# value at risk

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Risk Management in Trading by Davis Edwards

However, it is much harder to accurately guess the size of an extremely rare move. Rare moves are not well described by typical behavior because they have different root causes than normal price moves. WHAT IS VALUE-AT-RISK? Value‐at‐risk uses a factor common to all financial instruments (daily changes in value caused by mark‐to‐market accounting) to establish an apples‐to‐ apples comparison of size across a wide variety of instruments. It is typically pronounced “var” and rhymes with “car.” In some cases, it is abbreviated VaR or V@R to distinguish it from the mathematical abbreviation for variance, which is commonly abbreviated var. 144 RISK MANAGEMENT IN TRADING KEY CONCEPT: VALUE AT RISK (VAR) IS DEFINED MATHEMATICALLY Value‐at‐risk is typically defined as the maximum expected loss on a financial instrument, or a portfolio of financial instruments, over a given period of time and a given level of confidence.

(See Equation 6.3, Converting Volatility between Timeframes.) 150 RISK MANAGEMENT IN TRADING Timeframe Formula Weekly (5 trading days) Weekly Volatility = 5 Daily Volatility Monthly (21 trading days) Weekly Volatility = 21 Daily Volatility Annual (252 trading days) Annual Volatility = 252 Daily Volatility Monthly from Annual (12 months a year) Monthly Volatility = Weekly from Annual (52 weeks a year) Weekly Volatility = Annual Volatility (6.3) 12 Annual Volatility 52 PARAMETRIC VAR There are two main types of VAR, parametric VAR and non‐parametric VAR. The difference between the two is that parametric VAR assumes that returns will be normally distributed in the future. This substantially simplifies the math involved in combining positions into large portfolios and in converting between types of VAR. Non‐Parametric VAR allows more realistic assumptions but is typically more complicated and involves large‐scale computer simulation. Because it is simpler to use, and the limitations of parametric VAR are relatively unimportant for the purpose of setting position limits and calculating capital requirements, parametric VAR is the more common form of value‐at‐risk calculation. Common assumptions associated with parametric VAR are that returns are independent, identically distributed (have the same volatility each day), and normally distributed.

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

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?

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 .

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.

Analysis of Financial Time Series by Ruey S. Tsay

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.

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).

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

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.

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.

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

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.

Trading Risk: Enhanced Profitability Through Risk Control by Kenneth L. Grant

As is the case elsewhere, this limitation contains a hidden opportunity: I believe it is useful to compare correlations between securities across different time spans so as to gain a better The Risk Components of an Individual Portfolio 91 understanding of interactive pricing dynamics across the fullest range of available market conditions. VALUE AT RISK (VaR) Through the efforts of modern-day financial engineers, a new paradigm has emerged: It is now possible, nay, even fashionable, to combine the concepts of volatility and correlation into a single, portfolio-based exposure estimate. This work, most of which has been conducted over the past 15 or so years, is most broadly synthesized under the heading of Value at Risk, which is now thought of as the standard methodology for risk management in the financial services industry. The underlying objective is to aggregate all risks in a given portfolio in such a way as to produce a volatility statistic at the portfolio level boiled down to a single number that will characterize overall portfolio exposure.

So, whatever statistic you are currently employing as your benchmark exposure measurement, it must be mapped back into standard deviation units in order to produce meaningful outcomes. Perhaps the best alternative at your disposal in this regard is the results of a Value at Risk (VaR) calculation, which have the advantage of being based on current portfolio characteristics. If you have access to a VaR calculation, it is therefore possible to substitute this figure into the denominator of the Sharpe Ratio, as long as you take care to scale down the confidence interval statistic to the one standard deviation level (for example, if you are using a 95th percentile VaR, you can map it back into a one standard deviation figure by dividing by 1.96). If you choose not to use a VaR approach, the best alternative is simply to calculate a one standard deviation P/L volatility. Returning to our example, let us first assume that by our best estimate the portfolio is managed such that its projected, annualized volatility is 7%.

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

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.

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.

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

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.

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).

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

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.)

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.

Glossary of Symbols A B β c C C CA CE CE 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 PE 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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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

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.

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.

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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Optimization Methods in Finance by Gerard Cornuejols, Reha Tutuncu

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.

, 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.”

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

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.

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

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.

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.

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.

Monte Carlo Simulation and Finance by Don L. McLeish

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 ?

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.

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

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.

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 − .

(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.

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Python for Finance by Yuxing Yan

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.

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

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.

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Market Risk Analysis, Quantitative Methods in Finance by Carol Alexander

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.

