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**
Asset and Risk Management: Risk Oriented Finance
** by
Louis Esch,
Robert Kieffer,
Thierry Lopez

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asset allocation, Brownian motion, business continuity plan, business process, capital asset pricing model, computer age, corporate governance, discrete time, diversified portfolio, implied volatility, index fund, interest rate derivative, iterative process, P = NP, p-value, random walk, risk/return, shareholder value, statistical model, stochastic process, transaction costs, value at risk, Wiener process, yield curve, zero-coupon bond

xix xix xxi PART I THE MASSIVE CHANGES IN THE WORLD OF FINANCE Introduction 1 The Regulatory Context 1.1 Precautionary surveillance 1.2 The Basle Committee 1.2.1 General information 1.2.2 Basle II and the philosophy of operational risk 1.3 Accounting standards 1.3.1 Standard-setting organisations 1.3.2 The IASB 2 Changes in Financial Risk Management 2.1 Deﬁnitions 2.1.1 Typology of risks 2.1.2 Risk management methodology 2.2 Changes in ﬁnancial risk management 2.2.1 Towards an integrated risk management 2.2.2 The ‘cost’ of risk management 2.3 A new risk-return world 2.3.1 Towards a minimisation of risk for an anticipated return 2.3.2 Theoretical formalisation 1 2 3 3 3 3 5 9 9 9 11 11 11 19 21 21 25 26 26 26 vi Contents PART II EVALUATING FINANCIAL ASSETS Introduction 3 4 29 30 Equities 3.1 The basics 3.1.1 Return and risk 3.1.2 Market efﬁciency 3.1.3 Equity valuation models 3.2 Portfolio diversiﬁcation and management 3.2.1 Principles of diversiﬁcation 3.2.2 Diversiﬁcation and portfolio size 3.2.3 Markowitz model and critical line algorithm 3.2.4 Sharpe’s simple index model 3.2.5 Model with risk-free security 3.2.6 The Elton, Gruber and Padberg method of portfolio management 3.2.7 Utility theory and optimal portfolio selection 3.2.8 The market model 3.3 Model of ﬁnancial asset equilibrium and applications 3.3.1 Capital asset pricing model 3.3.2 Arbitrage pricing theory 3.3.3 Performance evaluation 3.3.4 Equity portfolio management strategies 3.4 Equity dynamic models 3.4.1 Deterministic models 3.4.2 Stochastic models 35 35 35 44 48 51 51 55 56 69 75 79 85 91 93 93 97 99 103 108 108 109 Bonds 4.1 Characteristics and valuation 4.1.1 Deﬁnitions 4.1.2 Return on bonds 4.1.3 Valuing a bond 4.2 Bonds and ﬁnancial risk 4.2.1 Sources of risk 4.2.2 Duration 4.2.3 Convexity 4.3 Deterministic structure of interest rates 4.3.1 Yield curves 4.3.2 Static interest rate structure 4.3.3 Dynamic interest rate structure 4.3.4 Deterministic model and stochastic model 4.4 Bond portfolio management strategies 4.4.1 Passive strategy: immunisation 4.4.2 Active strategy 4.5 Stochastic bond dynamic models 4.5.1 Arbitrage models with one state variable 4.5.2 The Vasicek model 115 115 115 116 119 119 119 121 127 129 129 130 132 134 135 135 137 138 139 142 Contents 4.5.3 The Cox, Ingersoll and Ross model 4.5.4 Stochastic duration 5 Options 5.1 Deﬁnitions 5.1.1 Characteristics 5.1.2 Use 5.2 Value of an option 5.2.1 Intrinsic value and time value 5.2.2 Volatility 5.2.3 Sensitivity parameters 5.2.4 General properties 5.3 Valuation models 5.3.1 Binomial model for equity options 5.3.2 Black and Scholes model for equity options 5.3.3 Other models of valuation 5.4 Strategies on options 5.4.1 Simple strategies 5.4.2 More complex strategies PART III GENERAL THEORY OF VaR Introduction vii 145 147 149 149 149 150 153 153 154 155 157 160 162 168 174 175 175 175 179 180 6 Theory of VaR 6.1 The concept of ‘risk per share’ 6.1.1 Standard measurement of risk linked to ﬁnancial products 6.1.2 Problems with these approaches to risk 6.1.3 Generalising the concept of ‘risk’ 6.2 VaR for a single asset 6.2.1 Value at Risk 6.2.2 Case of a normal distribution 6.3 VaR for a portfolio 6.3.1 General results 6.3.2 Components of the VaR of a portfolio 6.3.3 Incremental VaR 181 181 181 181 184 185 185 188 190 190 193 195 7 VaR Estimation Techniques 7.1 General questions in estimating VaR 7.1.1 The problem of estimation 7.1.2 Typology of estimation methods 7.2 Estimated variance–covariance matrix method 7.2.1 Identifying cash ﬂows in ﬁnancial assets 7.2.2 Mapping cashﬂows with standard maturity dates 7.2.3 Calculating VaR 7.3 Monte Carlo simulation 7.3.1 The Monte Carlo method and probability theory 7.3.2 Estimation method 199 199 199 200 202 203 205 209 216 216 218 viii Contents 7.4 Historical simulation 7.4.1 Basic methodology 7.4.2 The contribution of extreme value theory 7.5 Advantages and drawbacks 7.5.1 The theoretical viewpoint 7.5.2 The practical viewpoint 7.5.3 Synthesis 8 Setting Up a VaR Methodology 8.1 Putting together the database 8.1.1 Which data should be chosen?

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More speciﬁcally, this value at risk (for the duration t and the probability level q) is deﬁned as the amount (generally negative) termed VaR ∗ , so that the variation observed during the interval [0; t] will only be less than the average upward variation in |VaR ∗ | with a probability of (1 − q). Thus, if the expected variation is expressed as E(pt ), the deﬁnition Pr[pt − E(pt ) ≤ VaR ∗ ] = 1 − q. Or, again: Pr[pt > VaR ∗ + E(pt )] = q. It is evident that these two concepts are linked, as we evidently have VaR = VaR ∗ + E(pt ). 6.2.2 Case of a normal distribution In the speciﬁc case where the random variable pt follows a normal law with mean E(pt ) and standard deviation σ (pt ), the deﬁnition can be changed to: Pr VaR q − E(pt ) pt − E(pt ) ≤ =1−q σ (pt ) σ (pt ) VaR q − E(pt ) is the quantile of the standard normal σ (pt ) distribution, ordinarily expressed as z1−q .

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The interval [s; t] is thus replaced by the interval [0; t − s] and the variable p will now only have the duration of the interval as its index. We therefore have the following deﬁnitive deﬁnition: pt = pt − p0 . The ‘value at risk’ of the asset in question for the duration t and the probability level q is deﬁned as an amount termed VaR, so that the variation pt observed for the asset during the interval [0; t] will only be less than VaR with a probability of (1 − q): Pr[pt ≤ VaR] = 1 − q Or similarly: Pr[pt > VaR] = q By expressing as Fp and fp respectively the distribution function and density function of the random variable pt , we arrive at the deﬁnition of VaR in Figures 6.4 and 6.5. F∆p(x) 1 1–q VaR x Figure 6.4 Deﬁnition of VaR based on distribution function 5 In this chapter, the theory is presented on the basis of the value, the price of assets, portfolios etc.

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Analysis of Financial Time Series
** by
Ruey S. Tsay

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Asian financial crisis, asset allocation, Black-Scholes formula, Brownian motion, capital asset pricing model, compound rate of return, correlation coefficient, data acquisition, discrete time, frictionless, frictionless market, implied volatility, index arbitrage, Long Term Capital Management, market microstructure, martingale, p-value, pattern recognition, random walk, risk tolerance, short selling, statistical model, stochastic process, stochastic volatility, telemarketer, transaction costs, value at risk, volatility smile, Wiener process, yield curve

For example, for the monthly log returns of Example 9.4, a joint estimation of Eqs. (9.34)–(9.36) can be performed if the common factor xt = 0.769r1t + 0.605r2t is treated as given. 9.5 APPLICATION We illustrate the application of multivariate volatility models by considering the Value at Risk (VaR) of a financial position with multiple assets. Suppose that an investor holds a long position in the stocks of Cisco Systems and Intel Corporation each worth $1 million. We use the daily log returns for the two stocks from January 2, 1991 to December 31, 1999 to build volatility models. The VaR is computed using the 1-step ahead forecasts at the end of data span and 5% critical values. 386 MULTIVARIATE VOLATILITY MODELS Let VaR1 be the value at risk for holding the position on Cisco Systems stock and VaR2 for holding Intel stock. Results of Chapter 7 show that the overall daily VaR for the investor is VaR = VaR21 + VaR22 + 2ρVaR1 VaR2 . In this illustration, we consider three approaches to volatility modeling for calculating VaR. For simplicity, we do not report standard errors for the parameters involved or model checking statistics.

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Figure 7.1 shows the time plot of daily log returns of IBM stock from July 3, 1962 to December 31, 1998 for 9190 observations. 7.1 VALUE AT RISK There are several types of risk in financial markets. Credit risk, liquidity risk, and market risk are three examples. Value at risk (VaR) is mainly concerned with market risk. It is a single estimate of the amount by which an institution’s position in a risk category could decline due to general market movements during a given holding 256 257 -0.2 log return -0.1 0.0 0.1 VALUE AT RISK 1970 1980 year 1990 2000 Figure 7.1. Time plot of daily log returns of IBM stock from July 3, 1962 to December 31, 1998. period; see Duffie and Pan (1997) and Jorion (1997) for a general exposition of VaR. The measure can be used by financial institutions to assess their risks or by a regulatory committee to set margin requirements. In either case, VaR is used to ensure that the financial institutions can still be in business after a catastrophic event.

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Denote the cumulative distribution function (CDF) of V () by F (x). We define the VaR of a long position over the time horizon with probability p as p = Pr[V () ≤ VaR] = F (VaR). (7.1) 258 VALUE AT RISK Since the holder of a long financial position suffers a loss when V () < 0, the VaR defined in Eq. (7.1) typically assumes a negative value when p is small. The negative sign signifies a loss. From the definition, the probability that the holder would encounter a loss greater than or equal to VaR over the time horizon is p. Alternatively, VaR can be interpreted as follows. With probability (1 − p), the potential loss encountered by the holder of the financial position over the time horizon is less than or equal to VaR. The holder of a short position suffers a loss when the value of the asset increases [i.e., V () > 0]. The VaR is then defined as p = Pr[V () ≥ VaR] = 1 − Pr[V () ≤ VaR] = 1 − F (VaR).

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Red-Blooded Risk: The Secret History of Wall Street
** by
Aaron Brown,
Eric Kim

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Albert Einstein, algorithmic trading, Asian financial crisis, Atul Gawande, backtesting, Basel III, Benoit Mandelbrot, Bernie Madoff, Black Swan, capital asset pricing model, central bank independence, Checklist Manifesto, corporate governance, credit crunch, Credit Default Swap, disintermediation, distributed generation, diversification, diversified portfolio, Emanuel Derman, Eugene Fama: efficient market hypothesis, experimental subject, financial innovation, illegal immigration, implied volatility, index fund, Long Term Capital Management, loss aversion, margin call, market clearing, market fundamentalism, market microstructure, money: store of value / unit of account / medium of exchange, moral hazard, natural language processing, open economy, pre–internet, quantitative trading / quantitative ﬁnance, random walk, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, special drawing rights, statistical arbitrage, stochastic volatility, The Myth of the Rational Market, too big to fail, transaction costs, value at risk, yield curve

Statistical arbitrage Statistical Decision Functions (Wald) Statistical games Statistical reasoning, basic principles Statistics, history of Stigler, Steven Still Life with a Bridle (Herbert) Stock market crash: Monday, October 19, 1987 Stoller, Martin Stoller, Phil Stone Age Economics (Sahlins) Story of money: 1776, continental dollars Andrew Dexter generally government and paper paleonomics paper vs. metal property, exchange and risk transition what money does Strange Days Indeed (Wheen) Stress tests Sull, Donald Superposition Tail risk—extreme events Tale of High-Flying Speculation and America’s First Banking Collapse, A (Kamensky) Taleb, Nassim Tett, Gillian Thaler, Richard 13 Bankers ( Johnson) Thirty Years War Theory of Blackjack, The (Griffin) Thorp, Edward To Engineer Is Human (Petroski) “Tolling” swap Trading from Your Gut (Faith) Trading risk Transaction taxes Treasury bills/bonds Trust in Numbers (Porter) Tukey, John Tulips/tulipomania Unspeakable truths: good stuff beyond VaR limit parametric risk managers create risk risk managers should make sure firms fail Upside of Turbulence, The (Sull) Useless Arithmetic (Pilkey) Utility theory: change of numeraire and decision maker identity and declining marginal utility and extensions utility maximization Valuable boundary Value at risk (VaR). See also Historical simulation VaR back-testing beyond profit and loss birth of computing defined operationally illustration inside boundary middle office not measure of risk as orthodox method outside boundary parametric risk management and scaling factor validation and “VaR breaks” Value investors VaR. See Value at risk (VaR) Vega Vince, Ralph Virtual systems, experiments and VIX.

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To make this precise, I’m going to jump ahead and steal a concept that wasn’t fully fleshed out until 1992, value at risk (VaR). VaR is defined operationally. That means we specify a property VaR is supposed to have, and then try to figure out what number satisfies the property. For a 1 percent one-day VaR, the property is that one day in 100—1 percent of the time—a portfolio will lose more than the VaR amount over one day, assuming normal markets and no position changes in the portfolio. VaR can also be defined at different probability levels and over different time horizons. The 99 days in 100 in which markets are normal and you make money or lose less than the VaR amount are used as data for mathematical optimization. The two or three trading days a year that you lose more than VaR—called “VaR breaks”—or that have abnormal markets, are analyzed separately.

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After a few years, we didn’t trust any statistical result that didn’t have a clear numeraire and validated analysis of situations when the numeraire broke down. For financial trading applications, the standard process is: Estimate a 95 percent one-day value at risk each day before trading begins. You estimate every trading day, even if systems are down or data are missing. Compare actual daily profit and loss (P&L) against the VaR prediction when the daily P&L becomes available. Test for the correct number of VaR breaks, within statistical error. Test that the breaks are independent in time and independent of the level of VaR. Once you have a reliable VaR system, collect data within the VaR limit. Investigate days when you lose more than the VaR amount, but supplement the observations with hypothetical scenarios and days in the past when your current positions would have suffered large losses.

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Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues
** by
Alain Ruttiens

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algorithmic trading, asset allocation, asset-backed security, backtesting, banking crisis, Black Swan, Black-Scholes formula, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discounted cash flows, discrete time, diversification, fixed income, implied volatility, interest rate derivative, interest rate swap, margin call, market microstructure, martingale, p-value, passive investing, quantitative trading / quantitative ﬁnance, random walk, risk/return, Sharpe ratio, short selling, statistical model, stochastic process, stochastic volatility, time value of money, transaction costs, value at risk, volatility smile, Wiener process, yield curve, zero-coupon bond

In particular, if L = 0, that is, if it separates positive from negative returns, the Omega ratio corresponds to what has been introduced as the “Bernardo–Ledoit gain-loss ratio”.6 14.2 VaR OR VALUE-AT-RISK This section is mainly relative to a risk management tool with respect to market risk.7 The last sub-section concerns the case of the credit risk. The VaR is a risk measure that can be defined as the estimated possible loss, expressed as an amount of $(or any other currency), that can suffer a position or group of positions in financial market instruments, over a given horizon of time, with respect to some given probability level, called confidence level. The VaR measure thus rests on an assessment about the probability distributions of the prices of the instruments that compose the related risky position. Denoting c the confidence level, 1 − c = s the “significance level”, and P a position (or exposure) value, VaR computed on this position, with a confidence level of c, and from t to a horizon of t + τ, is such as (14.5) In plain English, for a confidence level c of, for example, 99%, hence a significance level s = 1%, there is 1% chance that the loss on the position is exceeding the VaR limit, and c = 99% chances that the loss is inferior to the VaR limit.

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short-term rates discount basis trading futures rate basis trading spot instruments skewness smiles, volatility smirks, volatility SML see security market line Sortino ratio sovereign bonds Spearman’s rank correlation coefficient special purpose vehicles (SPVs) specific risk speed sensitivity splines spot instruments bonds correlation modeling currencies forex swaps Gaussian hypothesis alternatives prices rates short-term rates volatility spreads SPVs see special purpose vehicles standardized futures contracts standard Wiener process see also dZ; general Wiener process stationarity stationary Markovian processes stochastic processes basis of Brownian motion definition of process diffusion processes discrete/continuous variables general Wiener process Markovian processes martingales probability reminders risk neutral probability standard Wiener process stationary/non-stationary processes terminology stock indexes basket options futures stock portfolios stock prices stock valuation book value method DCF method Gordon–Shapiro method real option method stocks without dividends stress tests Structural model Student distribution swaps bond duration conditional CRSs curves forwards ISDA second-generation swap points swap rate markets variance volatility see also forex swaps; interest rate swaps swaptions systematic factors Taiwan dollars (TWD) Taleb, Nassim Taylor series TE see Tracking Error term structure theoretical price forward foreign exchange futures theta time, continuous/discrete time horizon, VaR time value of option time-weighted rate of return (TWRR) Tiscali telecommunications Total total period, FRAs Toy see Black, Derman, Toy process Tracking Error (TE) tranches transfer functions Treasury bonds Treynor ratio trinomial trees TWD see Taiwan dollars TWRR see time-weighted rate of return Uhlenbeck see Ohrstein–Uhlenbeck unexpected credit loss United States dollars (USD) CRS swaps forward foreign exchange futures NDOs swap rates market volatility unwinding swaps USD see United States dollars valuation callable bonds credit derivatives IRSs stocks troubles value-at-risk (VaR) backtesting correlation troubles example important remarks methods parameters variants value-weighted indexes vanilla IRSs vanilla options vanilla swaps CRSs in-arrear swaps IRSs vanna VaR see value-at-risk variance-covariance method, VaR “variance gamma” process variance swaps Vasicek model VDAX index vega VIX index volatility annualized basket options correlation modeling curves delta-gamma neutral management derivatives dVega/dTime general Wiener process historical implied intraday volatility modeling option pricing practical issues realized models smiles smirks variance swaps vega volga vomma VXN index weather White see Hull and White model white noise AR process see also Brownian motion; standard Wiener process Wiener see general Wiener process; standard Wiener process WTI Crude Oil futures Yang–Zang volatility yield, convenience yield curves capital markets components CRS pricing cubic splines method definition EONIA/OIS swaps implied volatility interest rate options interpolations linear method methodology money markets points determination example polynomial curve methods swap curve swaps see also term structure yield to maturity (YTM) Z see dZ Zang see Yang–Zang volatility zero-coupon bonds zero-coupon rates see also spot instruments, rates zero-coupon swaps Z-score

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short-term rates discount basis trading futures rate basis trading spot instruments skewness smiles, volatility smirks, volatility SML see security market line Sortino ratio sovereign bonds Spearman’s rank correlation coefficient special purpose vehicles (SPVs) specific risk speed sensitivity splines spot instruments bonds correlation modeling currencies forex swaps Gaussian hypothesis alternatives prices rates short-term rates volatility spreads SPVs see special purpose vehicles standardized futures contracts standard Wiener process see also dZ; general Wiener process stationarity stationary Markovian processes stochastic processes basis of Brownian motion definition of process diffusion processes discrete/continuous variables general Wiener process Markovian processes martingales probability reminders risk neutral probability standard Wiener process stationary/non-stationary processes terminology stock indexes basket options futures stock portfolios stock prices stock valuation book value method DCF method Gordon–Shapiro method real option method stocks without dividends stress tests Structural model Student distribution swaps bond duration conditional CRSs curves forwards ISDA second-generation swap points swap rate markets variance volatility see also forex swaps; interest rate swaps swaptions systematic factors Taiwan dollars (TWD) Taleb, Nassim Taylor series TE see Tracking Error term structure theoretical price forward foreign exchange futures theta time, continuous/discrete time horizon, VaR time value of option time-weighted rate of return (TWRR) Tiscali telecommunications Total total period, FRAs Toy see Black, Derman, Toy process Tracking Error (TE) tranches transfer functions Treasury bonds Treynor ratio trinomial trees TWD see Taiwan dollars TWRR see time-weighted rate of return Uhlenbeck see Ohrstein–Uhlenbeck unexpected credit loss United States dollars (USD) CRS swaps forward foreign exchange futures NDOs swap rates market volatility unwinding swaps USD see United States dollars valuation callable bonds credit derivatives IRSs stocks troubles value-at-risk (VaR) backtesting correlation troubles example important remarks methods parameters variants value-weighted indexes vanilla IRSs vanilla options vanilla swaps CRSs in-arrear swaps IRSs vanna VaR see value-at-risk variance-covariance method, VaR “variance gamma” process variance swaps Vasicek model VDAX index vega VIX index volatility annualized basket options correlation modeling curves delta-gamma neutral management derivatives dVega/dTime general Wiener process historical implied intraday volatility modeling option pricing practical issues realized models smiles smirks variance swaps vega volga vomma VXN index weather White see Hull and White model white noise AR process see also Brownian motion; standard Wiener process Wiener see general Wiener process; standard Wiener process WTI Crude Oil futures Yang–Zang volatility yield, convenience yield curves capital markets components CRS pricing cubic splines method definition EONIA/OIS swaps implied volatility interest rate options interpolations linear method methodology money markets points determination example polynomial curve methods swap curve swaps see also term structure yield to maturity (YTM) Z see dZ Zang see Yang–Zang volatility zero-coupon bonds zero-coupon rates see also spot instruments, rates zero-coupon swaps Z-score

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Handbook of Modeling High-Frequency Data in Finance
** by
Frederi G. Viens,
Maria C. Mariani,
Ionut Florescu

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algorithmic trading, asset allocation, automated trading system, backtesting, Black-Scholes formula, Brownian motion, business process, continuous integration, corporate governance, discrete time, distributed generation, fixed income, Flash crash, housing crisis, implied volatility, incomplete markets, linear programming, mandelbrot fractal, market friction, market microstructure, martingale, Menlo Park, p-value, pattern recognition, performance metric, principal–agent problem, random walk, risk tolerance, risk/return, short selling, statistical model, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process

The method allows us to forecast the full pdf of the returns distribution, but for simplicity and concreteness, we focus here on forecasting VaR; other kinds of risk forecasts will be similar. 7.3.1 VALUE AT RISK DEFINITION 7.12 Value at Risk (VaR). Given α ∈ (0, 1), the value at risk at conﬁdence level α for loss L of a security or a portfolio is deﬁned as VaRα (L) = inf {l ∈ R : FL (l) ≥ α}, where FL is the cumulative distribution function of L. In probabilistic terms, VaR is a quantile of the loss distribution. Typical values for α are between 0.95 and 0.995. VaR can also be based on returns instead of losses, in which case α takes a small value such as 0.05 or 0.01. For example, intuitively, a 95% value at risk, VaR0.95 , is a level L such that a loss exceeding L has only a 5% chance of occurring. 7.3.2 DATA AND STYLIZED FACTS Given a set of daily closing prices for some index, we ﬁrst convert them into negative log returns and then would like to calibrate a skewed t distribution with the EM algorithm.

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See also Ordered lower-upper solution pair U-shape, of trade distributions, 42 Utility after retirement, 321 Utility estimations, 287 Utility functions, 296, 299 of power type, 305 Utility loss, 290 Value at risk (VaR), 163, 165, 176. See also VaR entries Value function, 304, 307, 312, 313 for the constant coefﬁcients case, 318 VaR error, 201. See also Value at risk (VaR) VaR estimates, based on Monte Carlo simulation, 199 VaRFixed , 213, 214, 215 VaR forecast(s), 210, 212 high-low frequency, 186 intraday, 202–203 VaR forecasting, 182 VaRHL , 213, 214, 215. See also HL estimator Index Variance, volatility of, 250–252 Variance estimator optimization, 286 Variance forecast, 206 Variance gamma (VG) distributions, 171 Variance-gamma (VG) model, 4, 8–9. See also VG MLE computing MME for, 10–11 empirical results for, 18–22 VaRTrue , 213, 214 VaR violations, 210 counting, 191–192 VG MLE, 6. See also Maximum likelihood estimators (MLEs); Variance-gamma (VG) model ﬁnite-sample performance of, 15–16 VG MME, ﬁnite-sample performance of, 14–15.

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See also CBOE entries calculation of, 98–99 Chronopoulou, Alexandra, xiii, 219 ‘‘Circuit breakers’’, 241 Citi data series, DFA and Hurst methods applied to, 155 City Group, Lévy ﬂight parameter for, 341 Classical risk forecast, 163 Classical time series analysis, 177 Combined Stochastic and Dirichlet problem, 317 Comparative analysis, 239–241 Compensation committees, 53 Compensation policy, 59 Complex models, 23 Compustat North America dataset, 54 Conditional density function, 173 Conditional distribution, 29, 30 Conditional expected returns, 181 Conditional normal distribution, density of, 173 Conditional VaR, 188–189, 207. See also Value at risk (VaR) 423 Conditional variances, 203, 206, 208 of the GARCH(1,1) process, 180 Conﬁdence intervals, for forecasts, 187–188 Consecutive trades, 129 Consensus indicators, 62 Constant coefﬁcient case, 311 Constant default correlation, 79–81 Constant default correlation model, 76 Constant rebalanced portfolio technical analysis (CRP-TA) trading algorithm, 65–66 Constant variance, 181 Constant volatility, 353 Constructed indices, comparison of, 106–107 Constructed volatility index (VIX).

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Commodity Trading Advisors: Risk, Performance Analysis, and Selection
** by
Greg N. Gregoriou,
Vassilios Karavas,
François-Serge Lhabitant,
Fabrice Douglas Rouah

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Asian financial crisis, asset allocation, backtesting, capital asset pricing model, collateralized debt obligation, commodity trading advisor, compound rate of return, constrained optimization, corporate governance, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, discrete time, distributed generation, diversification, diversified portfolio, dividend-yielding stocks, fixed income, high net worth, implied volatility, index arbitrage, index fund, interest rate swap, iterative process, linear programming, London Interbank Offered Rate, Long Term Capital Management, market fundamentalism, merger arbitrage, Mexican peso crisis / tequila crisis, p-value, Ponzi scheme, quantitative trading / quantitative ﬁnance, random walk, risk-adjusted returns, risk/return, Sharpe ratio, short selling, stochastic process, systematic trading, technology bubble, transaction costs, value at risk

Thus, investors needed a more precise measure of downside risk. With the value at risk (VaR) approach, it is possible to measure the amount of portfolio wealth that can be lost over a given period of time with a certain probability. VaR has become a widely used risk management tool. The Basel Accord of 1988, for example, requires commercial banks to compute VaR in setting their minimum capital requirements (see Jorion 2001). One of the main advantages of VaR is that it works across different asset classes such as stocks and bonds. Further, VaR often is used as an ex-post measure to evaluate the current exposure to market risk and determine whether this exposure should be reduced. Our objective consists in drawing the efficient frontiers based on the VaR framework. We also use the Cornish-Fisher (1937) expansion to adjust the traditional VaR with the skewness and kurtosis of the return distribution, which often deviates from normality.2 We call the VaR with the Cornish-Fisher expansion modified VaR.

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Our next step is to provide some Value at Risk analysis. 194 RISK AND MANAGED FUTURES INVESTING Diversified Excess Returns 15.00% 10.00% 5.00% 0.00% –5.00% –10.00% –20.00% –15.00% –10.00% –5.00% 0.00% 5.00% 10.00% 15.00% S&P 100 Excess Returns Diversified Trading Mimicking Portfolio Systematic Excess Returns FIGURE 9.6 Mimicking Portfolio Returns for the Barclay Diversified Trading Index 0.200 0.150 0.100 0.050 0.000 –0.050 –0.100 –0.175 –0.150 –0.125 –0.100 –0.075 –0.050 –0.025 0.000 0.025 0.050 0.075 0.100 0.125 S&P 100 Excess Returns Systematic Trading Mimicking Portfolio FIGURE 9.7 Mimicking Portfolio Returns for the Barclay Systematic Trading Index 195 MLMI Excess Returns Measuring the Long Volatility Strategies of Managed Futures 0.080 0.060 0.040 0.020 0.000 –0.020 –0.040 –0.060 –0.080 –0.175 –0.150 –0.125 –0.100 –0.075 –0.050 –0.025 0.000 0.025 0.050 0.075 0.100 0.125 S&P 100 Excess Returns MLM Index Mimicking Portfolio FIGURE 9.8 Mimicking Portfolio Returns for the MLM Index VALUE AT RISK FOR MANAGED FUTURES The main reason for building mimicking portfolios is to simulate the returns to trend-following strategies for developing risk estimates. Specifically, we can run Monte Carlo simulations with our mimicking portfolios and estimate value at risk (VaR). Armed with these data, we can estimate the probability of the risk of loss associated with long volatility strategies. This is important to help us understand the off-balance sheet risks associated with trend-following strategies. In addition, we can use Monte Carlo simulations to graph the frequency distribution of returns.

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Table 9.2 presents the results. For example, the one-month VaR for the Barclay Commodity Trading Index is −0.93 percent at a 1 percent confidence level and −0.69 percent at a 5 percent confidence level. This means that we can state with a 99 per- 196 RISK AND MANAGED FUTURES INVESTING TABLE 9.2 Monte Carlo Simulation of Value at Risk CTA Diversified Systematic MLM 1 Month VaR @ 1% Confidence Level 1 Month VaR @ 5% Confidence Level Maximum Loss −0.93% −1.46% −0.97% −1.18% −0.69% −1.31% −1.14% −1.99% −0.74% −1.35% −0.89% −1.64% Number of Simulations 10,000 10,000 10,000 10,000 cent (95 percent) level of confidence that the maximum loss sustained by a diversified CTA manager will not exceed 0.93 percent (0.69 percent) in any given month. Table 9.2 also contains the VaR for the other trend-following strategies.

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The Devil's Derivatives: The Untold Story of the Slick Traders and Hapless Regulators Who Almost Blew Up Wall Street . . . And Are Ready to Do It Again
** by
Nicholas Dunbar

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asset-backed security, bank run, banking crisis, Basel III, Black Swan, Black-Scholes formula, bonus culture, capital asset pricing model, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delayed gratification, diversification, Edmond Halley, facts on the ground, financial innovation, fixed income, George Akerlof, implied volatility, index fund, interest rate derivative, interest rate swap, Isaac Newton, Kenneth Rogoff, Long Term Capital Management, margin call, market bubble, Nick Leeson, Northern Rock, offshore financial centre, price mechanism, regulatory arbitrage, rent-seeking, Richard Thaler, risk tolerance, risk/return, Ronald Reagan, shareholder value, short selling, statistical model, The Chicago School, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, yield curve

Applying that bottom 5 percent of market outcomes to the bank’s current trading position gave them a number—value at risk (VAR)—which could serve as an assumption to be tested in the market. A day in which the performance was worse than VAR was called an “exception.” If the bank suffered through too many exceptions—a substantially greater fraction of days than one in twenty in which its performance was worse than VAR—then their assumptions about the markets were wrong. Armed with this scientific evidence, senior bankers could then step in and order their traders to cut positions. When Thieke told Fisher about VAR in early 1994, a mystery was suddenly solved. Seemingly unconnected events that spring—a jump in the dollar–yen exchange rate, a plunge in German bunds, and the March sell-off in Treasuries—were invisibly linked by the VAR models the banks were using. As the worst-case assumptions were breached in one market, banks would cut positions right across their portfolios to protect themselves from further losses.

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Because it relied on many simplifying assumptions and was not backed up by empirical evidence, Vasicek’s model was more of a provocative theoretical talking point than a practical, proven tool. And aside from leaning on Merton’s model, it didn’t provide an arbitrage recipe to enforce market pricing. But the invention of value at risk (VAR) in the 1990s provided a huge boost for the idea in practical terms. VAR, remember, was a method for sifting through trading book data to identify the worst that could happen in “normal” conditions—say, on nineteen out of twenty or ninety-nine out of one hundred trading days. At first sight, no one could expect VAR to apply to the opposite extreme: the opaque world of loans, which by definition were not traded, and stayed on a bank’s books until they either were paid back or had defaulted. Yet the pressure for lending banks to please shareholders led inexorably to the idea of trading credit risk, and thus the credit default swap.

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Morgan and elsewhere, the market-based world would soon figure out how to play these gatekeepers to get money at the price they wanted . . . and then use that to reap astounding profits. And in the process, they used credit default swaps to subvert—and nearly destroy—the financial system. CHAPTER TWO Going to the Mattresses In 1994, a new model for measuring risk—value at risk (VAR)—convinced large segments of the financial world that they were being too cautious in their investing. Another new financial tool, over-the-counter derivatives, seemed to cancel out unwanted risks by transferring them elsewhere. Thanks to VAR and OTC derivatives, the trading positions and profits of banks grew exponentially. In 1998, the fatal flaw of this paradigm was exposed by the collapse of LTCM, but traders and regulators learned the wrong lesson from that near-death experience, setting the financial world up for an even bigger cataclysm.

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The Mathematics of Banking and Finance
** by
Dennis W. Cox,
Michael A. A. Cox

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barriers to entry, Brownian motion, call centre, correlation coefficient, inventory management, iterative process, linear programming, meta analysis, meta-analysis, P = NP, pattern recognition, random walk, traveling salesman, value at risk

Given the difficulties inherent with data fitting and the underlying data integrity problem, a much lower level of accuracy is actually achieved – perhaps only 80%. 28.3 CALCULATING VALUE AT RISK Value at risk for a single position is calculated as: VaR = Sensitivity of position to change in market prices × Estimated change in price or VaR = Amount of the position × Volatility of the position = xσ where x is the position size and volatility, σ , is the proportion of the value of the position which may be lost over a given time horizon at the specified confidence level. When looking at exposure to two or more risks – e.g. the risk in a portfolio of two assets, say gold and euros – the risk measures must take account of the likely joint movements (or ‘correlations’) in the asset prices as well as the risks in the individual instruments. This can be written as: VaR = VaR21 + VaR22 + 2ρ12 VaR1 VaR2 where VaR1 is the value at risk arising from the first risk factor, VaR2 is the value at risk arising from the second risk factor, and ρ12 is the correlation between movements in the two risk factors.

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The functions are shown in Figures 27.11, 27.12 and 27.13 for σ = 2 and μ = 2, 4 and 6. 28 Value at Risk 28.1 INTRODUCTION Value at risk, or VaR is an attempt to estimate the greatest loss likely if a defined risk were to occur. For example, it could represent the loss in value of a portfolio of shares were a market slump to occur. Typically the way this works in practice is that the analyst calculates the greatest loss that would arise in 99% of all cases. That means that in 99% of cases the loss would actually exceed the amount of the calculated VaR, which is effectively a boundary value. This really is just a probabilistic statement. If a VaR is estimated to be £1 million with a 99% confidence, or a probability of 0.99, then a loss of more than £1 million might be expected on one day in every 100. Generally there will be a range of factors that could influence the VaR calculation.

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While we are giving an answer at a 99% confidence level, this does not mean that we are actually 99% confident in the analysis. When management improperly uses VaR figures, it is normally in the interpretation of the data arising that the business is let down. There are two percentages here – the 99% is based on the distribution and provides an element of analysis of the overall picture that has been estimated. The underlying data has an accuracy, which is certainly lower than 99% (i.e. there is only a 1% chance that the data will be unrepresentative or that the distribution selected will be inappropriate). Given the difficulties inherent with data fitting and the underlying data integrity problem, a much lower level of accuracy is actually achieved – perhaps only 80%. 28.3 CALCULATING VALUE AT RISK Value at risk for a single position is calculated as: VaR = Sensitivity of position to change in market prices × Estimated change in price or VaR = Amount of the position × Volatility of the position = xσ where x is the position size and volatility, σ , is the proportion of the value of the position which may be lost over a given time horizon at the specified confidence level.

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Mathematics for Finance: An Introduction to Financial Engineering
** by
Marek Capinski,
Tomasz Zastawniak

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Black-Scholes formula, Brownian motion, capital asset pricing model, cellular automata, delta neutral, discounted cash flows, discrete time, diversified portfolio, interest rate derivative, interest rate swap, locking in a profit, London Interbank Offered Rate, margin call, martingale, quantitative trading / quantitative ﬁnance, random walk, short selling, stochastic process, time value of money, transaction costs, value at risk, Wiener process, zero-coupon bond

In addition, they might prove expensive if transaction costs were included. 9.2 Hedging Business Risk We begin by introducing an alternative measure of risk, related to an intuitive understanding of risk as the size and likelihood of a possible loss. 202 Mathematics for Finance 9.2.1 Value at Risk Let us present the basic idea using a simple example. We buy a share of stock for S(0) = 100 dollars to sell it after one year. The selling price S(1) is random. We shall suﬀer a loss if S(1) < 100er , where r is the risk-free rate under continuous compounding. (The purchase can either be ﬁnanced by a loan, or, if the initial sum is already at our disposal, we take into account the foregone opportunity of a risk-free investment.) What is the probability of a loss being less than a given amount, for example, P (100er − S(1) < 20) = ? Let us reverse the question and ﬁx the probability, 95% say. Now we seek an amount such that the probability of a loss not exceeding this amount is 95%. This is referred to as Value at Risk at 95% conﬁdence level and denoted by VaR. (Other conﬁdence levels can also be used.)

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Such institutions are typically satisﬁed by the commission charged for their services, without taking an active position in the market. Next, we shall analyse methods of reducing undesirable risk stemming from certain business activities. Our case studies will be concerned with foreign exchange risk. It is possible to deal in a similar way with the risk resulting from unexpected future changes of various market variables such as commodity prices, interest rates or stock prices. We shall introduce a measure of risk called Value at Risk (VaR), which has recently become very popular. Derivative securities will be used to design portfolios with a view to reducing this kind of risk. Finally, we shall consider an application of options to manufacturing a levered investment, for which increased risk will be accompanied by high expected return. 191 192 Mathematics for Finance 9.1 Hedging Option Positions The writer of a European call option is exposed to risk, as the option may end up in the money.

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Glossary of Symbols A B β c C C CA CE E C Cov delta div div0 D D DA E E∗ f F gamma Φ k K i m ﬁxed income (risk free) security price; money market account bond price beta factor covariance call price; coupon value covariance matrix American call price European call price discounted European call price covariance Greek parameter delta dividend present value of dividends derivative security price; duration discounted derivative security price price of an American type derivative security expectation risk-neutral expectation futures price; payoﬀ of an option; forward rate forward price; future value; face value Greek parameter gamma cumulative binomial distribution logarithmic return return coupon rate compounding frequency; expected logarithmic return 305 306 Mathematics for Finance M m µ N N k ω Ω p p∗ P PA PE P E PA r rdiv re rF rho ρ S S σ t T τ theta u V Var VaR vega w w W x X y z market portfolio expected returns as a row matrix expected return cumulative normal distribution the number of k-element combinations out of N elements scenario probability space branching probability in a binomial tree risk-neutral probability put price; principal American put price European put price discounted European put price present value factor of an annuity interest rate dividend yield eﬀective rate risk-free return Greek parameter rho correlation risky security (stock) price discounted risky security (stock) price standard deviation; risk; volatility current time maturity time; expiry time; exercise time; delivery time time step Greek parameter theta row matrix with all entries 1 portfolio value; forward contract value, futures contract value variance value at risk Greek parameter vega symmetric random walk; weights in a portfolio weights in a portfolio as a row matrix Wiener process, Brownian motion position in a risky security strike price position in a ﬁxed income (risk free) security; yield of a bond position in a derivative security Index admissible – portfolio 5 – strategy 79, 88 American – call option 147 – derivative security – put option 147 amortised loan 30 annuity 29 arbitrage 7 at the money 169 attainable – portfolio 107 – set 107 183 basis – of a forward contract 128 – of a futures contract 140 basis point 218 bear spread 208 beta factor 121 binomial – distribution 57, 180 – tree model 7, 55, 81, 174, 238 Black–Derman–Toy model 260 Black–Scholes – equation 198 – formula 188 bond – at par 42, 249 – callable 255 – face value 39 – ﬁxed-coupon 255 – ﬂoating-coupon 255 – maturity date 39 – stripped 230 – unit 39 – with coupons 41 – zero-coupon 39 Brownian motion 69 bull spread 208 butterﬂy 208 – reversed 209 call option 13, 181 – American 147 – European 147, 188 callable bond 255 cap 258 Capital Asset Pricing Model 118 capital market line 118 caplet 258 CAPM 118 Central Limit Theorem 70 characteristic line 120 compounding – continuous 32 – discrete 25 – equivalent 36 – periodic 25 – preferable 36 conditional expectation 62 contingent claim 18, 85, 148 – American 183 – European 173 continuous compounding 32 continuous time limit 66 correlation coeﬃcient 99 coupon bond 41 coupon rate 249 307 308 covariance matrix 107 Cox–Ingersoll–Ross model 260 Cox–Ross–Rubinstein formula 181 cum-dividend price 292 delta 174, 192, 193, 197 delta hedging 192 delta neutral portfolio 192 delta-gamma hedging 199 delta-gamma neutral portfolio 198 delta-vega hedging 200 delta-vega neutral portfolio 198 derivative security 18, 85, 253 – American 183 – European 173 discount factor 24, 27, 33 discounted stock price 63 discounted value 24, 27 discrete compounding 25 distribution – binomial 57, 180 – log normal 71, 186 – normal 70, 186 diversiﬁable risk 122 dividend yield 131 divisibility 4, 74, 76, 87 duration 222 dynamic hedging 226 eﬀective rate 36 eﬃcient – frontier 115 – portfolio 115 equivalent compounding 36 European – call option 147, 181, 188 – derivative security 173 – put option 147, 181, 189 ex-coupon price 248 ex-dividend price 292 exercise – price 13, 147 – time 13, 147 expected return 10, 53, 97, 108 expiry time 147 face value 39 ﬁxed interest 255 ﬁxed-coupon bond 255 ﬂat term structure 229 ﬂoating interest 255 ﬂoating-coupon bond 255 ﬂoor 259 ﬂoorlet 259 Mathematics for Finance forward – contract 11, 125 – price 11, 125 – rate 233 fundamental theorem of asset pricing 83, 88 future value 22, 25 futures – contract 134 – price 134 gamma 197 Girsanov theorem 187 Greek parameters 197 growth factor 22, 25, 32 Heath–Jarrow–Morton model hedging – delta 192 – delta-gamma 199 – delta-vega 200 – dynamic 226 in the money 169 initial – forward rate 232 – margin 135 – term structure 229 instantaneous forward rate interest – compounded 25, 32 – ﬁxed 255 – ﬂoating 255 – simple 22 – variable 255 interest rate 22 interest rate option 254 interest rate swap 255 261 233 LIBID 232 LIBOR 232 line of best ﬁt 120 liquidity 4, 74, 77, 87 log normal distribution 71, 186 logarithmic return 34, 52 long forward position 11, 125 maintenance margin 135 margin call 135 market portfolio 119 market price of risk 212 marking to market 134 Markowitz bullet 113 martingale 63, 83 Index 309 martingale probability 63, 250 maturity date 39 minimum variance – line 109 – portfolio 108 money market 43, 235 no-arbitrage principle 7, 79, 88 normal distribution 70, 186 option – American 183 – at the money 169 – call 13, 147, 181, 188 – European 173, 181 – in the money 169 – interest rate 254 – intrinsic value 169 – out of the money 169 – payoﬀ 173 – put 18, 147, 181, 189 – time value 170 out of the money 169 par, bond trading at 42, 249 payoﬀ 148, 173 periodic compounding 25 perpetuity 24, 30 portfolio 76, 87 – admissible 5 – attainable 107 – delta neutral 192 – delta-gamma neutral 198 – delta-vega neutral 198 – expected return 108 – market 119 – variance 108 – vega neutral 197 positive part 148 predictable strategy 77, 88 preferable compounding 36 present value 24, 27 principal 22 put option 18, 181 – American 147 – European 147, 189 put-call parity 150 – estimates 153 random interest rates random walk 67 rate – coupon 249 – eﬀective 36 237 – forward 233 – – initial 232 – – instantaneous 233 – of interest 22 – of return 1, 49 – spot 229 regression line 120 residual random variable 121 residual variance 122 return 1, 49 – expected 53 – including dividends 50 – logarithmic 34, 52 reversed butterﬂy 209 rho 197 risk 10, 91 – diversiﬁable 122 – market price of 212 – systematic 122 – undiversiﬁable 122 risk premium 119, 123 risk-neutral – expectation 60, 83 – market 60 – probability 60, 83, 250 scenario 47 security market line 123 self-ﬁnancing strategy 76, 88 short forward position 11, 125 short rate 235 short selling 5, 74, 77, 87 simple interest 22 spot rate 229 Standard and Poor Index 141 state 238 stochastic calculus 71, 185 stochastic diﬀerential equation 71 stock index 141 stock price 47 strategy 76, 87 – admissible 79, 88 – predictable 77, 88 – self-ﬁnancing 76, 88 – value of 76, 87 strike price 13, 147 stripped bond 230 swap 256 swaption 258 systematic risk 122 term structure 229 theta 197 time value of money 21 310 trinomial tree model Mathematics for Finance 64 underlying 85, 147 undiversiﬁable risk 122 unit bond 39 value at risk 202 value of a portfolio 2 value of a strategy 76, 87 VaR 202 variable interest 255 Vasiček model 260 vega 197 vega neutral portfolio volatility 71 weights in a portfolio Wiener process 69 yield 216 yield to maturity 229 zero-coupon bond 39 197 94

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High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems
** by
Irene Aldridge

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algorithmic trading, asset allocation, asset-backed security, automated trading system, backtesting, Black Swan, Brownian motion, business process, capital asset pricing model, centralized clearinghouse, collapse of Lehman Brothers, collateralized debt obligation, collective bargaining, diversification, equity premium, fault tolerance, financial intermediation, fixed income, high net worth, implied volatility, index arbitrage, interest rate swap, inventory management, law of one price, Long Term Capital Management, Louis Bachelier, margin call, market friction, market microstructure, martingale, New Journalism, p-value, paper trading, performance metric, profit motive, purchasing power parity, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, short selling, Small Order Execution System, statistical arbitrage, statistical model, stochastic process, stochastic volatility, systematic trading, trade route, transaction costs, value at risk, yield curve

Bangia et al. (1999), for example, document that liquidity risk accounted for 17 percent of the market risk in long USD/THB positions in May 1997, and Le Saout (2002) estimates that liquidity risk can reach over 50 percent of total risk on selected securities in CAC40 stocks. 264 HIGH-FREQUENCY TRADING Bervas (2006) proposes the following liquidity-adjusted VaR measure: (17.7) VaR L = VaR + Liquidity Adjustment = VaR − µ S + zα σ S where VaR is the market risk value-at-risk discussed previously in this chapter, µS is the mean expected bid-ask spread, σ S is the standard deviation of the bid-ask spread, and zα is the confidence coefficient corresponding to the desired α– percent of the VaR estimation. Both µS and σ S can be estimated either from raw spread data or from the Roll (1984) model. Using Kyle’s λ measure, the VaR liquidity adjustment can be similarly computed through estimation of the mean and standard deviation of the trade volume: VaR L = VaR + Liquidity Adjustment = VaR − α̂ + λ̂(µNVOL + zα σ NVOL ) (17.8) where α̂ and λ̂ are estimated using OLS regression following Kyle (1985): Pt = α + λNVOLt + εt (17.9) Pt is the change in market price due to market impact of orders, and NVOLt is the difference between the buy and sell market depths in period t.

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Calmar Ratio (Young [1991]) Calmari = E [ri ]−r f Sterling Ratio (Kestner [1996]) Sterlingi = E [ri ]−r f N −1 MDi j Burke Ratio (Burke [1994]) Burkei = −MDi1 N k=1 E [ri ]−r f N k=1 MDi j 2 1/2 MDi1 is the maximum drawdown. N − N1 MDi j is the k=1 average maximum drawdown. 1/2 N 2 MDi j is a type k=1 of variance below the N th largest drawdown; accounts for very large losses. Value-at-risk–based measures. Value at risk (VaRi ) describes the possible loss of an investment, which is not exceeded with a given probability of 1 − α in a certain period. For normally distributed returns, VaRi = −(E [ri ] + zα σi ), where zα is the α-quantile of the standard normal distribution. (Continued) 54 HIGH-FREQUENCY TRADING TABLE 5.1 (Continued) E [r]−r f Excess return on value at risk (Dowd, [2000]) Excess R on VaR = Conditional Sharpe ratio (Agarwal and Naik [2004]) Conditional Sharpe = Modiﬁed Sharpe ratio (Gregoriou and Gueyie [2003]) Modiﬁed Sharpe = VaRi E [r]−r f C VaRi CVaRi = E [−rit |rit ≤ −VaRi ] E [r]−r f M VaRi Cornish-Fisher expansion is calculated as follows: Not suitable for non-normal returns.

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Finally, the Upside Potential ratio, produced by Sortino, van der Meer, and Plantinga (1999), measures the average return above the benchmark (the first higher partial moment) per unit of standard deviation of returns below the benchmark. Value-at-risk (VaR) measures also gained considerable popularity as metrics able to summarize the tail risk in a convenient point format within a statistical framework. The VaR measure essentially identifies the 90 percent, 95 percent, or 99 percent Z-score cutoff in distribution of returns (the metric is also often used on real dollar distributions of daily profit and loss). VaR companion measure, the conditional VaR (CVaR), also known as expected loss (EL), measures the average value of return within the cut-off tail. Of course, the original VaR assumes normal distributions of returns, whereas the returns are known to be fat-tailed. To address this issue, a modified VaR (MVaR) measure was proposed by Gregoriou and Gueyie (2003) and takes into account deviations from normality.

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Optimization Methods in Finance
** by
Gerard Cornuejols,
Reha Tutuncu

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asset allocation, call centre, constrained optimization, correlation coefficient, diversification, finite state, fixed income, frictionless, frictionless market, index fund, linear programming, Long Term Capital Management, passive investing, Sharpe ratio, transaction costs, value at risk, Y2K

When VaR is computed by generating scenarios, it turns out to be a non-smooth and nonconvex function of the positions in the investment portfolio. Therefore, when one tries to optimize VaR computed in this manner, multiple local optimizers are encountered, hindering the global optimization process. Another criticism on VaR is that it pays no attention to the magnitude of losses beyond the VaR value. This and other undesirable features of VaR led to the development of alternative risk measures. One well-known modification of VaR is obtained by computing the expected loss given that the loss exceeds VaR. This quantity is often called conditional Value-at-Risk or CVaR. There are several alternative names for this measure in the finance literature including Mean Expected Loss, Mean Shortfall, and Tail VaR. We now describe this risk measure in more detail and discuss how it can be optimized using linear programming techniques when the loss function is linear in the portfolio positions.

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, one day). Consider, for example, a random variable 3.3. RISK MEASURES: CONDITIONAL VALUE-AT-RISK 37 X that represents loss from an investment portfolio over a fixed period of time. A negative value for X indicates gains. Given a probability level α, α-VaR of the random variable X is given by the following relation: VaRα (X) := min{γ : P (X ≤ γ) ≥ α}. (3.11) The following figure illustrates the 0.95-VaR on a portfolio loss distribution plot: −4 1.4 x 10 VaR Probability Distribution Function 1.2 P(X) 1 0.8 0.6 0.4 0.2 5% 0 Loss VaR0.95(X) VaR is widely used by people in the financial industry and VaR calculators are common features in most financial software. Despite this popularity, VaR has one important undesirable property–it lacks subadditivity. Risk measures should respect the maxim “diversification reduces risk” and therefore, satisfy the following property: “The total risk of two different investment portfolios does not exceed the sum of the individual risks.”

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. , Kn } is a strictly convex function. 3.3 Risk Measures: Conditional Value-at-Risk Financial activities involve risk. Our stock or mutual fund holdings carry the risk of losing value due to market conditions. Even money invested in a bank carries a risk–that of the bank going bankrupt and never returning the money let alone some interest. While individuals generally just have to live with such risks, financial and other institutions can and very often must manage risk using sophisticated mathematical techniques. Managing risk requires a good understanding of risk which comes from quantitative risk measures that adequately reflect the vulnerabilities of a company. Perhaps the best-known risk measure is Value-at-Risk (VaR) developed by financial engineers at J.P. Morgan. VaR is a measure related to percentiles of loss distributions and represents the predicted maximum loss with a specified probability level (e.g., 95%) over a certain period of time (e.g., one day).

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Monte Carlo Simulation and Finance
** by
Don L. McLeish

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Black-Scholes formula, Brownian motion, capital asset pricing model, compound rate of return, discrete time, distributed generation, finite state, frictionless, frictionless market, implied volatility, incomplete markets, invention of the printing press, martingale, p-value, random walk, Sharpe ratio, short selling, stochastic process, stochastic volatility, the market place, transaction costs, value at risk, Wiener process, zero-coupon bond

VARIANCE REDUCTION TECHNIQUES independent with probability density function f (x) = c(1 + (x/b)2 )−2 (the re-scaled student distribution with 3 degrees of freedom). We wish to esP timate a weekly Value at Risk, V ar.95 , a value ev such that P [ 5i=1 Xi < v] = 0.95. If we wish to do this by simulation, suggest an appropriate method involving importance sampling. Implement and estimate the variance reduction. 10. Suppose three diﬀerent simulation estimators Y1 , Y2 , Y3 have means which depend on two unknown parameters θ1 , θ2 so that Y1 , Y2 , Y3 , are unbiased estimators of θ1 , θ1 + θ2 , θ2 respectively. Assume that var(Yi ) = 1, cov(Yi , Yj ) = −1/2 an we want to estimate the parameter θ1 . Should we use only the estimator Y1 which is the unbiased estimator of θ1 , or some linear combination of Y1 , Y2 , Y3 ?

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We can define conditional covariance using conditional expectation as cov(X, Y |Z) = E[XY |Z] − E[X|Z]E[Y |Z] VARIANCE REDUCTION FOR ONE-DIMENSIONAL MONTE-CARLO INTEGRATION.249 and conditional variance: var(X|Z) = E(X 2 |Z) − (E[X|Z])2 . The variance reduction through conditioning is justified by the following wellknown result: Theorem 41 (a)E(X) = E{E[X|Y ]} (b) cov(X, Y ) = E{cov(X, Y |Z)} + cov{E[X|Z], E[Y |Z]} (c) var(X) = E{var(X|Z)} + var{E[X|Z]} This theorem is used as follows. Suppose we are considering a candidate estimator θ̂, an unbiased estimator of θ. We also have an arbitrary random variable Z which is somehow related to θ̂. Suppose that we have chosen Z carefully so that we are able to calculate the conditional expectation T1 = E[θ̂|Z]. Then by part (a) of the above Theorem, T1 is also an unbiased estimator of θ. Define ε = θ̂ − T1 . By part (c), var(θ̂) = var(T1 ) + var(ε) and var(T1 ) = var(θ̂) − var(ε) < var(θ̂). In other words, for any variable Z, E[θ̂|Z] has the same expectation as does θ̂ but smaller variance and the decrease in variance is largest if Z and θ̂ are nearly independent, because in this case E[θ̂|Z] is close to a constant and its variance close to zero.

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It is easy to show once again that the estimator θ̂st is an unbiased estimator of θ, since E(θ̂st ) = aEf (V1 ) + (1 − a)Ef (V2 ) Z a Z 1 1 1 =a f (x) dx + (1 − a) f (x) dx a 1 − a 0 a Z 1 f (x)dx. = 0 Moreover, var(θ̂st ) = a2 var[f (V 1 )] + (1 − a)2 var[f (V 2 )] + 2a(1 − a)cov[f (V 1 ), f (V 2 )]. (4.10) Even when V1 , V2 are independent, so we obtain var(θ̂st ) = a2 var[f (V1 )] + (1 − a)2 var[f (V2 )], there may be a dramatic improvement in variance over crude Monte Carlo provided that the variability of f in each of the intervals [0, a] and [a, 1] is substantially less than in the whole interval [0, 1]. Let us return to the call option example above, with f defined by (4.6). 220 CHAPTER 4. VARIANCE REDUCTION TECHNIQUES Suppose for simplicity we choose independent values of V1 , V2 . In this case var(θ̂st ) = a2 var[f (V1 )] + (1 − a)2 var[f (V2 )]. (4.11) For example for a = .7, this results in a variance of about 0.046 obtained from the following F=a*fn(a*rand(1,500000))+(1-a)*fn(a+(1-a)*rand(1,500000)); var(F) and the variance of the sample mean of the components of the vector F is var(F)/length(F) or around 9.2 × 10−8 .

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Tools for Computational Finance
** by
Rüdiger Seydel

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bioinformatics, Black-Scholes formula, Brownian motion, continuous integration, discrete time, implied volatility, incomplete markets, interest rate swap, linear programming, London Interbank Offered Rate, mandelbrot fractal, martingale, random walk, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process, zero-coupon bond

One example is the Pareto distribution, which has tails behaving like x−α for large The thickness is measured by the kurtosis E((X − µ)4 )/σ 4 . The normal distribution has kurtosis 3. So the excess kurtoris is the diﬀerence to 3. Frequently, data of returns are characterized by large values of excess kurtosis. 8 52 Chapter 1 Modeling Tools for Financial Options x and a constant α > 0. A correct modeling of the tails is an integral basis for value at risk (VaR) calculations. For the risk aspect compare [BaN97], [Dowd98], [EKM97], [ArDEH99]. For distributions that match empirical data see [EK95], [Shi99], [BP00], [MRGS00], [BTT00]. Estimates of future values of the volatility are obtained by (G)ARCH methods, which work with different weights of the returns [Shi99], [Hull00], [Tsay02], [FHH04], [Rup04]. For calibration, the method of [CaM99] is recommendable.

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We denote the resulting antithetic variate by V − . By taking the average (3.21) VAV := 12 V + V − (AV for antithetic variate) we obtain a new approximation, which in many cases is more accurate than V . Since V and VAV are random variables we can only aim at Var(VAV ) < Var(V ) . In view of the properties of variance and covariance (equation (B1.7) in Appendix B1) we have Var(VAV ) = 14 Var(V + V − ) = 14 Var(V ) + 14 Var(V − ) + 12 Cov(V , V − ). From |Cov(X, Y )| ≤ (3.22) 1 [Var(X) + Var(Y )] 2 (follows from (B1.7)) we deduce Var(VAV ) ≤ 1 (Var(V ) + Var(V − )). 2 This shows that in the worst case only the eﬃciency is slightly deteriorated by the additional calculation of V − . The favorable situation is when the covariance is negative. Then (3.22) shows that the variance of VAV can become signiﬁcantly smaller than that of V and V − .

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(B1.4) −∞ The variance is deﬁned as the second central moment ∞ 2 2 (x − µ)2 f (x)dx . σ := Var(X) := E((X − µ) ) = (B1.5) −∞ A consequence is σ 2 = E(X 2 ) − µ2 . The expectation depends on the underlying probability measure P, which is sometimes emphasized by writing EP . Here and in the sequel we assume that the integrals exist. The square root σ = Var(X) is the standard deviation of X. For α, β ∈ IR and two random variables X, Y on the same probability space, expectation and variance satisfy E(αX + βY ) = αE(X) + βE(Y ) Var(αX + β) = Var(αX) = α2 Var(X). (B1.6) The covariance of two random variables X and Y is Cov(X, Y ) := E ((X − E(X))(Y − E(Y ))) = E(XY ) − E(X)E(Y ), from which Var(X ± Y ) = Var(X) + Var(Y ) ± 2Cov(X, Y ) (B1.7) B1 Essentials of Stochastics 255 follows. More general, the covariance between the components of a vector X is the matrix Cov(X) = E[(X − E(X))(X − E(X))tr ] = E(XX tr ) − E(X)E(X)tr , (B1.8) where the expectation E is applied to each component.

**
How Markets Fail: The Logic of Economic Calamities
** by
John Cassidy

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Albert Einstein, Andrei Shleifer, anti-communist, asset allocation, asset-backed security, availability heuristic, bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Black-Scholes formula, Bretton Woods, British Empire, capital asset pricing model, centralized clearinghouse, collateralized debt obligation, Columbine, conceptual framework, Corn Laws, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, Daniel Kahneman / Amos Tversky, debt deflation, diversification, Elliott wave, Eugene Fama: efficient market hypothesis, financial deregulation, financial innovation, Financial Instability Hypothesis, financial intermediation, full employment, George Akerlof, global supply chain, Haight Ashbury, hiring and firing, Hyman Minsky, income per capita, incomplete markets, index fund, invisible hand, John Nash: game theory, John von Neumann, Joseph Schumpeter, laissez-faire capitalism, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, mental accounting, Mikhail Gorbachev, Mont Pelerin Society, moral hazard, mortgage debt, Naomi Klein, Network effects, Nick Leeson, Northern Rock, paradox of thrift, Ponzi scheme, price discrimination, price stability, principal–agent problem, profit maximization, quantitative trading / quantitative ﬁnance, race to the bottom, Ralph Nader, RAND corporation, random walk, Renaissance Technologies, rent control, Richard Thaler, risk tolerance, risk-adjusted returns, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, shareholder value, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical model, technology bubble, The Chicago School, The Great Moderation, The Market for Lemons, The Wealth of Nations by Adam Smith, too big to fail, transaction costs, unorthodox policies, value at risk, Vanguard fund

In addition to offering an instant snapshot of the dangers a firm such as Morgan faced, VAR modeling provided a way for it to monitor changes in risk. For example, when a bank sells some Treasury bonds and buys some volatile technology stocks, its VAR rises by a certain amount, say $10 million, giving its management a precise read on how much extra risk it has taken on. “In contrast with traditional risk measures, VaR provides an aggregate view of a portfolio’s risk that accounts for leverage, correlations, and current positions,” Philippe Jorion, a professor of finance at the University of California, Irvine, wrote in his 1996 book, Value at Risk: The New Benchmark for Controlling Market Risk, which helped to popularize the methodology. “As a result, it is truly a forward looking risk measure.” According to Wall Street folklore, the concept of value-at-risk originated in the late 1980s, when, following the stock market crash of 1987, the late Sir Dennis Weatherstone, J.P.

…

The risk-management techniques that Merrill and many other big financial firms had adopted depended heavily on value-at-risk (VAR) models, which dated back to the 1990s, when they were promoted as a means of avoiding a repeat of previous financial blowups, such as the collapse of Barings Bank and the bankruptcy of Orange County. The keys to the appeal of the VAR (or “VaR”) methodology were its simplicity and its apparent precision. By following a fairly straightforward series of steps, the market-risk department of a bank could provide senior management with an exact dollar estimate of the firm’s losses under a worst-case scenario. In its 1994 annual report, for example, J.P. Morgan, one of the pioneers of the VAR methodology, revealed that the daily VAR of its trading book was $15 million at the 95 percent confidence level, which meant that the probability of its losing more than $15 million in any given trading session was less than one in twenty.

…

Rowe Price Tucker, Albert Tudor Fund Tufts University tulipmania Turning Point, The (Shmelev and Popov) Tversky, Amos Tyco Electronics Corporation UBS Financial Services United Kingdom Financial Services Authority Friedman in Hayek in health care in India Office Millennium Bridge project in moral philosophy in nineteenth century stimulus packages in Treasury of United Nations “Use of Knowledge in Society, The” (Hayek) U.S. Steel Corporation utilitarian philosophy utopian economics Greenspan and Keynes’s attack on reality-based economics versus triumph of market failures and; see also general equilibrium theory invisible hand rational expectations theory specific economists Value at Risk (Jorion) value-at-risk (VAR) models Vanguard Group Versailles, Treaty of Victoria, Queen of England Vienna, University of Vienna Circle Viniar, David Vinik, Jeffrey Volcker, Paul Voltaire von Neumann, John Wachovia Bank Wald, Abraham Wallace, Neil Wall Street Journal, The Wal-Mart Walras, Léon Walters, Alan Warren, Elizabeth Washington, George Washington Mutual Washington University School of Business Waxman, Henry Wealth of Nations, The (Smith) Weatherstone, Dennis Webvan Weill, Sanford “Sandy” Welch, Ivo Welch, Jack Wellesley College Wells Fargo Bank White, William White House Council of Economic Advisers Whither Socialism (Sitglitz) Whitney, Eli Williams, John D.

**
Python for Finance
** by
Yuxing Yan

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asset-backed security, business intelligence, capital asset pricing model, constrained optimization, correlation coefficient, distributed generation, diversified portfolio, implied volatility, market microstructure, P = NP, p-value, quantitative trading / quantitative ﬁnance, Sharpe ratio, time value of money, value at risk, volatility smile

See TORQ database trading strategies about 251 bear spread with calls 251 bear spread with puts 251 bull spread with calls 251 bull spread with puts 251 butterfly with calls 251, 256, 257 butterfly with puts 251 calendar spread 251, 254 [ 384 ] covered call 252 straddle 251-254 strangle 251 strap 251 strip 251 trading volume and closing price, viewing 156 trytond_account_statement module 91 trytond_currency module 91 trytond_project module 91 trytond_stock_forecast module 91 trytond_stock_split module 91 T-test about 193 equal means test, performing 194 equal variances test, performing 194 January effect, testing 195 performing 193, 194 ttest_1samp() function 111 tuple data type 39, 40 two strings combining 37 two-year price movement graphical representation 153, 154 type() function 36 spread (1984) 197, 198 V U uniform distribution random numbers, generating from 312, 313 unique() function 228, 317 Up-and-in option 337 up-and-in parity graphical representation 340-342 Up-and-out option 337 up-and-out parity graphical representation 340-342 upper() function 37, 38 U.S. Department of the Treasury URL 174 useful applications 52-week high and low trading strategy 196 Amihud's model for illiquidity (2002) 198, 199 Pastor and Stambaugh (2003) liquidity measure 199- 201 Roll's model to estimate Value at Risk. See VaR values assigning, to variables 24 vanilla options 335 VaR using 210, 211 variable deleting 27 initializing 17 unsigning 27 values, assigning to 24 values, displaying 24 variance-covariance matrix estimating 212, 214 optimization 214, 215 versions, Python finding 21 Visual financial statements URL 163 volatility about 348, 360 over two periods, equivalency testing 354 versus return, comparing 161, 162 volatility clustering 362, 363 volatility skewness 360, 362 volatility smile 360, 362 W web page data, retrieving from 180, 181 web page examples URL 163 while loop about 284 used, for estimating implied volatility 286, 287 X xlim() function 130 x.sum() dot function 107 [ 385 ] Y Yahoo!

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In this book, we use real-world data for various financial topics. For example, instead of showing how to run CAPM to estimate the beta (market risk), I show you how to estimate IBM, Apple, or Walmart's betas. Rather than just presenting formulae that shows you how to estimate a portfolio's return and risk, the Python programs are given to download real-world data, form various portfolios, and then estimate their returns and risk including Value at Risk (VaR). When I was a doctoral student, I learned the basic concept of volatility smiles. However, until writing this book, I had a chance to download real-world data to draw IBM's volatility smile. [2] Preface What this book covers Chapter 1, Introduction and Installation of Python, offers a short introduction, and explains how to install Python and covers other related issues such as how to launch and quit Python.

…

[ 163 ] Visual Finance via Matplotlib In Chapter 8, Statistical Analysis of Time Series, first we demonstrate how to retrieve historical time series data from several public data sources, such as Yahoo! Finance, Google Finance, Federal Reserve Data Library, and Prof. French's Data Library. Then, we discussed various statistical tests, such as T-test, F-test, and normality test. In addition, we presented Python programs to run capital asset pricing model (CAPM), run a Fama-French three-factor model, estimate the Roll (1984) spread, estimate Value at Risk (VaR) for individual stocks, and also estimate the Amihud (2002) illiquidity measure, and the Pastor and Stambaugh (2003) liquidity measure for portfolios. For the issue of anomaly in finance, we tested the existence of the socalled January effect. For high-frequency data, we explained briefly how to draw intra-day price movement and retrieved data from the Trade, Order, Report and Quote (TORQ) database and the Trade and Quote (TAQ) database.

**
Market Risk Analysis, Quantitative Methods in Finance
** by
Carol Alexander

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asset allocation, backtesting, barriers to entry, Brownian motion, capital asset pricing model, constrained optimization, credit crunch, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, implied volatility, interest rate swap, market friction, market microstructure, p-value, performance metric, quantitative trading / quantitative ﬁnance, random walk, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process, yield curve

The mean excess loss over a threshold u is defined by eu = EX − u X > u (I.3.67) If the excess over threshold has a generalized Pareto distribution (I.3.65) then the mean excess loss has a simple functional form, eu = β + u 1− (I.3.68) Generalized Pareto distributions have useful applications to value at risk (VaR) measurement. In particular, if the portfolio returns have a GPD distribution there are analytic expressions for the VaR and the expected tail loss (ETL), which is the average of all losses that exceed VaR. Probability and Statistics 105 Expected tail loss (also called conditional VaR) is often used for internal VaR measurement because it is a ‘coherent’ risk measure.21 By definition of the mean excess loss, ETL = VaR + eVaR (I.3.69) So to calculate the ETL from historical loss data we take the losses in excess of the VaR level, estimate the parameters β and of a generalized Pareto distribution and compute the quantity (I.3.68) with u = VaR. Adding this quantity to the VaR gives the ETL. Some examples of computing VaR and ETL under the generalized Pareto distribution are given in Sections IV.3.4 and IV.3.6.

…

(independent and identically distributed) variables central limit theorem 121 error process 148 financial modelling 186 GEV distribution 101 regression 148, 157, 175 stable distribution 106 stochastic process 134–5 Implicit function 185 Implied volatility 194, 196, 200–1 Implied volatility surface 200–1 Incremental change 31 Indefinite integral 15 Independent events 74 Independent and identically distributed (i.i.d.) variables central limit theorem 121 error process 148 financial modelling 186 GEV distribution 101 regression 148, 157, 175 stable distribution 106 stochastic process 134–5 284 Index Independent variable 72, 143 random 109–10, 115, 140 Index tracking regression model 182–3 Indicator function 6 Indices, laws 8 Indifference curves 248–9 Inequality constraint, minimum variance portfolio 245–6 Inference 72, 118–29, 141 central limit theorem 120–1 confidence intervals 72, 118–24 critical values 118–20, 122–3, 129 hypothesis tests 124–5 means 125–7 non-parametric tests 127–9 quantiles 118–20 variance 126–7 Inflexion points 14, 35 Information matrix 133, 203 Information ratio 257, 259 Instability, finite difference approximation 209–10 Integrated process, discrete time 134–6 Integration 3, 15–16, 35 Intensity, Poisson distribution 88 Interest rate 34, 171–3 Interest rate sensitivity 34 Interpolation 186, 193–200, 223 cubic spline 197–200 currency option 195–7 linear/bilinear 193–5 polynomial 195–7 Intrinsic value of option 215 Inverse function 6–7, 35 Inverse matrix 41, 43–4, 133 Investment bank 225 Investment 2, 256–7 Investor risk tolerance 230–1, 237 Irrational numbers 7 Isoquants 248 Iteration 186–93, 223 bisection method 187–8 gradient method 191–3 Newton–Raphson method 188–91 Itô’s lemma 138–9, 219 iTraxx Europe credit spread index 172 Jacobian matrix 202 Jarque–Bera normality test Jensen’s alpha 257–8 158 Joint density function 114–15 Joint distribution function 114–15 Joint probability 73 Jumps, Poisson process 139 Kappa indices 263–5 Kernel 106–7 Kolmogorov–Smirnoff test 128 Kuhn–Tucker conditions 30 Kurtosis 81–3, 94–6, 205–6 Lagrange multiplier (LM) test 124, 167 Lagrange multiplier 29–30, 244 Lagrangian function 29–30 Lattice 186, 210–16, 223 Laws of indices 8 Least squares OLS estimation 143–4, 146–50, 153–61, 163, 170–1, 176 problems 201–2 weighted 179 Leptokurtic density 82–3 Levenberg–Marquardt algorithm 202 Lévy distribution 105 Likelihood function 72, 130–31 MLE 72, 130–34, 141, 202–3 optimization 202–3 ratio test 124, 167 Linear function 4–5 Linear interpolation 193–5 Linear portfolios 33, 35 correlation matrix 55–60 covariance matrix 55–61 matrix algebra 55–61 P&L 57–8 returns 25, 56–8 volatility 57–8 Linear regression 143–84 Linear restrictions, hypothesis tests 165–6 Linear transformation 48 Linear utility function 233 LM (Lagrange multiplier) 29–30, 124, 167, 244 Local maxima 14, 28–9 Local minima 14, 28–9 Logarithmic utility function 232 Logarithm, natural 1, 9, 34–5 Log likelihood 131–2 Lognormal distribution 93–4, 213–14, 218–20 Log returns 16, 19–25 Index Long portfolio 3, 17, 238–40 Long-short portfolio 17, 20–1 Low discrepancy sequences 217 Lower triangular square matrix 62, 64 LR (likelihood ratio) test 124, 167 LU decomposition, matrix 63–4 Marginal densities 108–9 Marginal distributions 108–9 Marginal probability 73–4 Marginal utility 229–30 Market behaviour 180–1 Market beta 250 Market equilibrium 252 Market maker 2 Market microstructure 180 Market portfolio 250–1 Market risk premium, CAPM 253 Markets complete 212 regime-specific behaviour 96–7 Markowitz, Harry 226, 238, 266 Markowitz problem 200–1, 226, 244–5 Matrix algebra 37–70 application 38–47 decomposition 61–4, 70 definite matrix 37, 46–7, 54, 58–9, 70 determinant 41–3, 47 eigenvalues/vectors 37–8, 48–54, 59–61, 70 functions of several variables 27–31 general linear model 161–2 hypothesis testing 165–6 invariant 62 inverse 41, 43–4 law 39–40 linear portfolio 55–61 OLS estimation 159–61 PCA 64–70 product 39–40 quadratic form 37, 45–6, 54 regression 159–61, 165–6 simultaneous equation 44–5 singular matrix 40–1 terminology 38–9 Maxima 14, 28–31, 35 Maximum likelihood estimation (MLE) 72, 130–4, 141, 202–3 Mean confidence interval 123 Mean excess loss 104 Mean reverting process 136–7 Mean 78–9, 125–6, 127, 133–4 285 Mean square error 201 Mean–variance analysis 238 Mean–variance criterion, utility theory 234–7 Minima 14, 28–31, 35 Minimum variance portfolio 3, 240–7 Mixture distribution 94–7, 116–17, 203–6 MLE (maximum likelihood estimation) 72, 130–4, 141, 202–3 Modified duration 2 Modified Newton method 192–3 Moments probability distribution 78–83, 140 sample 82–3 Sharpe ratio 260–3 Monotonic function 13–14, 35 Monte Carlo simulation 129, 217–22 correlated simulation 220–2 empirical distribution 217–18 random numbers 217 time series of asset prices 218–20 Multicollinearity 170–3, 184 Multiple restrictions, hypothesis testing 166–7 Multivariate distributions 107–18, 140–1 bivariate 108–9, 116–17 bivariate normal mixture 116–17 continuous 114 correlation 111–14 covariance 110–2 independent random variables 109–10, 114 normal 115–17, 220–2 Student t 117–18 Multivariate linear regression 158–75 BHP Billiton Ltd 162–5, 169–70, 174–5 confidence interval 167–70 general linear model 161–2 hypothesis testing 163–6 matrix notation 159–61 multicollinearity 170–3, 184 multiple regression in Excel 163–4 OLS estimation 159–61 orthogonal regression 173–5 prediction 169–70 simple linear model 159–61 Multivariate Taylor expansion 34 Mutually exclusive events 73 Natural logarithm 9, 34–5 Natural spline 198 Negative definite matrix 46–7, 54 Newey–West standard error 176 286 Index Newton–Raphson iteration 188–91 Newton’s method 192 No arbitrage 2, 179–80, 211–12 Non-linear function 1–2 Non-linear hypothesis 167 Non-linear portfolio 33, 35 Non-parametric test 127–9 Normal confidence interval 119–20 Normal distribution 90–2 Jarque–Bera test 158 log likelihood 131–2 mixtures 94–7, 140–1, 203–6 multivariate 115–16, 220–2 standard 218–19 Normalized eigenvector 51–3 Normalized Student t distribution 99 Normal mixture distribution 94–7, 116–17, 140–1 EM algorithm 203–6 kurtosis 95–6 probabilities of variable 96–7 variance 94–6 Null hypothesis 124 Numerical methods 185–223 binomial lattice 210–6 inter/extrapolation 193–200 iteration 186–93 Objective function 29, 188 Offer price 2 Oil index, Amex 162–3, 169–70, 174 OLS (ordinary least squares) estimation 143–4, 146–50 autocorrelation 176 BHP Billiton Ltd case study 163 heteroscedasticity 176 matrix notation 159–61 multicollinearity 170–1 properties of estimator 155–8 regression in Excel 153–5 Omega statistic 263–5 One-sided confidence interval 119–20 Opportunity set 246–7, 251 Optimization 29–31, 200–6, 223 EM algorithm 203–6 least squares problems 201–2 likelihood methods 202–3 numerical methods 200–5 portfolio allocation 3, 181 Options 1–2 American 1, 215–16 Bermudan 1 call 1, 6 currency 195–7 European 1–2, 195–6, 212–13, 215–16 finite difference approximation 206–10 pay-off 6 plain vanilla 2 put 1 Ordinary least squares (OLS) estimation 143–4, 146–50 autocorrelation 176 BHP Billiton Ltd case study 163 heteroscedasticity 176 matrix notation 159–61 multicollinearity 170–1 properties of estimators 155–8 regression in Excel 153–5 Orthogonal matrix 53–4 Orthogonal regression 173–5 Orthogonal vector 39 Orthonormal matrix 53 Orthonormal vector 53 Out-of-sample testing 183 P&L (profit and loss) 3, 19 backtesting 183 continuous time 19 discrete time 19 financial returns 16, 19 volatility 57–8 Pairs trading 183 Parabola 4 Parameter notation 79–80 Pareto distribution 101, 103–5 Parsimonious regression model 153 Partial derivative 27–8, 35 Partial differential equation 2, 208–10 Pay-off, option 6 PCA (principal component analysis) 38, 64–70 definition 65–6 European equity indices 67–9 multicollinearity 171 representation 66–7 Peaks-over-threshold model 103–4 Percentage returns 16, 19–20, 58 Percentile 83–5, 195 Performance measures, RAPMs 256–65 Period log returns 23–5 Pi 7 Index Piecewise polynomial interpolation 197 Plain vanilla option 2 Points of inflexion 14, 35 Poisson distribution 87–9 Poisson process 88, 139 Polynomial interpolation 195–7 Population mean 123 Portfolio allocation 237–49, 266 diversification 238–40 efficient frontier 246–9, 251 Markowitz problem 244–5 minimum variance portfolio 240–7 optimal allocation 3, 181, 247–9 Portfolio holdings 17–18, 25–6 Portfolio mathematics 225–67 asset pricing theory 250–55 portfolio allocation 237–49, 266 RAPMs 256–67 utility theory 226–37, 266 Portfolios bond portfolio 37 delta-hedged 208 linear 25, 33, 35, 55–61 minimum variance 3, 240–7 non-linear 33, 35 rebalancing 17–18, 26, 248–9 returns 17–18, 20–1, 91–2 risk factors 33 risk free 211–12 stock portfolio 37 Portfolio volatility 3 Portfolio weights 3, 17, 25–6 Positive definite matrices 37, 46–7, 70 correlation matrix 58–9 covariance matrix 58–9 eigenvalues/vectors 54 stationary point 28–9 Posterior probability 74 Post-sample prediction 183 Power series expansion 9 Power utility functions 232–3 Prediction 169–70, 183 Price discovery 180 Prices ask price 2 asset price evolution 87 bid price 2 equity 172 generating time series 218–20 lognormal asset prices 213–14 market microstructure 180 offer price 2 stochastic process 137–9 Pricing arbitrage pricing theory 257 asset pricing theory 179–80, 250–55 European option 212–13 no arbitrage 211–13 Principal cofactors, determinants 41 Principal component analysis (PCA) 38, 64–70 definition 65–6 European equity index 67–9 multicollinearity 171 representation 66–7 Principal minors, determinants 41 Principle of portfolio diversification 240 Prior probability 74 Probability and statistics 71–141 basic concepts 72–85 inference 118–29 laws of probability 73–5 MLE 130–4 multivariate distributions 107–18 stochastic processes 134–9 univariate distribution 85–107 Profit and loss (P&L) 3, 19 backtesting 183 continuous time 19 discrete time 19 financial returns 16, 19 volatility 57–8 Prompt futures 194 Pseudo-random numbers 217 Put option 1, 212–13, 215–16 Quadratic convergence 188–9, 192 Quadratic form 37, 45–6, 54 Quadratic function 4–5, 233 Quantiles 83–5, 118–20, 195 Quartiles 83–5 Quasi-random numbers 217 Random numbers 89, 217 Random variables 71 density/distribution function 75 i.i.d. 101, 106, 121, 135, 148, 157, 175 independent 109–10, 116, 140–1 OLS estimators 155 sampling 79–80 Random walks 134–7 Ranking investments 256 287 288 Index RAPMs (risk adjusted performance measures) 256–67 CAPM 257–8 kappa indices 263–5 omega statistic 263–5 Sharpe ratio 250–1, 252, 257–63, 267 Sortino ratio 263–5 Realization, random variable 75 Realized variance 182 Rebalancing of portfolio 17–18, 26, 248–9 Recombining tree 210 Regime-specific market behaviour 96–7, 117 Regression 143–84 autocorrelation 175–9, 184 financial applications 179–83 heteroscedasticity 175–9, 184 linear 143–84 multivariate linear 158–75 OLS estimator properties 155–8 simple linear model 144–55 Relative frequency 77–8 Relative risk tolerance 231 Representation, PCA 66–7 Residuals 145–6, 157, 175–8 Residual sum of squares (RSS) 146, 148–50, 159–62 Resolution techniques 185–6 Restrictions, hypothesis testing 165–7 Returns 2–3, 16–26 absolute 58 active 92, 256 CAPM 253–4 compounding 22–3 continuous time 16–17 correlated simulations 220 discrete time 16–17, 22–5 equity index 96–7 geometric Brownian motion 21–2 linear portfolio 25, 56–8 log returns 16, 19–25 long-short portfolio 20–1 multivariate normal distribution 115–16 normal probability 91–2 P&L 19 percentage 16, 19–20, 59–61 period log 23–5 portfolio holdings/weights 17–18 risk free 2 sources 25–6 stochastic process 137–9 Ridge estimator, OLS 171 Risk active risk 256 diversifiable risk 181 portfolio 56–7 systematic risk 181, 250, 252 Risk adjusted performance measure (RAPM) 256–67 CAPM 257–8, 266 kappa indices 263–5 omega statistic 263–5 Sharpe ratio 251, 252, 257–63, 267 Sortino ratio 263–5 Risk averse investor 248 Risk aversion coefficients 231–4, 237 Risk factor sensitivities 33 Risk free investment 2 Risk free portfolio 211 Risk free returns 2 Risk loving investors 248–9 Risk neutral valuation 211–12 Risk preference 229–30 Risk reversal 195–7 Risk tolerance 230–1, 237 Robustness 171 Roots 3–9, 187 RSS (residual sum of squares) 146, 148–50, 159–62 S&P 100 index 242–4 S&P 500 index 204–5 Saddle point 14, 28 Sample 76–8, 82–3 Sampling distribution 140 Sampling random variable 79–80 Scalar product 39 Scaling law 106 Scatter plot 112–13, 144–5 SDE (stochastic differential equation) 136 Security market line (SML) 253–4 Self-financing portfolio 18 Sensitivities 1–2, 33–4 Sharpe ratio 257–63, 267 autocorrelation adjusted 259–62 CML 251, 252 generalized 262–3 higher moment adjusted 260–2 making decision 258 stochastic dominance 258–9 Sharpe, William 250 Short portfolio 3, 17 22, 134, Index Short sales 245–7 Short-term hedging 182 Significance level 124 Similarity transform 62 Similar matrices 62 Simple linear regression 144–55 ANOVA and goodness of fit 149–50 error process 148–9 Excel OLS estimation 153–5 hypothesis tests 151–2 matrix notation 159–61 OLS estimation 146–50 reporting estimated model 152–3 Simulation 186, 217–22 Simultaneous equations 44–5 Singular matrix 40–1 Skewness 81–3, 205–6 Smile fitting 196–7 SML (security market line) 253–4 Solver, Excel 186, 190–1, 246 Sortino ratio 263–5 Spectral decomposition 60–1, 70 Spline interpolation 197–200 Square matrix 38, 40–2, 61–4 Square-root-of-time scaling rule 106 Stable distribution 105–6 Standard deviation 80, 121 Standard error 80, 169 central limit theorem 121 mean/variance 133–4 regression 148–9 White’s robust 176 Standard error of the prediction 169 Standardized Student t distribution 99–100 Standard normal distribution 90, 218–19 Standard normal transformation 90 Standard uniform distribution 89 Stationary point 14–15, 28–31, 35 Stationary stochastic process 111–12, 134–6 Stationary time series 64–5 Statistical arbitrage strategy 182–3 Statistical bootstrap 218 Statistics and probability 71–141 basic concepts 72–85 inference 118–29 law of probability 73–5 MLE 130–4 multivariate distribution 107–18 stochastic process 134–9 univariate distribution 85–107 Step length 192 Stochastic differential equation (SDE) 22, 134, 136 Stochastic dominance 227, 258–9 Stochastic process 72, 134–9, 141 asset price/returns 137–9 integrated 134–6 mean reverting 136–7 Poisson process 139 random walks 136–7 stationary 111–12, 134–6 Stock portfolio 37 Straddle 195–6 Strangle 195–7 Strictly monotonic function 13–14, 35 Strict stochastic dominance 258 Structural break 175 Student t distribution 97–100, 140 confidence intervals 122–3 critical values 122–3 equality of means/variances 127 MLE 132 multivariate 117–18 regression 151–3, 165, 167–8 simulation 220–2 Sum of squared residual, OLS 146 Symmetric matrix 38, 47, 52–4, 61 Systematic risk 181, 250, 252 Tail index 102, 104 Taylor expansion 2–3, 31–4, 36 applications 33–4 approximation 31–4, 36 definition 32–3 multivariate 34 risk factor sensitivities 33 Theory of asset pricing 179–80, 250–55 Tic-by-tic data 180 Time series asset prices/returns 137–9, 218–20 lognormal asset prices 218–20 PCA 64–5 Poisson process 88 regression 144 stochastic process 134–9 Tobin’s separation theorem 250 Tolerance levels, iteration 188 Tolerance of risk 230–1, 237 Total derivative 31 Total sum of square (TSS) 149, 159–62 289 290 Index Total variation, PCA 66 Tower law for expectations 79 Traces of matrix 62 Tradable asset 1 Trading, regression model 182–3 Transition probability 211–13 Transitive preferences 226 Transposes of matrix 38 Trees 186, 209–11 Treynor ratio 257, 259 TSS (total sum of squares) 149, 159–62 Two-sided confidence interval 119–21 Unbiased estimation 79, 81, 156–7 Uncertainty 71 Unconstrained optimization 29 Undiversifiable risk 252 Uniform distribution 89 Unit matrix 40–1 Unit vector 46 Univariate distribution 85–107, 140 binomial 85–7, 212–13 exponential 87–9 generalized Pareto 101, 103–5 GEV 101–3 kernel 106–7 lognormal 93–4, 213–14, 218–20 normal 90–7, 115–16, 131–2, 140, 157–8, 203–6, 217–22 normal mixture 94–7, 140, 203–6 Poisson 87–9 sampling 100–1 stable 105–6 Student t 97–100, 122–3, 126, 132–3, 140–1, 151–3, 165–8, 220–2 uniform 89 Upper triangular square matrix 62, 64 Utility theory 226–37, 266 mean–variance criterion 234–7 properties 226–9 risk aversion coefficient 231–4, 237 risk preference 229–30 risk tolerance 230–1, 237 Value at risk (VaR) 104–6, 185, 194 Vanna–volga interpolation method 196 Variance ANOVA 143–4, 149–50, 154, 159–60, 164–5 confidence interval 123–4 forecasting 182 minimum variance portfolio 3, 240–7 mixture distribution 94–6 MLE 133 normal mixture distribution 95–6 portfolio volatility 3 probability distribution 79–81 realized 182 tests on variance 126–7 utility theory 234–7 VaR (value at risk) 104–6, 185, 194 Vector notation, functions of several variables 28 Vectors 28, 37–9, 48–54, 59–61, 70 Venn diagram 74–5 Volatility equity 3, 172–3 implied volatility 194, 196–7, 200–1 interpolation 194, 196–7 linear portfolio 57–8 long-only portfolio 238–40 minimum variance portfolio 240–4 portfolio variance 3 Volpi, Leonardo 70 Vstoxx index 172 Waiting time, Poisson process 88–9 Wald test 124, 167 Weakly stationary process 135 Weak stochastic dominance 258–9 Weibull distribution 103 Weighted least squares 179 Weights, portfolio 3, 17, 25–6 White’s heteroscedasticity test 177–8 White’s robust standard errors 176 Wiener process 22, 136 Yield 1, 197–200 Zero matrix 39 Z test 126

…

The allocations to risky assets that give portfolios with the minimum possible risk (as measured by the portfolio volatility) can only be determined analytically when there are no specific constraints on the allocations such as ‘no more than 5% of the capital should be allocated to US bonds’. The value at risk (VaR) of a portfolio has an analytic solution only under certain assumptions about the portfolio and its returns process. Otherwise we need to use a numerical method – usually simulation – to compute the VaR of a portfolio. The yield on a bond is the constant discount rate that, when applied to the future cash flows from the bond, gives its market price. Given the market price of a typical bond, we can only compute its yield using a numerical method. When we make realistic assumptions about the evolution of the underlying price, such as that the price process has a stochastic volatility, then the only way that we can find a theoretical price of an American option is using a numerical method such as finite differences or Monte Carlo simulations.