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.

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

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.

., 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.

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.

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

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.

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.

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.

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All the Devils Are Here by Bethany McLean

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.

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.

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.

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Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures by Frank J. Fabozzi

Recall that the 99% VaR of the loss distribution, for instance, is the loss value such that, with a 1% chance, the financial asset will have a loss bigger than 99% VaR over the given period. The VaR risk measure provides us with only a threshold. What loss could we expect if the 99% VaR level is broken? To answer this question, we must compute the expectation of losses conditional on the 99% VaR being exceeded:E[-Rt |-Rt > 99% VaR] where Rt denotes the return on a financial asset at time t and -Rt—the loss at time t. In the general case of VaR(1-α)100%, the conditional expectation above takes the formE[-Rt | -Rt > VaR(1-α)100%] and is known as the (1 - α)100% expected tail loss (ETL) or conditional value-at-risk (CVaR) if the return Rt has density. CONCEPTS EXPLAINED IN THIS CHAPTER (IN ORDER OF PRESENTATION) Conditional probabilities unconditional probabilities Marginal probabilities Independent events Dependent events Joint probability Multiplicative Rule of Probability Law of Total Probability Bayes’ rule Conditional parameters Conditional expectations Conditional variance Expected tail loss Conditional value-at-risk CHAPTER 16 Copula and Dependence Measures In previous chapters of this book, we introduced multivariate distributions that had distribution functions that could be presented as functions of their parameters and the values x of the state space; in other words, they could be given in closed form.175 In particular, we learned about the multivariate normal and multivariate t-distributions.

At q0.2 = 2, this area is exactly equal to 0.2. Value-at-Risk Let’s look at how quantiles are related to an important risk measure used by financial institutions called value-at-risk (VaR). Consider a portfolio consisting of financial assets. Suppose the return of this portfolio is given by rP. Denoting today’s portfolio value by P0, the value of the portfolio tomorrow is assumed to followFIGURE 13.2 Determining the 0.2-Quantile using the Cumulative Distribution Function P1 = P0 ⋅ e rP As is the case for quantiles, in general, VaR is associated with some level α Then, VaRα states that with probability 1 - α, the portfolio manager incurs a loss of VaRα or more. FIGURE 13.3 Determining the 0.2-Quantile of the Standard Normal Distribution with the Probability Density Function Computing the VaR of Various Distributions Let us set α = 0.99.

That is, for X defined on the probability space (Ω, A, P), the conditional variance is a random variable measurable with respect to the sub-σ-algebra, G, and denoted as var[X|G] such that its variance on each set of G is equal to the variance of X on the same set. For example, with the question “During recessionary periods, what is the variability in the number of corporate loans that default?,” we are looking to computevar[Number of default corporate loans | State of the economy = Recession] using the definition of variance from Chapter 13, we could equivalently express var[X|G] in terms of conditional expectations,var[X|G] = E[X2|G] + E[X|G]2 Expected Tail Loss In Chapter 13, we explained that the value-at-risk (VaR) is one risk measure employed in financial risk measurement and management. VaR is a feature of the unconditional distribution of financial losses (negative returns). Recall that the 99% VaR of the loss distribution, for instance, is the loss value such that, with a 1% chance, the financial asset will have a loss bigger than 99% VaR over the given period.

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

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.

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.

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).

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Market Sense and Nonsense by Jack D. Schwager

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.

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.

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?

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Frequently Asked Questions in Quantitative Finance by Paul Wilmott

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.

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.

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

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.

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.

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.

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

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.

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.

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

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).

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.

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

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.

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.

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.

The Trade Lifecycle: Behind the Scenes of the Trading Process (The Wiley Finance Series) by Robert P. Baker

The purpose of scenario analysis is to measure the risk caused by something unusual but not impossible occurring and to factor in some correlation between different types of market risk (as opposed to sensitivity analysis which perturbs each set of market data independently). Value at Risk (VaR) VaR is another risk measure. It attempts to state the maximum loss that will occur within a period of time. Since the maximum loss is in effect unlimited, the VaR puts a probability on the maximum loss occurring. For example, there is a 95% probability that the maximum one-day loss will be 12 million euros. In other words, 19 times out of 20 the loss will not exceed 12 million euros. The converse is that once every 20 times (about once a month) the loss will be more. It may not be very comforting to the board of a firm to know that VaR is likely to be exceeded once a month, but it is an industry standard measure and helps to make comparisons with other organisations to compare their risk exposures. Market Risk Control 137 Usually VaR is computed over an aggregation of trades in one division or from the whole organisation.