**
All the Devils Are Here
** by
Bethany McLean

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Asian financial crisis, asset-backed security, bank run, Black-Scholes formula, call centre, collateralized debt obligation, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Exxon Valdez, fear of failure, financial innovation, fixed income, high net worth, Home mortgage interest deduction, interest rate swap, laissez-faire capitalism, Long Term Capital Management, margin call, market bubble, market fundamentalism, Maui Hawaii, moral hazard, mortgage debt, Northern Rock, Own Your Own Home, Ponzi scheme, quantitative trading / quantitative ﬁnance, race to the bottom, risk/return, Ronald Reagan, Rosa Parks, shareholder value, short selling, South Sea Bubble, statistical model, telemarketer, too big to fail, value at risk

J.P. Morgan’s chief contribution in this area was something called the credit default swap. Its breakthrough risk model was called Value at Risk, or VaR. Both products quickly became tools that everyone on Wall Street relied on. What did these innovations have to do with subprime mortgages? Nothing, at first. J.P. Morgan and Ameriquest could have been operating on different planets, so little did they have to do with each other. But in time, Wall Street realized that the same principles that underlay J.P. Morgan’s risk model could be adapted to bestow coveted triple-A ratings on large chunks of complex new products created out of subprime mortgages. Firms could use VaR to persuade regulators—and themselves—that they were taking on very little risk, even as they were loading up on subprime securities.

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John Thain Co-COO under Paulson until 2003. Fabrice Tourre Mortgage trader under Sparks. Later named as a defendant in the SEC’s suit against the company. David Viniar CFO. J.P. Morgan Mark Brickell Lobbyist who fought derivatives regulation on behalf of J.P. Morgan and the International Swaps and Derivatives Association. President of ISDA from 1988 to 1992. Till Guldimann Executive who led the development of Value at Risk modeling and shared VaR with other banks. Blythe Masters Derivatives saleswoman who put together J.P. Morgan’s first credit default swap in 1994. Sir Dennis Weatherstone Chairman and CEO from 1990 to 1994. Merrill Lynch Michael Blum Executive charged with purchasing a mortgage company, First Franklin, in 2006. Served on Ownit’s board. John Breit Longtime Merrill Lynch risk manager who specialized in evaluating derivatives risk.

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Regulates securities firms, mutual funds, and other entities that trade stocks on behalf of investors. SMMEA: Secondary Mortgage Market Enhancement Act. The first of two laws passed in the 1980s to aid the new mortgage-backed securities market SIV: Structured investment vehicle. Thinly capitalized entities set up by banks and others to invest in securities. By the height of the boom, many ended up owning billions in CDOs and other mortgage-backed securities. VaR: Value at Risk. Key measure of risk developed by J.P. Morgan in the early 1990s. Prologue Stan O’Neal wanted to see him. How strange. It was September 2007. The two men hadn’t talked in years, certainly not since O’Neal had become CEO of Merrill Lynch in 2002. Back then, John Breit had been one of the company’s most powerful risk managers. A former physicist, Breit had been the head of market risk.

**
I.O.U.: Why Everyone Owes Everyone and No One Can Pay
** by
John Lanchester

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asset-backed security, bank run, banking crisis, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Black-Scholes formula, Celtic Tiger, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, diversified portfolio, double entry bookkeeping, Exxon Valdez, Fall of the Berlin Wall, financial deregulation, financial innovation, fixed income, George Akerlof, greed is good, hindsight bias, housing crisis, Hyman Minsky, interest rate swap, invisible hand, Jane Jacobs, John Maynard Keynes: Economic Possibilities for our Grandchildren, laissez-faire capitalism, liquidity trap, Long Term Capital Management, loss aversion, Martin Wolf, mortgage debt, mortgage tax deduction, mutually assured destruction, new economy, Nick Leeson, Northern Rock, Own Your Own Home, Ponzi scheme, quantitative easing, reserve currency, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Reagan, shareholder value, South Sea Bubble, statistical model, The Great Moderation, the payments system, too big to fail, tulip mania, value at risk

Such people understand that taking calculated risks is quite different from being rash.”6 He put this into practice by encouraging Bankers Trust to develop a precisely quantified measure of risk, a system which became known as risk-adjusted return on capital, or RAROC. RAROC offered a numerical analysis of risk and added to it a measure of the impact of that risk on a business’s profitability; just as portfolio management provided a way of assessing and optimizing the risk of a set of share holdings, RAROC did the same for a company’s or bank’s range of businesses. In time, however, the industry came to prefer a newer model of risk, called value at risk, or VAR. This was a statistical technique which really took off in the later 1980s, as a response to the Black Monday stock market crash of October 1987. On that occasion, many players were appalled by the speed and severity of their losses—losses which, it’s now thought, were in large part caused by computer programs running “portfolio insurance.” That was yet another invention, the brainchild of a young California academic named Hayne Leland, who worked out that thanks to the Black-Scholes equation and subsequent takeoff of the options industry, options could now be used to create a form of insurance against share prices dropping, not just one by one but across an entire investment portfolio.

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., 43, 54, 64, 74, 76–78 AIG bailout and, 76, 78 regulation and, 188–90 Treasury bills (T-bills), 29–30, 62, 103, 118, 144, 208 China’s investment in, 109, 176–77 Trichet, Jean-Claude, 92 Trillion Dollar Meltdown, The (Morris), 42 Troubled Assets Relief Program (TARP), 37, 189 Turner, Adair, 181 Tversky, Amos, 136–38, 141 UBS, 36, 120 uncertainty, 96 fair value theory and, 147–48 risk and, 55–56, 153, 163 United Kingdom, 9, 11–12, 18, 28–29, 61, 122–24, 134, 139, 194–202, 216–18 banking in, 5, 11, 32–36, 38–40, 51–54, 76–77, 89, 94, 120, 146, 180, 194–96, 199, 202, 204–6, 211–12, 217, 227–28 bill of, 220–22, 224 and City of London, 21–22, 32, 195–97, 200, 217–18 credit ratings and, 123–24, 209 derivatives and, 72, 200–201 financial vs. industrial interests in, 196–99 free-market capitalism in, 14–15, 21, 230 GDP of, 32, 214, 220 Goodwin’s pension and, 76–77 housing in, 38, 87–98, 110, 122, 177–78 interest rates in, 102, 177–80 personal debt in, 221–22 prosperity of, 214, 216 regulation in, 21–22, 105n, 180–82, 194–96, 199–201, 218 United Nations, 4 United States, 17–22, 34, 62–71, 120–31, 134n, 165, 199–201 AIG bailout and, 76–78 banks of, 36–37, 39–40, 43, 63–71, 73, 75, 77–78, 84, 116, 120–21, 127, 150, 152, 163, 183, 185, 190, 195, 204, 211–12, 219–20, 225, 227–28 bill of, 219–20 China’s investment in, 109, 176–77 credit and, 109, 123–24, 195, 208–9, 211 free-market capitalism in, 14–15, 230 housing in, 37, 82–86, 95, 97–101, 109–10, 114–15, 122, 125–31, 157–58, 163 interest rates in, 102, 107–8, 173–77 regulation in, 181, 184–92, 195, 199–200, 223–24, 227 urban desolation in, 81–86 value, values, 42, 74–75, 78–80, 103–4, 179, 181, 217–18, 220, 227 bonds and, 61, 103 derivatives and, 38, 48–49, 185, 201 housing and, 28–29, 71, 90, 92–95, 111, 176 investing and, 60–61, 104, 198 LTCM and, 55–56 notional, 38, 48–49, 80 value at risk (VAR), 151–57, 162–63 Vietnam War, 18, 220 Viniar, David, 163 volatility, 20, 158 risk and, 47–48, 148–50, 161 Volcker, Paul, 20 Waldrow, Mary, 127 Wall Street, 22, 53, 64, 129, 188 Washington Post, The, 18 wealth, 4, 10, 19–21, 64, 204, 206 financial industry’s ascent and, 20–21 in free-market capitalism, 15, 19, 230 housing and, 87, 90, 121 Keynes’s predictions on, 214–15 in West, 218–19 Weatherstone, Dennis, 152 Wells Fargo, 84, 127 Wessex Water, 105n West, 14–18, 43, 213, 231 conflict between Communist bloc and, 16–18 free-market capitalism in, 14–15, 17, 21, 23 wealth in, 218–19 wheat, 49n, 52 When Genius Failed (Lowenstein), 161 Williams, John Burr, 147 Wilson, Lashawn, 130–31 Wire, The, 83–84 World Bank, 58, 65, 69 * GDP, which will be mentioned quite a few times in this story, sounds complicated but isn’t: it’s nothing more than the value of all the goods and services produced in an economy.

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The most thoughtful advocates of VAR at times sound oddly like its critics. Philippe Jorion is a California-based French economist who took part in a famous-to-quants exchange with Nassim Taleb in April 1997. Jorion made a number of measured points about the usefulness of VAR and then disagreed with Taleb about some specific issues to do with how well VAR predicted unusual and non-bell-curvy phenomena. A wobbly speedometer, Jorion said, was more useful than no speedometer at all. Then he came to this moderate and sensible-sounding conclusion: It seems premature to describe VAR as “charlatanism.” In spite of naysayers, VAR is an essential component of sound risk management systems. VAR gives an estimate of potential losses given market risks. In the end, the greatest benefit of VAR lies in the imposition of a structured methodology for critically thinking about risk.

**
The Crisis of Crowding: Quant Copycats, Ugly Models, and the New Crash Normal
** by
Ludwig B. Chincarini

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affirmative action, asset-backed security, automated trading system, bank run, banking crisis, Basel III, Bernie Madoff, Black-Scholes formula, buttonwood tree, Carmen Reinhart, central bank independence, collapse of Lehman Brothers, collateralized debt obligation, collective bargaining, corporate governance, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discounted cash flows, diversification, diversified portfolio, family office, financial innovation, financial intermediation, fixed income, Flash crash, full employment, Gini coefficient, high net worth, hindsight bias, housing crisis, implied volatility, income inequality, interest rate derivative, interest rate swap, labour mobility, liquidity trap, London Interbank Offered Rate, Long Term Capital Management, low skilled workers, margin call, market design, market fundamentalism, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, mortgage debt, Northern Rock, Occupy movement, oil shock, price stability, quantitative easing, quantitative hedge fund, quantitative trading / quantitative ﬁnance, Ralph Waldo Emerson, regulatory arbitrage, Renaissance Technologies, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Reagan, Sharpe ratio, short selling, sovereign wealth fund, speech recognition, statistical arbitrage, statistical model, systematic trading, The Great Moderation, too big to fail, transaction costs, value at risk, yield curve, zero-coupon bond

Good models could generate more complicated security-price distributions, but might also ultimately measure risks more accurately.3 Risk models’ failure to account for crowding and interconnectedness also played an important role in risk misvaluation during 2008’s financial crisis.4 VaR There are limitations to VaR, stress testing, or any other risk management system. LTCM’s risk management system rested on selecting a portfolio with a large number of low-volatility trades, all with very low correlations to one another. The portfolio had a very low estimated value-at-risk (VaR) before the fund collapsed in August and September 1998. Extremely large directional bets often bring down traders and hedge funds, but this wasn’t the case for LTCM. LTCM’s failure illustrates some of the limitations of VaR analysis and stress testing—as well as the impossibility of stress testing the unimaginable. VaR analysis is nothing new. In its simplest form, it involves using a return process’s standard deviation to estimate how much a trader or portfolio manager might lose if one event or another takes place.

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If traders measured this correlation inaccurately and correlations across strategies were in fact higher than estimated, the fund’s loss risk was much larger. A simple value-at-risk (VaR) formula for the above structure is: (A.9) where represents the expected return of the levered portfolio, represents the standard deviation of the levered portfolio, Vt represents the initial portfolio value, and k represents the confidence level critical value, assuming a normal distribution (i.e., k = 1.96 for a 97.5% confidence interval).9 Table A.1 presents the potential VaR calculations at a 99% confidence level for a normal distribution (k = 2.33) and a capital base of $4.8B (the amount that LTCM had at the beginning of 1998). The VaR numbers are presented as monthly numbers. Given the correlation coefficient, this represents what might have been expected to occur in any given month at LTCM. TABLE A.1 Sensitivity of VaR to Strategy Correlations Table A.1 shows that an unlevered fund’s standard deviation was 0.0951% per month and 0.6723% per month with a correlation of 0 and 1 respectively.

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What’s more, lenders may decide to stop lending to a fund, forcing a leveraged portfolio to sell positions, further exacerbating its losses. Measuring Risk Measuring risk is difficult. Portfolio returns come from a return distribution. That distribution may include a –100% return, which means losing the entire portfolio. Thus, one way to measure risk is to measure the worst-case scenario: losing everything. That doesn’t tell us very much about more typical risks. A more useful risk measurement uses a portfolio’s value-at-risk (VaR). This measure gives an estimate of the largest losses a portfolio is likely to suffer in a given period in all but truly exceptional circumstances. The calculation depends on a host of inputs, including the portfolio’s expected return, the portfolio’s volatility, and the fund manager’s degree of confidence in the largest loss. Oftentimes the inputs, like the expected return, volatility, and trade correlation, come from historical data.

**
How I Became a Quant: Insights From 25 of Wall Street's Elite
** by
Richard R. Lindsey,
Barry Schachter

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Albert Einstein, algorithmic trading, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, asset allocation, asset-backed security, backtesting, bank run, banking crisis, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, business process, buy low sell high, capital asset pricing model, centre right, collateralized debt obligation, corporate governance, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, discounted cash flows, disintermediation, diversification, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, full employment, George Akerlof, Gordon Gekko, hiring and firing, implied volatility, index fund, interest rate derivative, interest rate swap, John von Neumann, linear programming, Loma Prieta earthquake, Long Term Capital Management, margin call, market friction, market microstructure, martingale, merger arbitrage, Nick Leeson, P = NP, pattern recognition, pensions crisis, performance metric, prediction markets, profit maximization, purchasing power parity, quantitative trading / quantitative ﬁnance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Richard Feynman, Richard Stallman, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, sorting algorithm, statistical arbitrage, statistical model, stem cell, Steven Levy, stochastic process, systematic trading, technology bubble, The Great Moderation, the scientific method, too big to fail, trade route, transaction costs, transfer pricing, value at risk, volatility smile, Wiener process, yield curve, young professional

Since this time, savvy investors have begun to employ several compensating techniques in order to accommodate the peculiarities of hedge fund data, including conditional value at risk (CVaR) in recognition of the distinctly nonsymmetric, lefttail-skewed, reality of hedge fund investing;18 resampled optimization in recognition of the frailties of error estimation and the fact that life is, sadly, out of sample;19 and double secret probation mechanisms for developing and incorporating forward-looking views on return, volatility, and correlation. The second culprit VaR has been used, and is in my experience still used, to substantiate the assumption of risk that, in a qualitative JWPR007-Lindsey 196 April 30, 2007 18:3 h ow i b e cam e a quant framework, would be unacceptable. The most recent example that I observed (a.k.a. lost money as a result of) involved a commodity manager who went home on a Friday afternoon with a reported daily VaR of approximately 5 percent.

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This nonquant manager is still in business, in a hedge fund whereas the “smarter” quant trader is not. This goes to show that sometimes the business model is more important than the quantitative model. JWPR007-Lindsey May 7, 2007 17:9 Julian Shaw 235 The Strange Evolution of Value at Risk In the beginning, VaR calculations were usually based on the assumption of a multivariate normal distribution of a large number of market risk factors, a method generally known as variance-covariance or VCV. The variances and covariances of these factors were estimated with complex GARCH models (or particularizations of GARCH such as exponential smoothing). What is the situation today? Are today’s VaR models even more complex? No, they are much simpler! Almost everyone, even at JP Morgan where the multivariate normal approach was invented, has switched to an approach so simple even my mother can understand—historical simulation, or HistSim.

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Journal of Financial Engineering (December 1998). Value at Risk, in the Handbook of Risk Management and Analysis, Volume I: Measuring and Managing Financial Risks. Ed. Carol Alexander (New York: John Wiley & Sons, 1998). “Portfolio Credit Risk”, Economic Policy Review, Federal Reserve Bank of New York (October 1998). Wilson, Thomas. “CreditPortfolioViewTM : Technical Documentation.” McKinsey & Company, 1998. Wilson, Thomas. “Managing Credit Portfolio Risk, Parts I and II.” Risk (September–October 1997). Wilson, Thomas. “Credit Portfolio Risk, Parts I and II.” Journal of Lending and Credit Risk Management (August–September 1997). Wilson, Thomas. “Plugging the Gap.” Risk (November 1994) (development of a delta-gamma VaR method). Wilson, Thomas. “Debunking the Myths.” Risk (April 1994) (application of factor analysis to VaR calculations for multicurrency term structures).

**
The New Science of Asset Allocation: Risk Management in a Multi-Asset World
** by
Thomas Schneeweis,
Garry B. Crowder,
Hossein Kazemi

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asset allocation, backtesting, Bernie Madoff, Black Swan, capital asset pricing model, collateralized debt obligation, commodity trading advisor, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, diversified portfolio, fixed income, high net worth, implied volatility, index fund, interest rate swap, invisible hand, market microstructure, merger arbitrage, moral hazard, passive investing, Richard Feynman, Richard Feynman, Richard Feynman: Challenger O-ring, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, short selling, statistical model, systematic trading, technology bubble, the market place, Thomas Kuhn: the structure of scientific revolutions, transaction costs, value at risk, yield curve

In this section, we use value at risk (VaR) to measure a portfolio’s overall risk. Then we show how the VaR of a portfolio can be decomposed so one could know how allocation to each asset class contributes to the total risk of the portfolio. In this way, the portfolio manager can balance the potential return from each allocation by the contribution of the allocation to the total risk of the portfolio. As was pointed out in Chapter 2, the VaR of a portfolio measures its potential losses due to market risks. In particular, the daily VaR of a portfolio at the confidence level of α states that the portfolio will not suffer a loss greater than VaR with probability of α. Let Var(Rp) denote the perperiod VaR of a portfolio. Then this measure of total risk can be decomposed as follows: VaR( Rp ) = MVaR( R1 ) × w1 + MVaR( R2 ) × w2 + … + MVaR(RN ) × wN where MVaR(Ri) is the marginal VaR of asset class i and it measures the contribution of one unit of asset class i to the total VaR of the portfolio.

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For example, Surplus-at-Risk (SAR)/Liability Driven Investment (LDI) often seeks to minimize risk relative to liabilities, rather than broad, return based benchmarks with the goal of delivering nominal, inflation-linked, or wagelinked defined benefits. VALUE AT RISK A chapter on risk and what it is would not be complete (and it never is) without a mention of the concept of “value at risk” or VaR. For a given portfolio, probability, and time horizon, VaR is defined as the loss that is expected to be exceeded with the given probability, over the given time horizon under normal market conditions assuming that there is no portfolio rebalancing. For example, if a portfolio of stocks has a one-day VaR of $1 million at the 95% confidence level, then there is 5% chance that the one- 35 Measuring Risk day loss of the portfolio could exceed $1 million assuming normal market conditions and no intra day rebalancing.

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The question remains, however, as to how best to ensure that those making the regulations, those creating the products, those selling the products, and those purchasing the products have any real level of financial knowledge. How to educate, how to inform, how to reeducate, and how to reinform is the struggle for the next decade. ■ ■ NOTE 1. There is considerable research on alternative means of tracking and evaluating the potential volatility of existing fund strategies and overall portfolio risk. The generic term given to such analysis often falls under the classification of VaR (value at risk), which often offers a simplified forecast of the probability of losing more than x dollars of asset value. The entire area of monitoring and evaluating fund risk is constantly evolving, and readers are directed to articles in academic (The Journal of Alternative Investments) and practitioner press to track changes and advances in the field. APPENDIX Risk and Return of Asset Classes and Risk Factors Through Business Cycles This appendix presents graphs of risks and returns of major asset classes through time.

**
Market Sense and Nonsense
** by
Jack D. Schwager

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asset allocation, Bernie Madoff, Brownian motion, collateralized debt obligation, commodity trading advisor, conceptual framework, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, diversification, diversified portfolio, fixed income, high net worth, implied volatility, index arbitrage, index fund, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, market fundamentalism, merger arbitrage, pattern recognition, performance metric, pets.com, Ponzi scheme, quantitative trading / quantitative ﬁnance, random walk, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sharpe ratio, short selling, statistical arbitrage, statistical model, transaction costs, two-sided market, value at risk, yield curve

It is not a sufficient indicator because in some cases, high volatility may be due to large gains while losses are well controlled. The Problem with Value at Risk (VaR) Value at risk (VaR) is a worst-case loss estimate that is most prone to serious error in worst-case situations. The VaR can be defined as the loss threshold that will not be exceeded within a specified time interval at some high confidence level (typically, 95 percent or 99 percent). The VaR can be stated in either dollar or percentage terms. For example, a 3.2 percent daily VaR at the 99 percent confidence level would imply that the daily loss is expected to exceed 3.2 percent on only 1 out of 100 days. To convert a VaR from daily to monthly, we multiply it by 4.69, the square root of 22 (the approximate number of trading days in a month). Therefore the 3.2 percent daily VaR would also imply that the monthly loss is expected to exceed 15.0 percent (3.2% × 4.69) only once out of every 100 months.

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Reality: For portfolios with significant illiquid holdings, the value that would be realized if the portfolio had to be liquidated might be considerably lower than implied by market prices because of the slippage that would occur in exiting positions. Investment Misconception 14: Value at risk (VaR) provides a good indication of worst-case risk. Reality: VaR may severely understate worst-case risk when the look-back period used to calculate this statistic is not representative of the future volatility and correlation levels of the portfolio holdings. Following transitions from benign market environments to liquidation-type markets, realized losses can far exceed the thresholds implied by previous VaR levels. By the time VaR adequately adjusts to the new high-risk environment, larger-than-anticipated losses may already have been realized. Investment Insights Standard risk measures are often poor indicators of actual risk.

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Hedge Funds: Relative Performance of the Past Highest-Return Strategy Why Do Past High-Return Sectors and Strategy Styles Perform So Poorly? Wait a Minute. Do We Mean to Imply . . .? Investment Insights Chapter 4: The Mismeasurement of Risk Worse Than Nothing Volatility as a Risk Measure The Source of the Problem Hidden Risk Evaluating Hidden Risk The Confusion between Volatility and Risk The Problem with Value at Risk (VaR) Asset Risk: Why Appearances May Be Deceiving, or Price Matters Investment Insights Chapter 5: Why Volatility Is Not Just about Risk, and the Case of Leveraged ETFs Leveraged ETFs: What You Get May Not Be What You Expect Investment Insights Chapter 6: Track Record Pitfalls Hidden Risk The Data Relevance Pitfall When Good Past Performance Is Bad The Apples-and-Oranges Pitfall Longer Track Records Could Be Less Relevant Investment Insights Chapter 7: Sense and Nonsense about Pro Forma Statistics Investment Insights Chapter 8: How to Evaluate Past Performance Why Return Alone Is Meaningless Risk-Adjusted Return Measures Visual Performance Evaluation Investment Insights Chapter 9: Correlation: Facts and Fallacies Correlation Defined Correlation Shows Linear Relationships The Coefficient of Determination (r2) Spurious (Nonsense) Correlations Misconceptions about Correlation Focusing on the Down Months Correlation versus Beta Investment Insights Part Two: Hedge Funds as an Investment Chapter 10: The Origin of Hedge Funds Chapter 11: Hedge Funds 101 Differences between Hedge Funds and Mutual Funds Types of Hedge Funds Correlation with Equities Chapter 12: Hedge Fund Investing: Perception and Reality The Rationale for Hedge Fund Investment Advantages of Incorporating Hedge Funds in a Portfolio The Special Case of Managed Futures Single-Fund Risk Investment Insights Chapter 13: Fear of Hedge Funds: It’s Only Human A Parable Fear of Hedge Funds Chapter 14: The Paradox of Hedge Fund of Funds Underperformance Investment Insights Chapter 15: The Leverage Fallacy The Folly of Arbitrary Investment Rules Leverage and Investor Preference When Leverage Is Dangerous Investment Insights Chapter 16: Managed Accounts: An Investor-Friendly Alternative to Funds The Essential Difference between Managed Accounts and Funds The Major Advantages of a Managed Account Individual Managed Accounts versus Indirect Managed Account Investment Why Would Managers Agree to Managed Accounts?

**
Currency Wars: The Making of the Next Gobal Crisis
** by
James Rickards

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Asian financial crisis, bank run, Benoit Mandelbrot, Berlin Wall, Big bang: deregulation of the City of London, Black Swan, borderless world, Bretton Woods, BRICs, British Empire, business climate, capital controls, Carmen Reinhart, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, Daniel Kahneman / Amos Tversky, Deng Xiaoping, diversification, diversified portfolio, Fall of the Berlin Wall, family office, financial innovation, floating exchange rates, full employment, game design, German hyperinflation, Gini coefficient, global rebalancing, global reserve currency, high net worth, income inequality, interest rate derivative, Kenneth Rogoff, labour mobility, laissez-faire capitalism, liquidity trap, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Mexican peso crisis / tequila crisis, money: store of value / unit of account / medium of exchange, Network effects, New Journalism, Nixon shock, offshore financial centre, oil shock, open economy, paradox of thrift, price mechanism, price stability, private sector deleveraging, quantitative easing, race to the bottom, RAND corporation, rent-seeking, reserve currency, Ronald Reagan, sovereign wealth fund, special drawing rights, special economic zone, The Myth of the Rational Market, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, time value of money, too big to fail, value at risk, War on Poverty, Washington Consensus

The application of these flawed theories to actual capital markets activity contributed to the 1987 stock market crash, the 1998 implosion of Long-Term Capital Management and the greatest catastrophe of all—the Panic of 2008. One contagious virus that spread the financial economics disease was known as value at risk, or VaR. Value at risk is the method Wall Street used to manage risk in the decade leading up to the Panic of 2008 and it is still in widespread use today. It is a way to measure risk in an overall portfolio—certain risky positions are offset against other positions to reduce risk, and VaR claims to measure that offset. For example, a long position in ten-year Treasury notes might be offset by a short position in five-year Treasury notes so that the net risk, according to VaR, is much less than either of the separate risks of the notes. There is no limit to the number of complicated offsetting baskets that can be constructed. The mathematics quickly become daunting, because clear relationships such as longs and shorts in the same bond give way to the multiple relationships of many items in the hedging basket.

…

The mathematics quickly become daunting, because clear relationships such as longs and shorts in the same bond give way to the multiple relationships of many items in the hedging basket. Value at risk is the mathematical culmination of fifty years of financial economics. Importantly, it assumes that future relationships between prices will resemble the past. VaR assumes that price fluctuations are random and that risk is embedded in net positions—long minus short—instead of gross positions. VaR carries the intellectual baggage of efficient markets and normal distributions into the world of risk management. The role of VaR in causing the Panic of 2008 is immense but has never been thoroughly explored. The Financial Crisis Inquiry Commission barely considered trading risk models. The highly conflicted and fraudulent roles of mortgage brokers, investment bankers and ratings agencies have been extensively examined. Yet the role of VaR has remained hidden. In many ways, VaR was the invisible thread that ran through all the excesses that led to the collapse.

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Yet the role of VaR has remained hidden. In many ways, VaR was the invisible thread that ran through all the excesses that led to the collapse. What was it that allowed the banks, ratings agencies and investors to assume that their positions were safe? What was it that gave the Federal Reserve and the SEC comfort that the banks and brokers had adequate capital? Why did bank risk managers continually assure their CEOs and boards of directors that everything was under control? The answers revolve around value at risk and its related models. The VaR models gave the all clear to higher leverage and massive off–balance sheet exposures. Since the regulators did not know as much about VaR as the banks, they were in no position to question the risk assessments. Regulators allowed the banks to self-regulate when it came to risk and leverage.

**
Frequently Asked Questions in Quantitative Finance
** by
Paul Wilmott

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Albert Einstein, asset allocation, Black-Scholes formula, Brownian motion, butterfly effect, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discrete time, diversified portfolio, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Norbert Wiener, quantitative trading / quantitative ﬁnance, random walk, regulatory arbitrage, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, urban planning, value at risk, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond

John Wiley & Sons What is Value at Risk and How is it Used? Short Answer Value at Risk, or VaR for short, is a measure of the amount that could be lost from a position, portfolio, desk, bank, etc. VaR is generally understood to mean the maximum loss an investment could incur at a given confidence level over a specified time horizon. There are other risk measures used in practice but this is the simplest and most common. Example An equity derivatives hedge fund estimates that its Value at Risk over one day at the 95% confidence level is $500,000. This is interpreted as one day out of 20 the fund expects to lose more than half a million dollars. Long Answer VaR calculations often assume that returns are normally distributed over the time horizon of interest. Inputs for a VaR calculation will include details of the portfolio composition, the time horizon, and parameters governing the distribution of the underlyings.

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The branch of mathematics involving the random evolution of a quantities usually in continuous time commonly associated with models of the financial markets and derivatives. To be contrasted with deterministic. Structured products Contracts designed to meet the specific investment criteria of a client, in terms of market view, risk and return. Swap A general term for an over-the-counter contract in which there are exchanges of cashflows between two parties. See page 324. Swaptions An option on a swap. They are commonly Bermudan exercise. See page 324. VaR Value at Risk, an estimate of the potential downside from one’s investments. See pages 40 and 48. Variance swap A contract in which there is an exchange of the realized variance over a specified period and a fixed amount. See page 325. Volatility The annualized standard deviation of returns of an asset. The most important quantity in derivatives pricing. Difficult to estimate and forecast, there are many competing models for the behaviour of volatility.

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Degree of confidence Number of standard deviations from the mean 99% 2.326342 98% 2.053748 97% 1.88079 96% 1.750686 95% 1.644853 90% 1.281551 Of course, there are also valid criticisms as well. • It does not tell you what the loss will be beyond the VaR value • VaR is concerned with typical market conditions, not the extreme events • It uses historical data, “like driving a car by looking in the rear-view mirror only” • Within the time horizon positions could change dramatically (due to normal trading or due to hedging or expiration of derivatives) A common criticism of traditional VaR has been that it does not satisfy all of certain commonsense criteria. Artzner et al. (1997) specify criteria that make a risk measure coherent. And VaR as described above is not coherent. Prudence would suggest that other risk-measurement methods are used in conjunction with VaR, including but not limited to, stress testing under different real and hypothetical scenarios, including the stressing of volatility especially for portfolios containing derivatives.

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Inside the House of Money: Top Hedge Fund Traders on Profiting in a Global Market
** by
Steven Drobny

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How much could I lose?”We also use a subjective limit of “If this happens, we get out.”We manage all of our position sizes individually, then aggregate them based on worst-case moves. We look at value at risk (VAR), but if there’s a very high VAR I know I have much larger risk on because VAR is dampening. In a concentrated portfolio, like a lot of commodities portfolios, I think it’s incredibly dangerous to manage off a VAR number. If you have a thousand traders, like a Goldman Sachs, a VAR calculation can make sense because you have enough diversification to give you something statistically significant. VAR assumes that there is some positive/negative correlation between commodities. If I am long $100 of aluminum and short $100 of copper, and copper is more volatile, it would show me that I have a net risk of, say, $20 from the copper, choosing an arbitrary dollar amount.

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Indeed, we will take the positions in areas where Barclays doesn’t have any natural presence or exposure, such as New Zealand, for example. Our risk is not limited to Barclays’ outstanding liabilities.We are actively managing risk and seeking a positive absolute return while being limited by the firm’s value at risk (VAR) model, regulatory capital limits, and balance sheet limits. We look to maximize current income for a given unit of risk. As a result, we tend to be in the front end of the yield curve as opposed to the back end because it’s better to roll one billion one-year notes for 10 years than to buy 100 million 10-year bonds ceteris paribus.The VAR would be the same if they had the same volatility but with the one-year notes, you get much more current income. By concentrating risk in the front end of the yield curve, the only thing that can really make me right or wrong is a central bank.

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For example, in the fourth quarter of 2004 we recognized the growing imbalances in the United States and the need for a higher savings rate and thus a weaker dollar.We looked at those macro factors and positioned ourselves through foreign exchange and bonds. Foreign exchange was clearly the best trade, but again, we’re not really a global macro fund so it’s hard for us to have all of our risk in foreign exchange. In this example, we put a total of 2 percent of our value at risk (VAR) THE FIXED INCOME SPECIALISTS 317 into that macro view, with 60 basis points of VAR going toward short USD, long euro FX, and 70 basis points each in long European bonds and short U.S. bonds. This trade structure captured the idea of slow domestic demand in Europe, higher short rates in the United States, and a weaker dollar.We expressed quite a lot of the bond side through options because European interest rate volatility was very cheap.

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What Happened to Goldman Sachs: An Insider's Story of Organizational Drift and Its Unintended Consequences
** by
Steven G. Mandis

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algorithmic trading, Berlin Wall, bonus culture, BRICs, business process, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, disintermediation, diversification, Emanuel Derman, financial innovation, fixed income, friendly fire, Goldman Sachs: Vampire Squid, high net worth, housing crisis, London Whale, Long Term Capital Management, merger arbitrage, new economy, passive investing, performance metric, risk tolerance, Ronald Reagan, Saturday Night Live, shareholder value, short selling, sovereign wealth fund, The Nature of the Firm, too big to fail, value at risk

As mentioned earlier, Goldman had learned from its 1994 experience. Value at Risk, Models, and Risk Management Models are widely used in risk management to synthesize risk and help analysts, investors, and company boards determine acceptable trading parameters under different scenarios. Value at risk (VaR) is a widely used measure of the risk of loss on a specific portfolio of financial assets, expressed in terms of a probability of losing a given percentage of the value of a portfolio—in mark-to-market value—over a certain time. For example, if a portfolio of stocks has a one-day 5 percent VaR of $1 million, there is a 0.05 probability that the portfolio will fall in value by more than $1 million over a one-day period. Informally, a loss of $1 million or more on this portfolio is expected on one day in twenty. Typically, banks report the VaR by risk type (e.g., interest rates, equity prices, currency rates, and commodity prices).

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Interviews confirmed the level of dissonance at Goldman, even as a publicly traded firm, in discussing and understanding that the output of the models was and is unique to Goldman, which meant the firm was not as dependent on the models as were other firms, and that, combined with what sociologists call a “heterarchical structure” (less hierarchy in the chain of command than in many firms) and the trading experience of its top executives, gave Goldman an edge.8 The more intense scrutiny of the models and risk factors led Goldman’s top executives to pick up on market signals that other firms’ executives missed.9 As Emanuel Derman, the former head of the quantitative risk strategies group at Goldman and now a professor at Columbia, wrote, at Goldman, “Even if you insist on representing risk with a single number, VaR isn’t the best one … As a result, though we [Goldman] used VaR, we didn’t make it our religion.”10 (Meanwhile, at other firms, measures like “VaR [value at risk] … became institutionalized,” as the New York Times’ Joe Nocera put it. “Corporate chieftains like Stanley O’Neal at Merrill Lynch and Charles Prince at Citigroup pushed their divisions to take more risk because they were being left behind in the race for trading profits. All over Wall Street, VaR numbers increased.”11) Even though VaR has flaws, it is the only relatively consistent risk data that is publicly reported from the various banks, which is why I analyzed it. When analyzing the publicly reported data from 2000 to 2010 for Goldman and its peers, what stands out is that Goldman’s standard deviation of VaR is higher (meaning that the level of the total VaR was more varied) than most other firms, implying that Goldman more dynamically managed risk than its peers over the time period.

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Typically, banks report the VaR by risk type (e.g., interest rates, equity prices, currency rates, and commodity prices). VaR may be an unsatisfactory risk metric, but it has become an industry standard. Wall Street equity analysts expect banks to provide risk (VaR) calculations quarterly, and they talk about risk increasing, or decreasing, depending on the output of the models. The models and VaR calculations, however, make numerous assumptions, some of which proved over time to be invalid, making it dangerous to rely on or extrapolate too much on VaR. Analysts and investors (and boards of directors) overrely on VAR as a measurement of risk, and therefore management teams do also, one of the external influences of being a public company. Yet the overreliance on VaR, one of the key measures employed in risk management, is controversial. Some of the claims made about it include that it “[ignores] 2,500 years of experience in favor of untested models built by non-traders; was charlatanism because it claimed to estimate the risks of rare events, which is impossible; gave false confidence; would be exploited by traders.”6 Comparing VaR to “an airbag that works all the time, except when you have a car accident,” David Einhorn, the hedge fund manager who profited from shorting Lehman stock, charged that VaR also led to excessive risk-taking and leverage at financial institutions before the crisis and is “potentially catastrophic when its use creates a false sense of security among senior executives and watchdogs.”7 Leading up to the crisis most of Wall Street essentially used the same models and metrics for risk management, particularly VaR (an effect of being public—analysts and investors compare VaR between firms in analyzing performance).

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Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
** by
William Poundstone

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LTCM used a sophisticated form of the industry standard risk reporting system, VaR or “Value at Risk.” After the Black Monday crash of 1987, investment bank J. P. Morgan became concerned with getting a handle on risk. Derivatives, interest rate swaps, and repurchase agreements had changed the financial landscape so much that it was no longer a simple thing for a bank executive (much less a client) to understand what risks the people in the firm were taking. Morgan’s management wanted an executive summary. It would be a number or numbers (just not too many numbers) that executives could look at every morning. Looking at the numbers would reassure the execs that the bank was not assuming too much risk. Two of Morgan’s analysts, Til Guldimann and Jacques Longerstaey, devised Value at Risk. The concept is as simple as it can be. Compute how much a portfolio stands to lose within a given time frame, and with what probability.

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When the investor scans the figures and raises no fuss, he has implicitly signed off on those risks. Should something terrible happen later on, the money manager can always pull out the VaR report, point to cell D18, the 5 percent risk of a 37 percent loss. As a ritual between portfolio manager and client, calculating VaR is not such a bad idea in a litigious society where many well-off people don’t know much math. In October 1994, LTCM sent its investors a document comparing projected returns to risks. One reported factoid: In order to make a 25 percent annual return, the fund would have to assume a 1 percent chance of losing 20 percent or more of the fund’s value in a year. A 20-percent-or-more loss was the worst case considered. The chapter on Value at Risk in the popular finance textbook Paul Wilmott Introduces Quantitative Finance begins with a cartoon of the author shrugging.

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Compute how much a portfolio stands to lose within a given time frame, and with what probability. A VaR report might say that there is a 1-in-20 chance that a portfolio will lose $1.64 million or more in the next day of trading. Want more numbers? VaR’s got as many numbers as you want. Make a spreadsheet. The cells of the spreadsheet are the possible losses, for different time periods or various thresholds of likelihood. Throw in color charts, print it out on the good paper, and hand it to the client. Morgan’s management liked the idea. Practically everyone else did, too. Other banks began hiring “risk managers” to prepare daily VaR reports. The Basel Committee on Banking Supervision—head-quartered in the city of the Bernoullis—endorsed VaR as a means of determining capital requirements for banks. VaR migrated downstream to private investment managers. By calculating VaR, a money manager shows the client that she is serious about managing risk.

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Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined
** by
Lasse Heje Pedersen

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algorithmic trading, Andrei Shleifer, asset allocation, backtesting, bank run, banking crisis, barriers to entry, Black-Scholes formula, Brownian motion, buy low sell high, capital asset pricing model, commodity trading advisor, conceptual framework, corporate governance, credit crunch, Credit Default Swap, currency peg, David Ricardo: comparative advantage, declining real wages, discounted cash flows, diversification, diversified portfolio, Emanuel Derman, equity premium, Eugene Fama: efficient market hypothesis, fixed income, Flash crash, floating exchange rates, frictionless, frictionless market, Gordon Gekko, implied volatility, index arbitrage, index fund, interest rate swap, late capitalism, law of one price, Long Term Capital Management, margin call, market clearing, market design, market friction, merger arbitrage, mortgage debt, New Journalism, paper trading, passive investing, price discovery process, price stability, purchasing power parity, quantitative easing, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, Richard Thaler, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, systematic trading, technology bubble, time value of money, total factor productivity, transaction costs, value at risk, Vanguard fund, yield curve, zero-coupon bond

To compute the volatility of a large portfolio, hedge funds need to account for correlations across assets, which can be accomplished by simulating the overall portfolio or by using a statistical model such as a factor model. Another measure of risk is value-at-risk (VaR), which attempts to capture tail risk (non-normality). The VaR measures the maximum loss with a certain confidence, as seen in figure 4.1 below. For example, the VaR is the most that you can lose with a 95% or 99% confidence. For instance, a hedge fund has a one-day 95% VaR of $10 million if A simple way to estimate VaR is to line up past returns, sort them by magnitude, and find a return that has 5% worse days and 95% better days. This is the 95% VaR, since, if history repeats itself, you will lose less than this number with 95% certainty. You can estimate the VaR by looking at your past returns, but if your positions have changed a lot, this can be rather misleading.

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You can estimate the VaR by looking at your past returns, but if your positions have changed a lot, this can be rather misleading. In that case, it may be more accurate to look at your current positions and simulate returns on these positions over, say, the past three years. Figure 4.1. Value-at-risk. The x-axis has the possible outcomes for the return, and the y-axis has the corresponding probability density. One issue with the VaR is that it does not depend on how much you lose if you do lose more than the VaR. The magnitude of these extreme tail losses is, in principle, captured by the risk measure called the expected shortfall (ES). The expected shortfall is the expected loss, given that you are losing more than the VaR: Another measure of risk is the stress loss. This measure is computed by performing various stress tests, that is, simulated portfolio returns during various scenarios, and then considering the worst-case loss in these scenarios.

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A hedge fund may therefore want to minimize the risk that its drawdown will become worse than some prespecified maximum acceptable drawdown (MADD), say, 25%.1 If the current drawdown is given by DDt, then one sensible drawdown control policy is The right-hand-side of this inequality is the distance between the maximum acceptable drawdown and the current drawdown, that is, the largest acceptable loss given the amount already lost. The left-hand-side is the value-at-risk, that is, the most that can be lost given the current positions and current market risk, at a certain confidence level. Hence, the drawdown policy states that the risk must be small enough that losses do not push drawdowns beyond the MADD, with a certain confidence. If this inequality is violated, the hedge fund should reduce risk, that is, unwind positions such that the VaR comes down to a level that satisfies the inequality. Once the strategies have recovered and the drawdown is reduced, the risk can be increased again. To make this drawdown system operational, one must choose a MADD and also the type of VaR measure to use on the left-hand side (i.e., the time period and the confidence level).

**
Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives
** by
Satyajit Das

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accounting loophole / creative accounting, Albert Einstein, Asian financial crisis, asset-backed security, Black Swan, Black-Scholes formula, Bretton Woods, BRICs, Brownian motion, business process, buy low sell high, call centre, capital asset pricing model, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, currency peg, disintermediation, diversification, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, Haight Ashbury, high net worth, implied volatility, index arbitrage, index card, index fund, interest rate derivative, interest rate swap, Isaac Newton, job satisfaction, locking in a profit, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Marshall McLuhan, mass affluent, merger arbitrage, Mexican peso crisis / tequila crisis, moral hazard, mutually assured destruction, new economy, New Journalism, Nick Leeson, offshore financial centre, oil shock, Parkinson's law, placebo effect, Ponzi scheme, purchasing power parity, quantitative trading / quantitative ﬁnance, random walk, regulatory arbitrage, risk-adjusted returns, risk/return, shareholder value, short selling, South Sea Bubble, statistical model, technology bubble, the medium is the message, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, volatility smile, yield curve, Yogi Berra, zero-coupon bond

Were the numbers actually correct? Were all the positions that the bank held correctly included? What did the number actually mean? What was it used for? The answers to these questions are inevitably vague. Like religious matters, faith is key. The reader of the Report had no way of verifying whether it was correct. You have to believe in the thing. The holy liturgy of risk is built around a concept known as VAR – ‘value at risk’. Sceptics refer to it as ‘Variable And wRong’. There is also DEAR – ‘daily earning at risk’. The concepts all go back to Carl Frederich Gauss, a nineteenth century German mathematician of rare genius. The Gaussian distribution lies at the centre of modern finance, especially risk management and financial modelling. It is commonly and mistakenly referred to as a ‘normal’ distribution, but there is nothing ‘normal’ about it.

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However, the text is different. 6 ‘What Worries Warren’ (3 March 2003) Fortune. 13_INDEX.QXD 17/2/06 4:44 pm Page 325 Index accounting rules 139, 221, 228, 257 Accounting Standards Board 33 accrual accounting 139 active fund management 111 actuaries 107–10, 205, 289 Advance Corporation Tax 242 agency business 123–4, 129 agency theory 117 airline profits 140–1 Alaska 319 Allen, Woody 20 Allied Irish Bank 143 Allied Lyons 98 alternative investment strategies 112, 308 American Express 291 analysts, role of 62–4 anchor effect 136 Anderson, Rolf 92–4 annuities 204–5 ANZ Bank 277 Aquinas, Thomas 137 arbitrage 33, 38–40, 99, 114, 137–8, 171–2, 245–8, 253–5, 290, 293–6 arbitration 307 Argentina 45 arithmophobia 177 ‘armpit theory’ 303 Armstrong World Industries 274 arrears assets 225 Ashanti Goldfields 97–8, 114 Asian financial crisis (1997) 4, 9, 44–5, 115, 144, 166, 172, 207, 235, 245, 252, 310, 319 asset consultants 115–17, 281 ‘asset growth’ strategy 255 asset swaps 230–2 assets under management (AUM) 113–4, 117 assignment of loans 267–8 AT&T 275 attribution of earnings 148 auditors 144 Australia 222–4, 254–5, 261–2 back office functions 65–6 back-to-back loans 35, 40 backwardation 96 Banca Popolare di Intra 298 Bank of America 298, 303 Bank of International Settlements 50–1, 281 Bank of Japan 220 Bankers’ Trust (BT) 59, 72, 101–2, 149, 217–18, 232, 268–71, 298, 301, 319 banking regulations 155, 159, 162, 164, 281, 286, 288 banking services 34; see also commercial banks; investment banks bankruptcy 276–7 Banque Paribas 37–8, 232 Barclays Bank 121–2, 297–8 13_INDEX.QXD 17/2/06 326 4:44 pm Page 326 Index Baring, Peter 151 Baring Brothers 51, 143, 151–2, 155 ‘Basel 2’ proposal 159 basis risk 28, 42, 274 Bear Stearns 173 bearer eurodollar collateralized securities (BECS) 231–3 ‘behavioural finance’ 136 Berkshire Hathaway 19 Bermudan options 205, 227 Bernstein, Peter 167 binomial option pricing model 196 Bismarck, Otto von 108 Black, Fischer 22, 42, 160, 185, 189–90, 193, 195, 197, 209, 215 Black–Scholes formula for option pricing 22, 185, 194–5 Black–Scholes–Merton model 160, 189–93, 196–7 ‘black swan’ hypothesis 130 Blair, Tony 223 Bogle, John 116 Bohr, Niels 122 Bond, Sir John 148 ‘bond floor’ concept 251–4 bonding 75–6, 168, 181 bonuses 146–51, 244, 262, 284–5 Brady Commission 203 brand awareness and brand equity 124, 236 Brazil 302 Bretton Woods system 33 bribery 80, 303 British Sky Broadcasting (BSB) 247–8 Brittain, Alfred 72 broad index secured trust offerings (BISTROs) 284–5 brokers 69, 309 Brown, Robert 161 bubbles 210, 310, 319 Buconero 299 Buffet, Warren 12, 19–20, 50, 110–11, 136, 173, 246, 316 business process reorganization 72 business risk 159 Business Week 130 buy-backs 249 ‘call’ options 25, 90, 99, 101, 131, 190, 196 callable bonds 227–9, 256 capital asset pricing model (CAPM) 111 capital flow 30 capital guarantees 257–8 capital structure arbitrage 296 Capote, Truman 87 carbon trading 320 ‘carry cost’ model 188 ‘carry’ trades 131–3, 171 cash accounting 139 catastrophe bonds 212, 320 caveat emptor principle 27, 272 Cayman Islands 233–4 Cazenove (company) 152 CDO2 292 Cemex 249–50 chaos theory 209, 312 Chase Manhattan Bank 143, 299 Chicago Board Options Exchange 195 Chicago Board of Trade (CBOT) 25–6, 34 chief risk officers 177 China 23–5, 276, 302–4 China Club, Hong Kong 318 Chinese walls 249, 261, 280 chrematophobia 177 Citibank and Citigroup 37–8, 43, 71, 79, 94, 134–5, 149, 174, 238–9 Citron, Robert 124–5, 212–17 client relationships 58–9 Clinton, Bill 223 Coats, Craig 168–9 collateral requirements 215–16 collateralized bond obligations (CBOs) 282 collateralized debt obligations (CDOs) 45, 282–99 13_INDEX.QXD 17/2/06 4:44 pm Page 327 Index collateralized fund obligations (CFOs) 292 collateralized loan obligations (CLOs) 283–5, 288 commercial banks 265–7 commoditization 236 commodity collateralized obligations (CCOs) 292 commodity prices 304 Commonwealth Bank of Australia 255 compliance officers 65 computer systems 54, 155, 197–8 concentration risk 271, 287 conferences with clients 59 confidence levels 164 confidentiality 226 Conseco 279–80 contagion crises 291 contango 96 contingent conversion convertibles (co-cos) 257 contingent payment convertibles (co-pays) 257 Continental Illinois 34 ‘convergence’ trading 170 convertible bonds 250–60 correlations 163–6, 294–5; see also default correlations corruption 303 CORVUS 297 Cox, John 196–7 credit cycle 291 credit default swaps (CDSs) 271–84, 293, 299 credit derivatives 129, 150, 265–72, 282, 295, 299–300 Credit Derivatives Market Practices Committee 273, 275, 280–1 credit models 294, 296 credit ratings 256–7, 270, 287–8, 297–8, 304 credit reserves 140 credit risk 158, 265–74, 281–95, 299 327 credit spreads 114, 172–5, 296 Credit Suisse 70, 106, 167 credit trading 293–5 CRH Capital 309 critical events 164–6 Croesus 137 cross-ruffing 142 cubic splines 189 currency options 98, 218, 319 custom repackaged asset vehicles (CRAVEs) 233 daily earning at risk (DEAR) concept 160 Daiwa Bank 142 Daiwa Europe 277 Danish Oil and Natural Gas 296 data scrubbing 142 dealers, work of 87–8, 124–8, 133, 167, 206, 229–37, 262, 295–6; see also traders ‘death swap’ strategy 110 decentralization 72 decision-making, scientific 182 default correlations 270–1 defaults 277–9, 287, 291, 293, 296, 299 DEFCON scale 156–7 ‘Delta 1’ options 243 delta hedging 42, 200 Deming, W.E. 98, 101 Denmark 38 deregulation, financial 34 derivatives trading 5–6, 12–14, 18–72, 79, 88–9, 99–115, 123–31, 139–41, 150, 153, 155, 175, 184–9, 206–8, 211–14, 217–19, 230, 233, 257, 262–3, 307, 316, 319–20; see also equity derivatives Derman, Emmanuel 185, 198–9 Deutsche Bank 70, 104, 150, 247–8, 274, 277 devaluations 80–1, 89, 203–4, 319 13_INDEX.QXD 17/2/06 4:44 pm Page 328 328 Index dilution of share capital 241 DINKs 313 Disney Corporation 91–8 diversification 72, 110–11, 166, 299 dividend yield 243 ‘Dr Evil’ trade 135 dollar premium 35 downsizing 73 Drexel Burnham Lambert (DBL) 282 dual currency bonds 220–3; see also reverse dual currency bonds earthquakes, bonds linked to 212 efficient markets hypothesis 22, 31, 111, 203 electronic trading 126–30, 134 ‘embeddos’ 218 emerging markets 3–4, 44, 115, 132–3, 142, 212, 226, 297 Enron 54, 142, 250, 298 enterprise risk management (ERM) 176 equity capital management 249 equity collateralized obligations (ECOs) 292 equity derivatives 241–2, 246–9, 257–62 equity index 137–8 equity investment, retail market in 258–9 equity investors’ risk 286–8 equity options 253–4 equity swaps 247–8 euro currency 171, 206, 237 European Bank for Reconstruction and Development 297 European currency units 93 European Union 247–8 Exchange Rate Mechanism, European 204 exchangeable bonds 260 expatriate postings 81–2 expert witnesses 310–12 extrapolation 189, 205 extreme value theory 166 fads of management science 72–4 ‘fairway bonds’ 225 Fama, Eugene 22, 111, 194 ‘fat tail’ events 163–4 Federal Accounting Standards Board 266 Federal Home Loans Bank 213 Federal National Mortgage Association 213 Federal Reserve Bank 20, 173 Federal Reserve Board 132 ‘Ferraris’ 232 financial engineering 228, 230, 233, 249–50, 262, 269 Financial Services Authority (FSA), Japan 106, 238 Financial Services Authority (FSA), UK 15, 135 firewalls 235–6 firing of staff 84–5 First Interstate Ltd 34–5 ‘flat’ organizations 72 ‘flat’ positions 159 floaters 231–2; see also inverse floaters ‘flow’ trading 60–1, 129 Ford Motors 282, 296 forecasting 135–6, 190 forward contracts 24–33, 90, 97, 124, 131, 188 fugu fish 239 fund management 109–17, 286, 300 futures see forward contracts Galbraith, John Kenneth 121 gamma risk 200–2, 294 Gauss, Carl Friedrich 160–2 General Motors 279, 296 General Reinsurance 20 geometric Brownian motion (GBM) 161 Ghana 98 Gibson Greeting Cards 44 Glass-Steagall Act 34 gold borrowings 132 13_INDEX.QXD 17/2/06 4:44 pm Page 329 Index gold sales 97, 137 Goldman Sachs 34, 71, 93, 150, 173, 185 ‘golfing holiday bonds’ 224 Greenspan, Alan 6, 9, 19–21, 29, 43, 47, 50, 53, 62, 132, 159, 170, 215, 223, 308 Greenwich NatWest 298 Gross, Bill 19 Guangdong International Trust and Investment Corporation (GITIC) 276–7 guaranteed annuity option (GAO) contracts 204–5 Gutenfreund, John 168–9 gyosei shido 106 Haghani, Victor 168 Hamanaka, Yasuo 142 Hamburgische Landesbank 297 Hammersmith and Fulham, London Borough of 66–7 ‘hara-kiri’ swaps 39 Hartley, L.P. 163 Hawkins, Greg 168 ‘heaven and hell’ bonds 218 hedge funds 44, 88–9, 113–14, 167, 170–5, 200–2, 206, 253–4, 262–3, 282, 292, 296, 300, 308–9 hedge ratio 264 hedging 24–8, 31, 38–42, 60, 87–100, 184, 195–200, 205–7, 214, 221, 229, 252, 269, 281, 293–4, 310 Heisenberg, Werner 122 ‘hell bonds’ 218 Herman, Clement (‘Crem’) 45–9, 77, 84, 309 Herodotus 137, 178 high net worth individuals (HNWIs) 237–8, 286 Hilibrand, Lawrence 168 Hill Samuel 231–2 329 The Hitchhiker’s Guide to the Galaxy 189 Homer, Sidney 184 Hong Kong 9, 303–4 ‘hot tubbing’ 311–12 HSBC Bank 148 HSH Nordbank 297–8 Hudson, Kevin 102 Hufschmid, Hans 77–8 IBM 36, 218, 260 ICI 34 Iguchi, Toshihude 142 incubators 309 independent valuation 142 indexed currency option notes (ICONs) 218 India 302 Indonesia 5, 9, 19, 26, 55, 80–2, 105, 146, 219–20, 252, 305 initial public offerings 33, 64, 261 inside information and insider trading 133, 241, 248–9 insurance companies 107–10, 117, 119, 150, 192–3, 204–5, 221, 223, 282, 286, 300; see also reinsurance companies insurance law 272 Intel 260 intellectual property in financial products 226 Intercontinental Hotels Group (IHG) 285–6 International Accounting Standards 33 International Securities Market Association 106 International Swap Dealers Association (ISDA) 273, 275, 279, 281 Internet stock and the Internet boom 64, 112, 259, 261, 310, 319 interpolation of interest rates 141–2, 189 inverse floaters 46–51, 213–16, 225, 232–3 13_INDEX.QXD 17/2/06 4:44 pm Page 330 330 Index investment banks 34–8, 62, 64, 67, 71, 127–8, 172, 198, 206, 216–17, 234, 265–7, 298, 309 investment managers 43–4 investment styles 111–14 irrational decisions 136 Italy 106–7 Ito’s Lemma 194 Japan 39, 43, 82–3, 92, 94, 98–9, 101, 106, 132, 142, 145–6, 157, 212, 217–25, 228, 269–70 Jensen, Michael 117 Jett, Joseph 143 JP Morgan (company) 72, 150, 152, 160, 162, 249–50, 268–9, 284–5, 299; see also Morgan Guaranty junk bonds 231, 279, 282, 291, 296–7 JWM Associates 175 Kahneman, Daniel 136 Kaplanis, Costas 174 Kassouf, Sheen 253 Kaufman, Henry 62 Kerkorian, Kirk 296 Keynes, J.M. 167, 175, 198 Keynesianism 5 Kidder Peabody 143 Kleinwort Benson 40 Korea 9, 226, 278 Kozeny, Viktor 121 Krasker, William 168 Kreiger, Andy 319 Kyoto Protocol 320 Lavin, Jack 102 law of large numbers 192 Leeson, Nick 51, 131, 143, 151 legal opinions 47, 219–20, 235, 273–4 Leibowitz, Martin 184 Leland, Hayne 42, 202 Lend Lease Corporation 261–2 leptokurtic conditions 163 leverage 31–2, 48–50, 54, 99, 102–3, 114, 131–2, 171–5, 213–14, 247, 270–3, 291, 295, 305, 308 Lewis, Kenneth 303 Lewis, Michael 77–8 life insurance 204–5 Lintner, John 111 liquidity options 175 liquidity risk 158, 173 litigation 297–8 Ljunggren, Bernt 38–40 London Inter-Bank Offered Rate (LIBOR) 6, 37 ‘long first coupon’ strategy 39 Long Term Capital Management (LTCM) 44, 51, 62, 77–8, 84, 114, 166–75, 187, 206, 210, 215–18, 263–4, 309–10 Long Term Credit Bank of Japan 94 LOR (company) 202 Louisiana Purchase 319 low exercise price options (LEPOs) 261 Maastricht Treaty and criteria 106–7 McLuhan, Marshall 134 McNamara, Robert 182 macro-economic indicators, derivatives linked to 319 Mahathir Mohammed 31 Malaysia 9 management consultants 72–3 Manchester United 152 mandatory convertibles 255 Marakanond, Rerngchai 302 margin calls 97–8, 175 ‘market neutral’ investment strategy 114 market risk 158, 173, 265 marketable eurodollar collateralized securities (MECS) 232 Markowitz, Harry 110 mark-to-market accounting 10, 100, 139–41, 145, 150, 174, 215–16, 228, 244, 266, 292, 295, 298 Marx, Groucho 24, 57, 67, 117, 308 13_INDEX.QXD 17/2/06 4:44 pm Page 331 Index mathematics applied to financial instruments 209–10; see also ‘quants’ matrix structures 72 Meckling, Herbert 117 Melamed, Leo 34, 211 merchant banks 38 Meriwether, John 167–9, 172–5 Merrill Lynch 124, 150, 217, 232 Merton, Robert 22, 42, 168–70, 175, 185, 189–90, 193–7, 210 Messier, Marie 247 Metallgesellschaft 95–7 Mexico 44 mezzanine finance 285–8, 291–7 MG Refining and Marketing 95–8, 114 Microsoft 53 Mill, Stuart 130 Miller, Merton 22, 101, 194 Milliken, Michael 282 Ministry of Finance, Japan 222 misogyny 75–7 mis-selling 238, 297–8 Mitchell, Edison 70 Mitchell & Butler 275–6 models financial 42–3, 141–2, 163–4, 173–5, 181–4, 189, 198–9, 205–10 of business processes 73–5 see also credit models Modest, David 168 momentum investment 111 monetization 260–1 monopolies in financial trading 124 moral hazard 151, 280, 291 Morgan Guaranty 37–8, 221, 232 Morgan Stanley 76, 150 mortgage-backed securities (MBSs) 282–3 Moscow, City of 277 moves of staff between firms 150, 244 Mozer, Paul 169 Mullins, David 168–70 multi-skilling 73 331 Mumbai 3 Murdoch, Rupert 247 Nabisco 220 Napoleon 113 NASDAQ index 64, 112 Nash, Ogden 306 National Australia Bank 144, 178 National Rifle Association 29 NatWest Bank 144–5, 198 Niederhoffer, Victor 130 ‘Nero’ 7, 31, 45–9, 60, 77, 82–3, 88–9, 110, 118–19, 125, 128, 292 NERVA 297 New Zealand 319 Newman, Frank 104 news, financial 133–4 News Corporation 247 Newton, Isaac 162, 210 Nippon Credit Bank 106, 271 Nixon, Richard 33 Nomura Securities 218 normal distribution 160–3, 193, 199 Northern Electric 248 O’Brien, John 202 Occam, William 188 off-balance sheet transactions 32–3, 99, 234, 273, 282 ‘offsites’ 74–5 oil prices 30, 33, 89–90, 95–7 ‘omitted variable’ bias 209–10 operational risk 158, 176 opinion shopping 47 options 9, 21–2, 25–6, 32, 42, 90, 98, 124, 197, 229 pricing 185, 189–98, 202 Orange County 16, 44, 50, 124–57, 212–17, 232–3 orphan subsidiaries 234 over-the-counter (OTC) market 26, 34, 53, 95, 124, 126 overvaluation 64 13_INDEX.QXD 17/2/06 4:44 pm Page 332 332 Index ‘overwhelming force’ strategy 134–5 Owen, Martin 145 ownership, ‘legal’ and ‘economic’ 247 parallel loans 35 pari-mutuel auction system 319 Parkinson’s Law 136 Parmalat 250, 298–9 Partnoy, Frank 87 pension funds 43, 108–10, 115, 204–5, 255 People’s Bank of China (PBOC) 276–7 Peters’ Principle 71 petrodollars 71 Pétrus (restaurant) 121 Philippines, the 9 phobophobia 177 Piga, Gustavo 106 PIMCO 19 Plaza Accord 38, 94, 99, 220 plutophobia 177 pollution quotas 320 ‘portable alpha’ strategy 115 portfolio insurance 112, 202–3, 294 power reverse dual currency (PRDC) bonds 226–30 PowerPoint 75 preferred exchangeable resettable listed shares (PERLS) 255 presentations of business models 75 to clients 57, 185 prime brokerage 309 Prince, Charles 238 privatization 205 privity of contract 273 Proctor & Gamble (P&G) 44, 101–4, 155, 298, 301 product disclosure statements (PDSs) 48–9 profit smoothing 140 ‘programme’ issuers 234–5 proprietary (‘prop’) trading 60, 62, 64, 130, 174, 254 publicly available information (PAI) 277 ‘puff’ effect 148 purchasing power parity theory 92 ‘put’ options 90, 131, 256 ‘quants’ 183–9, 198, 208, 294 Raabe, Matthew 217 Ramsay, Gordon 121 range notes 225 real estate 91, 219 regulatory arbitrage 33 reinsurance companies 288–9 ‘relative value’ trading 131, 170–1, 310 Reliance Insurance 91–2 repackaging (‘repack’) business 230–6, 282, 290 replication in option pricing 195–9, 202 dynamic 200 research provided to clients 58, 62–4, 184 reserves, use of 140 reset preference shares 254–7 restructuring of loans 279–81 retail equity products 258–9 reverse convertibles 258–9 reverse dual currency bonds 223–30 ‘revolver’ loans 284–5 risk, financial, types of 158 risk adjusted return on capital (RAROC) 268, 290 risk conservation principle 229–30 risk management 65, 153–79, 184, 187, 201, 267 risk models 163–4, 173–5 riskless portfolios 196–7 RJ Reynolds (company) 220–1 rogue traders 176, 313–16 Rosenfield, Eric 168 Ross, Stephen 196–7, 202 Roth, Don 38 Rothschild, Mayer Amshel 267 Royal Bank of Scotland 298 Rubinstein, Mark 42, 196–7 13_INDEX.QXD 17/2/06 4:44 pm Page 333 Index Rumsfeld, Donald 12, 134, 306 Rusnak, John 143 Russia 45, 80, 166, 172–3, 274, 302 sales staff 55–60, 64–5, 125, 129, 217 Salomon Brothers 20, 36, 54, 62, 167–9, 174, 184 Sandor, Richard 34 Sanford, Charles 72, 269 Sanford, Eugene 269 Schieffelin, Allison 76 Scholes, Myron 22, 42, 168–71, 175, 185, 189–90, 193–7, 263–4 Seagram Group 247 Securities and Exchange Commission, US 64, 304 Securities and Futures Authority, UK 249 securitization 282–90 ‘security design’ 254–7 self-regulation 155 sex discrimination 76 share options 250–1 Sharpe, William 111 short selling 30–1, 114 Singapore 9 single-tranche CDOs 293–4, 299 ‘Sisters of Perpetual Ecstasy’ 234 SITCOMs 313 Six Continents (6C) 275–6 ‘smile’ effect 145 ‘snake’ currency system 203 ‘softing’ arrangements 117 Solon 137 Soros, George 44, 130, 253, 318–19 South Sea Bubble 210 special purpose asset repackaging companies (SPARCs) 233 special purpose vehicles (SPVs) 231–4, 282–6, 290, 293 speculation 29–31, 42, 67, 87, 108, 130 ‘spinning’ 64 333 Spitzer, Eliot 64 spread 41, 103; see also credit spreads stack hedges 96 Stamenson, Michael 124–5 standard deviation 161, 193, 195, 199 Steinberg, Sol 91 stock market booms 258, 260 stock market crashes 42–3, 168, 203, 257, 259, 319 straddles or strangles 131 strategy in banking 70 stress testing 164–6 stripping of convertible bonds 253–4 structured investment products 44, 112, 115, 118, 128, 211–39, 298 structured note asset packages (SNAPs) 233 Stuart SC 18, 307, 316–18 Styblo Bleder, Tanya 153 Suharto, Thojib 81–2 Sumitomo Corporation 100, 142 Sun Tzu 61 Svensk Exportkredit (SEK) 38–9 swaps 5–10, 26, 35–40, 107, 188, 211; see also equity swaps ‘swaptions’ 205–6 Swiss Bank Corporation (SBC) 248–9 Swiss banks 108, 305 ‘Swiss cheese theory’ 176 synthetic securitization 284–5, 288–90 systemic risk 151 Takeover Panel 248–9 Taleb, Nassim 130, 136, 167 target redemption notes 225–6 tax and tax credits 171, 242–7, 260–3 Taylor, Frederick 98, 101 team-building exercises 76 team moves 149 technical analysis 60–1, 135 television programmes about money 53, 62–3 Thailand 9, 80, 302–5 13_INDEX.QXD 17/2/06 4:44 pm Page 334 334 Index Thatcher, Margaret 205 Thorp, Edward 253 tobashi trades 105–7 Tokyo Disneyland 92, 212 top managers 72–3 total return swaps 246–8, 269 tracking error 138 traders in financial products 59–65, 129–31, 135–6, 140, 148, 151, 168, 185–6, 198; see also dealers trading limits 42, 157, 201 trading rooms 53–4, 64, 68, 75–7, 184–7, 208 Trafalgar House 248 tranching 286–9, 292, 296 transparency 26, 117, 126, 129–30, 310 Treynor, Jack 111 trust investment enhanced return securities (TIERS) 216, 233 trust obligation participating securities (TOPS) 232 TXU Europe 279 UBS Global Asset Management 110, 150, 263–4, 274 uncertainty principle 122–3 unique selling propositions 118 unit trusts 109 university education 187 unspecified fund obligations (UFOs) 292 ‘upfronting’ of income 139, 151 Valéry, Paul 163 valuation 64, 142–6 value at risk (VAR) concept 160–7, 173 value investing 111 Vanguard 116 vanity bonds 230 variance 161 Vietnam War 182, 195 Virgin Islands 233–4 Vivendi 247–8 volatility of bond prices 197 of interest rates 144–5 of share prices 161–8, 172–5, 192–3, 199 Volcker, Paul 20, 33 ‘warehouses’ 40–2, 139 warrants arbitrage 99–101 weather, bonds linked to 212, 320 Weatherstone, Dennis 72, 268 Weil, Gotscal & Manges 298 Weill, Sandy 174 Westdeutsche Genosenschafts Zentralbank 143 Westminster Group 34–5 Westpac 261–2 Wheat, Allen 70, 72, 106, 167 Wojniflower, Albert 62 World Bank 4, 36, 38 World Food Programme 320 Worldcom 250, 298 Wriston, Walter 71 WTI (West Texas Intermediate) contracts 28–30 yield curves 103, 188–9, 213, 215 yield enhancement 112, 213, 269 ‘yield hogs’ 43 zaiteku 98–101, 104–5 zero coupon bonds 221–2, 257–8

…

DAS_C06.QXP 8/7/06 162 4:43 PM Page 162 Tr a d e r s , G u n s & M o n e y VAR revolves around the stupid question that I asked Ray so many years ago. VAR calculations look at the distribution of price changes in the past. For example, if you look at a share over a year then you find that most of the time the share price moved up or down a small amount. On some days you might get a large change and occasionally a very large price change. You can arrange the price change from largest fall to largest rise. If you then assume that the price changes fit a normal distribution then you can calculate what the probability of a particular size price change is. This means you can also answer questions like, ‘What is the likely maximum price change at a specific probability level, say 99%, one in 100 days?’ VAR signifies the maximum amount that you could lose as a result of market price moves for a given probability over a fixed time.

**
Austerity: The History of a Dangerous Idea
** by
Mark Blyth

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accounting loophole / creative accounting, balance sheet recession, bank run, banking crisis, Black Swan, Bretton Woods, capital controls, Carmen Reinhart, Celtic Tiger, central bank independence, centre right, collateralized debt obligation, correlation does not imply causation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency peg, debt deflation, deindustrialization, disintermediation, diversification, en.wikipedia.org, ending welfare as we know it, Eugene Fama: efficient market hypothesis, eurozone crisis, financial repression, fixed income, floating exchange rates, Fractional reserve banking, full employment, German hyperinflation, Gini coefficient, global reserve currency, Growth in a Time of Debt, Hyman Minsky, income inequality, interest rate swap, invisible hand, Irish property bubble, Joseph Schumpeter, Kenneth Rogoff, liquidationism / Banker’s doctrine / the Treasury view, Long Term Capital Management, market bubble, market clearing, Martin Wolf, moral hazard, mortgage debt, mortgage tax deduction, Occupy movement, offshore financial centre, paradox of thrift, price stability, quantitative easing, rent-seeking, reserve currency, road to serfdom, savings glut, short selling, structural adjustment programs, The Great Moderation, The Myth of the Rational Market, The Wealth of Nations by Adam Smith, Tobin tax, too big to fail, unorthodox policies, value at risk, Washington Consensus

Figure 2.1 The “Normal” Distribution of probable events Change the variable from height to default probability, and you can see how such a way of thinking about the likelihood of future events could be of great use to banks as they tried to risk-adjust their portfolios and positions. The piece of technology that allowed banks to do this is known as Value at Risk (VaR) analysis, which is part of a larger class of mathematical models designed to help banks manage risk. What VaR does is generate a figure (a VaR number) for how much a firm can win or lose on an individual trade. By summing VaR numbers, one can estimate a firm’s total exposure. Consider the following example. What was the worst that could have happened to the US housing market in 2008? As in the height example, the answer depends on a data sample that calibrates the model. Prior to 2007, the worst downturn firms had data on was the result of the mortgage defaults in Texas in the 1980s, when houses lost 40 percent of their value.

…

., 168 Sweden as a welfare state, 214 austerity in, 17, 178–180, 191–193, 204, 206 economic recovery in the 1930s in, 126 expansionary contraction in, 209–210, 211 fiscal adjustment in, 173 Swedish Social Democrats, (SAP), 191 thirty-year bond in, 210–211 systemic risk, 44 Tabellini, Guido “Positive Theory of Fiscal Deficits and Government Debt in a Democracy, A”, 167 tail risk, 44 See also systemic risk Takahashi, Korekiyo, 199 Taleb, Nassim Nicolas, 32, 33, 34 “Tales of Fiscal Adjustment” (Alesina and Ardanga), 171, 205, 208, 209 Target Two payments, 91 Taylor, Alan, 73 Tax Justice Network, 244 Thatcher, Margaret, 15 “there is no alternative”, 98, 171–173, 175, 231 ThyssenKrupp, 132 Tilford, Simon, 83 “too big to bail,” 49, 51–93, 74, 82 European banks as, 83, 90, 92 “too big to fail”, 6, 16, 45, 47–50, 82, 231 Tooze, Adam, 196 Trichet, Jean Claude, 60 as president of the ECB, 176 on Greece and Ireland, 235 See also European Central Bank United Kingdom, 1 and the gold standard, 185, 189–191 asset footprint of top banks, 83 austerity in, 17, 122–125, 126, 178–180 and the global economy in the 1920s and 1930s, 184–189, 189–121 banking crisis in, 52 cost of, 45 depression in, 204 Eurozone Ten-Year Government Bond Yields, 80 fig. 3.2 Gordon Brown economics policy, 5, 59 housing bubble, 66–67 Lawson boom, 208 “Memoranda on Certain Proposals Relating to Unemployment” (UK White Paper), 122, 124 New Liberalism, 117–119 “Treasury view”, 101, 163–165 war debts to the United States, 185 United States, 2 AAA credit rating, 1, 2–3 Agricultural Adjustment Act, 188 and current economic conditions, 213 and printing its own money, 11 and recycling foreign savings, 11–12 and the Austrian School of economics, 121, 143–145, 148–152 and the gold standard, 188 assets of large banks in, 6 austerity in, 17, 119–122, 178–180, 187–189 “Banker’s doctrine”, 101 banking system of, 6 cost of crisis, 45, 52 Bush administration economics policy, 5, 58–59 capital-flow cycle in, 11 Congressional Research Service (CRS), 213 debt-ceiling agreement, 3 depression in, 188 Federal Reserve, 6, 157 federal taxes, 242–243 liberalism in, 119–122 liquidationism in, 119–122, 204 National Industrial Recovery Act, 188 repo market, 15–16, 24–25 rise in real estate prices in, 27 Securities and Exchange Commission, 49 Simson-Bowles Commission, 122, 122–125 Social Security Act, 188 stimulus in, 55 stop in capital flow in 1929, 190 Treasury bills, 25 Troubled Asset Relief Program, 58–59, 230 and American politics involvement, 59 Wagner’s Act, 188 Wall Street Crash of 1929, 204, 238 Washington Consensus, 142, 161–162, 165 Value at Risk (VaR) analysis, 34–38 Vienna agreement, 221 Viniar, David, 32 Wade, Robert, 13 Wagner, Richard, 156 Wartin, Christian, 137 Watson Institute for International Studies, ix “We Can Conquer Unemployment” (Lloyd George), 123, 24 “Wealth of Nations, The”, 109, 112 welfare, xi, 58 welfare state foundation for, 117 Wells Fargo, 48 Whyte, Philip, 83 Williamson, John, 161, 162 World Bank, 163, 210, 211 World Economic Outlook, 212

…

Indeed, the probability that all your mortgage bonds will go bad or that a very large bank will go bust is absurdly small, ten sigma or more, again, so long as you think that the probability distribution you face is normally distributed. Your VaR number, once calculated, would reflect this. Nassim Taleb never bought into this line of thinking. He had been a critic of VaR models as far back as 1997, arguing that they systematically underestimated the probability of high-impact, low-probability events. He argued that the thin tails of the Gaussian worked for height but not for finance, where the tails were “fat.” The probabilities associated with fat tails do not get exponentially smaller, so outlier events are much more frequent than your model allows you to imagine. This is why ten-sigma events actually happen nine years apart. Taleb’s 2006 book The Black Swan, published before the crisis, turned these criticisms of VaR into a full-blown attack on the way banks and governments think about risk.

**
Age of Greed: The Triumph of Finance and the Decline of America, 1970 to the Present
** by
Jeff Madrick

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accounting loophole / creative accounting, Asian financial crisis, bank run, Bretton Woods, capital controls, collapse of Lehman Brothers, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, desegregation, disintermediation, diversified portfolio, Donald Trump, financial deregulation, fixed income, floating exchange rates, Frederick Winslow Taylor, full employment, George Akerlof, Hyman Minsky, income inequality, index fund, inflation targeting, inventory management, invisible hand, laissez-faire capitalism, locking in a profit, Long Term Capital Management, market bubble, minimum wage unemployment, Mont Pelerin Society, moral hazard, mortgage debt, new economy, North Sea oil, Northern Rock, oil shock, price stability, quantitative easing, Ralph Nader, rent control, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, Ronald Reagan: Tear down this wall, shareholder value, short selling, Silicon Valley, Simon Kuznets, technology bubble, Telecommunications Act of 1996, The Chicago School, The Great Moderation, too big to fail, union organizing, V2 rocket, value at risk, Vanguard fund, War on Poverty, Washington Consensus, Y2K, Yom Kippur War

They called it Value at Risk, or VAR. For example, VAR might find that a loss of 25 percent of a portfolio of assets would occur only once in twenty-five times. If the investment firm had more than enough capital to cover the maximum likely to be lost, according to VAR, it could feel comfortable borrowing still more to raise investment levels. For portfolio managers, VAR became invaluable. If VAR was too high, it could sell assets, or specifically, the more volatile assets. Diversifying assets was also thought to be a key way to reduce VAR, because different kinds of securities—say a California state bond and a Michigan state bond—rose or fell at different times; mixing securities usually meant less volatility overall. The managers could also buy hedges—offsetting investments—to reduce VAR. International regulators also placed their faith in VAR.

…

., prl.1, prl.2, 7.1 Trump, Donald Tsai, Gerald Tudor Investment Tunney, John, 7.1, 7.2 Turner, Ed Turner, Ted, 8.1, 8.2, 8.3, 8.4, 8.5, 13.1 Turner Broadcasting Network (TNT), 8.1, 8.2, 8.3 Tuttle, Holmes Twentieth Century Fox, 7.1, 8.1, 8.2 Two Lucky People (Friedman and Friedman), 2.1 Tyco, 17.1, 17.2 Tynan, Kenneth UBS, 19.1, 19.2, 19.3, 19.4 Uhler, James Carvel, prl.1, prl.2 Uhler, Lewis, ix–x, prl.1, prl.2, 2.1, 7.1, 7.2 underwriters, 1.1, 6.1, 13.1, 13.2, 16.1, 16.2, 16.3, 17.1, 17.2, 17.3, 17.4, 17.5, 17.6, 17.7, 18.1, 19.1 unemployment insurance, 2.1, 2.2, 7.1 unemployment rate, prl.1, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 3.1, 3.2, 4.1, 6.1, 8.1, 8.2, 9.1, 9.2, 9.3, 9.4, 9.5, 10.1, 11.1, 11.2, 11.3, 11.4, 12.1, 12.2, 12.3, 14.1, 14.2, 14.3, 14.4, 14.5, 17.1, 19.1, 19.2, 19.3, 19.4, 19.5, 19.6 United Technologies, 4.1, 5.1 Unruh, Jesse Updike, John uranium, 4.1, 5.1, 14.1 Utah International, 4.1, 5.1, 5.2, 12.1, 12.2 Value at Risk (VAR), 15.1, 15.2, 15.3, 15.4, 15.5, 17.1, 17.2 Vanguard Funds Van Horn, Rob Versailles, Treaty of (1919) Veterans Administration (VA), 18.1, 18.2 Viacom, 8.1, 16.1 Vietnam War, prl.1, 1.1, 2.1, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 7.1, 10.1, 12.1, 19.1 Vilar, Alberto Viner, Jacob, 2.1, 2.2 Vinson & Elkins Volcker, Paul, 11.1, 11.2; background of, 3.1, 6.1, 11.3; in Carter administration, 11.4, 11.5, 11.6; as Federal Reserve chairman, itr.1, 6.2, 6.3, 6.4, 9.1, 9.2, 11.7, 13.1, 13.2, 13.3, 14.1, 15.1, 18.1, 19.1, 19.2; Greenspan compared with, 14.2, 14.3, 14.4, 14.5, 14.6; inflation policy of, 6.5, 6.6, 6.7, 6.8, 9.3, 11.8, 11.9, 11.10, 11.11, 11.12, 11.13, 11.14, 11.15, 11.16, 11.17, 14.7, 14.8; interest rates policy of, 6.9, 6.10, 9.4, 11.18, 11.19, 11.20, 11.21, 11.22, 15.2, 18.2, 18.3; in Reagan administration, 11.23, 11.24, 11.25; tax policy of, 11.26, 11.27, 11.28; as Treasury undersecretary, 3.2, 3.3, 6.11, 6.12, 6.13, 9.5, 9.6; unemployment rate and, 11.29, 11.30 Voorhis, Jerry Vranos, Michael, 12.1, 18.1 Wachtel, Paul wage controls, 2.1, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 14.1 wage levels, itr.1, prl.1, prl.2, prl.3, 1.1, 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 4.1, 4.2, 8.1, 8.2, 9.1, 9.2, 9.3, 10.1, 10.2, 11.1, 11.2, 11.3, 11.4, 11.5, 12.1, 12.2, 13.1, 14.1, 14.2, 14.3, 16.1, 17.1, 17.2, 19.1, 19.2 Walker, Charls Wall, Danny Wallace, George Wallich, Henry Wall Street, x, 1.1, 1.2, 1.3, 1.4, 3.1, 4.1, 6.1, 8.1, 8.2, 8.3, 9.1, 9.2, 9.3, 11.1, 12.1, 12.2, 12.3, 12.4, 13.1, 13.2, 13.3, 13.4, 13.5, 14.1, 14.2, 14.3, 14.4, 14.5, 15.1, 15.2, 15.3, 15.4, 15.5, 15.6, 16.1, 16.2, 16.3, 16.4, 16.5, 16.6, 17.1, 17.2, 18.1, 19.1, 19.2, 19.3, 19.4, 19.5, 19.6, 19.7, 19.8, 19.9, 19.10, 19.11, 19.12, 19.13, 19.14 Wall Street Journal, 2.1, 6.1, 16.1, 16.2, 17.1, 17.2 Wal-Mart, 8.1, 8.2 Walras, Léon Walters, Barbara Walton, Bud Walton, Sam, 8.1, 8.2, 12.1 Warner, Douglas, III Warner-Amex Cable, 8.1, 8.2 Warner Bros., 7.1, 8.1, 8.2 Warner Bros.

…

International regulators also placed their faith in VAR. The Bank for International Settlements (BIS) headquartered in Basel, Switzerland, in what were known as the Basel Agreements, set capital requirements for bankers according to the VAR of their portfolio of assets. Commercial banks, too, now trading actively for their portfolios, used VAR. The Meriwether group used VAR to calm concerns of Salomon management that they were leveraging too aggressively. If the quants had a sure way to measure the risk they were taking, they could justify borrowing still more. All seemed entirely under control in the late 1980s and early 1990s, even as the economy entered another recession and federal budget deficits reached new heights. But VAR also had drawbacks that were neglected in periods when markets were generally operating predictably. VAR worked when history repeated itself fairly closely.