Once a calculation engine has been built and tested, it is easy to apply any set of market data and get results. This lends itself to scenario analysis which, in essence, is a process of generating the market data you want to use, valuing with that market data and comparing the results. Some typical scenarios: Bump all market data up by 5%. Set all market data to be at its lowest value for the past month. Set volatility of spot prices to 15%. Assume all credit recovery rates fall to 5%. Value at Risk (VaR) VaR is a type of worst-case valuation – over the next day (week, month, …) with an unchanged portfolio asking how bad could the valuation get? Typically this is done on a portfolio basis and requires, in addition to a valuation model, a model of the variability (volatility) of the driving variables (interest and exchange rates, equity prices, etc.) and their relationship (correlation). (See Chapter 11.)

Greater disclosure by banks of how risk-weighted exposures are calculated and used. The overall effect should be to reduce benefits of internal models and increase banks’ costs. Also, by increasing the capital required, banks will be driven to reassess pricing and whether it is worth continuing to offer certain products. In October 2013, the Basel Committee published a paper proposing: a move from the standard Value at Risk (VaR) calculation to that of Expected Shortfall. This will increase capital charges simpler boundary between the trading and banking book extending time horizons for liquidation of exposures in stressed market conditions a tougher approach to allowing benefits of hedging. 206 THE TRADE LIFECYCLE Effect of regulation in practice Naturally the actual business of trading is impacted by the weight of regulation.

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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

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.

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.

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

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.

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.

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).

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

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.

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.

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The Greed Merchants: How the Investment Banks Exploited the System by Philip Augar

Computers make all this possible; no longer is risk assessed with a series of phone calls and a quick tally on a scratch pad.’11 At the same time as risk management procedures became more structured, value-at-risk (VAR) was adopted as the industry’s risk modelling tool. VAR is based on a paper called ‘Portfolio Selection’ published in the Journal of Finance in 1952 by Professor Harry Markowitz, which explored how investors could construct portfolios in order to optimize expected returns for a given level of risk. These techniques were taken up by asset managers, but it was not until 1993, when the Group of Thirty coined the term value-at-risk in a report on risk management for derivatives dealers, that they spread to investment banks. Then in 1994, the year the bond market crash pushed risk further up management’s agenda, J. P. Morgan launched its free RiskMetrics service, which further promoted the use of VAR. The following year the Basle Committee on Banking Supervision based its market risk capital requirements for banks on VAR and over the next year or two VAR became the industry standard for risk management in financial institutions, corporate treasuries, commodities firms and energy traders.12 As we saw in the previous chapter, VAR is a statistical technique to measure market risk.