**
My Life as a Quant: Reflections on Physics and Finance
** by
Emanuel Derman

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Berlin Wall, bioinformatics, Black-Scholes formula, Brownian motion, capital asset pricing model, Claude Shannon: information theory, Emanuel Derman, fixed income, Gödel, Escher, Bach, haute couture, hiring and firing, implied volatility, interest rate derivative, Jeff Bezos, John von Neumann, law of one price, linked data, Long Term Capital Management, moral hazard, Murray Gell-Mann, pre–internet, publish or perish, quantitative trading / quantitative ﬁnance, Richard Feynman, Sharpe ratio, statistical arbitrage, statistical model, Stephen Hawking, Steve Jobs, stochastic volatility, technology bubble, transaction costs, value at risk, volatility smile, Y2K, yield curve, zero-coupon bond

Most days, a desk was likely to gain or lose small amounts, but there was always some chance of a potentially large loss. To quantify the notion of risk, we and almost everyone else on the Street used the socalled daily VaR, orValue at Risk, the dollar loss threshold above which greater losses would occur with a probability no larger than 0.4 percent, or 1 chance in 250. This corresponded to about one trading day in a year. VaR is therefore the 99.6 percentile loss. So, for example, a Val", of $50MM for the Equities Division meant that there was only a one-intwo-fifty chance that more money than this would be lost on any given day in the year. Invented in 1994 by the J. P. Morgan bank, VaR is an unsatisfactory risk metric that has somehow become an industry standard. We estimated our daily VaR by running nightly simulations of the changes in the prices of the portfolio held by each trading desk. These simulations were huge computer programs that used the past statistics of each desk's assets to estimate the distribution of possible values the portfolio might take in the future.

…

We are ignorant of the true probabilities-the extreme tails of stock and bond price distributions, not to mention the overall distributions of complex securities like swaptions or weather derivatives, are poorly understood and may not even be stationary. Even if you insist on representing risk with a single number, VaR isn't the best one. Percentiles don't reflect the psychology of risk perception very well-two different securities can each have their own small percentile losses that combine to produce a greater percentile loss for the portfolio. The VaR of a portfolio can therefore be greater than the VaR of its components, in counterintuitive contradiction with the idea that diversification diminishes risk. As a result, though we used VaR, we didn't make it our religion. We were pantheists, praying to many parallel risk gods. For example, we had all lived through various market meltdowns-the 1987 stock market crash, the 1998 Russian default crisis-whose reoccurrence would cause great losses even though we had no idea of their probability.

…

With those estimates we could predict the distribution of each desk's portfolio value a day later. We produced VaRs for each desk, then for each group of desks in a common trading area, then for each division, and finally for the entire firm, generating a hierarchy of potential one-day losses that gave a view of the firm's riskiness from top to bottom. Each day, like clockwork, we computed and reported the VaR for the firm and its parts. Several times a week senior members of our group met with each division's risk committee, and once a week, in an unpleasantly early 7:30 A.M. global conference call, we met with the central risk committee who fine-tuned the entire firm's risk by setting limits on VaR. During turbulent times they lowered the cap and during quiet times they raised it. The aim was to take the appropriate amount of risk for the economic environment, not to eliminate it.

**
Fool's Gold: How the Bold Dream of a Small Tribe at J.P. Morgan Was Corrupted by Wall Street Greed and Unleashed a Catastrophe
** by
Gillian Tett

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accounting loophole / creative accounting, asset-backed security, bank run, banking crisis, Black-Scholes formula, Bretton Woods, business climate, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, easy for humans, difficult for computers, financial innovation, fixed income, housing crisis, interest rate derivative, interest rate swap, locking in a profit, Long Term Capital Management, McMansion, mortgage debt, North Sea oil, Northern Rock, Renaissance Technologies, risk tolerance, Robert Shiller, Robert Shiller, short selling, sovereign wealth fund, statistical model, The Great Moderation, too big to fail, value at risk, yield curve

Government bureaucrats should not be the sheriffs or high priests of this world; bankers and their lawyers were better informed, and they had strong incentives to comply. Like a hunter-gatherer tribe, all derivatives traders had an equal interest in upholding the norms. That was why any recommendation the G30 report might make about legislation to institute regulation was to be fought, argued Brickell, tooth and nail. Another key factor that influenced how J.P. Morgan bankers and others viewed regulation was the development of an idea known as value at risk, or VaR. In previous decades, banks had taken an ad hoc attitude toward measuring risk. They extended loans to customers they liked, withheld them from those they did not, and tried to prevent their traders from engaging in any market activity that looked too risky, but without trying to quantify those dangers with precision. In the 1980s, though, Charles Sanford, an innovative financier at Bankers Trust, had developed the industry’s first full-fledged system for measuring the level of credit and market risk, known as RAROC.

…

Weatherstone decided he wanted more, and he asked a team of quantitative experts to develop a technique that could measure how much money the bank stood to lose each day if the markets turned sour. It was the first time that any bank had ever done that, with the notable exception of Bankers Trust. For several months the so-called quants played around with ideas until they coalesced around the concept of value at risk (VaR). They decided that the goal should be to work out how much money the bank could expect to lose, with a probability of 95 percent, on any given day. The 95 percent was an accommodation to the hard reality that there would always be some risk in the markets that the models wouldn’t be able to account for. Weatherstone and his quants reckoned there was little point in trying to run a business in a manner that would create obsessive worry about very worst-case scenarios.

…

It was not enough, he declared, to look at the dangers that might beset narrow “silos” of the bank or to simply subcontract risk management to one department. Nor could risk be reduced to a few mathematical models. Fifteen years earlier, when Dennis Weatherstone ran the bank, J.P. Morgan had invented the concept of VaR and then disseminated it to the rest of the industry. It was a notable legacy. However, Dimon had no intention of giving undue veneration to VaR. Dimon (like Weatherstone) deemed mathematical models to be useful tools, but only when they were treated as a compass, not an oracle. Models could not do your thinking for you. The only safe way to use VaR, or so Dimon believed, was alongside numerous other analytical tools—including the human brain. By late 2004, speculation that Dimon was about to oust Harrison was rampant. “Yond Cassius has a lean and hungry look…such men are dangerous,” Brad Hintz, an analyst at Sanford C.

**
Money and Power: How Goldman Sachs Came to Rule the World
** by
William D. Cohan

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asset-backed security, Bernie Madoff, buttonwood tree, collateralized debt obligation, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, diversified portfolio, fear of failure, financial innovation, fixed income, Ford paid five dollars a day, Goldman Sachs: Vampire Squid, Gordon Gekko, high net worth, hiring and firing, hive mind, Hyman Minsky, interest rate swap, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, merger arbitrage, moral hazard, mortgage debt, paper trading, passive investing, Ponzi scheme, price stability, profit maximization, risk tolerance, Ronald Reagan, Saturday Night Live, South Sea Bubble, time value of money, too big to fail, traveling salesman, value at risk, yield curve, Yogi Berra

Later that night, Sparks responded to Winkelried that there was “[b]ad news everywhere” including that NovaStar, a subprime mortgage originator, announced bad earnings and lost one-third of its market value in one day and that Wells Fargo had fired more than three hundred people from its subprime mortgage origination business. But, he was happy to report, Goldman was “net short, but mostly in single name CDS and some tranched index vs the s[a]me index longs. We are working to cover more, but liquidity makes it tough. Volatility is causing our VAR [value at risk] numbers to grow dramatically,” which soon enough would make Goldman’s top brass concerned about the level of the firm’s capital being committed to these trades. Not surprisingly, in the midst of all of this intellectual and financial jousting in the market, Goldman’s senior executives occasionally wavered from the clear message that Viniar delivered in December 2006. At one point before the magnitude of the problem became crystalline, Viniar thought that Goldman had become too bearish and insisted that the firm’s traders reverse course somewhat.

…

by Goldman Sachs, see Goldman Sachs, deals and underwriting of Medina’s judicial ruling on on mortgages risks of Union Investment Management United Aircraft United Cigar Manufacturers’ Corporation United Corporation United Technologies University Hill Foundation Univis Lens Co. Unocal, 11.1, 11.2, 11.3, 11.4, 11.5 UPI USG Corp. U.S. Steel utility bonds, 1.1, 5.1, 5.2 Utley, Kristine value-at-risk (VAR) system, 14.1, 20.1, 20.2, 22.1, 22.2, 22.3, 22.4, 23.1 Vanderbilt, Cornelius Vanity Fair, 17.1, 23.1, 24.1 van Praag, Lucas, 17.1, 17.2, 22.1, 22.2 Venice Victor, Ed Vietnam War Viniar, David, prl.1, 3.1, 18.1, 18.2, 19.1, 19.2, 19.3, 20.1, 20.2, 21.1, 21.2, 21.3, 21.4, 21.5, 21.6, 22.1, 22.2, 22.3, 22.4, 22.5, 22.6, 22.7, 23.1, 24.1 Senate testimony of, prl.1, prl.2, prl.3 Vogel, Jack, 7.1, 7.2, 7.3, 7.4 Vogel, Matthew Vogelstein, John Volcker, Paul, 13.1, 18.1, 18.2, 19.1 Voltaire Vranos, Michael Wachovia, financial troubles of Wachtell, Lipton, Rosen & Katz, 11.1, 11.2, 11.3 Waldorf-Astoria Hotel, 4.1, 7.1 Walgreens Walker, Doak Wall Street Journal, 5.1, 7.1, 7.2, 7.3, 7.4, 7.5, 8.1, 10.1, 12.1, 15.1, 16.1, 16.2, 17.1, 17.2, 18.1, 19.1, 20.1, 20.2, 20.3, 22.1, 23.1, 23.2, 23.3 article on M&A business, 9.1, 9.2, 9.3 on insider training scandal, 11.1, 11.2, 11.3, 11.4 Wall Street Letter, 12.1 Walt Disney Company, 7.1, 11.1, 17.1 Wambold, Ali Warburg Pincus Warner, Ernestine Warner, Douglas “Sandy,” 16.1, 16.2, 16.3 Warner Bros.

…

Salem quickly understood Birnbaum’s point. “[I] do think that is a real concern,” he replied. “[H]ow quickly can you work with [the VAR police] to get them to revise our VAR to a more realistic number?” Birnbaum replied that he had a meeting with them on Tuesday, where apparently he was able to get the VAR limit of $110 million extended until August 21. But, on August 13, when VAR for trading overall had increased to $159 million, from $150 million, Viniar was explicit. “No comment necessary,” he wrote. “Get it down.” Gary Cohn echoed Viniar’s comment two days later, after the trading VAR had increased to $165 million. “There is no room for debate,” he wrote. “We must get down now.” The concern about the rising VAR on the mortgage trading desk revealed a larger debate then percolating around Goldman: how to take advantage of the misery being felt by other firms as the mortgage markets started to collapse.

**
Them And Us: Politics, Greed And Inequality - Why We Need A Fair Society
** by
Will Hutton

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Andrei Shleifer, asset-backed security, bank run, banking crisis, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Bretton Woods, capital controls, carbon footprint, Carmen Reinhart, Cass Sunstein, centre right, choice architecture, cloud computing, collective bargaining, conceptual framework, Corn Laws, corporate governance, credit crunch, Credit Default Swap, debt deflation, decarbonisation, Deng Xiaoping, discovery of DNA, discovery of the americas, discrete time, diversification, double helix, Edward Glaeser, financial deregulation, financial innovation, financial intermediation, first-past-the-post, floating exchange rates, Francis Fukuyama: the end of history, Frank Levy and Richard Murnane: The New Division of Labor, full employment, George Akerlof, Gini coefficient, global supply chain, Growth in a Time of Debt, Hyman Minsky, I think there is a world market for maybe five computers, income inequality, inflation targeting, interest rate swap, invisible hand, Isaac Newton, James Dyson, James Watt: steam engine, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, knowledge economy, knowledge worker, labour market flexibility, Long Term Capital Management, Louis Pasteur, low-wage service sector, mandelbrot fractal, margin call, market fundamentalism, Martin Wolf, means of production, Mikhail Gorbachev, millennium bug, moral hazard, mortgage debt, new economy, Northern Rock, offshore financial centre, open economy, Plutocrats, plutocrats, price discrimination, private sector deleveraging, purchasing power parity, quantitative easing, race to the bottom, railway mania, random walk, rent-seeking, reserve currency, Richard Thaler, rising living standards, Robert Shiller, Robert Shiller, Ronald Reagan, Rory Sutherland, shareholder value, short selling, Silicon Valley, Skype, South Sea Bubble, Steve Jobs, The Market for Lemons, the market place, The Myth of the Rational Market, the payments system, the scientific method, The Wealth of Nations by Adam Smith, too big to fail, unpaid internship, value at risk, Washington Consensus, working poor, éminence grise

As bank balance sheets varied so much from day to day, depending on what they were financing and to what degree they had laid off the financing to other banks, it was important to track the value at risk each day. In the late 1980s Dennis Weatherstone, the CEO of JP Morgan, instituted regular reporting at 4.15 p.m., after trading had closed, of the level of risk that the bank was running in all parts of its business.32 One could attach risk weightings to loans, but that was only partially helpful. What Weatherstone wanted to know was how much money the bank would lose if it were hit by a big event outside the normal distribution of events. Such events are statistically improbable but still possible. But would they present too much risk, and bring down the whole bank? This led to the development of mathematically computed value at risk (VaR), which was based on the same assumptions about random walks, efficient markets and bell curves that had been used when pricing derivatives.

…

Now, with the benefit of hindsight, it seems obvious that larger banks that are deemed too big to fail should be obliged to carry more capital to underwrite their business. In 2004 the view of both regulators and the bankers themselves was that the large banks would have more diversified risks, and so needed less capital. The claim was also made that they utilised sophisticated risk-management techniques, notably value at risk (VaR), which allegedly allowed them to assess risk more accurately than smaller banks and thus had a more carefully calibrated view of the amount of capital they needed. The argument went that such banks should be permitted to assess the riskiness of their own loans and then negotiate their capital needs with the regulator. In other words, Basel 2 gave the green light to an unchecked credit explosion.

…

., 156–7 Oxbridge/top university entry, 293–4, 306 Oxford University, 261 Page, Scott, 204 Paine, Tom, 347 Pareto, Vilfredo, 201–2 Paribas, 152, 187 Parkinson, Lance-Bombardier Ben, 13 participation, political, 35, 86, 96, 99 Paulson, Henry, 177 Paulson, John, 103, 167–8 pay of executives and bankers, 3–4, 5, 6–7, 22, 66–7, 138, 387; bonuses, 6, 25–6, 41, 174–5, 176, 179, 208, 242, 249, 388; high levels/rises of, 6–7, 13, 25, 82–3, 94, 172–6, 216, 296, 387, 393; Peter Mandelson on, 24; post-crash/bail-outs, 176, 216; in private equity houses, 248; remuneration committees, 6, 82, 83, 176; shared capitalism and, 66, 93; spurious justifications for, 42, 78, 82–3, 94, 176, 216 pension, state, 81, 372, 373 pension funds, 240, 242 Pettis, Michael, 379–80 pharmaceutical industry, 219, 255, 263, 265, 267–8 Phelps, Edmund, 275 philanthropy and charitable giving, 13, 25, 280 Philippines, 168 Philippon, Thomas, 172–3 Philips Electronics, Royal, 256 Pimco, 177 piracy, 101–2 Plato, 39, 44 Player, Gary, 76 pluralist state/society, x, 35, 99, 113, 233, 331, 350, 394 Poland, 67, 254 political parties, 13–14, 340, 341, 345, 390; see also under entries for individual parties political system, British: see also democracy; centralised constitution, 14–15, 35, 217, 334; coalitions as a good thing, 345–6; decline of class-based politics, 341; devolving of power to Cardiff and Edinburgh, 15, 334; expenses scandal, 3, 14, 217, 313, 341; history of (to late nineteenth-century), 124–30; lack of departmental coordination, 335, 336, 337; long-term policy making and, 217; monarchy and, 15, 312, 336; politicians’ lack of experience outside politics, 338; required reforms of, 344–8; select committee system, 339–40; settlement (of 1689), 125; sovereignty and, 223, 346, 347, 378; urgent need for reform, 35, 36–7, 218, 344; voter-politician disengagement, 217–18, 310, 311, 313–14, 340 Pommerehne, Werner, 60 population levels, world, 36 Portsmouth Football Club, 352 Portugal, 108, 109, 121, 377 poverty, 278–9; child development and, 288–90; circumstantial causes of, 26, 283–4; Conservative Party and, 279; ‘deserving’/’undeserving’ poor, 276, 277–8, 280, 284, 297, 301; Enlightenment views on, 53, 55–6; need for asset ownership, 301–3, 304; political left and, 78–83; the poor viewed as a race apart, 285–7; as relative not absolute, 55, 84; Adam Smith on, 55, 84; structure of market economy and, 78–9, 83; view that the poor deserve to be poor, 25, 52–3, 80, 83, 281, 285–8, 297, 301, 387; worldwide, 383, 384 Power2010 website, 340–1 PR companies and media, 322, 323 Press Complaints Commission (PCC), 325, 327, 331–2, 348 preventative medicine, 371 Price, Lance, 328, 340 Price, Mark, 93 Prince, Chuck, 184 printing press, 109, 110–11 prisoners, early release of, 11 private-equity firms, 6, 28–9, 158, 172, 177, 179, 205, 244–9, 374 Procter & Gamble, 167, 255 productive entrepreneurship, 6, 22–3, 28, 29–30, 33, 61–2, 63, 78, 84, 136, 298; in British history (to 1850), 28, 124, 126–7, 129; due desert/fairness and, 102–3, 105–6, 112, 223, 272, 393; general-purpose technologies (GPTs) and, 107–11, 112, 117, 126–7, 134, 228–9, 256, 261, 384 property market: baby boomer generation and, 372–3; Barker Review, 185; boom in, 5, 143, 161, 183–4, 185–7, 221; bust (1989-91), 161, 163; buy-to-let market, 186; commercial property, 7, 356, 359, 363; demutualisation of building societies, 156, 186; deregulation (1971) and, 161; Japanese crunch (1989-92) and, 361–2; need for tax on profits from home ownership, 308–9, 373–4; property as national obsession, 187; residential mortgages, 7, 183–4, 186, 356, 359, 363; securitised loans based mortgages, 171, 186, 188; shadow banking system and, 171, 172; ‘subprime’ mortgages, 64, 152, 161, 186, 203 proportionality, 4, 24, 26, 35, 38, 39–40, 44–6, 51, 84, 218; see also desert, due, concept of; contributory/discretionary benefits and, 63; diplomacy/ international relations and, 385–6; job seeker’s allowance as transgression of, 81; left wing politics and, 80; luck and, 73–7, 273; policy responses to crash and, 215–16; poverty relief systems and, 80–1; profit and, 40, 388; types of entrepreneurship and, 61–2, 63 protectionism, 36, 358, 376–7, 378, 379, 382, 386 Prussia, 128 Public Accounts Committee, 340 Purnell, James, 338 quantitative easing, 176 Quayle, Dan, 177 race, disadvantage and, 290 railways, 9, 28, 105, 109–10, 126 Rand, Ayn, 145, 234 Rawls, John, 57, 58, 63, 73, 78 Reagan, Ronald, 135, 163 recession, xi, 3, 8, 9, 138, 153, 210, 223, 335; of 1979-81 period, 161; efficacy of fiscal policy, 367–8; VAT decrease (2009) and, 366–7 reciprocity, 43, 45, 82, 86, 90, 143, 271, 304, 382; see also desert, due, concept of; proportionality Reckitt Benckiser, 82–3 Regional Development Agencies, 21 regulation: see also Bank of England; Financial Services Authority (FSA); Bank of International Settlements (BIS), 169, 182; Basel system, 158, 160, 163, 169, 170–1, 196, 385; big as beautiful in global banking, 201–2; Big Bang (1986), 90, 162; by-passing of, 137, 187; capital requirements/ratios, 162–3, 170–1, 208; dismantling of post-war system, 149, 158, 159–63; economists’ doubts over deregulation, 163; example of China, 160; failure to prevent crash, 154, 197, 198–9; Glass-Steagall abolition (1999), 170, 202–3; light-touch, 5, 32, 138, 151, 162, 198–9; New Deal rules (1930s), 159, 162; in pharmaceutical industry, 267–8; as pro-business tool, 268–70; proposed Financial Policy Committee, 208; required reforms of, 267, 269–70, 376, 377, 384, 392; reserve requirements scrapped (1979), 208; task of banking authorities, 157; Top Runner programme in Japan, 269 Reinhart, Carmen, 214, 356 Repo 105 technique, 181 Reshef, Ariell, 172–3 Reuters, 322, 331 riches and wealth, 11–13, 272–3, 283–4, 387–8; see also pay of executives and bankers; the rich as deserving of their wealth, 25–6, 52, 278, 296–7 Rickards, James, 194 risk, 149, 158, 165, 298–302, 352–3; credit default swaps and, 151, 152, 166–8, 170, 171, 175, 176, 191, 203, 207; derivatives and see derivatives; distinction between uncertainty and, 189–90, 191, 192–3, 196–7; employment insurance concept, 298–9, 301, 374; management, 165, 170, 171, 189, 191–2, 193–4, 195–6, 202, 203, 210, 354; securitisation and, 32, 147, 165, 169, 171, 186, 188, 196; structured investment vehicles and, 151, 165, 169, 171, 188; value at risk (VaR), 171, 192, 195, 196 Risley, Todd, 289 Ritchie, Andrew, 103 Ritter, Scott, 329 Robinson, Sir Gerry, 295 Rogoff, Ken, 214, 356 rogue states, 36 Rolling Stones, 247 Rolls-Royce, 219, 231 Rome, classical, 45, 74, 108, 116 Roosevelt, Franklin D., 133, 300 Rothermere, Viscount, 327 Rousseau, Jean-Jacques, 56, 58, 112 Rousseau, Peter, 256 Rowling, J.K., 64, 65 Rowthorn, Robert, 292, 363 Royal Bank of Scotland (RBS), 25, 150, 152, 157, 173, 181, 199, 251, 259; collapse of, 7, 137, 150, 158, 175–6, 202, 203, 204; Sir Fred Goodwin and, 7, 150, 176, 340 Rubin, Robert, 174, 177, 183 rule of law, x, 4, 220, 235 Russell, Bertrand, 189 Russia, 127, 134–5, 169, 201, 354–5, 385; fall of communism, 135, 140; oligarchs, 30, 65, 135 Rwandan genocide, 71 Ryanair, 233 sailing ships, three-masted, 108 Sandbrook, Dominic, 22 Sands, Peter (CEO of Standard Chartered Bank), 26 Sarkozy, Nicolas, 51, 377 Sassoon, Sir James, 178 Scholes, Myron, 169, 191, 193 Schumpeter, Joseph, 62, 67, 111 science and technology: capitalist dynamism and, 27–8, 31, 112–13; digitalisation, 34, 231, 320, 349, 350; the Enlightenment and, 31, 108–9, 112–13, 116–17, 121, 126–7; general-purpose technologies (GPTs), 107–11, 112, 117, 126–7, 134, 228–9, 256, 261, 384; increased pace of advance, 228–9, 253, 297; nanotechnology, 232; New Labour improvements, 21; new opportunities and, 33–4, 228–9, 231–3; new technologies, 232, 233, 240; universities and, 261–5 Scotland, devolving of power to, 15, 334 Scott, James, 114–15 Scott Bader, 93 Scott Trust, 327 Second World War, 134, 313 Securities and Exchanges Commission, 151, 167–8 securitisation, 32, 147, 165, 169, 171, 186, 187, 196 self-determination, 85–6 self-employment, 86 self-interest, 59, 60, 78 Sen, Amartya, 51, 232, 275 service sector, 8, 291, 341, 355 shadow banking system, 148, 153, 157–8, 170, 171, 172, 187 Shakespeare, William, 39, 274, 351 shareholders, 156, 197, 216–17, 240–4, 250 Sher, George, 46, 50, 51 Sherman Act (USA, 1890), 133 Sherraden, Michael, 301 Shiller, Robert, 43, 298, 299 Shimer, Robert, 299 Shleifer, Andrei, 62, 63, 92 short selling, 103 Sicilian mafia, 101, 105 Simon, Herbert, 222 Simpson, George, 142–3 single mothers, 17, 53, 287 sixth form education, 306 Sky (broadcasting company), 30, 318, 330, 389 Skype, 253 Slim, Carlos, 30 Sloan School of Management, 195 Slumdog Millionaire, 283 Smith, Adam, 55, 84, 104, 112, 121, 122, 126, 145–6 Smith, John, 148 Snoddy, Ray, 322 Snow, John, 177 social capital, 88–9, 92 social class, 78, 130, 230, 304, 343, 388; childcare and, 278, 288–90; continued importance of, 271, 283–96; decline of class-based politics, 341; education and, 13, 17, 223, 264–5, 272–3, 274, 276, 292–5, 304, 308; historical development of, 56–8, 109, 115–16, 122, 123–5, 127–8, 199; New Labour and, 271, 277–9; working-class opinion, 16, 143 social investment, 10, 19, 20–1, 279, 280–1 social polarisation, 9–16, 34–5, 223, 271–4, 282–5, 286–97, 342; Conservative reforms (1979-97) and, 275–6; New Labour and, 277–9; private education and, 13, 223, 264–5, 272–3, 276, 283–4, 293–5, 304; required reforms for reduction of, 297–309 social security benefits, 277, 278, 299–301, 328; contributory, 63, 81, 283; flexicurity social system, 299–301, 304, 374; to immigrants, 81–2, 282, 283, 284; job seeker’s allowance, 81, 281, 298, 301; New Labour and ‘undeserving’ claimants, 143, 277–8; non-contributory, 63, 79, 81, 82; targeting of/two-tier system, 277, 281 socialism, 22, 32, 38, 75, 138, 144, 145, 394 Soham murder case, 10, 339 Solomon Brothers, 173 Sony, 254–5 Soros, George, 166 Sorrell, Martin, 349 Soskice, David, 342–3 South Korea, 168, 358–9 South Sea Bubble, 125–6 Spain, 123–4, 207, 358–9, 371, 377 Spamann, Holger, 198 special purpose vehicles, 181 Spitzer, Matthew, 60 sport, cheating in, 23 stakeholder capitalism, x, 148–9 Standard Oil, 130–1, 132 state, British: anti-statism, 20, 22, 233–4, 235, 311; big finance’s penetration of, 176, 178–80; ‘choice architecture’ and, 238, 252; desired level of involvement, 234–5; domination of by media, 14, 16, 221, 338, 339, 343; facilitation of fairness, ix–x, 391–2, 394–5; investment in knowledge, 28, 31, 40, 220, 235, 261, 265; need for government as employer of last resort, 300; need for hybrid financial system, 244, 249–52; need for intervention in markets, 219–22, 229–30, 235–9, 252, 392; need for reshaping of, 34; pluralism, x, 35, 99, 113, 233, 331, 350, 394; public ownership, 32, 240; target-setting in, 91–2; threats to civil liberty and, 340 steam engine, 110, 126 Steinmueller, W.

**
The Default Line: The Inside Story of People, Banks and Entire Nations on the Edge
** by
Faisal Islam

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Asian financial crisis, asset-backed security, balance sheet recession, bank run, banking crisis, Basel III, Ben Bernanke: helicopter money, Berlin Wall, Big bang: deregulation of the City of London, British Empire, capital controls, carbon footprint, Celtic Tiger, central bank independence, centre right, collapse of Lehman Brothers, credit crunch, Credit Default Swap, crony capitalism, dark matter, deindustrialization, Deng Xiaoping, disintermediation, energy security, Eugene Fama: efficient market hypothesis, eurozone crisis, financial deregulation, financial innovation, financial repression, floating exchange rates, forensic accounting, forward guidance, full employment, ghettoisation, global rebalancing, global reserve currency, hiring and firing, inflation targeting, Irish property bubble, Just-in-time delivery, labour market flexibility, London Whale, Long Term Capital Management, margin call, market clearing, megacity, Mikhail Gorbachev, mini-job, mittelstand, moral hazard, mortgage debt, mortgage tax deduction, mutually assured destruction, North Sea oil, Northern Rock, offshore financial centre, open economy, paradox of thrift, pension reform, price mechanism, price stability, profit motive, quantitative easing, quantitative trading / quantitative ﬁnance, race to the bottom, regulatory arbitrage, reserve currency, reshoring, rising living standards, Ronald Reagan, savings glut, shareholder value, sovereign wealth fund, The Chicago School, the payments system, too big to fail, trade route, transaction costs, two tier labour market, unorthodox policies, uranium enrichment, urban planning, value at risk, working-age population

They can wreak havoc, from earthquakes and power outages, to depressions and financial crises. Failing to recognise those tail events – being fooled by randomness – risks catastrophic policy error.’ But – no surprise – normal distributions are hard-wired into economics and quantitative financial modelling. The towering example of this is value-at-risk (VaR), the measure used by banks and regulators to assess risk on their trading books, and to set limits on traders. VaR is supposed to tell a bank and its regulators how much a trading portfolio will make on 99 per cent or sometimes 95 per cent of trading days. Remember that at the time Northern Rock and its competitors were going crazy, credit risk was migrating off balance sheets and out of the regulated loan book and into the trading book. The regulatory dam was a flawed set of equations rooted in normal distributions, and the notion that a limited history of past pricing patterns could be extrapolated into the future.

…

Morgan itself discovered in May 2012 that the ‘London Whale’ corporate credit portfolio that was assessed with a 95 per cent VaR of $67 million in early 2012 had lost them $2 billion within weeks. In its February 2008 annual results, RBS calculated a 95 per cent VaR on its trading book at £45.7 million. The disastrous purchase of the toxic asset-laden ABN Amro had increased that measure by just £6 million. A footnote did warn: ‘VaR using a 95 per cent confidence level does not reflect the extent of potential losses beyond that percentile.’ And sure enough, just a few months later, the losses on the trading book in 2008 topped £12 billion. A basic problem is that past trading performance is no guide to the future. VaR models were routinely specified to assume that the very recent past is the best guide to the future. Before long VaR came to be seen, quite incorrectly, as an upper-end assessment of likely losses.

…

But global regulators demanded banks calculate, and sure enough the familiar pattern of misinterpreting, gaming and reverse engineering formulae was quickly applied to VaR. The Financial Times quoted Goldman Sachs’ chief financial officer during the 2007 credit crunch as saying that twenty-five standard deviation moves were happening several days in a row. To put that in context, he was suggesting that occurrences that his financial model suggested would only happen once in a period of many trillions of lifetimes of the universe, were actually happening every day. The ‘fatal flaw’ of VaR, as Haldane argues, is that it is silent about the tail risk. A trader could be given a so-called 99 per cent VaR limit of $10 million, but VaR would be blind to the trader’s construction of a portfolio that gave a 1 per cent chance of a $1 billion loss. J. P.

**
The Concepts and Practice of Mathematical Finance
** by
Mark S. Joshi

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Black-Scholes formula, Brownian motion, correlation coefficient, Credit Default Swap, delta neutral, discrete time, Emanuel Derman, implied volatility, incomplete markets, interest rate derivative, interest rate swap, London Interbank Offered Rate, martingale, millennium bug, quantitative trading / quantitative ﬁnance, short selling, stochastic process, stochastic volatility, the market place, time value of money, transaction costs, value at risk, volatility smile, yield curve, zero-coupon bond

Skew A normalization of the third moment of a random variable: E((X - E(X))3) Var(X)3/2 Stochastic A fancy word for random. Stock See share. Strike The price that an options allows an asset to be ought or sold for. Swap A contract to swap a fixed stream of interest rate payments for a floating stream of interest rate payments. The fixed rate is called the strike of the swap. Swap rate The rate such that a swap with that strike has zero value. Swaption The option but not the obligation to enter into a swap. Theta The derivative of the price of an instrument with respect to time. Trigger option An option that requires the holder to buy or sell an asset at a fixed price according to the level of some reference rate. Value at risk (or VAR) The amount that a portfolio can lose over some period of time with a given probability.

…

Value at risk (or VAR) The amount that a portfolio can lose over some period of time with a given probability. For example, the amount the bank can lose in one day with 5% probability. VAR Short for value at risk. Variance Variance is defined as Var(X) _ ]E((X - ]E(X))2). Vanna The derivative of the Vega with respect to the underlying. Vega The derivative of the price of an instrument with respect to volatility. Yield The effective interest rate receivable by purchasing a bond. (There are lots of different sorts of yields.) Yield curve Another name for a discount curve. Zero-coupon bond A bond which pays no coupons. Appendix B Computer projects B1 Introduction In this appendix, we look at some basic methods of simulating financially important mathematical functions, and then list a number of projects the reader is encouraged to try for himself. Ultimately, quantitative analysis is about the implementation of financial models not the theory, and the reader will not have truly learnt the topic until he, or she, has programmed a few models.

…

Index N, 65 N(0, 1), 57 N(µ, a2), 98 or-field, 458 accreting notional, 429 admissible exercise strategy, see exercise strategy, admissible almost, 257 almost surely, 99 American, 10 American option, see option, American amortising notional, 429 annualized rates, 302 annuity, 308 .anti-thetic sampling, 192 arbitrage, 19-20, 27-29,429 and bounding option prices, 29-39 arbitrage-free price, 45, 46 arbitrageur, 12-13, 18 Arrow-Debreu security, 152 at-the-forward, 31 at-the-money, 30, 66 auto cap, 429 bank, 12 barrier option, see option, barrier basis point, 429 basket option, 261 Bermudan option, see option, Bermudan Bermudan swaption, see swaption, Bermudan BGM, 429 implementation of, 450-453 BGM model, 322-355 automatic calibration to co-terminal swaptions, 342 long steps, 337 running a simulation, 337-342 BGM/J, 429 BGM/J model, see BGM model bid-offer spread, 21 Black formula, 173, 310-311 approximate linearity, 356 approximation for swaption pricing under BGM model, 341 Black-Scholes formula, see option, call, Black-Scholes formula for Black-Scholes density, 188 Black-Scholes equation, 69, 160, 161 for options on dividend-paying assets, 123 higher-dimensional, 271 informal derivation of, 114-116 rigorous derivation, 116-119 solution of, 119-121 with time-dependent parameters, 164 Black-Scholes formula, 65 Black-Scholes model, 74, 113, 430 Black-Scholes price, 19 Black-Scholes model, 76 bond, 4 6, 430 callable, 301 convertible, 7, 430 corporate, 7 government, 1 premium, 2 riskless, 5, 7 zero-coupon, 5, 24-26, 28, 302, 433 Brownian bridge, 230 Brownian motion, 97-100, 101, 107, 142, 260, 430 correlated, 263 higher-dimensional, 261-263 Buffett, Warren, 2 bushy tree, see tree, non-recombining calibration to vanilla options using jump-diffusion, 377 call, 301 call option, see option, call callable bond, see bond, callable cap, 309, 430 caplet, 309-311, 430 strike of, 309 caption, 326, 430 cash bond, 26, 430 Central Limit theorem, 56, 60 Central Limit Theorem, 64 Central Limit theorem, 278,463 central method, 238 533 Index 534 CEV, see constant elasticity of variance chain rule, 106 for stochastic calculus, 109 characteristic function, 408 Cholesky decomposition, 227 cliquet, 425, 430 call, 425 optional, 426 put, 425 CMS, see swap, constant maturity co-initial, 317, 340 co-terminal, 317, 340 commodities, 123 complete market, 152, 430 compound optionality, 426 conditional probability, 460 consol, 430 constant elasticity of variance, 113 constant elasticity of variance process, 355 constant maturity swap, see swap, constant maturity contingent claim, 152, 430 continuously compounding rate, 25, 26 control variate and pricing of Bermudan swaptions, 351 on a tree, 288 convenience yield, 123 convexity, 35-37, 81 as a function of spot price in a log-type model, 383 correlation, 466 between forward rates, 321, 335 correlation matrix, 268, 466 cost of carry, 123 coupon, 4, 301, 430 covariance, 466 covariance matrix, 466 and implementing BGM, 343 crash, 10, 86 credit default swap, 23 credit rating, 316, 430 cumulative distribution function, 461 cumulative normal function, 65, 435, 437 default, 1 deflated, 168 Delta, 76, 80,430 and static replication, 246, 248 Black-Scholes formula for call option, 80 integral expression for, 189 Delta hedging, see hedging, Delta dependent, 461 derivative, 10, 430 credit, 11 weather, 11 Derman-Kani implied tree, 381 deterministic future smile, 244, 426 digital, 430 digital option, see option, digital dimensionality, 224, 438 dimensionality reduction, 229 discount curve, 431 discretely compounding money market account, 324 displaced diffusion model, 355 distribution log-normal, see log-normal distribution diversifiable risk, 431 diversification, 8 dividend, 7, 431 scrip, 25 dividend rate, 25 dividends and the Black-Scholes equation, 121-123 drift, 60, 111 of a forward rate under BGM, 330 real-world, 64 Dupire model, 381 dynamic replication, see replication, dynamic early exercise, 68 equivalent martingale measure for a tree with jumps, 363 equivalent probability measures, see probability measure, equivalence European, 10 European contingent claim, 116 exercise, 10 exercise boundary, 289 exercise region, 289 exercise strategy admissible, 286 expectation, 431, 462 conditional, 155 fat tails, 85, 431, 464 Feynman-Kac theorem, 161 fickle, 377 filtration, 143, 154, 162 first variation, see variation, first fixed leg, 306 fixed rate, 431 floating, 300 floating leg, 306 floating rate, 431 floating smile, see smile, floating floor, 309,431 floorlet, 309, 431 floortion, 326, 431 forward contract, 9, 22, 181, 431 and risk-neutrality, 137 value of, 26 forward price, 26, 31 forward rates, 303-305 forward-rate agreement, 23, 304, 431 Fourier transform, 395, 408 FRA, see forward-rate agreement free boundary value problem, 290 Gamma, 77, 80, 431 and static replication, 246, 248 Black-Scholes formula for a call option, 80 non-negativity of, 384 Index Gamma distribution, 402 Gamma function, 402 incomplete, 405 Gaussian distribution, 57, 103 Gaussian random variable synthesis of, 191 gearing, 300 geometric Brownian motion, 111, 114 gilt, 314 Girsanov transformation, 214 Girsanov's theorem, 158, 166, 210-213, 368, 390, 431 higher-dimensional, 267-271 Greeks, 77-83, 431 and static replication, 246, 248 computation of on a tree, 186 of multi-look options, 236-238 heat equation, 119, 120-121 Heath, Jarrow & Morton, 322 hedger, 12-13, 18 hedging, 4, 8, 11, 67-68, 431, 441 and martingale pricing, 162-164 Delta, 18-19, 68, 73, 76, 115, 118, 162 exotic option under jump-diffusion, 535 Ito's Lemma, 106-110 application of, 111-114 multi-dimensional, 264 joint density function, 464 joint law of minimum and terminal value of a Brownian motion with drift, 213 without drift, 208 jump-diffusion model, 87, 364-381 and deterministic future smiles, 244 and replication of American options, 293 price of vanilla options as a function of jump intensity, 374 pricing by risk-neutral evaluation, 364-367 jump-diffusion process, 361 jumps, 86-88 jumps on a tree, 362 Kappa, 79 knock in, 202 knock out, 202 knock-in option, see option, barrier knock-out option, see option, barrier kurtosis, 85, 432, 464 375 Gamma, 77 in a one-step tree, 44-45 in a three-state model, 49 in a two-step model, 51 of exotic options, 424 vanilla options in a jump-diffusion world, 372 Vega, 79 hedging strategy, 17-18, 44, 76 stop-loss, 143 hedging, discrete, 76 HJM model, 322 homogeneity, 274, 281, 383 implied volatility, see volatility, implied importance sampling, 193 in-the-money, 30 incomplete, 431 incomplete market, 50, 361, 367-375, 389, 390 incomplete model, 89 incremental path generation, see path generation, incremental independent, 461 information, 2, 4, 113, 140-145, 162, 401 conditioning on, 145 insider trading, 3 insurance, 12 inverse cumulative normal function, 192, 435, 436 inverse floater, 359 Ito, 97 Ito calculus higher-dimensional, 261, 263-266 Ito process, 106, 154 law of large numbers, 69, 191, 462 law of the minimum of a Brownian motion drift, 215, 216 law of the unconscious statistician, 463 Leibniz rule, 110 leveraging, 300 LIBID, 432 LIBOR, 302, 315, 432 LIBOR market model, 322 LIBOR-in-arrears, 312-313 LIBOR-in-arrears caplet pricing by BGM, 326 LIBOR-in-arrears FRA pricing by BGM, 326 likelihood ratio, 195, 237 liquidity, 21 Lloyds, 6 log-normal distribution, 61 log-normal model, 58 approximation by a tree, see tree, approximating a log-normal model for stock price movements, 112 log-type model, 382-385 long, 21, 432 low-discrepancy numbers, 193 the pricing of exotic options, 445-447 lucky paths, 369 marginal distribution, 465 Margrabe option, see option, Margrabe market efficiency, 2-4 weak, 3, 4, 99 market maker, 74 market model, 432 market price of risk, 89, 112 Index 536 Markov property, 3, 98, 99 strong, 210 martingale, 129, 145, 432 and no arbitrage, 146 continuous, 154-160 discrete, 146 higher-dimensional, 267 martingale measure, 148 choice of, 376 uniqueness, 150 martingale pricing and time-dependent parameters, 164-165 based on the forward, 172-175 continuous, 157-160 discrete, 145-154 equivalence to PDE method, 161-162 with dividend-paying assets, 171 martingale representation theorem, 162 maturity, 5 maximal foresight, 296 mean-reverting process, 390 measure change, 368 model risk, 244 moment, 432 moment matching, 193 and pricing of Asian options, 231-233 money-market account, 26, 114, 430 moneyness, 385 monotonicity theorem, 27 Monte Carlo simulation, 69, 462 and price of exotic options using a jump-diffusion model, 379 and pricing of European options, 191 computation of Greeks, 194-195 variance reduction, 192 Moro, 435 mortgage, 301 multi-look option, see option, multi-look Name, 6 natural payoff, 330 NFLWVR, 132, 135 no free lunch principle, 19 no free lunch with vanishing risk, see NFLWVR no-arbitrage, 45 non-recombining tree, see tree, non-recombining normal distribution, see Gaussian distribution, 461 notional, 304 numeral e, 168, 174, 310, 312, 314, 324 change of, 167 numerical integration and pricing of European options, 187-190 option, 9-12 American, 68, 144, 284, 429 boundary conditions for PDE, 290 lower bounds by Monte Carlo, 293-295 PDE pricing, 289-291 pricing on a tree, 287-289 replication of, 291-293 seller's price, 297 theoretical price of, 287 upper bounds by Monte Carlo, 295-297 American digital, 219 American put, 219 Asian, 222, 429 pricing by PDE or tree, 233-234 static replication of, 249-251 barrier, 69, 429 definition, 202-204 price of down-and-out call, 217, 218 basket, 261, 429 Bermudan, 284,429 binary, 429 call, 10, 181, 430 American, 32 Black-Scholes formula for, 65, 160 down-and-in, 202 down-and-out, 202 formula for price in jump-diffusion model, 366, 367 pay-off, 29 perpetual American, 299 pricing under Black-Scholes, 114 chooser, 294 continuous barrier expectation pricing of, 207-208, 216-219 PDE pricing of, 205-207 static replication of, 244-247, 252-256 static replication of down-and-out put, 244-246 continuous double barrier static replication, 246-247 digital, 83, 257 call, 83 put, 83 digital call, 181 Black-Scholes formula for price of, 183 digital put, 181 Black-Scholes formula for price of, 183 discrete barrier, 222 static replication of, 247-249 double digital, 130 European, 431 exotic, 10, 87 Monte Carlo, 444445 pricing under jump-diffusion, 379-381 knock-in, 431 knock-out, 69, 432 Margrabe, 260, 273-275 model-independent bounds on price, 29-39 multi-look, 223 Parisian, 432 path-dependent, 223 and risk-neutral pricing, 223-225 static replication of, 249-251 power call, 182 put, 10, 181,432 Black-Scholes formula for, 65 pay-off, 30 Index quanto, 260, 275-280 static replication of up-and-in put with barrier at strike, 251-252 trigger, 433 vanilla, 10 with multiple exercise dates, 284 out-of-the-money, 30 path dependence weak, 225 path generation, 226-230 incremental, 228 using spectral theory, 228 path-dependent exotic option, see option, path-dependent pathwise method, 195, 236 PDE methods and the pricing of European options, 195-196 Poisson process, 364 positive semi-definite, 467 positivity, 7, 28 predictable, 162 predictor-corrector, 340 present valuing, 302 previsible, 370 pricing arbitrage-free, 22 principal, 5, 301 probability risk-neutral, see risk-neutral probability probability density function, 461 probability measure, 458 equivalence, 147 product rule for Ito processes, 110 pseudo-square root, 468 put option, see option, put put-call parity, 30, 65, 67 put-call symmetry, 252-256 quadratic variation, 100, see variation, quadratic quanto call, 277 quanto drift, 276 quanto forward, 277 quanto option, see option, quanto quasi Monte Carlo, 194 Radon-Nikodym, 214 Radon-Nikodym derivative, 213 random time, 88, 143 random variable, 459 real-world drift, see drift, real-world recombining trees implementing, 443 reflection principle, 208-210 replication, 23, 116 and dividends, 122 and the pricing of European options, 196-198 classification of methods, 257 dynamic, 198, 257 in a one-step tree, 48-49 537 in a three-state model, 50 semi-static and jump-diffusion models, 381 static, 198 feeble, 257 mezzo, 257 strong, 243, 257 weak, 243, 257 repo, 315 restricted stochastic-volatility model, see Dupire model reverse option, 320 reversing pair, 319 Rho, 79 rho, 432 risk, 1-2, 8, 9 diversifiable, 8-9 purity of, 9 risk neutral, 19 risk premium, 46, 60, 64, 111, 119,432 risk-neutral distribution, 64 risk-neutral density as second derivative of call price, 137 in Black-Scholes world, 139 risk-neutral expectation, 64 risk-neutral measure, 148, 432 completeness, 166 existence of, 129 uniqueness, 166 risk-neutral pricing, 64 65, 140 higher-dimensional, 267-271 risk-neutral probability, 47, 52, 54, 59, 128 risk-neutral valuation, 59 in a one-step tree, 45-48 in a three-state model, 50 in jump models, 86 two-step model, 52 riskless, 1 riskless asset, 28 Rogers method for upper bounds by Monte Carlo, 295, 350 sample space, 458 self-financing portfolio, 28, 116-117, 128, 163, 369 dynamic, 28 share, 6-7, 432 share split, 57 short, 432 short rate, 25, 433 short selling, 21 simplex method, 295 skew, 433, 464 smile, 74-77 displaced-diffusion, 356,420 equity, 421 floating, 88, 385, 407, 413-414 foreign exchange, 413 FX, 424 interest-rate, 355-357, 424 jump-diffusion, 378, 415 sticky, 88, 413-414 sticky-delta, 413 538 smile (cont.) stochastic volatility, 398, 416 time dependence, 414-415 Variance Gamma, 406,417 smile dynamics Deiman-Kani, 420 displaced-diffusion, 420 Dupire model, 420 equity, 421 FX, 424 interest-rate, 424 jump-diffusion, 415 market, 413-415 model, 415-421 stochastic volatility, 416 Variance Gamma, 417 smoothing operator, 120 spectral theory, 228 speculator, 12, 18 split share, see share split spot price, 31 square root of a matrix, 467 standard error, 191 standard deviation, 463 static replication, see replication, static stepping methods for Monte Carlo, 439 stochastic, 433 stochastic calculus, 97 stochastic differential equation, 105 for square of Brownian motion, 107 stochastic process, 102-106, 141 stochastic volatility, 88, 389 and risk-neutral pricing, 390-393 implied, 400 pricing by Monte Carlo, 391-394 pricing by PDE and transform methods, 395-398 stochastic volatility smiles, see smile, stochastic volatility stock, 6-7, 433 stop loss hedging strategy, 18 stopping time, 143, 286, 346 straddle, 182, 257 Index lower bound via local optimization, 347 lower bounds by BGM, 345-349 pricing by BGM, 325 upper bounds by BGM, 349-352 cash-settled, 327 European, 310 price of, 313-314 payer's, 309,432 pricing by BGM, 323 receiver's, 309, 432 swaptions rapid approximation to price in a BGM model, 340 Taylor's theorem, 67, 80, 108 term structure of implied volatilities, 334 terminal decorrelation, 339, 352 Theta, 79, 433 and static replication, 246, 248 time homogeneity, 33, 333 time value of money, 24-26 time-dependent volatility and pricing of multi-look options, 235 Tower Law, 155 trading volatility, see volatility, trading of trading volume, 401 transaction costs, 21, 76, 90, 91 trapezium method, 188 tree with multiple time steps, 50-55 and pricing of European options, 183-186 and time-dependent volatility, 184 approximating a log-normal model, 60-68 approximating a normal model, 55-58 higher-dimensional, 277-280 non-recombining, 184 one-step, 44-50 risk-neutral behaviour, 61 trinomial, 184 with interest rates, 58-59 trigger FRA, 318 trigger swap, 325 pricing by BGM, 325 trinomial tree, see tree, trinomial strike, 10, 433 strong static replication, see replication, static, strong sub-replication, 369-375 super-replication, 369-375 swap, 300, 305-309, 433 constant maturity, 328 payer's, 306, 432 pricing by BGM, 323 receiver's, 306, 432 value of, 308 swap rate, 433 swap-rate market model, 340 swaption, 301, 309, 433 Bermudan, 301, 310, 342 and factor reduction, 352-355 lower bound via global optimization, 347 underlying, 10 uniform distribution, 461 valuation risk-neutral, see risk-neutral valuation value at risk, 433 Vanna, 433 VAR, 433 variance, 433, 463 Variance Gamma mean rate, 402 variance rate, 403 Variance Gamma density, 408 Variance Gamma model, 88, 404-407 and deterministic future smiles, 244 Variance Gamma process, 401-403 Index variation, 157, 367 first, 99, 367, 409 quadratic, 368 second, see variation, quadratic Vega, 79, 82, 433 integral expression for, 189 Vega hedging, see hedging, Vega volatility, 60, 65, 66, 73-74, 111 Black-Scholes formula as linear function of, 66 forward, 426 implied, 73, 197 instantaneous curve, 320, 333 539 root-mean-square, 320 time-dependence and tree-pricing, 294 trading of, 73 volatility surface, 363 weak static replication, see replication, static, weak Wiener measure, 141, 142 yield, 5, 24, 433 annualized, 25 yield curve, 319, 433 zero-coupon bond, see bond, zero-coupon