Rothschild 31–2 narcissism, organizational 198 NASDAQ index 12, 13 National Association of Securities Dealers (NASD) 185, 188, 201 National City Bank 6–7 Neuer Markt 73–4 New York Stock Exchange 187–8, 201, 205 Office of Federal Home Loan Oversight 80 Office of Risk Assessment 205 O’Kelly, Gene 200–201 oligopoly 102 O’Neal, Stanley 23, 61, 135–6 Ong, Belita 11–12 options, definition of 77 output of investment banks, evaluation of 63–5, 85, 100 over-the-counter derivatives 77–8, 81, 89 Paine Webber 45 Parmalat 84, 161 Partnoy, Frank 41, 181–2, 209 Paulson, Henry 197, 206 Pecora, Judge Ferdinand 85 Perella, Joseph 43 perfect competition 102 Pitt, Harvey 187 Plender, John 208 PNC Financial 81–2 political connections 181–4, 209 prices 86–7, 97–8, 100–101, 172 advisory work 90–91, 94–5, 96–7 basis point pricing 91–3 collusion 93–8, 100–103 derivatives 88–9 and fund managers 192 negotiation, lack of 176–8, 179 under oligopoly 102 pre-announcement movements, shares 122 share trading 87–8, 89 strategic pricing 94–5, 98 underwriting 89–90, 92, 94–6 prime brokerage 133 private equity 132 privatization, UK 181 product development 131–4 product range 33 profits 51–2, 61–2 and compensation 60, 99–100 diverting attention from 95 falling, implications of 209–10 identification of 192–3 outlook for 209–10 return on equity (ROE) 54–7, 58 source of 166–7 programme trades 87, 88 proprietary trading 114–19, 192, 206, 211–12 prospect theory 180 Prudential-Bache Securities 11 Prudential plc 82 Public Company Accounting Oversight Board 200 Purcell, Philip 14, 22, 23–4, 39, 138, 205–6 Quattrone, Frank 19–20, 137–8, 151 Qwest 82 Racketeer-Influenced Corrupt Organizations law (RICO) 10, 26 recession, post-2001 13–14 Reed, John 189 regulation 7–8, 20, 81, 183, 185–90, 199 and bundling 193 integrated structure, failure to reform 22, 23, 24 and lobbying 209 recent 19, 200–203, 205, 209–10 regulatory arbitrage 185 relationship banking, demise of 35–6, 152–3, 170 research 66–7, 68, 69, 140–41, 145, 146 independent 69, 201–2, 204 internal position of 196 see also analysts Restoring Trust: Investment in the Twenty-First Century 194 returns 49–51, 61–2, 99–100, 165–6 and analysts’ recommendations 67 compensation 58–60, 99–100, 165–6 and cost of equity capital 57–8 excess, source of 166–7 falling, implications of 209–10 margins 52–3, 88–9, 119 outlook for 209–10 profits 51–2 return on equity (ROE) 54–7, 58, 61 risk management 111–13, 125–31 risk premium 55, 56 Ritter, Professor Jay 71, 89–90, 94–5, 179 Rogers, John 68 Roosevelt, President Franklin D. 7 Roye, Paul 191 Rubin, Robert 42, 182–3 salaries see compensation Salomon Brothers 11, 34, 37, 41–2, 137, 148–9 cynicism, culture of 152, 153 losses, 1994 128 and WorldCom 121 Salomon Smith Barney 17, 41, 150–51, 195 Sanford Bernstein 32 Sants, Hector 170–71, 189 Sarbanes-Oxley Act (2002) 19, 200–201, 209 Sassoon, James 184 Saunders, Ernest 11 scandals see corruption/malpractice Schapiro, Mary 188 Schroders 42 Securities and Exchange Commission (SEC) 7, 19, 21, 23, 185–7, 205 Securities Industry Association 183 securitization 78 securitized bonds 46 settlements paid by investment banks 19, 20, 23, 24, 38, 39, 42, 43, 201, 207 share prices, pre-announcement movements 122 shareholder activism 203–4 shareholder value 8–9, 63, 169 shareholders, and corporate control 163–4, 203–4 Sherman Anti-Trust Act (1890) 5–6, 8 Smith, Adam 86, 171–2 Smith, David 171 Smith, Professor Roy 195 Smith Barney 40, 41 Southern Peru Copper Corp 91 special purpose entities/vehicles (SPEs/SPVs) 78, 82, 83 ‘specialists’ 115–16 ‘spinning’ 17–18, 43, 137, 160 Spitzer, Eliot 15, 65–6 inquiry headed by 15, 16–17, 21, 22, 24, 38, 200 whispering campaign against 23 status of investment banking 4–5, 12, 18 Stevenson, Lord 175 Stiglitz, Joseph 12, 64, 176, 182–3 stock exchanges, structural reform 212 stock markets bull market mentality 3–5, 12–13, 64, 65, 71–3 performance of 63–4 public interest in 12 stock options 176 new accounting rules 201, 209 Stonehill, Charles 147–8 structural reform 211–15 Sudarsanam, Professor Sudi 76 Summers, Lawrence 63 swaps 77, 132 Sykes, Sir Richard 210 taxation, 401K amendment 9 team ethos 124–5 Thain, John 188, 209 Time Warner 13, 14, 76–7 Tomlinson, Lindsay 194 transaction banking 152–3, 170 transaction costs 67 Travelers 41 treasurers (company), and derivatives 80 Treasury bond scandal 41–2 ‘Triple Play’ 121 Truman, President Harry S. 7 trustees, mutual/pension funds 191–2 UBS 31, 32, 37 underwriting fees 89–90, 92, 94–6 value-at-risk (VAR) 117, 129–31 volatility of markets, and performance of investment banks 24–5, 51–2, 57–8 Wall Street 9 Wall Street Crash 6–7 Walter, Professor Ingo 195 Wasserman, Ed 18 Wasserstein, Bruce 31, 43, 77 Weill, Sanford 195 Welch, Jack 45 Wertheim 147 Wheat, Allen 59, 137 WorldCom 17, 121, 150–51, 161 Zumwinkel, Klaus 178–9

The investment banks disclose value-at-risk data, which gives some clue as to the scale of activities; but everyone’s model is slightly different and it is not possible to estimate what profits the stated value-at-risk might generate. The average daily value-at-risk of the large investment banks varied in 2003 from, for example, \$15m at Bear Stearns to \$58m at Goldman Sachs. As Goldman Sachs said, ‘This means that there is a 1 in 20 chance that daily trading net revenues will fall below the expected daily trading net revenue by an amount at least as large as the reported value-at-risk.’21 Even with annual trading revenues of over \$10 billion, this is a far from negligible risk but there is some protection from shareholders’ equity, which is several hundred times value-at-risk – and of course from the Edge, which substantially reduces the real risk.