**
The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street
** by
Justin Fox

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Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, bank run, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, capital asset pricing model, card file, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discovery of the americas, diversification, diversified portfolio, Edward Glaeser, endowment effect, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, floating exchange rates, George Akerlof, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, invisible hand, Isaac Newton, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market design, New Journalism, Nikolai Kondratiev, Paul Lévy, pension reform, performance metric, Ponzi scheme, prediction markets, pushing on a string, quantitative trading / quantitative ﬁnance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, South Sea Bubble, statistical model, The Chicago School, The Myth of the Rational Market, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas L Friedman, Thorstein Veblen, Tobin tax, transaction costs, tulip mania, value at risk, Vanguard fund, volatility smile, Yogi Berra

In the early 1990s, as banks and their customers struggled to get a handle on the risks posed by their derivatives deals, most turned to an approach called “value at risk,” or VaR. This name was new—coined at J. P. Morgan in the 1980s—but it described what Harry Markowitz had dubbed “semi-variance” in 1959. It was the downside risk, a quantitative measure of how much a portfolio could drop on a bad day. It was possible to estimate a value at risk that took into account some of the wondrous and fat-tailed behavior of actual financial markets, but that required guesswork and judgment. To persuade a wary CEO to green-light a derivatives deal or convince a bank regulator that capital reserves were enough to cover potential losses, one needed a standardized VaR model like the RiskMetrics version peddled by J. P. Morgan. Even a good VaR model yielded only a partial picture of the true risks facing a bank or corporation or investor, and there were those who found this alarming.

…

“Measuring events that are unmeasurable can sometimes make things worse,” said Nassim Nicholas Taleb, a derivatives trader who—after making a mint in the 1987 crash—emerged as the most outspoken VaR critic in the mid-1990s. “A measuring process that lowers your anxiety level can mislead you into a false sense of security.” Take this argument to its extreme, though, and there’s no point in trying to measure financial risk at all. A happy mean must exist between quantification and judgment—even if it’s seldom attained in the real world. Taleb’s harder-to-argue-away concern was that widespread use of VaR made markets riskier. A drop in the price of a security raised the value at risk of a portfolio containing that security. If a bank or hedge fund was trying to keep the VaR below a certain level, it might then have to sell off other securities to push the VaR back down. That put downward pressure on the prices of those other securities, which in turn threatened to start the cycle over again.

…

., 146–47, 214, 216–21, 222–23, 230, 240, 242, 328 3Com, 262 three-factor model, 209–10 tight prior equilibrium, 89–90 Time Warner, 267 Tito, Dennis, 152 Tobin, James, 244, 302 Tobin tax, 244 trade deficits, 230 Travelers, 241 Treasury Inflation-Protected Securities (TIPS), 19 Treynor, Jack, 83–85, 88, 122–23, 125–27, 132, 139, 141, 149, 329 Trilling, Lionel, 91 Tsai, Gerry, 120, 124–25, 166 tuberculosis, 4, 12–13, 16 tulip market, 15–16 Tullock, Gordon, 159 Tversky, Amos, 176–77, 183, 185–86, 191–92, 201, 289, 291, 316, 329 “Uncertainty, Evolution and Economic Theory,” 93 United Kingdom, 40, 48 University of California, Irvine, 216 University of California, Los Angeles (UCLA), 86 University of Chicago (Chicago School of Economics) and academic isolation, 89–90 early growth of, 94–97 and efficient market hypothesis, xiii and experimental economics, 190 and Follies event, 287–89 founding of, 94–97 and Hayek, 92 and hostile takeovers, 167–68 and Knight, 84–85 and market efficiency, 101–5 and Miller, 237 and Mitchell, 31 and portfolio theory, 169 and the rational market hypothesis, 180 and role of businesses, 268 and Samuelson, 60–61 and unmanaged funds, 111 University of Chicago Law School, 157–58 University of Chicago Press, 90–91 University of Rochester, 107, 169, 275 Unruh, Jesse, 272, 273 U.S. and Foreign Securities Corp., 114 U.S. Congress, 137–38, 276, 280, 313–14 U.S. Department of Agriculture, 195 U.S. Department of Labor, 138 U.S. House of Representatives, 40 U.S. Naval Research Laboratory, 67 U.S. Senate, 40, 123–24 U.S. Steel, 15, 277 U.S. Supreme Court, 276 “The Use of Knowledge in Society” (Hayek), 91–92 utility theory, 10, 30, 51–52, 75 value at risk (VaR), 238–39 value investing, 116–18, 206, 215–16, 226, 255, 260 Vanguard, 129, 131 variance, 134–35, 138–39 Veblen, Thorstein, 30–31, 33–34, 76, 157 Viniar, David, 316 Vishny, Robert, 252–55, 300 volatility, 138–39, 144–45, 197, 233–34 Von Neumann-Morgenstern expected utility, 51–52, 54, 75, 80, 176–77, 193 wage controls, 136–37 Waldmann, Robert, 251 Waldrop, Mitchell, 302, 304–5 The Wall Street Journal, 15, 17–18, 26, 112, 163, 219, 224, 231–32, 235, 262–63 Wall $treet Week, 163 Wallis, W.

**
The Misbehavior of Markets
** by
Benoit Mandelbrot

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Albert Einstein, asset allocation, Augustin-Louis Cauchy, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black-Scholes formula, British Empire, Brownian motion, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, Elliott wave, equity premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, new economy, paper trading, passive investing, Paul Lévy, Plutocrats, plutocrats, price mechanism, quantitative trading / quantitative ﬁnance, Ralph Nelson Elliott, RAND corporation, random walk, risk tolerance, Robert Shiller, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, volatility smile

Time flexibility of market behavior with Titman, Sheridan Tobin, James Topology Trading ranges technical analysis with Trading time Transactions of the American Society of Civil Engineers Tree rings Treynor, Jack Trigonometry Turbulence bursts/pauses of da Vinci on financial heresy of long-term dependence with market behavior with metaphor of Puget Sound currents scaling pattern with wind Ulysses (Joyce) University of British Columbia University of Chicago University of Maryland University of Nottingham University of Paris University of Washington Upensky, J.V. U.S. Agriculture Department U.S. Commodity Futures Trading Commission U.S. Financial Executives Research Foundation U.S. Geological Survey Value at Risk (VAR) Van Ness, John VAR. See Value at Risk Variance Variance gamma process VIX Volatility clustering of Volatility surface Voss, R.F. Wall Street Journal Wallis, James R. Water Resources Research Williams, Albert L. Wind tunnel Wind turbulence World Trade Center attack Zigzag generator fractal geometry with Zipf, George Kingsley formula of power law slope of word frequencies of Zurich Copyright © 2004 by Benoit B.

…

The old methods are inadequate, they agree. So what should replace them? One of the standard methods relies on—guess what?—Brownian motion. The same false assumptions that underestimate stock-market risk, mis-price options, build bad portfolios, and generally misconstrue the financial world are also built into the standard risk software used by many of the world’s banks. The method is called Value at Risk, or VAR, and it works like this. You start off by deciding how “safe” you need to be. Say you set a 95 percent confidence level. That means you want to structure your bank’s investments so there is, by your models, a 95 percent probability that the losses will stay below the danger point, and only a 5 percent chance they will break through it. To use an example suggested by some Citigroup analysts, suppose you want to check the risk of your euro-dollar positions.

…

It is only in the infrequent moments of high turbulence that the theory founders—and at such moments, who can guard against a hostile takeover, a bankruptcy or other financial act of God? Such reasoning, of course, is little comfort to those wiped out on one of those “improbable,” violent trading days. But the financial industry is supremely pragmatic. While it may genuflect to the old icons, it invests its research dollars in the search for newer, better gods. “Exotic” options, “guaranteed-return” products, “value-at-risk” analysis, and other Wall Street creations have all benefited from this search. Central bankers, too, are pragmatic. After years of accepting the old ways, they have been pushing since 1998 for new, more realistic mathematical models by which a bank should evaluate its risk. These so-called Basle II rules will force many banks to change the way they calculate how much capital they set aside as a cushion against financial catastrophe.

**
Hedge Fund Market Wizards
** by
Jack D. Schwager

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asset-backed security, backtesting, banking crisis, barriers to entry, Bernie Madoff, Black-Scholes formula, British Empire, Claude Shannon: information theory, cloud computing, collateralized debt obligation, commodity trading advisor, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, diversification, diversified portfolio, family office, financial independence, fixed income, Flash crash, hindsight bias, implied volatility, index fund, James Dyson, Long Term Capital Management, margin call, market bubble, market fundamentalism, merger arbitrage, oil shock, pattern recognition, pets.com, Ponzi scheme, private sector deleveraging, quantitative easing, quantitative trading / quantitative ﬁnance, risk tolerance, risk-adjusted returns, risk/return, riskless arbitrage, Sharpe ratio, short selling, statistical arbitrage, Steve Jobs, systematic trading, technology bubble, transaction costs, value at risk, yield curve

In terms of volatility-adjusted leverage, their risk exposure had actually gone up. I notice that you use VAR as a risk measurement. Aren’t you concerned that it can sometimes be very misleading regarding portfolio risk? Value at Risk (VAR) can be defined as the loss threshold that will not be exceeded within a specified time interval at some high confidence level (typically, 95 percent or 99 percent). The VAR can be stated in either dollar or percentage terms. For example, a 3.2 percent daily VAR at the 99 percent confidence level would imply that the daily loss is expected to exceed 3.2 percent on only 1 out of 100 days. To convert a VAR from daily to monthly, we multiply it by the square root of 22 (the approximate number of trading days in a month). Therefore the 3.2 percent daily VAR would also imply that the monthly loss is expected to exceed 15.0 percent (3.2 percent × 4.69) only once out of every 100 months.

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See also Dot-com bubble TED spread Thames River Capital Management Thorp, Edward firsts achieved by gambling experiments and strategies option pricing model statistical arbitrage strategy warrant pricing model Time arbitrage Time horizons Time value Trade implementation Traders, hiring Trade size. See also Kelly criterion Trading around a position Trading book rules Trading pits, changes since electronic trading Trading rules vs. guidelines Trading style development Trend following Trend-neutral model Trend vs. countertrend methodologies Trinity Industries 200-day moving average Tyco Value and Special Situation Investing course Value at Risk (VAR) Value investing Value Investors Club Value-weighted indexes Vidich, Joe Volatility Volatility assumption Volatility vs. risk Warburg Securities Warrants Weighted indexes Wells Fargo Williams, Greyson Wolfe, Tom Woodriff, Jaffray on data mining on fund capacity statistical prediction research Woodriff Trading Worst of option XLP index You Can Be a Stock Market Genius (Greenblatt)

…

Therefore the 3.2 percent daily VAR would also imply that the monthly loss is expected to exceed 15.0 percent (3.2 percent × 4.69) only once out of every 100 months. The convenient thing about VAR is that it provides a worst-case loss estimate for a portfolio of mixed investments and adapts to the specific holdings as the portfolio composition changes. There are several ways of calculating VAR, but they all depend on the volatility and correlations of the portfolio holdings during a past look-back period—and therein lies the rub. The VAR provides a worst-case loss estimate assuming future volatility and correlation levels look like the past. The main reason the VAR gets a bad name is because people don’t understand it. VAR does exactly what it says on the tin. Which is? It tells you how volatile your current portfolio was in the past. That is all. VAR is entirely backward looking. You have to recognize that the future will be different.

**
A Colossal Failure of Common Sense: The Inside Story of the Collapse of Lehman Brothers
** by
Lawrence G. Mcdonald,
Patrick Robinson

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asset-backed security, bank run, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, diversification, fixed income, high net worth, hiring and firing, if you build it, they will come, London Interbank Offered Rate, Long Term Capital Management, margin call, moral hazard, mortgage debt, naked short selling, new economy, Ronald Reagan, short selling, sovereign wealth fund, value at risk

Risk managers in Lehman Brothers were guided, advised, regulated, trapped, imprisoned, and threatened on pain of torture and death by a tyrant who stood in their back office with a bullwhip and branding irons. His name was VaR. His strength was beyond that of a normal man; he could terrify legions and lay down the law in a manner that made empires shudder. VaR had a brain the size of a caraway seed and the imagination of a parsnip. The acronym that provides his name comes from value at risk, a technique used to estimate the probability of portfolio losses based on the statistical analysis of historical price trends and volatilities. It measures the worst expected loss under normal market conditions over a specific time interval at a given confidence level. Which means it measures both fear and optimism. In this particular instance, VaR knew that the market had no problem with the confidence level of those who bought CDOs. There was as yet no volatility in this market.

…

The one great flaw with VaR was its insistence on putting heavy emphasis on recent volatility. This meant that if a security did not have a history of volatility, it would irrevocably be marked as riskless despite the fact that it currently gazed into the abyss. VaR was a prisoner of its own guidelines. And like all systems that place too much faith in a philosophy, especially one as widely used on a global scale as VaR, it ends up with too much power and influence. It ended up ruling the department it was supposed to assist, because at Lehman no one wanted to be the renegade who stepped over the sacred VaR guidelines. Should there be a disaster, there could be only one scapegoat: the man who kicked over the traces and failed to obey the tried-and-true rules of VaR. Therefore, right or wrong, VaR was obeyed.

…

The CDOs were fine because they fell within the no-volatility rules, they were AAA-rated, and there had never been a default. But Delta was another story: much lower-rated because of the bankruptcy, a shaky history with the unions, operational problems because of the rise of jet fuels, undercutting by no-frills rivals, and a questionable future. When the risk management guys ran Delta through the computer program, the damn thing nearly blew up. Result: love CDOs, hate Delta. Verdict: VaR was a bonehead. It’s just a goddamned machine. And it’s only as good as the information it’s given. You cannot implicitly rely on it. And our risk management guys never should have idly switched off their own brains and paid attention only to the friggin’ robot. Still, that stupid piece of equipment, with its blinking lights, colored screens, and softly lit keyboard, was not the only brain around Lehman that was ignoring all of us.

**
Financial Market Meltdown: Everything You Need to Know to Understand and Survive the Global Credit Crisis
** by
Kevin Mellyn

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asset-backed security, bank run, banking crisis, Bernie Madoff, bonus culture, Bretton Woods, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, disintermediation, diversification, fiat currency, financial deregulation, financial innovation, financial intermediation, fixed income, Francis Fukuyama: the end of history, global reserve currency, Home mortgage interest deduction, Isaac Newton, joint-stock company, liquidity trap, London Interbank Offered Rate, margin call, market clearing, moral hazard, mortgage tax deduction, Northern Rock, offshore financial centre, paradox of thrift, pattern recognition, pension reform, pets.com, Plutocrats, plutocrats, Ponzi scheme, profit maximization, pushing on a string, reserve currency, risk tolerance, risk-adjusted returns, road to serfdom, Ronald Reagan, shareholder value, Silicon Valley, South Sea Bubble, statistical model, The Great Moderation, the payments system, too big to fail, value at risk, very high income, War on Poverty, Y2K, yield curve

Events like Pearl Harbor and the attacks of 9/11 were considered extremely remote by experts until they actually happened. TRIUMPH OF RISK SCIENCE VAR models were designed to allow banks to control the risks they were taking in a very scientific and rigorous manner. Until the events that began to unfold in the summer of 2007, almost everyone considered the mathematical measurement and modeling of risk to be a great advance over the traditional judgment-based approach. Banks and investment banks spent tens of millions of dollars on computer systems that allowed the exposure to risk of every line of business, down to loan portfolios and trading positions, to be calculated. Many banks were capable of producing daily reports that summed up the value at risk of the entire institution on a daily basis. These VAR reports were reviewed by top management and taken seriously by them and the risk management committees of their boards.

…

Banks became seized with a superstitious belief that complex mathematical models could better manage financial risk and return than human judgment. This thinking went well beyond the FICO score or the models used by the rating agencies to ‘‘stress test’’ default probabilities. Banks came to believe that they could design and implement data-driven ‘‘scientific’’ risk systems. The key concepts were ‘‘value at risk’’ or VAR and ‘‘risk adjusted return on capital’’ or RAROC. The basic idea was simple. Every loan, trading position, or operating exposure such as fraud or computer systems failure involved risks that Financial Innovation Made Easy could be identified and quantified with some precision across the whole institution. Risks were quantified by measuring the potential gap between the expected income from a loan or investment and the income actually received if things went wrong.

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See Stocks silver, xv, xvi, 8, 34, 83, 95 197 198 Index Sixteenth Amendment (to US constitution), 181 Smith, Adam, 179–180 Social Security, 23, 157 Socialism, 124–126, 182–183, 188–189 South Sea Bubble, 137 sovereign immunity, 151 sovereign lending, 151–152 speculation, 53, 109, 132, 138 Spitzer, Eliot, 138 stimulus and crisis management in US, Japan, 114, 169, 172 stocks, x–xi, xix, 3, 7, 13, 20, 22, 25, 27, 42, 49, 50–55, 60, 70–73, 80, 87, 137, 139, 142, 165, 167–168, 188; defined, 46; in Great Depression, 109–110; stock exchange, 88–89; stock prices, 47; versus bonds, 48; why stocks are risky, 47 Strong, Benjamin (‘‘Ben Strong’’), 105–106, 108–111 ‘‘structured finance,’’ 60, 64–68, 72, 133, 175–176, 185 sub prime, 55, 63–64, 176, 185 SVA (Shareholder Value Added), 71 Sweden banking crisis, 166 TARP (Troubled Asset Relief Program), 170 technology in banking and finance, xviii, 11, 40, 61–62, 70, 100, 117, 184 Term Loans, defined, 38–39; history, 143, 146 Thatcher, Margaret, 182, 184, 188 Thrift. See S&L ‘‘Too Big To Fail’’ doctrine, 159, 174 ‘‘Toxic Assets,’’ 72 Uniform Commercial Code, 38 U.S. Treasury, 44, 156, 158, 163, 173 VAR (Value at Risk), explained, 68; uses and abuses of, 69, 71 venture capital, 26–27 ‘‘volatility’’ (of financial markets, of stock and bond prices), 48–49 Volcker, Paul and end of the Great Inflation, 130, 140 Von Clemm, Michael, and Eurodollar CD, 149 Wall Street (short hand for financial economy), 1, 18–19, 22, 24, 57, 91, 102, 104–106, 138–140, 156–157, 159, 176–177, 183, 185 Warburg, Sigmund, and Eurodollar markets, 151 ‘‘working capital’’ and bank lending, 61, 143 World Bank, 115 Wriston, Walt, 149, 151–52; and the invention of the Certificate of Deposit, 145 Zombinakis, Minos, and Eurodollar markets, 148, 151 About the Author KEVIN MELLYN has over 30 years of experience in banking and consulting in London and New York with special emphasis on wholesale financial markets and their supporting technologies and infrastructure.

**
Paper Promises
** by
Philip Coggan

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accounting loophole / creative accounting, balance sheet recession, bank run, banking crisis, barriers to entry, Berlin Wall, Bernie Madoff, Black Swan, Bretton Woods, British Empire, call centre, capital controls, Carmen Reinhart, carried interest, Celtic Tiger, central bank independence, collapse of Lehman Brothers, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, debt deflation, delayed gratification, diversified portfolio, eurozone crisis, Fall of the Berlin Wall, falling living standards, fear of failure, financial innovation, financial repression, fixed income, floating exchange rates, full employment, German hyperinflation, global reserve currency, hiring and firing, Hyman Minsky, income inequality, inflation targeting, Isaac Newton, joint-stock company, Kenneth Rogoff, labour market flexibility, Long Term Capital Management, manufacturing employment, market bubble, market clearing, Martin Wolf, money: store of value / unit of account / medium of exchange, moral hazard, mortgage debt, Nick Leeson, Northern Rock, oil shale / tar sands, paradox of thrift, peak oil, pension reform, Plutocrats, plutocrats, Ponzi scheme, price stability, principal–agent problem, purchasing power parity, quantitative easing, QWERTY keyboard, railway mania, regulatory arbitrage, reserve currency, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Reagan, savings glut, short selling, South Sea Bubble, sovereign wealth fund, special drawing rights, The Chicago School, The Great Moderation, The Wealth of Nations by Adam Smith, time value of money, too big to fail, trade route, tulip mania, value at risk, Washington Consensus, women in the workforce

The more complex the product, the harder it was for investors to see the price. The result was fat fees for the banking sector. But perhaps the banks deceived themselves in the long run. One particular risk measure, called value-at-risk (VAR), got built into the system in the wake of Black Monday. Dennis Weatherstone, the chief executive of J P Morgan, was disturbed by the events of 1987. He asked his team to provide a measure of how much the bank was exposed to sudden market movements. VAR was developed to provide that information; it aimed to measure the maximum loss the bank could suffer on 95 per cent (in some cases 99 per cent) of all trading days. Some see the use of VAR as contributing to the crisis by providing false comfort to bank executives. Author Pablo Triana compared the method to a passenger airbag that works 95 per cent of the time, but not during the vital 5 per cent of occasions when your car has a crash.23 Nassim Nicholas Taleb writes of the ‘ludic fallacy’, the belief that the odds of market movements can be rigorously computed, like the odds of winning a poker hand.24 The problem, as Taleb points out, is that the range of probabilities is not known in advance.

…

Rubin, Robert Rueff, Jacques Rumsfeld, Donald Russia Sack, Alexander St Augustine Saint-Simon, duc de Salamis (city) Santelli, Rick Sarkozy, Nicholas Saudi Arabia savings savings glut Sbrancia, Belen Schacht, Hjalmar Scholes, Myron shale gas Second Bank of the United States Second World War Securities and Exchange Commission seignorage Shakespeare, William share options Shiller, Robert short-selling silver Singapore Sloan, Alfred Smith, Adam Smith, Fred Smithers & Co Smithsonian agreement Snowden, Philip Socialist Party of Greece social security Société Générale solidus Solon of Athens Soros, George sound money South Africa South Korea South Sea bubble sovereign debt crisis Soviet Union Spain special drawing right speculation, speculators Stability and Growth pact stagnation Standard & Poor’s sterling Stewart, Jimmy Stiglitz, Joseph stock markets stop-go cycle store of value Strauss-Kahn, Dominque Strong, Benjamin sub-prime lending Suez canal crisis Suharto, President of Indonesia Sumerians supply-side reforms Supreme Court (US) Sutton, Willie Sweden Swiss franc Swiss National Bank Switzerland Sylla, Richard Taiwan Taleb, Nassim Nicholas taxpayers Taylor, John tea party (US) Temin, Peter Thackeray, William Makepeace Thailand Thatcher, Margaret third world debt crisis Tiernan, Tommy Times Square, New York tobacco as currency treasury bills treasury bonds Treaty of Versailles trente glorieuses Triana, Pablo Triffin, Robert Triffin dilemma ‘trilemma’ of currency policy Truck Act True Finn party Truman, Harry S tulip mania Turkey Turner, Adair Twain, Mark unit of account usury value-at-risk (VAR) Vanguard Vanity Fair Venice Vietnam War vigilantes, bond market Viniar, David Volcker, Paul Voltaire Wagner, Adolph Wall Street Wall Street Crash of 1929 Wal-Mart wampum Warburton, Peter Warren, George Washington consensus Weatherstone, Dennis Weimar inflation Weimar Republic Weinberg, Sidney West Germany whales’ teeth White, Harry Dexter William of Orange Wilson, Harold Wirtschaftswunder Wizard of Oz, The Wolf, Martin Women Empowering Women Woodward, Bob Woolley, Paul World Bank Wriston, Walter Xinhua agency Yale University yen yield on debt yield on shares Zambia zero interest rates Zimbabwe Zoellick, Robert Philip Coggan is the Buttonwood columnist of the Economist.

…

Extreme outliers (below 1 foot or over 10 feet) are unknown. In markets, we get ‘fat tails’ of the bell curve, or more extreme examples than one might expect. David Viniar, chief financial officer of Goldman Sachs, said in August 2007, ‘We were seeing things that were 25-standard deviation moves, several days in a row.’25 Since, under a bell curve, 25-standard deviations have an infinitesimal chance of occurring, this shows that the VAR model was simply wrong. Of course, modellers can allow for different probability distributions than the bell curve. But they still don’t know which distribution will occur. Take too cautious a view and you will take little risk, and some other investment bank will take all the profits. To the aggressive heads of investment banks like Dick Fuld and Jimmy Cayne, this was the clinching argument. Those who advocated caution were not being team players.

**
Trend Following: How Great Traders Make Millions in Up or Down Markets
** by
Michael W. Covel

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Albert Einstein, asset allocation, Atul Gawande, backtesting, Bernie Madoff, Black Swan, buy low sell high, capital asset pricing model, Clayton Christensen, commodity trading advisor, correlation coefficient, Daniel Kahneman / Amos Tversky, delayed gratification, deliberate practice, diversification, diversified portfolio, Elliott wave, Emanuel Derman, Eugene Fama: efficient market hypothesis, fiat currency, fixed income, game design, hindsight bias, housing crisis, index fund, Isaac Newton, John Nash: game theory, linear programming, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, market fundamentalism, market microstructure, mental accounting, Nash equilibrium, new economy, Nick Leeson, Ponzi scheme, prediction markets, random walk, Renaissance Technologies, Richard Feynman, Richard Feynman, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, South Sea Bubble, Stephen Hawking, systematic trading, the scientific method, Thomas L Friedman, too big to fail, transaction costs, upwardly mobile, value at risk, Vanguard fund, volatility arbitrage, William of Occam

It is difficult. We are influenced heavily by standard finance theory that revolves almost entirely around normal distribution worship. Michael Mauboussin and Kristen Bartholdson see clearly the state of affairs: “Normal distributions are the bedrock of finance, including the random walk, capital asset pricing, value-at-risk, and Black-Scholes models. Value-at-risk (VaR) models, for example, attempt to quantify how much loss a portfolio may suffer with a given probability. While there are various forms of VaR models, a basic version relies on standard deviation as a measure of risk. Given a normal distribution, it is relatively straightforward to measure standard deviation, and hence risk. However, if price changes are not normally distributed, standard deviation can be a very misleading proxy for risk.”14 Chapter 8 • Science of Trading The problem with using standard deviation as a risk measurement can be seen with the example where two traders have similar standard deviations, but might show entirely different distribution of returns.

…

See stocks, trend following and success of, 15-17 understand and explaining to clients, 280-281 Tropin, Ken, 271, 274, 289 trusting numbers, 18 truth, refusal of, and behavioral finance, 196 TTP (Trading Tribe Process), 203 Turtles, 78-79, 281 correlation, 113-114 selection process, 79-83 Tversky, Amos, 189 U.S. dollar trading, 128, 136, 139, 162 U.S. National Agricultural Library, 53 U.S. T-Bond chart (1998), trend-followers and, 159 UBS, 156 Ueland, Brenda, 24 uncertainty, reaction to, 197 understanding trend following, 280-281 upside volatility, 102-105 value-at-risk (VAR) models, 180 van Stolk, Mark, 262 Vandergrift, Justin, 110, 132-134, 255 Vanguard, 295 VAR (value-at-risk) models, 180 Varanedoe, J. Kirk T., 214 Vician, Thomas, Jr., 40, 66, 243, 272 volatility, 99-105 measuring, 180 risk versus, 104 upside volatility, 102-105 Voltaire, xvii von Metternich, Klemens, 270 von Mises, Ludwig, xviii, 3, 97, 99, 202, 264 Wachtel, Larry, 235 Waksman, Sol, 253 Watts, Dickson, 92 Weaver, Earl, 182 web sites, 397 Weill, Sandy, 156 Weintraub, Neal T., 233 Wells, Herbert George (H.G.), 225 Welton, Patrick, 15 what to trade, 254-256 when to buy/sell, 259-262 whipsaws, 263 Wigdor, Paul, 126 Wilcox, Cole, 268, 307 William of Occam, 213 Williams, Ted, 261 winners Long-Term Capital Management (LTCM) collapse, 156-164 losers versus, 123-125 “The Winners and Losers of the Zero-Sum Game: The Origins of Trading Profits, Price Efficiency and Market Liquidity” (white paper) (Harris), 115 winning investment philosophies, 4-6 winning positions, when to exit, 263-265 Winton Capital Management, 29, 372-373 Winton Futures Fund, 230 “The Winton Papers” (Harding), 31 Wittgenstein, Ludwig, 395 Womack, Kent, 241 The World is Flat (Friedman), 143 WorldCom, 241 Wright, Charlie, 244 Yahoo!

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Terence (Publius Terentius Afer), Source: Andria (I, 5, 32) Trend Following (Updated Edition): Learn to Make Millions in Up or Down Markets • People place too much emphasis on the short-term performance of trend followers. They draw conclusions about one month’s performance and forget to look at the long term. Just like a batting average, which can have short-term streaks over the course of a season, trend followers have streaks. Trend following performance does deviate from averages, but over time there is remarkable consistency. • Value-at-risk (VAR) models measure volatility, not risk. If you rely on VAR as a risk measure you are in trouble. • Hunt Taylor, Director of Investments, Stern Investment Holdings, states: “I’m wondering when statisticians are going to figure out that the statistical probability of improbable losses are absolutely the worst predictors of the regularity with which they’ll occur. I mean, the single worst descriptor of negative events is the hundred-year flood.

**
The Big Short: Inside the Doomsday Machine
** by
Michael Lewis

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Asperger Syndrome, asset-backed security, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversified portfolio, facts on the ground, financial innovation, fixed income, forensic accounting, Gordon Gekko, high net worth, housing crisis, illegal immigration, income inequality, index fund, interest rate swap, London Interbank Offered Rate, Long Term Capital Management, medical residency, moral hazard, mortgage debt, pets.com, Ponzi scheme, Potemkin village, quantitative trading / quantitative ﬁnance, short selling, Silicon Valley, too big to fail, value at risk, Vanguard fund

Howie Hubler's proprietary trading group was of course required to supply information about its trades to both upper management and risk management, but the information the traders supplied disguised the nature of their risk. The $16 billion in subprime risk Hubler had taken on showed up in Morgan Stanley's risk reports inside a bucket marked "triple A"--which is to say, they might as well have been U.S. Treasury bonds. They showed up again in a calculation known as value at risk (VaR). The tool most commonly used by Wall Street management to figure out what their traders had just done, VaR measured only the degree to which a given stock or bond had jumped around in the past, with the recent movements receiving a greater emphasis than movements in the more distant past. Having never fluctuated much in value, triple-A-rated subprime-backed CDOs registered on Morgan Stanley's internal reports as virtually riskless. In March 2007 Hubler's traders prepared a presentation, delivered by Hubler's bosses to Morgan Stanley's board of directors, that boasted of their "great structural position" in the subprime mortgage market.

…

It is fair to say that our risk management division did not stress those losses as well.* It's just simple as that. Those are big fat tail risks that caught us hard, right. That's what happened. TANONA: Okay. Fair enough. I guess the other thing I would question. I am surprised that your trading VaR stayed stable in the quarter given this level of loss, and given that I would suspect that these were trading assets. So can you help me understand why your VaR didn't increase in the quarter dramatically?+ MACK: Bill, I think VaR is a very good representation of liquid trading risk. But in terms of the (inaudible) of that, I am very happy to get back to you on that when we have been out of this, because I can't answer that at the moment. The meaningless flow of words might have left the audience with the sense that it was incapable of parsing the deep complexity of Morgan Stanley's bond trading business.

**
Extreme Money: Masters of the Universe and the Cult of Risk
** by
Satyajit Das

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affirmative action, Albert Einstein, algorithmic trading, Andy Kessler, Asian financial crisis, asset allocation, asset-backed security, bank run, banking crisis, banks create money, Basel III, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, Big bang: deregulation of the City of London, Black Swan, Bonfire of the Vanities, bonus culture, Bretton Woods, BRICs, British Empire, capital asset pricing model, Carmen Reinhart, carried interest, Celtic Tiger, clean water, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, debt deflation, Deng Xiaoping, deskilling, discrete time, diversification, diversified portfolio, Doomsday Clock, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, eurozone crisis, Fall of the Berlin Wall, financial independence, financial innovation, fixed income, full employment, global reserve currency, Goldman Sachs: Vampire Squid, Gordon Gekko, greed is good, happiness index / gross national happiness, haute cuisine, high net worth, Hyman Minsky, index fund, interest rate swap, invention of the wheel, invisible hand, Isaac Newton, job automation, Johann Wolfgang von Goethe, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, Kevin Kelly, labour market flexibility, laissez-faire capitalism, load shedding, locking in a profit, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, Martin Wolf, merger arbitrage, Mikhail Gorbachev, Milgram experiment, Mont Pelerin Society, moral hazard, mortgage debt, mortgage tax deduction, mutually assured destruction, Naomi Klein, Network effects, new economy, Nick Leeson, Nixon shock, Northern Rock, nuclear winter, oil shock, Own Your Own Home, pets.com, Plutocrats, plutocrats, Ponzi scheme, price anchoring, price stability, profit maximization, quantitative easing, quantitative trading / quantitative ﬁnance, Ralph Nader, RAND corporation, random walk, Ray Kurzweil, regulatory arbitrage, rent control, rent-seeking, reserve currency, Richard Feynman, Richard Feynman, Richard Thaler, risk-adjusted returns, risk/return, road to serfdom, Robert Shiller, Robert Shiller, Rod Stewart played at Stephen Schwarzman birthday party, rolodex, Ronald Reagan, Ronald Reagan: Tear down this wall, savings glut, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, Slavoj Žižek, South Sea Bubble, special economic zone, statistical model, Stephen Hawking, Steve Jobs, The Chicago School, The Great Moderation, the market place, the medium is the message, The Myth of the Rational Market, The Nature of the Firm, The Predators' Ball, The Wealth of Nations by Adam Smith, Thorstein Veblen, too big to fail, trickle-down economics, Turing test, Upton Sinclair, value at risk, Yogi Berra, zero-coupon bond

The BSM model and Markowitz’s work evolved into risk quantification modes, such as value at risk (VAR) models. VAR signifies the maximum amount that you can lose, statistically, as a result of market moves for a given probability over a fixed time. If you own shares over a year, then most of the time the share price moves up or down a small amount. On some days you may get a large or very large price change. VAR ranks the price changes from largest fall to largest rise. Assuming that prices follow a random walk and price changes fit a normal distribution, you can calculate the probability of a particular size price change. You can answer questions like what is the likely maximum price change and loss on your holding at a specific probability level, say 99 percent, which equates to 1 day out of 100 days. A VAR figure of $50 million at 99 percent over a 10-day holding period means that the bank has a 99 percent probability that it will not suffer a loss of more than $50 million over a 10-day period.

…

MacKenzie, An Engine, Not a Camera: 136. 14. Bernstein, Capital Ideas: 143. 15. Quoted in ibid: 48. 16. MacKenzie, An Engine, Not a Camera: 79. 17. Ibid: 79, 80. 18. Ibid: 80. 19. Ibid: 83, 84. 20. Joel Stern “Let’s abandon earnings per share” (18 December 1972) Wall Street Journal. 21. MacKenzie, An Engine, Not a Camera: 254. 22. Barry Schachter “An irreverent guide to value at risk” (August 1997) Financial Engineering News 1/1 (www.debtonnet.com/newdon/files/marketinformation/var-guide.asp). 23. Quoted in Fox, The Myth of the Rational Market: 191. 24. Quoted in ibid: 260. 25. Paul De Grauwe, Leonardo Iania and Pablo Rovira Kaltwasser “How abnormal was the stock market in October 2008?” (11 November 2008) (www.eurointelligence.com/article.581+M5f21b8d26a3.0.html). 26. Stephen Hawking, during a 1994 debate with Roger Penrose at the Isaac Newton Institute for Mathematical Sciences, University of Cambridge; in Stephen Hawking and Roger Penrose (1996) The Nature of Space and Time, Princeton University Press, New Jersey: 26. 27.

…

Treasury bonds, 87 UBS, 201 UK Financial Services Act (2001), 279 UK House of Commons, 288 ultra prosperity, 99 uncertainty, 366 unintended consequences, 130 United Airlines (UAL), 166 United States debt levels as a percentage of GDP, 265 domestic corporate profits, 276 universal banks, 75 University of California at Berkeley, 42 University of Chicago, 34, 101, 104 collaboration between Black and Scholes, 121 University of Surrey, 363 Unocal, 137 Updike, John, 27, 46, 363 Urbanek, Zdener, 91 urbanization, 38 Urdu, 22 ushinawareta junen (the lost decade), 39 usuries, 32 V vacancy rates, commercial real estate, 349 VADM (very accurately defined maturity) bonds, 178 value accounting, 286-287 of commodities, 24 of modern money, 35 stocks, 58 value at risk (VAR) models, 125 Van der Starr, Cornelius, 230 Van Riper, Paul, 264 Vanguard Group, 123 Vanity Fair, 324 vapidity of life, 328 VAT (value added tax), 262 Veblen, Thorstein, 41, 52, 245 Veil, Jean, 229 velocity of capital, 69 Velvet Revolution (1989), 359 vertical segmentation, 170. See also tranches Vertin, James, 123 Viagra, 326 video, financial news, 91-99 Vienna landmark, 163 Vietnam War, 30, 274 Viniar, David, 126, 198 Virgil, 338 virtual loans, 195-196 volatility, 254 hedge funds, 246 LCTM, 250 of currencies, 125 Volcker rule, 353 Volcker, Paul, 78, 145, 352, 359 Volkswagen (VW), 55, 146, 257 Volvo AB, 343 von Bismarck.

**
Valuation: Measuring and Managing the Value of Companies
** by
Tim Koller,
McKinsey,
Company Inc.,
Marc Goedhart,
David Wessels,
Barbara Schwimmer,
Franziska Manoury

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air freight, barriers to entry, Basel III, BRICs, business climate, business process, capital asset pricing model, capital controls, cloud computing, compound rate of return, conceptual framework, corporate governance, corporate social responsibility, credit crunch, Credit Default Swap, discounted cash flows, distributed generation, diversified portfolio, energy security, equity premium, index fund, iterative process, Long Term Capital Management, market bubble, market friction, meta analysis, meta-analysis, new economy, p-value, performance metric, Ponzi scheme, price anchoring, purchasing power parity, quantitative easing, risk/return, Robert Shiller, Robert Shiller, shareholder value, six sigma, sovereign wealth fund, speech recognition, technology bubble, time value of money, too big to fail, transaction costs, transfer pricing, value at risk, yield curve, zero-coupon bond

Estimate the risk weighting and RWA for each of the loan categories in such a way that your estimate fits the reported RWA for all loans (€202 billion in this example). r Market risk is a bank’s exposure to changes in interest rates, stock prices, currency rates, and commodity prices. It is typically related to its value at risk (VaR), which is the maximum loss for the bank under a worst-case scenario of a given probability for these market prices. For an approximation, use the reported VaR over several years to estimate the bank’s RWA as a percentage of VaR (242 percent in the example). r Operational risk is all risk that is neither market nor credit risk. It is usu- ally related to a bank’s net revenues (net interest income plus net other income). Use the bank’s average revenues over the previous year(s) to estimate RWA per unit of revenue (155 percent in the example). Based on your forecasts for growth across different loan categories, VaR requirements for trading activities, and a bank’s net revenues, you can estimate the total RWA in each future year.

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You can think of a bank’s trading results as driven by the size of its trading positions, the risk taken in trading (as measured by the total VaR), and the trading result per unit of risk (measured by return on VaR). The ratio of VaR to net trading position is an indication of the relative risk taking in trading. The more risk a bank takes in trading, the higher the expected trading return should be, as well as the required risk capital. The required equity risk capital EXHIBIT 34.15 Value Drivers: Trading Activities (Simplified) Key value drivers 2 Return on VaR1 1 TTrading position: Net trading position (assets minus liabilities) 2 Return on VaR: Relative trading result 3 VaR/net trading assets: Relative trading risk 4 Operating expenses: E.g., driven by number of traders relative to trading assets and bonuses paid out on trading proﬁts 5 Equity: Required equity levels 6 Growth: Growth of trading volumes 7 COE: Cost of equity 1 Trading result Trading liabilities Trading assets Coost/i t n come m 4 Operating expenses1 Return on equity 3 VaR/net trading assets 6 Value creation 5 Growth Capital ratio Equity 7 Cost of equity 1 After taxes. 782 BANKS for the trading activities follows from the VaR (and RWA), as discussed earlier in the chapter.

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In December 2010, new regulatory requirements for capital adequacy were specified in the Basel III guidelines, replacing the 2007 Basel II accords, which were no longer considered adequate in the wake of the 2008 and 2010 financial crises.15 The new guidelines are being gradually implemented by banks across the world between 2013 and 2019. 15 The Basel accords are recommendations on laws and regulations for banking and are issued by the Basel Committee on Banking Supervision (BCBS). 778 BANKS EXHIBIT 34.13 Estimating Risk-Weighted Assets (RWA) for a Large European Bank billion Reported RWA Asset category 2013 Loans to countries Loans to banks Loans to corporations Residential mortgages Other consumer loans Overall Operational risk Market risk Credit risk Year Estimated RWA parameters, % Loans outstanding RWA 16,228 25,100 147,242 148,076 45,440 382,086 202,219 Standardized Standardized Allocated RWA/loans RWA RWA 10 35 35 35 75 Year VaR trading book RWA Estimated RWA/ VaR 2013 19,564 47,259 242 Year Revenues RWA Estimated RWA/ revenues 2013 32,826 50,891 155 1,623 8,785 51,535 51,827 34,080 147,489 2,220 12,016 70,486 70,885 46,613 202,219 Estimated RWA/loans 14 48 48 48 103 53 Basel III specifies rules for banks regarding how much equity capital they must hold based on the bank’s so-called risk-weighted assets (RWA).16 The level of RWA is driven by the riskiness of a bank’s asset portfolio and its trading book.

**
How the City Really Works: The Definitive Guide to Money and Investing in London's Square Mile
** by
Alexander Davidson

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accounting loophole / creative accounting, algorithmic trading, asset allocation, asset-backed security, bank run, banking crisis, barriers to entry, Big bang: deregulation of the City of London, capital asset pricing model, central bank independence, corporate governance, Credit Default Swap, dematerialisation, discounted cash flows, diversified portfolio, double entry bookkeeping, Edward Lloyd's coffeehouse, Elliott wave, Exxon Valdez, forensic accounting, global reserve currency, high net worth, index fund, inflation targeting, interest rate derivative, interest rate swap, London Interbank Offered Rate, Long Term Capital Management, margin call, market fundamentalism, Nick Leeson, North Sea oil, Northern Rock, pension reform, Piper Alpha, price stability, purchasing power parity, Real Time Gross Settlement, reserve currency, shareholder value, short selling, The Wealth of Nations by Adam Smith, transaction costs, value at risk, yield curve, zero-coupon bond

Banks are now more sensitive to internal risk and have tighter procedures, including ‘know your client’. Problems and fraud The problem with derivatives is not in the product itself, but in how it is sold or managed. If a company is to trade in derivatives, it must understand their value. Software data will calculate the value at risk, known as VAR, which is how much the company is willing to lose at any time. The VAR changes daily. Banks have thousands of loans on their books, both receiving and giving. They 68 HOW THE CITY REALLY WORKS __________________________________ need good systems and procedures to determine VAR, and this is an underlying complexity. There are always rogue traders, or treasurers of companies who do not behave responsibly. An overzealous derivatives salesman could go to an unaware company treasurer and say: ‘Swap your ﬁxed rate for a variable rate loan.

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Index 419 fraud 204 9/11 terrorist attacks 31, 218, 242, 243, 254, 257 Abbey National 22 ABN AMRO 103 accounting and governance 232–38 scandals 232 Accounting Standards Board (ASB) 236 administration 17 Allianz 207 Alternative Investment Market (AIM) 44–45, 131, 183, 238 Amaranth Advisors 170 analysts 172–78 fundamental 172–74 others 177–78 Spitzer impact 174–75 technical 175–77 anti-fraud agencies Assets Recovery Agency 211–13 City of London Police 209 Financial Services Authority 208 Financial Crime and Intelligence Division 208 Insurance Fraud Bureau 209 Insurance Fraud Investigators Group 209 International Association of Insurance Fraud Agencies 207, 210, 218 National Criminal Intelligence Service 210 Serious Fraud Ofﬁce 213–15 Serious Organised Crime Agency 210–11 asset ﬁnance 24–25 Association of Investment Companies 167 backwardation 101 bad debt, collection of 26–28 Banco Santander Central Hispano 22 Bank for International Settlements (BIS) 17, 27, 85, 98, 114 bank guarantee 23 Bank of Credit and Commerce International (BCCI) 10, 214 Bank of England 6, 10–17 Court of the 11 credit risk warning 98 framework for sterling money markets 81 Governor 11, 13, 14 history 10, 15–16 Inﬂation Report 14 inﬂation targeting 12–13 interest rates and 12 international liaison 17 lender of last resort 15–17 Market Abuse Directive (MAD) 16 monetary policy and 12–15 Monetary Policy Committee (MPC) 13–14 Open-market operations 15, 82 repo rate 12, 15 role 11–12 RTGS (Real Time Gross Settlement) 143 statutory immunity 11 supervisory role 11 Bank of England Act 1988 11, 12 Bank of England Quarterly Model (BEQM) 14 Banking Act 1933 see Glass-Steagall Act banks commercial 5 investment 5 Barclays Bank 20 Barings 11, 15, 68, 186, 299 Barlow Clowes case 214 Barron’s 99 base rate see repo rate Basel Committee for Banking Supervision (BCBS) 27–28 ____________________________________________________ INDEX 303 Basel I 27 Basel II 27–28, 56 Bear Stearns 95, 97 BearingPoint 97 bill of exchange 26 Bingham, Lord Justice 10–11 Blue Arrow trial 214 BNP Paribas 145, 150 bond issues see credit products book runners 51, 92 Borsa Italiana 8, 139 bps 90 British Bankers’ Association 20, 96, 97 building societies 22–23 demutualisation 22 Building Societies Association 22 Capital Asset Pricing Model (CAPM) see discounted cash ﬂow analysis capital gains tax 73, 75, 163, 168 capital raising markets 42–46 mergers and acquisitions (M&A) 56–58 see also ﬂotation, bond issues Capital Requirements Directive 28, 94 central securities depository (CSD) 145 international (ICSD) 145 Central Warrants Trading Service 73 Chancellor of the Exchequer 12, 13, 229 Chicago Mercantile Exchange 65 Citigroup 136, 145, 150 City of London 4–9 Big Bang 7 deﬁnition 4 employment in 8–9 ﬁnancial markets 5 geography 4–5 history 6–7 services offered 4 world leader 5–6 clearing 140, 141–42 Clearing House Automated Payment System (CHAPS) 143 Clearstream Banking Luxembourg 92, 145 commercial banking 5, 18–28 bad loans and capital adequacy 26–28 banking cards 21 building societies 22–23 credit collection 25–26 ﬁnance raising 23–25 history 18–19 overdrafts 23 role today 19–21 commodities market 99–109 exchange-traded commodities 101 ﬂuctuations 100 futures 100 hard commodities energy 102 non-ferrous metals 102–04 precious metal 104–06 soft commodities cocoa 107 coffee 106 sugar 107 Companies Act 2006 204, 223, 236 conﬂict of interests 7 consolidation 138–39 Consumer Price Index (CPI) 13 contango 101 Continuous Linked Settlement (CLS) 119 corporate governance 223–38 best practice 231 Cadbury Code 224 Combined Code 43, 225 compliance 230 deﬁnition 223 Directors’ Remuneration Report Regulations 226 EU developments 230 European auditing rules 234–35 Greenbury Committee 224–25 Higgs and Smith reports 227 International Financial Reporting Standards (IFRS) 237–38 Listing Rules 228–29 Model Code 229 Myners Report 229 OECD Principles 226 operating and ﬁnancial review (OFR) 235– 36 revised Combined Code 227–28 Sarbanes–Oxley Act 233–34 Turnbull Report 225 credit cards 21 zero-per-cent cards 21 credit collection 25–26 factoring and invoice discounting 26 trade ﬁnance 25–26 credit derivatives 96–97 back ofﬁce issues 97 credit default swap (CDS) 96–97 credit products asset-backed securities 94 bonds 90–91 collateralised debt obligations 94–95 collateralised loan obligation 95 covered bonds 93 equity convertibles 93 international debt securities 92–93 304 INDEX ____________________________________________________ junk bonds 91 zero-coupon bonds 93 credit rating agencies 91 Credit Suisse 5, 136, 193 CREST system 141, 142–44 dark liquidity pools 138 Debt Management Ofﬁce 82, 86 Department of Trade and Industry (DTI) 235, 251, 282 derivatives 60–77 asset classes 60 bilateral settlement 66 cash and 60–61 central counterparty clearing 65–66 contracts for difference 76–77, 129 covered warrants 72–73 futures 71–72 hedging and speculation 67 on-exchange vs OTC derivatives 63–65 options 69–71 Black-Scholes model 70 call option 70 equity option 70–71 index options 71 put option 70 problems and fraud 67–68 retail investors and 69–77 spread betting 73–75 transactions forward (future) 61–62 option 62 spot 61 swap 62–63 useful websites 75 Deutsche Bank 136 Deutsche Börse 64, 138 discounted cash ﬂow analysis (DCF) 39 dividend 29 domestic ﬁnancial services complaint and compensation 279–80 ﬁnancial advisors 277–78 Insurance Mediation Directive 278–79 investments with life insurance 275–76 life insurance term 275 whole-of-life 274–75 NEWICOB 279 property and mortgages 273–74 protection products 275 savings products 276–77 Dow theory 175 easyJet 67 EDX London 66 Egg 20, 21 Elliott Wave Theory 176 Enron 67, 114, 186, 232, 233 enterprise investment schemes 167–68 Equiduct 133–34, 137 Equitable Life 282 equities 29–35 market indices 32–33 market inﬂuencers 40–41 nominee accounts 31 shares 29–32 stockbrokers 33–34 valuation 35–41 equity transparency 64 Eurex 64, 65 Euro Overnight Index Average (EURONIA) 85 euro, the 17, 115 Eurobond 6, 92 Euroclear Bank 92, 146, 148–49 Euronext.liffe 5, 60, 65, 71 European Central Bank (ECB) 16, 17, 84, 148 European Central Counterparty (EuroCCP) 136 European Code of Conduct 146–47, 150 European Exchange Rate Mechanism 114 European Harmonised Index of Consumer Prices 13 European Union Capital Requirements Directive 199 Market Abuse Directive (MAD) 16, 196 Market in Financial Instruments Directive (MiFID) 64, 197–99 Money Laundering Directive 219 Prospectus Directive 196–97 Transparency Directive 197 exchange controls 6 expectation theory 172 Exxon Valdez 250 factoring see credit collection Factors and Discounters Association 26 Fair & Clear Group 145–46 Federal Deposit Insurance Corporation 17 Federation of European Securities Exchanges 137 Fighting Fraud Together 200–01 ﬁnance, raising 23–25 asset 24–25 committed 23 project ﬁnance 24 recourse loan 24 syndicated loan 23–24 uncommitted 23 Financial Action Task Force on Money Laundering (FATF) 217–18 ﬁnancial communications 179–89 ____________________________________________________ INDEX 305 advertising 189 corporate information ﬂow 185 primary information providers (PIPs) 185 investor relations 183–84 journalists 185–89 public relations 179–183 black PR’ 182–83 tipsters 187–89 City Slickers case 188–89 Financial Ombudsman Service (FOS) 165, 279–80 ﬁnancial ratios 36–39 dividend cover 37 earnings per share (EPS) 36 EBITDA 38 enterprise multiple 38 gearing 38 net asset value (NAV) 38 price/earnings (P/E) 37 price-to-sales ratio 37 return on capital employed (ROCE) 38 see also discounted cash ﬂow analysis Financial Reporting Council (FRC) 224, 228, 234, 236 Financial Services Act 1986 191–92 Financial Services Action Plan 8, 195 Financial Services and Markets Act 2001 192 Financial Services and Markets Tribunal 94 Financial Services Authority (FSA) 5, 8, 31, 44, 67, 94, 97, 103, 171, 189, 192–99 competition review 132 insurance industry 240 money laundering and 219 objectives 192 regulatory role 192–95 powers 193 principles-based 194–95 Financial Services Compensation Scheme (FSCS) 17, 165, 280 Financial Services Modernisation Act 19 ﬁnancial services regulation 190–99 see also Financial Services Authority Financial Times 9, 298 First Direct 20 ﬂipping 53 ﬂotation beauty parade 51 book build 52 early secondary market trading 53 grey market 52, 74 initial public offering (IPO) 47–53 pre-marketing 51–52 pricing 52–53 specialist types of share issue accelerated book build 54 bought deal 54 deeply discounted rights issue 55 introduction 55 placing 55 placing and open offer 55 rights issues 54–55 underwriting 52 foreign exchange 109–120 brokers 113 dealers 113 default risk 119 electronic trading 117 exchange rate 115 ICAP Knowledge Centre 120 investors 113–14 transaction types derivatives 116–17 spot market 115–16 Foreign Exchange Joint Standing Committee 112 forward rate agreement 85 fraud 200–15 advanced fee frauds 204–05 boiler rooms 201–04 Regulation S 202 future regulation 215 identity theft 205–06 insurance fraud 206–08 see also anti-fraud agencies Fraud Act 2006 200 FTSE 100 32, 36, 58, 122, 189, 227, 233 FTSE 250 32, 122 FTSE All-Share Index 32, 122 FTSE Group 131 FTSE SmallCap Index 32 FTSE Sterling Corporate Bond Index 33 Futures and Options Association 131 Generally Accepted Accounting Principles (GAAP) 237, 257 gilts 33, 86–88 Giovanni Group 146 Glass-Steagall Act 7, 19 Global Bond Market Forum 64 Goldman Sachs 136 government bonds see gilts Guinness case 214 Halifax Bank 20 hedge funds 8, 77, 97, 156–57 derivatives-based arbitrage 156 ﬁxed-income arbitrage 157 Hemscott 35 HM Revenue and Customs 55, 211 HSBC 20, 103 Hurricane Hugo 250 306 INDEX ____________________________________________________ Hurricane Katrina 2, 67, 242 ICE Futures 5, 66, 102 Individual Capital Adequacy Standards (ICAS) 244 inﬂation 12–14 cost-push 12 deﬁnition 12 demand-pull 12 quarterly Inﬂation Report 14 initial public offering (IPO) 47–53 institutional investors 155–58 fund managers 155–56 hedge fund managers 156–57 insurance companies 157 pension funds 158 insurance industry London and 240 market 239–40 protection and indemnity associations 241 reform 245 regulation 243 contingent commissions 243 contract certainty 243 ICAS and Solvency II 244–45 types 240–41 underwriting process 241–42 see also Lloyd’s of London, reinsurance Intercontinental Exchange 5 interest equalisation tax 6 interest rate products debt securities 82–83, 92–93 bill of exchange 83 certiﬁcate of deposit 83 debt instrument 83 euro bill 82 ﬂoating rate note 83 local authority bill 83 T-bills 82 derivatives 85 forward rate agreements (FRAs) 85–86 government bonds (gilts) 86–89 money markets 81–82 repos 84 International Financial Reporting Standards (IFRS) 58, 86, 173, 237–38 International Financial Services London (IFSL) 5, 64, 86, 92, 112 International Monetary Fund 17 International Securities Exchange 138 International Swap Dealers Association 63 International Swaps and Derivatives Association 63 International Underwriting Association (IUA) 240 investment banking 5, 47–59 mergers and acquisitions (M&A) 56–58 see also capital raising investment companies 164–69 real estate 169 split capital 166–67 venture capital 167–68 investment funds 159–64 charges 163 investment strategy 164 fund of funds scheme 164 manager-of-managers scheme 164 open-ended investment companies (OEICs) 159 selection criteria 163 total expense ratio (TER) 164 unit trusts 159 Investment Management Association 156 Investment Management Regulatory Organisation 11 Johnson Matthey Bankers Limited 15–16 Joint Money Laundering Steering Group 221 KAS Bank 145 LCH.Clearnet Limited 66, 140 letter of credit (LOC) 23, 25–26 liability-driven investment 158 Listing Rules 43, 167, 173, 225, 228–29 Lloyd’s of London 8, 246–59 capital backing 249 chain of security 252–255 Central Fund 253 Corporation of Lloyd’s 248–49, 253 Equitas Reinsurance Ltd 251, 252, 255–56 Franchise Performance Directorate 256 future 258–59 Hardship Committee 251 history 246–47, 250–52 international licenses 258 Lioncover 252, 256 Member’s Agent Pooling Arrangement (MAPA) 249, 251 Names 248, one-year accounting 257 regulation 257 solvency ratio 255 syndicate capacity 249–50 syndicates 27 loans 23–24 recourse loan 24 syndicated loan 23–24 London Interbank Offered Rate (LIBOR) 74, 76 ____________________________________________________ INDEX 307 London Stock Exchange (LSE) 7, 8, 22, 29, 32, 64 Alternative Investment Market (AIM) 32 Main Market 42–43, 55 statistics 41 trading facilities 122–27 market makers 125–27 SETSmm 122, 123, 124 SETSqx 124 Stock Exchange Electronic Trading Service (SETS) 122–25 TradElect 124–25 users 127–29 Louvre Accord 114 Markets in Financial Instruments Directive (MiFID) 64, 121, 124, 125, 130, 144, 197–99, 277 best execution policy 130–31 Maxwell, Robert 186, 214, 282 mergers and acquisitions 56–58 current speculation 57–58 disclosure and regulation 58–59 Panel on Takeovers and Mergers 57 ‘white knight’ 57 ‘white squire’ 57 Merrill Lynch 136, 174, 186, 254 money laundering 216–22 Egmont Group 218 hawala system 217 know your client (KYC) 217, 218 size of the problem 222 three stages of laundering 216 Morgan Stanley 5, 136 multilateral trading facilities Chi-X 134–35, 141 Project Turquoise 136, 141 Munich Re 207 Nasdaq 124, 138 National Strategy for Financial Capability 269 National Westminster Bank 20 Nationwide Building Society 221 net operating cash ﬂow (NOCF) see discounted cash ﬂow analysis New York Federal Reserve Bank (Fed) 16 Nomads 45 normal market share (NMS) 132–33 Northern Rock 16 Nymex Europe 102 NYSE Euronext 124, 138, 145 options see derivatives Oxera 52 Parmalat 67, 232 pensions alternatively secured pension 290 annuities 288–89 occupational pension ﬁnal salary scheme 285–86 money purchase scheme 286 personal account 287 personal pension self-invested personal pension 288 stakeholder pension 288 state pension 283 unsecured pension 289–90 Pensions Act 2007 283 phishing 200 Piper Alpha oil disaster 250 PLUS Markets Group 32, 45–46 as alternative to LSE 45–46, 131–33 deal with OMX 132 relationship to Ofex 46 pooled investments exchange-traded funds (ETF) 169 hedge funds 169–71 see also investment companies, investment funds post-trade services 140–50 clearing 140, 141–42 safekeeping and custody 143–44 registrar services 144 settlement 140, 142–43 real-time process 142 Proceeds of Crime Act 2003 (POCA) 211, 219, 220–21 Professional Securities Market 43–44 Prudential 20 purchasing power parity 118–19 reinsurance 260–68 cat bonds 264–65 dispute resolution 268 doctrines 263 ﬁnancial reinsurance 263–64 incurred but not reported (IBNR) claims insurance securitisation 265 non-proportional 261 offshore requirements 267 proportional 261 Reinsurance Directive 266–67 retrocession 262 types of contract facultative 262 treaty 262 retail banking 20 retail investors 151–155 Retail Prices Index (RPI) 13, 87 264 308 INDEX ____________________________________________________ Retail Service Provider (RSP) network Reuters 35 Royal Bank of Scotland 20, 79, 221 73 Sarbanes–Oxley Act 233–34 securities 5, 29 Securities and Futures Authority 11 self-regulatory organisations (SROs) 192 Serious Crime Bill 213 settlement 11, 31, 140, 142–43 shareholder, rights of 29 shares investment in 29–32 nominee accounts 31 valuation 35–39 ratios 36–39 see also ﬂotation short selling 31–32, 73, 100, 157 Society for Worldwide Interbank Financial Telecommunications (SWIFT) 119 Solvency II 244–245 Soros, George 114, 115 Specialist Fund Market 44 ‘square mile’ 4 stamp duty 72, 75, 166 Sterling Overnight Index Average (SONIA) 85 Stock Exchange Automated Quotation System (SEAQ) 7, 121, 126 Stock Exchange Electronic Trading Service (SETS) see Lloyd’s of London stock market 29–33 stockbrokers 33–34 advisory 33 discretionary 33–34 execution-only 34 stocks see shares sub-prime mortgage crisis 16, 89, 94, 274 superequivalence 43 suspicious activity reports (SARs) 212, 219–22 swaps market 7 interest rates 56 swaptions 68 systematic internalisers (SI) 137–38 Target2-Securities 147–48, 150 The Times 35, 53, 291 share price tables 36–37, 40 tip sheets 33 trading platforms, electronic 80, 97, 113, 117 tranche trading 123 Treasury Select Committee 14 trend theory 175–76 UBS Warburg 103, 136 UK Listing Authority 44 Undertakings for Collective Investments in Transferable Securities (UCITS) 156 United Capital Asset Management 95 value at risk (VAR) virtual banks 20 virt-x 140 67–68 weighted-average cost of capital (WACC) see discounted cash ﬂow analysis wholesale banking 20 wholesale markets 78–80 banks 78–79 interdealer brokers 79–80 investors 79 Woolwich Bank 20 WorldCom 67, 232 Index of Advertisers Aberdeen Asset Management PLC xiii–xv Birkbeck University of London xl–xlii BPP xliv–xlvi Brewin Dolphin Investment Banking 48–50 Cass Business School xxi–xxiv Cater Allen Private Bank 180–81 CB Richard Ellis Ltd 270–71 CDP xlviii–l Charles Schwab UK Ltd lvi–lviii City Jet Ltd x–xii The City of London inside front cover EBS Dealing Resource International 110–11 Edelman xx ESCP-EAP European School of Management vi ICAS (The Inst. of Chartered Accountants of Scotland) xxx JP Morgan Asset Management 160–62 London Business School xvi–xviii London City Airport vii–viii Morgan Lewis xxix Securities & Investments Institute ii The Share Centre 30, 152–54 Smithﬁeld Bar and Grill lii–liv TD Waterhouse xxxii–xxxiv University of East London xxxvi–xxxviii

**
What They Do With Your Money: How the Financial System Fails Us, and How to Fix It
** by
Stephen Davis,
Jon Lukomnik,
David Pitt-Watson

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Admiral Zheng, banking crisis, Basel III, Bernie Madoff, Black Swan, centralized clearinghouse, clean water, corporate governance, correlation does not imply causation, credit crunch, Credit Default Swap, crowdsourcing, David Brooks, Dissolution of the Soviet Union, diversification, diversified portfolio, en.wikipedia.org, financial innovation, financial intermediation, Flash crash, income inequality, index fund, invisible hand, London Whale, Long Term Capital Management, moral hazard, Northern Rock, passive investing, performance metric, Ponzi scheme, principal–agent problem, rent-seeking, Ronald Coase, shareholder value, Silicon Valley, South Sea Bubble, sovereign wealth fund, statistical model, Steve Jobs, the market place, The Wealth of Nations by Adam Smith, transaction costs, Upton Sinclair, value at risk, WikiLeaks

We have all read, for example, about car crashes caused by drivers following obviously flawed directions coming from their navigation systems. Somehow, our natural skepticism is dampened by sophisticated technology. Perhaps the most widespread mathematical modeling system used by the finance sector is “value at risk,” or “VaR,” as it is known in trading rooms and risk management offices. Don’t let the jargon intimidate you; value at risk is exactly what it sounds. It tries to predict, given how you are investing your money, how much value you lose, and with what probability, over any specified time period. VaR analysis might tell you, for instance, that over the next year you can be 95 percent sure that your portfolio will not lose more than 10 percent. Using clever statistics, you can see the probability of the property market going up when shares go down, or the other way around, or of stock A moving in lockstep with stock B.

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See also High-frequency trading Trading platforms, that protect investors, 88–89 Transaction costs, 127, 169–70, 255n4 Transparency: in governance, 97–100, 224 in People’s Pension, 203–4, 207–8 of financial institutions, 229–30 regarding fees, 53–54, 60 regulation requiring, 146 Trillium, 77 Triodos Bank, 111 TripAdvisor, 127 Trust, 256n14 finance industry and, 56, 187 financial system and, 176–77 globalization and, 186–87 in government, 141 markets and, 178, 181 Trustee boards, of pension funds, 105–6 Trustee Network, 121 Trustees, 105–6, 108–9, 137–38, 140, 205, 207, 224–25, 229 Twitter, 114, 115, 116 Uncertainty, risk and, 172, 261n35 Unequal treaties, 168–69 United Airlines, 114–15 United Kingdom: financial services as percent of economy, 16 index funds, 57 investor coalitions, 89 laws to protect shareholders, 152 switch to defined contribution plans, 197–98 trust in finance industry, 56 women on corporate boards, 247n45 United Nations Principles for Responsible Investment (UN PRI), 58, 90, 112, 117, 140, 207 UN Environment Program, Finance Initiative, 138 United States: defined benefit funds, 105 defined contribution plans, 100, 102 director elections, 79 disclosure rules, 97–98 fiduciary duty and brokers, 256n23 flash crash, 51–52 fund governance regulation, 107–8 index funds, 57 investor coalitions, 90 lack of corporate governance code, 205, 267n3 regulation in aftermath of financial crisis, 124 stock market crash (2013), 51 switch to defined contribution plans, 197–98 tax liability for executive pay, 69, 85 trust in finance industry, 56 women on corporate boards, 247n45 US Office of the Comptroller, 108 US Commodity Futures Trading Commission, 52 US Department of Labor, 60, 107, 139–40 University of Oxford, 190 University students, governance reform and, 121–22 Urwin, Roger, 206 Value at risk (VaR), 39–40 Values, economies and, 178 Van Clieaf, Mark, 68 van der Vondel, Joost, 262n49 Vanguard, 6, 139, 235n24 Volcker, Paul, 267n1 von Hayek, Friedrich, 165 Voting: derivatives and, 80, 82–83, 93 disclosure of, 93, 108, 120, 121, 140, 207 for directors, 78–79 fund managers and, 75–77 individual investors and, 91, 120, 223 Vulture investors, 248n50 Wall Street Journal (newspaper), 29, 52 Wallace, Robert, 14, 199–202, 209 Walras, Leon, 159–60 Walter, Elisse, 88 Warren, Elizabeth, 129, 130 Washington, George, 157 The Wealth of Nations (Smith), 158, 161 Webb, David, 115 Weber, Max, 167 Webster, Alexander, 14, 199–202, 209 Weisman, Andrew, 37, 38 White, William, 259n5 Williamson, Michael, 59 Williamson, Oliver, 262n52 Women, on corporate boards, 247n45 Wong, Simon, 104 World Bank, 73, 151 World Economic Forum, 103–4 World Federation of Exchanges, 64–65 WorldCom, 44 www.corpgov.net, 116–17 Yahoo!

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See Liability-driven investing (LDI) Legislation on corporate governance, 9–10 Lehman Brothers, 25 Lemming standard, 137–38 Lenders, financial system as intermediator between borrowers and, 17, 19–22, 47, 74, 211–15 Leverage ratio, 215 Levitt, Arthur, 28 Liability-driven investing (LDI), 54–56, 264n2 Liar loans, 47 Libor, 257n32 Limited liability company, 21, 184–85, 237n7 Lincoln, Abraham, 157 LinkedIn, 116 Lipsey, Richard, 236n34 Lipton, Martin, 8 Liquidity, 17 Liquidity crisis, 74 Llewellyn, Karl, 262n52 Loans, classification of risk, 129, 175, 212–13 Long-Term Capital Management, 38, 164, 260n20 Long-term growth, emphasizing, 223 Long-term investment, 148: evergreen direct investing, 87 tax policy encouraging, 92, 223–24 Longevity risk, 194–95 Loopholes, regulation and exploitation of, 130 Lorsch, Jay, 8 MacDonald, Tim, 59, 87 Macey, Jon, 249n3 Macroeconomics, 179 Madoff, Bernard, 105 Mann, Harinder, 263n1, 266n28 Mao Tse Tung, 157 Marginal cost, 160 Marginal value, 160 Market capitalization, 45–46 Market discipline, 152–53, 258n46 Market economies, 142, 177, 181 regulation of, 125–28 Market institutions, 170 Markets: creating fiduciary behavior and, 152–53 regulation and, 125–28, 134 transaction costs and, 169–70 trust and, 178, 181 Marshall, Alfred, 177 Marx, Karl, 159 Mathematical modeling: atomized regulation and, 130 liability-driven investing and, 55–56 narrowness of, 153 overreliance on theoretical, 168–71 publishing economic research and, 189–90 recalibration of, 264n9 value at risk, 39–40 weakness of, 40–44. See also Economic modeling Max Planck Institute for Research on Collective Goods, 215 McRitchie, James, 116–17 Mercer, 122 Merrill Lynch, 44 Merton, Robert, 260n20 MFS Technologies, 82 Microeconomics, 179, 181–82 Millstein Center for Corporate Governance and Performance, 265n13 Millstein, Ira, 8 Minow, Nell, 207 Mirvis, Theodore, 8 Misalignment indicators, 104 Molinari, Claire, 112 Money managers, using collective action to allow focus on benefits for all, 89–90 “The Monkey Business Illusion” (video), 174 Monks, Bob, 62 Moral hazard, 73 Morality: economics and, 158 trade, 177 Morningstar, 34, 35, 36–37, 101, 122, 208, 225 Mortgages: chain of agents involved in, 31–32 subprime, 38, 40, 47 Murninghan, Marcy, 122 Mutual funds: agency capitalism and, 77–78 boards of, 205–6, 265n14 chain of agents in, 31 disclosure rules, 97 duration of holdings, 243n4, 258n41 failure to protect investors’ interests, 6–7 governance and performance of, 101–4, 224–25 grassroots campaigns influencing, 117 self-evaluation of, 110 votes on shareholder resolutions, 102 Mylan Laboratories, 81 Myopia, 66, 68 National Employment Savings Trust (NEST), 111, 206, 208 National governance code, 205, 265n13 Navalny, Alexei, 115–16 NEST.

**
The Invisible Hands: Top Hedge Fund Traders on Bubbles, Crashes, and Real Money
** by
Steven Drobny

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Albert Einstein, Asian financial crisis, asset allocation, asset-backed security, backtesting, banking crisis, Bernie Madoff, Black Swan, Bretton Woods, BRICs, British Empire, business process, capital asset pricing model, capital controls, central bank independence, collateralized debt obligation, Commodity Super-Cycle, commodity trading advisor, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency peg, debt deflation, diversification, diversified portfolio, equity premium, family office, fiat currency, fixed income, follow your passion, full employment, Hyman Minsky, implied volatility, index fund, inflation targeting, interest rate swap, inventory management, invisible hand, London Interbank Offered Rate, Long Term Capital Management, market bubble, market fundamentalism, market microstructure, moral hazard, North Sea oil, open economy, peak oil, pension reform, Ponzi scheme, prediction markets, price discovery process, price stability, private sector deleveraging, profit motive, purchasing power parity, quantitative easing, random walk, reserve currency, risk tolerance, risk-adjusted returns, risk/return, savings glut, Sharpe ratio, short selling, sovereign wealth fund, special drawing rights, statistical arbitrage, stochastic volatility, The Great Moderation, time value of money, too big to fail, transaction costs, unbiased observer, value at risk, Vanguard fund, yield curve

A great book that describes this process is The Alchemy of Finance by George Soros, in which he describes and demonstrates how he uses hypothesis formation and testing, ideas that come from the philosopher Karl Popper. Can you give me an example of how this process works in practice? Some people can trade markets using only numbers, prices on a screen, but this approach does not work for me. The numbers have to mean something—I have to understand the fundamental drivers behind the numbers. And while fundamentals are important, they are only one of many important inputs to the process. Just as a Value-at-Risk (VaR) model alone cannot tell you what your overall risk is, economic analysis alone cannot tell you where the bond market should be. Let us use an interest rate trade around central bank policy as a straightforward example to illustrate my process. Economic drivers will create the framework: What is the outlook for growth, inflation, employment, and other key variables? What will the reaction of the central bank be?

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Trade design, portfolio diversity, and risk management are just as important as being right about the markets, if not more so. At least that is how it has worked for me. Having said that, the commodities markets have been conducive to this approach in recent years. Still, I believe the key is running a fairly diverse portfolio of good risk-versus-reward trades coupled with very careful risk management on a portfolio level. It is important to have limits on VaR (value at risk), on margin-to-equity, portfolio P&L volatility, sector risk, individual position risk, vega, theta and premium spent if you trade a lot of options. It is also extremely important to delever the portfolio when you’re losing money in order to preserve capital. What’s the difference between being a prop trader and being a hedge fund manager? A prop trader is someone who speculates by taking a lot of risk, without necessarily thinking about capital preservation as rule number one.

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-centric equity portfolio U.S. dollar China, challenge reserve currency status decline role status U.S. equities annualized returns/volatility overpricing U.S. equity centric portfolio (protection), foreign currency diversification (usage) U.S. government budget, balance (1931-1932) defaulting, risk pricing U.S. government bonds annualized returns/volatility performance yield U.S. National Labor Relations Board (NLRB), corporate pension ruling U.S. public/private pension fund assets growth inflation, impact U.S. TIPS (2008-2009) U.S. Treasuries investment purchase worthlessness U.S. Treasury bonds (1987-1988) markets, protest Notes Valuation examination importance Valuation-driven tactical asset allocation models, time frame (increase) Value-at-Risk (VaR) calculation model Value-driven fundamental models, belief Vanguard 500 Index Funds (VFINX) return Vega, limits Venture capital opportunities, cash flow production Vision macro Visualization VIX, Fed funds (relationship) VIX Index (2007-2009) Volatility adjustment collapse dampening explanation usage Volcker, Paul Wages, transmission Washington State Investment Board West Texas Intermediate (WTI) crude World financial system, collapse World Trade Organization (WTO), China entry Wyatt, Watson Wynn, Steve credit bubble, recognition creditworthiness diversification perspective feedback, usage future correlations, usage historical correlations, usage interview lessons macro scenario, preparation money making ability multiple scenarios, tracking psychology, importance risk capital, reduction skill, recognition Swedish bond market, forward market introduction time horizon, alteration volatilities, usage Yale Asset Class, results Yale Endowment Investment Committee long-term investment popularity/usage Yale Model Yale University, endowments annual long-term performance control (Swensen) decline equity returns portfolio composition Yield curves, impact Zero-sum game, alpha extraction (relationship) Zimbabwe hyperinflation inflation/equities (2005-2008) market

**
Conspiracy of Fools: A True Story
** by
Kurt Eichenwald

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Asian financial crisis, Burning Man, estate planning, forensic accounting, Long Term Capital Management, margin call, Negawatt, new economy, oil shock, price stability, pushing on a string, Ronald Reagan, transaction costs, value at risk, young professional

The result was, if the possible loss grew, the traders might have to sell positions for cash even if they were making money. Now, the fluctuations in California were playing havoc with the formula, known as value at risk, or VAR. One perverse effect was that even if the traders stopped trading, they still might hit the risk limits. Whalley called Skilling to let him know the dilemma. The directors would need to kick up the VAR limit by about 30 percent to maintain current positions, he said. “No problem,” Skilling said. “I’ll take care of it.” This was just administrative, Skilling figured. He telephoned Pug Winokur, the head of the finance committee. “We’re going to need to make a request to the board for additional VAR,” Skilling said, giving the 30 percent estimate. “Well,” Winokur said, “we’ll have to talk about this at the board meeting.” Skilling paused.

…

“I just got a call from John Duncan about you wanting to get a VAR increase,” he said. “What’s going on?” John Duncan? Why was the head of the board’s executive committee calling Lay? “I don’t know what’s going on, Ken,” Skilling said. “I told Pug we were going to ask for an increase in VAR. It’s just a mathematical function, because of the increase in volatility.” Lay sat down. “Well, there’s something else going on. I mean, the directors are all talking among themselves.” This is ridiculous. “Ken, the position we have in VAR is just one-tenth of the risk we were taking in India. We’ve gone through hoops to tell them how VAR works. But they can approve a project in India in a twenty-two-minute phone call. There’s something wrong here.” Skilling set his jaw. He knew what this was about. It wasn’t VAR. It wasn’t risk. It was him.

…

The whole interview struck Skilling as unpleasant. This wasn’t the collaborative effort, the chance to expound on his views that he had been hoping for. These lawyers clearly thought he was responsible. He couldn’t believe it. “Would it surprise you to find out Fastow made about thirty-five million dollars from LJM in the last two years?” McLucas asked. Skilling shrugged. “Depends on what he had at risk,” he said. “You guys should do a value-at-risk analysis.” They haggled over the LJM approval sheets. Fastow had told the board that Skilling was approving each deal, McLucas said. That wasn’t the process, Skilling retorted. Only Causey and Buy were formally meant to approve each deal. McLucas brought out an approval sheet for a deal named Margaux, the sole LJM transaction signed by Skilling. “You signed this one,” McLucas said. “There is a list of questions with answers, and you signed it.”

**
Getting a Job in Hedge Funds: An Inside Look at How Funds Hire
** by
Adam Zoia,
Aaron Finkel

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backtesting, barriers to entry, collateralized debt obligation, commodity trading advisor, Credit Default Swap, credit default swaps / collateralized debt obligations, discounted cash flows, family office, fixed income, high net worth, interest rate derivative, interest rate swap, Long Term Capital Management, merger arbitrage, offshore financial centre, random walk, Renaissance Technologies, risk-adjusted returns, rolodex, short selling, side project, statistical arbitrage, systematic trading, unpaid internship, value at risk, yield curve, yield management

SAMPLE JOB SEARCHES To further illustrate what hedge funds look for when hiring various types of risk managers, we thought it would be helpful to include some job specifications from actual searches. Search 1: Hedge Fund Risk Analyst Note: This fund has a director of risk management who is looking for an additional resource (risk analyst) to join his team and develop within the firm. Description • Responsible for periodic report production, including: • Value at risk (VaR) and volatility reporting by portfolio. • Back-testing and historical performance measurement. • Portfolio segmentation analysis. • Factor analysis reporting. • Position level: • Expected return by position. • Risk analysis by position. • Marginal impact. • Relative risk/reward performance: • Stress testing. c07.indd 91 1/10/08 11:08:07 AM 92 Getting a Job in Hedge Funds • Correlation and concentration reporting by name, sector, and industry. • Responsible for the development and maintenance of a risk management database: • Creation of a centralized risk management database repository. • Daily data extraction from trading systems (Eze Castle) and accounting systems (VPM). • Maintenance of a security master and entity master tables. • Sourcing and storage of market pricing information. • Data cleaning and standardization. • Automation of data feeds from the risk management database to other applications (e.g., RiskMetrics) or models. • Supporting portfolio analysis: • Position and portfolio volatility analysis. • Correlation and factor model development. • Relative risk-adjusted performance measurement. • Historical and prospective analysis. • Analysis by position, portfolio, strategy, and so on. • Ad hoc analysis of portfolio.

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EXPERIENCE 2003–2006 BULGE-BRACKET INVESTMENT BANK New York, NY Client Portfolio Strategy – Risk Management • Consulted on risk management for large institutional fixed income trading clients and numerous smaller REIT, and credit arbitrage portfolios. • Modeled financial data including scenario total returns across large asset/liability portfolios, risk management metrics and VaR, derivative hedging strategies, duration of bank deposits, portable alpha, and CORE+ portfolios. Firm Proprietary Trading – Risk Management • Project analysis of trading risk issues and P&L across the entire firm’s trading business, working under the Global Head of Market Risk and reporting to the executive committee. • Redeveloped reporting of main risk metrics (delta, gamma, vega, P&L, VaR, scenarios, etc.) to better highlight emerging risk factors, new trades, and business concerns across firm’s equity derivatives business, including market making, arbitrage, and structured and exotic derivatives. • Designed risk management procedures for growing billion-dollar hedge-fund-linked derivative structures. 2002 SMALL HEDGE FUND New York, NY Analyst – Investment Research • Performed fundamental analysis and made investment recommendations for event-driven hedge fund investigating opportunities in distressed debt, turnaround, merger, and spin-off situations. • Financial statement analysis, including FCF modeling, capital structure analysis, reviews of bond covenants, indentures, and footnotes in order to develop a valuation assessment. 1997–2001 Technology Industry Held front office positions in sales and consulting at Intel, Net Perceptions, and Euro RSCG.

**
The Quants
** by
Scott Patterson

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Albert Einstein, asset allocation, automated trading system, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, buttonwood tree, buy low sell high, capital asset pricing model, centralized clearinghouse, Claude Shannon: information theory, cloud computing, collapse of Lehman Brothers, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, Doomsday Clock, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Gordon Gekko, greed is good, Haight Ashbury, index fund, invention of the telegraph, invisible hand, Isaac Newton, job automation, John Nash: game theory, law of one price, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, merger arbitrage, NetJets, new economy, offshore financial centre, Paul Lévy, Ponzi scheme, quantitative hedge fund, quantitative trading / quantitative ﬁnance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Sergey Aleynikov, short selling, South Sea Bubble, speech recognition, statistical arbitrage, The Chicago School, The Great Moderation, The Predators' Ball, too big to fail, transaction costs, value at risk, volatility smile, yield curve, éminence grise

P. Morgan quants created measured the daily volatility of the firm’s positions and then translated that volatility into a dollar amount. It was a statistical distribution of average volatility based on Brownian motion. Plotted on a graph, that volatility looked like a bell curve. The result was a model they called value-at-risk, or VAR. It was a metric showing the amount of money the bank could lose over a twenty-four-hour period within a 95 percent probability. The powerful VAR radar system had a dangerous allure. If risk could be quantified, it also could be controlled through sophisticated hedging strategies. This belief can be seen in LTCM’s October 1993 prospectus: “The reduction in the Portfolio Company’s volatility through hedging could permit the leveraging up of the resulting position to the same expected level of volatility as an unhedged position, but with a larger expected return.”

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When losses mount, leveraged investors such as Long-Term are forced to sell, lest their losses overwhelm them. When a firm has to sell in a market without buyers, prices run to the extremes beyond the bell curve.” Prices for everything from stocks to currencies to bonds held by LTCM moved in a bizarre fashion that defied logic. LTCM had relied on complex hedging strategies, massive hairballs of derivatives, and risk management tools such as VAR to allow it to leverage up to the maximum amount possible. By carefully hedging its holdings, LTCM could reduce its capital, otherwise known as equity. That freed up cash to make other bets. As Myron Scholes explained before the disaster struck: “I like to think of equity as an all-purpose risk cushion. The more I have, the less risk I have, because I can’t get hurt. On the other hand, if I have systematic hedging—a more targeted approach—that’s interesting because there’s a trade-off: it’s costly to hedge, but it’s also costly to use equity.”

…

Weinstein remained outwardly calm, quietly brooding in his office overlooking Wall Street. But the losses were piling up rapidly and soon topped $1 billion. He pleaded with Deutsche’s risk managers to let him purchase more swaps so he could better hedge his positions, but the word had come down from on high: buying wasn’t allowed, only selling. Perversely, the bank’s risk models, such as the notorious VAR used by all Wall Street banks, instructed traders to exit short positions, including credit default swaps. Weinstein knew that was crazy, but the quants in charge of risk couldn’t be argued with. “Step away from the model,” he begged. “The only way for me to get out of this is to be short. If the market is falling and you’re losing money, that means you are long the market—and you need to short it, as fast as possible.”

**
Obliquity: Why Our Goals Are Best Achieved Indirectly
** by
John Kay

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Andrew Wiles, Asian financial crisis, Berlin Wall, bonus culture, British Empire, business process, Cass Sunstein, computer age, credit crunch, Daniel Kahneman / Amos Tversky, discounted cash flows, discovery of penicillin, diversification, Donald Trump, Fall of the Berlin Wall, financial innovation, Gordon Gekko, greed is good, invention of the telephone, invisible hand, Jane Jacobs, Long Term Capital Management, Louis Pasteur, market fundamentalism, Nash equilibrium, pattern recognition, purchasing power parity, RAND corporation, regulatory arbitrage, shareholder value, Simon Singh, Steve Jobs, The Death and Life of Great American Cities, The Predators' Ball, The Wealth of Nations by Adam Smith, ultimatum game, urban planning, value at risk

In the first decade of the twenty-first century banks persuaded themselves that risk management could be treated as a problem that was closed, determinate and calculable—like working out when the bus will arrive. We, and they, learned that they were wrong. The most widely used template in the banking industry was called “value at risk” (VAR) and elaborated by JPMorgan. The bank published the details and subsequently spun off a business, RiskMetrics, which promotes it still.2 These risk models are based on analysis of the volatility of individual assets or asset classes and—crucially—on correlations, the relationships among the behaviors of different assets. The standard assumptions of most value-at-risk models are that the dispersion of investment returns follows the normal distribution, the bell curve that characterizes so many natural and social phenomena, and that future correlations will reproduce past ones.

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root method Rotella, Bob Rousseau, Jean-Jacques rules Saint-Gobain salesmen Salomon Brothers Samuelson, Paul Santa Maria del Fiore cathedral Scholes, Myron science scorecard Scottish Enlightenment Sculley, John Sears securities selfish gene September 11 attacks (2001) shareholder value share options Sieff, Israel Sierra Leone Simon, Herbert simplification Singapore Singer Smith, Adam Smith, Ed Smith, Will SmithKline soccer (English football) social contract socialism social issues socialist realism sociopaths Solon Sony Sony Walkman Soros, George Soviet Union sports Stalin, Joseph “Still Muddling, Not Yet Through” (Lindblom) Stockdale, James Stockdale Paradox stock prices Stone, Oliver successive limited comparison sudoku Sugar, Alan Sunbeam Sunstein, Cass Super Cub motorcycles superstition surgery survival sustainability Taleb, Nassim Nicholas Tankel, Stanley target goals teaching quality assessment technology see also computers teleological fallacy telephones Tellus tennis Tetlock, Philip Tet Offensive (1968) Thales of Miletus Thornton, Charles Bates “Tex” tic-tac-toe Tolstoy, Leo transnational corporations transportation Travelers Treasury, U.S. trials Trump, Donald TRW 2001: A Space Odyssey Typhoon (Conrad) ultimatum games uncertainty United Nations United States Unités d’Habitation unplanned evolution urban planning value at risk (VAR) van Gogh, Vincent van Meegeren, Han Vasari, Giorgio Vermeer, Johannes Victorian era Vietnam War Vioxx volatility Wall Street Walton, Sam Wason, Peter Wason test wealth Wealth of Nations, The (Smith) Weill, Sandy Weir, Peter Welch, Jack Whately, Archbishop What Is to Be Done? (Lenin) Whitehead, John Whitman, Walt Whiz Kids Wilde, Oscar Wild One, The Wiles, Andrew Williams, Robin wind farms Wolfe, James World Bank World Economic Forum World War II Yeats, William Butler Yellowstone National Park Young Hare, The (Dürer) Zaire Zantac Zeneca zero tolerance About the Author John Kay is a visiting professor at the London School of Economics and a fellow of St John’s College, University of Oxford.

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–Aug. 1960), pp. 45–56. 4 Carl W. Stern and George Stalk, eds., Perspectives on Strategy from the Boston Consulting Group (New York: John Wiley, 1998). 5 For similar illusions, see http://www.planetperplex.com/en/item131. Chapter 12: Abstraction—Why Models Are Imperfect Descriptions of Reality 1 Jorge Luis Borges, A Universal History of Infamy (Harmondsworth, UK: Penguin, 1975), p. 131. 2 Value at risk is a group of related models that compute the maximum potential change in value of a portfolio of assets under “normal” market conditions. (See also: JPMorgan and Reuters, RiskMetrics—Technical Document, 4th ed. (New York: Morgan Guaranty Trust Company of New York, 1996); Joe Nocera, “Risk Management,” New York Times, January 4, 2009.) 3 Bruce Pandolfini, Kasparov and Deep Blue: The Historic Chess Match Between Man and Machine (New York: Simon & Schuster, 1997). 4 David G.

**
Nerds on Wall Street: Math, Machines and Wired Markets
** by
David J. Leinweber

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AI winter, algorithmic trading, asset allocation, banking crisis, barriers to entry, Big bang: deregulation of the City of London, butterfly effect, buttonwood tree, buy low sell high, capital asset pricing model, citizen journalism, collateralized debt obligation, corporate governance, Craig Reynolds: boids flock, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Danny Hillis, demand response, disintermediation, distributed generation, diversification, diversified portfolio, Emanuel Derman, en.wikipedia.org, experimental economics, financial innovation, Gordon Gekko, implied volatility, index arbitrage, index fund, information retrieval, Internet Archive, John Nash: game theory, Khan Academy, load shedding, Long Term Capital Management, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, market fragmentation, market microstructure, Mars Rover, moral hazard, mutually assured destruction, natural language processing, Network effects, optical character recognition, paper trading, passive investing, pez dispenser, phenotype, prediction markets, quantitative hedge fund, quantitative trading / quantitative ﬁnance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Renaissance Technologies, Richard Stallman, risk tolerance, risk-adjusted returns, risk/return, Ronald Reagan, semantic web, Sharpe ratio, short selling, Silicon Valley, Small Order Execution System, smart grid, smart meter, social web, South Sea Bubble, statistical arbitrage, statistical model, Steve Jobs, Steven Levy, Tacoma Narrows Bridge, the scientific method, The Wisdom of Crowds, time value of money, too big to fail, transaction costs, Turing machine, Upton Sinclair, value at risk, Vernor Vinge, yield curve, Yogi Berra

Robert Almgren and Neil Chriss made that major step in their 2000 paper “Optimal Execution of Portfolio Transactions.”15 It explicitly included the risk aversion of traders, and introduced the idea of liquidity-adjusted value at risk as a metric for trading strategies. Okay, let’s call this Algos 201, but again, the authors do a fine job explaining this for the mathematically inclined. This work has been very widely adopted in today’s algo systems. From the abstract: We consider the execution of portfolio transactions with the aim of minimizing a combination of volatility risk and transaction costs arising from permanent and temporary market impact. For a simple linear cost model, we explicitly construct the efficient frontier in the space of time-dependent liquidation strategies, which have minimum expected cost for a given level of uncertainty. We may then select optimal strategies either by minimizing a quadratic utility function, or minimizing Value at Risk . . . , that explicitly considers the tradeoff between volatility risk and liquidation costs.

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It is a better use of computational resources to get rid of them early. Variants on the chromosomes5 used for the forecasting models, as seen in Figure 8.4, allowed for higher levels of flexibility. The simplest Basic—Variables fixed in advance AVG1 SBP gene LAG1 AVG2 LAG2 AVG1 BRP gene LAG1 AVG2 LAG2 Snappy Version—Variables and transforms coded VAR ID X FORM AVG1 LAG1 AVG2 LAG2 VAR ID Really Snappy Version—As above, plus variation in algebraic form PRED ID PRED ID OP VAR ID X FORM VAR ID X FORM AVG1 AVG1 LAG1 LAG1 AVG2 AVG2 LAG2 LAG2 Figure 8.4 Chromosomes for Global Tactical Asset Allocation (GTAA) and Tactical Currency Allocation (TCA) Models Perils and Pr omise of Evolutionary Computation on Wall Str eet 193 chromosomes assumed that the standard predictor variables used in the existing models were utilized, and only the transforms were adjusted.

**
How to Kick Ass on Wall Street
** by
Andy Kessler

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Andy Kessler, Bernie Madoff, buttonwood tree, call centre, collateralized debt obligation, family office, fixed income, hiring and firing, invention of the wheel, invisible hand, London Whale, margin call, NetJets, Nick Leeson, pets.com, risk tolerance, Silicon Valley, sovereign wealth fund, time value of money, too big to fail, value at risk

Great way to generate good will and cash bonuses. But even the smartest traders get fooled. Maybe the smartest get fooled the most. Markets get irrational. Every trader worth their salt knows this or learns it quickly. The old adage is that the market can stay irrational longer than you can stay solvent. This is why firms put trading limits on traders or cumulatively trading desks. There is a firm-wide limit, known as VaR or Value at Risk – the most a firm could lose on any given day. The better you get trading, the higher your personal limit and the bigger chunk of the firm’s capital you get to play with and turn into more money (or end up as a smoking hole in the ground, see Nick Leeson and JP Morgan’s London Whale.) Bond trading is a little different, but not much. Again, trading government bonds and munis and corporate debt is mostly facilitating trades for clients.

**
The Ascent of Money: A Financial History of the World
** by
Niall Ferguson

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Admiral Zheng, Andrei Shleifer, Asian financial crisis, asset allocation, asset-backed security, Atahualpa, bank run, banking crisis, banks create money, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, BRICs, British Empire, capital asset pricing model, capital controls, Carmen Reinhart, Cass Sunstein, central bank independence, collateralized debt obligation, colonial exploitation, Corn Laws, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, currency peg, Daniel Kahneman / Amos Tversky, deglobalization, diversification, diversified portfolio, double entry bookkeeping, Edmond Halley, Edward Glaeser, Edward Lloyd's coffeehouse, financial innovation, financial intermediation, fixed income, floating exchange rates, Fractional reserve banking, Francisco Pizarro, full employment, German hyperinflation, Hernando de Soto, high net worth, hindsight bias, Home mortgage interest deduction, Hyman Minsky, income inequality, interest rate swap, Isaac Newton, iterative process, joint-stock company, joint-stock limited liability company, Joseph Schumpeter, Kenneth Rogoff, knowledge economy, labour mobility, London Interbank Offered Rate, Long Term Capital Management, market bubble, market fundamentalism, means of production, Mikhail Gorbachev, money: store of value / unit of account / medium of exchange, moral hazard, mortgage debt, mortgage tax deduction, Naomi Klein, Nick Leeson, Northern Rock, pension reform, price anchoring, price stability, principal–agent problem, probability theory / Blaise Pascal / Pierre de Fermat, profit motive, quantitative hedge fund, RAND corporation, random walk, rent control, rent-seeking, reserve currency, Richard Thaler, Robert Shiller, Robert Shiller, Ronald Reagan, savings glut, seigniorage, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spice trade, structural adjustment programs, technology bubble, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Malthus, Thorstein Veblen, too big to fail, transaction costs, value at risk, Washington Consensus, Yom Kippur War

Meriwether echoed this view: ‘The nature of the world had changed, and we hadn’t recognized it.’98 In particular, because many other firms had begun trying to copy Long-Term’s strategies, when things went wrong it was not just the Long-Term portfolio that was hit; it was as if an entire super-portfolio was haemorrhaging.99 There was a herd-like stampede for the exits, with senior managers at the big banks insisting that positions be closed down at any price. Everything suddenly went down at once. As one leading London hedge fund manager later put it to Meriwether: ‘John, you were the correlation.’ There was, however, another reason why LTCM failed. The firm’s value at risk (VaR) models had implied that the loss Long-Term suffered in August was so unlikely that it ought never to have happened in the entire life of the universe. But that was because the models were working with just five years’ worth of data. If the models had gone back even eleven years, they would have captured the 1987 stock market crash. If they had gone back eighty years they would have captured the last great Russian default, after the 1917 Revolution.

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United Kingdom see Britain United Netherlands East India Company see VOC United Provinces: bond market 75 currencies in 48 and East India Company see VOC and Mississippi Bubble 153-5 power of 3 rentiers in 75 rivalry between provinces 129 see also Netherlands, The United States of America: ageing population 219-21 ‘American empire’ 309-10 banking system 57-8 British investment in 293 budget deficit 118 currency policy 338 debt and bankruptcy in 59-61 defence industry 317 depression see depressions divisions in society see race divisions France and see Louisiana government bonds 323 health care and insurance 61 home ownership see property/ real estate and IMF and World Bank 309-12 immigration and population 286 imports 10 incomes 1-2 industrialization 285 inflation 108 insurance 199 international borrowing 334-5 overseas aid and investment 305-7 public ignorance about finance 10-12 real estate see property/real estate recession prospects 8 savings 333-5 social divisions see race divisions stock market 6 as subprime superpower 282 use of economic hit men 309-11 welfare system 11 and Second World War 205-6 and First World War 101-2 universities 195 Uriburu, José F. 110 Uruk 31 US Army Corps of Engineers 183 USSR see Russia/USSR US Steel 349 usury 35-6 utility companies 169 see also energy industry utility and probability 189-90 utopianism 17-18 Value at Risk (VaR) models 325 . Vatican 42 Veblen, Thorstein 348 Velasco, Carmen 279 Venezuela 26 Venice 33-8 and bonds 72-3 ghetto 34 Medici in 42 and money-lending 33-8 and Oriental influences 33 San Moise 126 Vernon S&L 255 Versailles Treaty 102-3 Vicksburg 92 Victoria, Queen 238 Vienna 101 Vietnam War 307n. violence, in absence of money 18-19 ‘virtual’ money see electronic money VOC (Dutch/United East India Company) 128-37 shares in 129-30 structure 128-9 volatility: alleged death of 6 projected return of 356 see also investors; stock markets Volcker, Paul 166 Voltaire 145 voting rights see electoral reform wage cuts 160 Wallace, Robert 190-95 Wall Street crash 158-63 war: and capitalist system 297-8 causing ‘bankruptcy of nations’ 297 and commodity markets and prices 10 conditions for 304 finance for 1 globalization and 338-40 and industrial change 348 and inflation see inflation and insurance see insurance and money 1 probabilities 183 and trade 134 war bonds 101-2 and welfare state 202-4 see also bonds and bond markets War Damage Corporation 206 War Loans 295 Washington, D.C. 306 Washington Consensus 308 Washington Mutual 266 Waterloo, Battle of 3 Watkins, Sherron 171-2 wealthy 26 weapons see arms; technological innovation; war weather: derivatives 227-8 extreme 6; see also disasters and stock markets 159 Webster, Alexander 190-95 welfare state 199-211 backlash against 215 dismantling of 211 and economy 209-11 and war see war Wellington, Duke of 80-1 Western Union 317 Westminster, Duke of 234 wheat prices see grain widows and orphans 192-4 William of Orange 75 Williamson, John 308n.

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bl Under the Basel I rules agreed in 1988, assets of banks are divided into five categories according to credit risk, carrying risk weights ranging from zero (for example, home country government bonds) to 100 per cent (corporate debt). International banks are required to hold capital equal to 8 per cent of their risk-weighted assets. Basel II, first published in 2004 but only gradually being adopted around the world, sets out more complex rules, distinguishing between credit risk, operational risk and market risk, the last of which mandates the use of value at risk (VaR) models. Ironically, in the light of 2007-8, liquidity risk is combined with other risks under the heading ‘residual risk’. Such rules inevitably conflict with the incentive all banks have to minimize their capital and hence raise their return on equity. bm In Andrew Lo’s words: ‘Hedge funds are the Galapagos Islands of finance . . . The rate of innovation, evolution, competition, adaptation, births and deaths, the whole range of evolutionary phenomena, occurs at an extraordinarily rapid clip.’

**
The Black Box Society: The Secret Algorithms That Control Money and Information
** by
Frank Pasquale

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Affordable Care Act / Obamacare, algorithmic trading, Amazon Mechanical Turk, asset-backed security, Atul Gawande, bank run, barriers to entry, Berlin Wall, Bernie Madoff, Black Swan, bonus culture, Brian Krebs, call centre, Capital in the Twenty-First Century by Thomas Piketty, Chelsea Manning, cloud computing, collateralized debt obligation, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, crowdsourcing, cryptocurrency, Debian, don't be evil, Edward Snowden, en.wikipedia.org, Fall of the Berlin Wall, Filter Bubble, financial innovation, Flash crash, full employment, Goldman Sachs: Vampire Squid, Google Earth, Hernando de Soto, High speed trading, hiring and firing, housing crisis, informal economy, information retrieval, interest rate swap, Internet of things, invisible hand, Jaron Lanier, Jeff Bezos, job automation, Julian Assange, Kevin Kelly, knowledge worker, Kodak vs Instagram, kremlinology, late fees, London Interbank Offered Rate, London Whale, Mark Zuckerberg, mobile money, moral hazard, new economy, Nicholas Carr, offshore financial centre, PageRank, pattern recognition, precariat, profit maximization, profit motive, quantitative easing, race to the bottom, recommendation engine, regulatory arbitrage, risk-adjusted returns, search engine result page, shareholder value, Silicon Valley, Snapchat, Spread Networks laid a new fibre optics cable between New York and Chicago, statistical arbitrage, statistical model, Steven Levy, the scientific method, too big to fail, transaction costs, two-sided market, universal basic income, Upton Sinclair, value at risk, WikiLeaks

“Financial engineers” crafted “swaps” of risk,55 encouraging quants (and regulators) to try to estimate it in ever more precise ways.56 A credit default swap (CDS), for instance, transfers the risk of nonpayment to a third party, which promises to pay you (the first party) in case the debtor (the second party) does not.57 This innovation was celebrated as a landmark of “price discovery,” a day-by-day (or even second-by-second) tracking of exactly how likely an entity was to default.58 114 THE BLACK BOX SOCIETY As with credit scores, the risk modeling here was deeply fallible, another misapplication of natural science methods to an essentially social science of finance. “Value at Risk” models purported to predict with at least 95 percent certainty how much a firm could lose if market prices changed. But the models had to assume the stability of certain kinds of human behavior, which could change in response to widespread adoption of the models themselves. Furthermore, many models gave little weight to the possibility that housing prices would fall across the nation. Just as an unduly high credit score could help a consumer get a loan he had no chance of paying back, an overly generous model could help a bank garner capital to fund projects of dubious value.

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Jake Bernstein and Jesse Eisinger, “Banks’ Self-Dealing Super- Charged Finanical Crisis,” Pro Publica, August 26, 2010, at http://www.propublica.org /article /banks-self-dealing-super-charged-fi nancial-crisis. 104. Jaron Lanier, You Are Not a Gadget: A Manifesto (New York: Alfred A. Knopf, 2010), 96. 105. U.S. Senate Permanent Subcommittee on Investigations, JPMorgan Chase Whale Trades: A Case History of Derivatives Risks and Abuses (2013), 8. (“In the case of the CIO VaR, after analysts concluded the existing model was too conservative and overstated risk, an alternative CIO model was hurriedly adopted in late January 2012, while the CIO was in breach of its own and the bankwide VaR limit. The CIO’s new model immediately lowered the SCP’s VaR by 50%, enabling the CIO not only to end its breach, but to engage in substantially more risky derivatives trading. Months later, the bank determined that the model was improperly implemented, requiring error-prone manual data entry and incorporating formula and calculation errors.”) 106.

**
13 Bankers: The Wall Street Takeover and the Next Financial Meltdown
** by
Simon Johnson,
James Kwak

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Andrei Shleifer, Asian financial crisis, asset-backed security, bank run, banking crisis, Bernie Madoff, Bonfire of the Vanities, bonus culture, capital controls, Carmen Reinhart, central bank independence, collapse of Lehman Brothers, collateralized debt obligation, corporate governance, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, Edward Glaeser, Eugene Fama: efficient market hypothesis, financial deregulation, financial innovation, financial intermediation, financial repression, fixed income, George Akerlof, Gordon Gekko, greed is good, Home mortgage interest deduction, Hyman Minsky, income per capita, interest rate derivative, interest rate swap, Kenneth Rogoff, laissez-faire capitalism, late fees, Long Term Capital Management, market bubble, market fundamentalism, Martin Wolf, moral hazard, mortgage tax deduction, Ponzi scheme, price stability, profit maximization, race to the bottom, regulatory arbitrage, rent-seeking, Robert Shiller, Robert Shiller, Ronald Reagan, Saturday Night Live, sovereign wealth fund, The Myth of the Rational Market, too big to fail, transaction costs, value at risk, yield curve

Quoted in Jenny Anderson, “Despite Bailouts, Business as Usual at Goldman,” The New York Times, August 5, 2009, available at http://www.nytimes.com/2009/08/06/business/06goldman.html. 71. Felix Salmon, “Chart of the Day: Goldman VaR,” Reuters, July 15, 2009, available at http://blogs.reuters.com/felix-salmon/2009/07/15/chart-of-the-day-goldman-var/. See also Andrew Ross Sorkin, “Taking a Chance on Risk, Again,” DealBook Blog, The New York Times, September 17, 2009, available at http://dealbook.blogs.nytimes.com/2009/09/17/taking-a-chance-on-risk-again/. While VaR—value-at-risk—is a poor way of estimating potential losses under extreme market conditions, it does measure the change in the riskiness of a portfolio relative to historical data. 72. Quoted in Simon Clark and Caroline Binham, “Profit ‘Is Not Satanic,’ Barclays CEO Varley Says,” Bloomberg, November 3, 2009, available at http://www.bloomberg.com/apps/news?

…

JPMorgan Chase, Goldman Sachs, and Morgan Stanley alone accounted for 42 percent of the market for equity underwriting in the first half of 2009.69 Finally, Goldman was making money the oldfashioned way—by taking on more risk. As the bank’s president, Gary Cohn, said in August 2009, “Our risk appetite continues to grow year on year, quarter on quarter, as our balance sheet and liquidity continue to grow.”70 And Goldman’s value-at-risk—a quantitative measure of the amount it stood to lose on a given day—after dipping slightly in summer 2008, continued to climb throughout the crisis to levels in 2009 five times as high as in 2002.71 However, the clearest indication that Wall Street was back to business as usual was the amount of money earmarked for bonuses. In the first half of 2009, Goldman Sachs set aside $11.4 billion for employee compensation—an annual rate of over $750,000 per employee and near the record levels of the boom.

**
The End of Accounting and the Path Forward for Investors and Managers (Wiley Finance)
** by
Feng Gu

Amazon: amazon.com — amazon.co.uk — amazon.de — amazon.fr

Affordable Care Act / Obamacare, barriers to entry, business process, Claude Shannon: information theory, Clayton Christensen, conceptual framework, corporate governance, Daniel Kahneman / Amos Tversky, discounted cash flows, diversified portfolio, double entry bookkeeping, Exxon Valdez, financial innovation, fixed income, hydraulic fracturing, index fund, inventory management, Joseph Schumpeter, knowledge economy, moral hazard, new economy, obamacare, quantitative easing, quantitative trading / quantitative ﬁnance, QWERTY keyboard, race to the bottom, risk/return, Robert Shiller, Robert Shiller, shareholder value, Steve Jobs, The Great Moderation, value at risk

Strategic Resources & Consequences Report: Case No. 2 159 The Resource Preservation part of the Resources & Consequences Report (mid-column) should accordingly provide sufficient information enabling investors to evaluate the effectiveness of the company’s risk management, and the extent of risk exposure. Narrative, but not boilerplate, discussion of management’s risk mitigation strategies, with quantitative indicators, like proportion of exposure and premium ceded to reinsurers, along with traditional risk measures, such as VAR (value at risk) should be provided in the Resources & Consequences Report. As for regulatory risk, relevant information includes the status of major rate increase applications and regulators’ moves to impose new coverage on the company. Here, as elsewhere, it’s important to perceive the proposed Report as an integrated system, rather than a list of disparate indicators. Accordingly, other information in the Report, particularly on patterns in the frequency and severity of claims and customer’s rate of renewing policies, also shed light on important insurance risk dimensions.

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Such price gyrations strongly affect companies’ strategy and financial results—Apache (February 25, 2015, presentation) reported that the recent 190 SO, WHAT’S TO BE DONE? 38 percent oil price decrease caused a 17 percent decline of cash flows—and puts heavy pressure on exploration and production decisions (shutting off operations when prices drop below breakeven?). It is important, therefore, to provide investors with quantitative risk indicators, akin to VAR (value at risk) financial measures, to indicate the sensitivity of cash flows and sales to expected changes in the prices of oil and gas. You surely don’t have to warn investors that oil and gas price volatility affects operations; they know it. But how about quantifying for them the sensitivity of operations to prospective price changes, allowing investors to assess the riskiness of operations and the company’s future growth?

**
Foolproof: Why Safety Can Be Dangerous and How Danger Makes Us Safe
** by
Greg Ip

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Affordable Care Act / Obamacare, Air France Flight 447, air freight, airport security, Asian financial crisis, asset-backed security, bank run, banking crisis, Bretton Woods, capital controls, central bank independence, cloud computing, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, currency peg, Daniel Kahneman / Amos Tversky, diversified portfolio, double helix, endowment effect, Exxon Valdez, financial deregulation, financial innovation, Financial Instability Hypothesis, floating exchange rates, full employment, global supply chain, hindsight bias, Hyman Minsky, Joseph Schumpeter, Kenneth Rogoff, London Whale, Long Term Capital Management, market bubble, moral hazard, Network effects, new economy, offshore financial centre, paradox of thrift, pets.com, Ponzi scheme, quantitative easing, Ralph Nader, Richard Thaler, risk tolerance, Ronald Reagan, savings glut, technology bubble, The Great Moderation, too big to fail, transaction costs, union organizing, Unsafe at Any Speed, value at risk

Our environment evolves, and successfully preventing one type of risk may simply funnel it elsewhere, to reemerge, like a mutated bacteria, in more virulent fashion. In fact, bacteria illustrate this. Millions of people become sick or die each year because excessive use of antibiotics causes bacteria to mutate into resistant strains. The systems we’ve developed to learn from history can unintentionally magnify this tendency. Financial institutions, for example, monitor their risk with a formula called “value at risk,” or VaR. Vastly simplified, VaR asks how much money would be lost if securities or interest rates fluctuate as much as they did at their most volatile moment in the recent past. A long period of calm will thus naturally lead a bank to raise its exposure. As that exposure grows, so does the potential loss if volatility exceeds expectations. Those losses will in turn trigger a rush to sell those securities, making the volatility even worse.

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Expected Returns: An Investor's Guide to Harvesting Market Rewards
** by
Antti Ilmanen

Amazon: amazon.com — amazon.co.uk — amazon.de — amazon.fr

Andrei Shleifer, asset allocation, asset-backed security, availability heuristic, backtesting, balance sheet recession, bank run, banking crisis, barriers to entry, Bernie Madoff, Black Swan, Bretton Woods, buy low sell high, capital asset pricing model, capital controls, Carmen Reinhart, central bank independence, collateralized debt obligation, commodity trading advisor, corporate governance, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, debt deflation, deglobalization, delta neutral, demand response, discounted cash flows, disintermediation, diversification, diversified portfolio, dividend-yielding stocks, equity premium, Eugene Fama: efficient market hypothesis, fiat currency, financial deregulation, financial innovation, financial intermediation, fixed income, Flash crash, framing effect, frictionless, frictionless market, George Akerlof, global reserve currency, Google Earth, high net worth, hindsight bias, Hyman Minsky, implied volatility, income inequality, incomplete markets, index fund, inflation targeting, interest rate swap, invisible hand, Kenneth Rogoff, laissez-faire capitalism, law of one price, Long Term Capital Management, loss aversion, margin call, market bubble, market clearing, market friction, market fundamentalism, market microstructure, mental accounting, merger arbitrage, mittelstand, moral hazard, New Journalism, oil shock, p-value, passive investing, performance metric, Ponzi scheme, prediction markets, price anchoring, price stability, principal–agent problem, private sector deleveraging, purchasing power parity, quantitative easing, quantitative trading / quantitative ﬁnance, random walk, reserve currency, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, riskless arbitrage, Robert Shiller, Robert Shiller, savings glut, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, stochastic volatility, systematic trading, The Great Moderation, The Myth of the Rational Market, too big to fail, transaction costs, tulip mania, value at risk, volatility arbitrage, volatility smile, working-age population, Y2K, yield curve, zero-coupon bond

Antti Ilmanen Bad Homburg, November 2010 Abbreviations and acronyms AM Arithmetic Mean ATM At The Money (option) AUM Assets Under Management BEI Break-Even Inflation BF Behavioral Finance B/P Book/Price, book-to-market ratio BRP Bond Risk Premium, term premium B-S Black–Scholes C-P BRP Cochrane–Piazzesi Bond Risk Premium CAPM Capital Asset Pricing Model CAY Consumption wealth ratio CB Central Bank CCW Covered Call Writing CDO Collateralized Debt Obligation CDS Credit Default Swap CF Cash Flow CFNAI Chicago Fed National Activity Index CFO Chief Financial Officer CMD Commodity (futures) CPIyoy Consumer Price Inflation year on year CRB Commodity Research Bureau CRP Credit Risk Premium (over Treasury bond) CRRA Constant Relative Risk Aversion CTA Commodity Trading Advisor DDM Dividend Discount Model DJ CS Dow Jones Credit Suisse DMS Dimson–Marsh–Staunton D/P Dividend/Price (ratio), dividend yield DR Diversification Return E( ) Expected (conditional expectation) EMH Efficient Markets Hypothesis E/P Earnings/Price ratio, earnings yield EPS Earnings Per Share ERP Equity Risk Premium ERPB Equity Risk Premium over Bond (Treasury) ERPC Equity Risk Premium over Cash (Treasury bill) F Forward price or futures price FF Fama–French FI Fixed Income FoF Fund of Funds FX Foreign eXchange G Growth rate GARCH Generalized AutoRegressive Conditional Heteroskedasticity GC General Collateral repo rate (money market interest rate) GDP Gross Domestic Product GM Geometric Mean, also compound annual return GP General Partner GSCI Goldman Sachs Commodity Index H Holding-period return HF Hedge Fund HFR Hedge Fund Research HML High Minus Low, a value measure, also VMG HNWI High Net Worth Individual HPA House Price Appreciation (rate) HY High Yield, speculative-rated debt IG Investment Grade (rated debt) ILLIQ Measure of a stock’s illiquidity: average absolute daily return over a month divided by dollar volume IPO Initial Public Offering IR Information Ratio IRP Inflation Risk Premium ISM Business confidence index ITM In The Money (option) JGB Japanese Government Bond K-W BRP Kim–Wright Bond Risk Premium LIBOR London InterBank Offered Rate, a popular bank deposit rate LP Limited Partner LSV Lakonishok–Shleifer–Vishny LtA Limits to Arbitrage LTCM Long-Term Capital Management MA Moving Average MBS (fixed rate, residential) Mortgage-Backed Securities MIT-CRE MIT Center for Real Estate MOM Equity MOMentum proxy MSCI Morgan Stanley Capital International MU Marginal Utility NBER National Bureau of Economic Research NCREIF National Council of Real Estate Investment Fiduciaries OAS Option-Adjusted (credit) Spread OTM Out of The Money (option) P Price P/B Price/Book (valuation ratio) P/E Price/Earnings (valuation ratio) PE Private Equity PEH Pure Expectations Hypothesis PT Prospect Theory r Excess return R Real (rate) RE Real Estate REITs Real Estate Investment Trusts RWH Random Walk Hypothesis S Spot price, spot rate SBRP Survey-based Bond Risk Premium SDF Stochastic Discount Factor SMB Small Minus Big, size premium proxy SR Sharpe Ratio SWF Sovereign Wealth Fund TED Treasury–Eurodollar (deposit) rate spread in money markets TIPS Treasury Inflation-Protected Securities, real bonds UIP Uncovered Interest Parity (hypothesis) VaR Value at Risk VC Venture Capital VIX A popular measure of the implied volatility of S&P 500 index options VMG Value Minus Growth, equity value premium proxy WDRA Wealth-Dependent Risk Aversion X Cash flow Y Yield YC Yield Curve (steepness), term spread YTM Yield To Maturity YTW Yield To Worst Disclaimer Antti Ilmanen is a Senior Portfolio Manager at Brevan Howard, one of Europe’s largest hedge fund managers.

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Principal–agent problems shorten horizons from both sides, a phenomenon that can make the long-horizon investor lose his natural edge. Market turmoil in 1998 and 2007–2008 taught us additional features that should discourage arbitrage activities—VaR-based risk management and crowded trade risk:• Risk management systems that make sense for any one investor can increase systemic risk. A vicious circle can arise when rising risks (in VaR models or in other reactive risk measures) trigger mandatory or voluntary position reductions (but the problem is much worse if mandatory); widespread liquidations can destabilize the markets and require further reductions. Procyclical regulatory capital requirements have a similar impact. • If many leveraged arbitrageurs have similar positions, the desire of some of them to liquidate positions can cause a rush to the exit that makes even fundamentally unrelated positions move temporarily in lockstep—against the arbitrageurs.

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In an ideal world of zero-autocorrelated returns and no trading costs, very frequent rebalancing makes sense because it reduces both tracking error and (typically negative) covariance drag. However, the presence of trading costs and, possibly, short-term return momentum make longer rebalancing intervals more attractive. A close cousin: Volatility targeting Instead of targeting certain nominal weights, leveraged investors often target some overall volatility level and certain relative volatility (or VaR contribution) weights for strategies or asset classes. Indeed, return volatility is a more natural measurement unit (than dollar allocation) for strategies or assets whose unlevered standalone volatilities differ hugely. HFs use various ways of scaling or targeting volatility to improve their portfolios. When trading a long–short position, pairwise volatility scaling (weighting long and short legs by their empirical volatilities or betas) reduces and (if risk estimates are accurate) potentially eliminates the position’s market directionality.

**
Planet Ponzi
** by
Mitch Feierstein

Amazon: amazon.com — amazon.co.uk — amazon.de — amazon.fr

Affordable Care Act / Obamacare, Albert Einstein, Asian financial crisis, asset-backed security, bank run, banking crisis, barriers to entry, Bernie Madoff, centre right, collapse of Lehman Brothers, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, disintermediation, diversification, Donald Trump, energy security, eurozone crisis, financial innovation, financial intermediation, Flash crash, floating exchange rates, frictionless, frictionless market, high net worth, High speed trading, illegal immigration, income inequality, interest rate swap, invention of agriculture, Long Term Capital Management, moral hazard, mortgage debt, Northern Rock, obamacare, offshore financial centre, oil shock, pensions crisis, Plutocrats, plutocrats, Ponzi scheme, price anchoring, price stability, purchasing power parity, quantitative easing, risk tolerance, Robert Shiller, Robert Shiller, Ronald Reagan, too big to fail, trickle-down economics, value at risk, yield curve

And there’s only one way to avoid it: only play with stuff that you really, truly understand. And stick close to actual market pricing, because only then do you stay close to reality. Long tail risk There’s a variant on risk quantification which carries its own separate hazards. Back in the 1990s, JP Morgan—then and now, one of the best-run banks on the market—invented a risk management technology which measured ‘value at risk’ or VAR. That is, it could tell you how much money you would stand to lose on your entire portfolio if interest rates rose a little, or if the yen fell a little, and so on. The technology was a terrific innovation, and became widespread across the market. But it had a limitation. It could only predict likely losses under likely scenarios. It was a way of measuring the losses you’d be exposed to 95 times out of 100, perhaps even 99 times out of 100.

…

Of course, that’s information any decently managed financial institution needs—an essential part of the information that enables it to manage its ordinary risks as accurately as possible. Ninety-nine times out of a hundred, when you come into work, you won’t find a tornado flying around your dealing room. But ordinary risks are not the risks which are going to bury your firm—and the whole of Western capitalism—under a mountain of excessive debts and lousy assets. VAR technology was so dangerous because the technology was so good—95% of the time. As it happened, JP Morgan was never suckered by its own creation. The firm remembered what it could do and what it could not do. Management wanted to build a ‘fortress balance sheet’ that would withstand the 1 in 10,000 chance, as well as the 95 in 100 one. So they did. When the first credit crisis hit, JP Morgan shipped some water, but not much.

**
Too big to fail: the inside story of how Wall Street and Washington fought to save the financial system from crisis--and themselves
** by
Andrew Ross Sorkin

Amazon: amazon.com — amazon.co.uk — amazon.de — amazon.fr

affirmative action, Asian financial crisis, Berlin Wall, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, Fall of the Berlin Wall, fear of failure, fixed income, Goldman Sachs: Vampire Squid, housing crisis, indoor plumbing, invisible hand, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, Mikhail Gorbachev, moral hazard, NetJets, Northern Rock, oil shock, paper trading, risk tolerance, rolodex, Ronald Reagan, savings glut, shareholder value, short selling, sovereign wealth fund, supply-chain management, too big to fail, value at risk, éminence grise

For Goldman, even as a bank holding company, it was back to business as usual. The real question about Goldman’s success, which could be asked about other firms as well, is this: How should regulators respond to continued risk taking—which generates enormous profits—when the government and taxpayers provide an implicit, if not explicit, guarantee of its business? Indeed, in Goldman’s second quarter of 2009, its VaR, or value-at-risk, on any given day had risen to an all-time high of $245 million. (A year earlier that figure had been $184 million.) Goldman’s trades have so far paid off, but what if it had bet the wrong way? For better or worse, Goldman, like so many of the nation’s largest financial institutions, remains too big to fail. 339 Could the financial crisis have been avoided? That is the $1.1 trillion question —the price tag of the bailout thus far.

**
MacroWikinomics: Rebooting Business and the World
** by
Don Tapscott,
Anthony D. Williams

Amazon: amazon.com — amazon.co.uk — amazon.de — amazon.fr

accounting loophole / creative accounting, airport security, Andrew Keen, augmented reality, Ayatollah Khomeini, barriers to entry, bioinformatics, Bretton Woods, business climate, business process, car-free, carbon footprint, citizen journalism, Clayton Christensen, clean water, Climategate, Climatic Research Unit, cloud computing, collaborative editing, collapse of Lehman Brothers, collateralized debt obligation, colonial rule, corporate governance, corporate social responsibility, crowdsourcing, death of newspapers, demographic transition, distributed generation, don't be evil, en.wikipedia.org, energy security, energy transition, Exxon Valdez, failed state, fault tolerance, financial innovation, Galaxy Zoo, game design, global village, Google Earth, Hans Rosling, hive mind, Home mortgage interest deduction, interchangeable parts, Internet of things, invention of movable type, Isaac Newton, James Watt: steam engine, Jaron Lanier, jimmy wales, Joseph Schumpeter, Julian Assange, Kevin Kelly, knowledge economy, knowledge worker, Marshall McLuhan, medical bankruptcy, megacity, mortgage tax deduction, Netflix Prize, new economy, Nicholas Carr, oil shock, online collectivism, open borders, open economy, pattern recognition, peer-to-peer lending, personalized medicine, Ray Kurzweil, RFID, ride hailing / ride sharing, Ronald Reagan, scientific mainstream, shareholder value, Silicon Valley, Skype, smart grid, smart meter, social graph, social web, software patent, Steve Jobs, text mining, the scientific method, The Wisdom of Crowds, transaction costs, transfer pricing, University of East Anglia, urban sprawl, value at risk, WikiLeaks, X Prize, young professional, Zipcar

Can investors and others ever again believe the stated profits or losses of any financial institution, its purported capital base and financial soundness, when these numbers are based on secret and opaque models that are derived from mathematics so complex that even the company’s executive management does not understand them? Going forward, the mathematics behind the value and risk calculations for new financial instruments should be open and vetted by a crowd of experts, applying the wisdom of many to the problem. They should know, for example, whether the VaR (Value at Risk) analysis is based on information from only a couple of years, which would not cover the consequences of a once-in-a-generation event. The underlying data and the algorithms for complex derivatives such as collateralized debt obligations should be placed on the Internet, where investors could “fly over” and “drill down” into an instrument’s underlying assets. With full data, they could readily graph the payment history and correlate information such as employment histories, recent appreciations (or depreciations), location, neighborhood pricings, delinquency patterns, and recent neighborhood offer and sales activities.