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

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.

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Model Thinker: What You Need to Know to Make Data Work for You by Scott E. Page

While the Polya process reveals the core idea that interactions produce path dependence, we need more realistic models for that insight to guide action. Value at Risk and Volatility We can interpret the standard deviation in a time series of data as volatility. Investments in stocks, real estate, and privately held businesses all exhibit volatility. Value at risk (VaR) measures the probability of a loss of a given amount during a specific time period. An investment with a one-year 5% VaR of \$10,000 has a 5% probability of losing more than \$10,000 at the end of one year.10 Banks use VaR calculations to determine the amount of assets that must be kept on hand to avoid bankruptcy. For example, to secure an investment with a two-week 40% VaR of \$100,000, an investor may be asked to hold \$100,000 in cash. If an investment follows a simple random walk with an increase or decrease of size M each period, then it has an N period 2.5% VaR of .11 Thus, an investment that randomly goes up or down \$1,000 each day has a nine-day 2.5% VaR of \$6,000, and a one-year 2.5% VaR of \$38,000.

total value, 108 Tractatus Logico-Philosophicus (Wittgenstein), 6 training sets, 87 transition probabilities, 190, 191, 351 transition rule, 182 transition-to-addiction model, 341 transitivity, in rational-actor model, 49 TROLL, 260 Troubled Asset Relief Program (TARP), 21–22 truth-telling, 285 TurboTax, 76 Tversky, Amos, 51–52 two-dimensional median, 233 typhoid, 140 uncertainty, 144 unconditional generosity, 303 uniform distribution, 149, 150 uniqueness, rational choice and, 50 United States Air Force, 10–11 utility functions, 48–49 vaccination threshold, 138 valence attributes, in hedonic competition model, 237 valuation error, defining, 35 value, 332 last-on-the-bus, 108, 115 many-model thinking for, 241–242 of signals, 301–302 value at risk (VaR), 170 value function, 108 VaR. See value at risk variables dependent, 84 independent, 84 multiple-variable regression, 88–89 multivariable linear models, 87–90 omitted, 84–85 variance in normal distribution, 60–61 percentage of, 34 veto players, 234–236 Vinlanders, 270 volatility long-tailed distributions and, 77–78 VaR and, 170 voluntary participation, 285 von Neumann, John, 95 Voronoi neighborhoods, 231 spatial competition model with, 231 (fig.) Wainer, Howard, 63 Walmart, 78 Waltz, Kenneth, 313 Warbler males, 260 wasteful subsistence behavior, 303 weak ties, 125 weak types, 299, 301 weights, 307 in hedonic competition model, 237 West, Geoffrey, 69 Wilhelm, Kaiser, 167 William III (King), 211 Williams, Serena, 319 wisdom hierarchy, 8–12 data in, 7 information in, 7 wisdom of crowds, 30 Wittgenstein, Ludwig, 6 Wolfram’s classes, 147, 148 (fig.)

If an investment follows a simple random walk with an increase or decrease of size M each period, then it has an N period 2.5% VaR of .11 Thus, an investment that randomly goes up or down \$1,000 each day has a nine-day 2.5% VaR of \$6,000, and a one-year 2.5% VaR of \$38,000. Notice that VaR increases linearly in the size of the steps but that it increases like the square root of the number of periods. We can use the formula for VAR to explain why the FDIC only requires that banks hold around 2% of their assets in cash overnight, but banks require that consumers put down 20% deposits on houses. The duration on the overnight loans is one day. Home loans can last for over a decade. The square root of three thousand and sixty-five days is approximately sixty. Here, we have assumed a normal random walk. Analysts calculating VaR often consider the past empirical distribution of returns. If the empirical distribution has a longer tail, that is, if it includes more large events, then VAR would increase as large events are more likely.

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The Road to Ruin: The Global Elites' Secret Plan for the Next Financial Crisis by James Rickards

The prevailing theory is called value at risk, or VaR. This theory assumes that risk in long and short positions is netted, the degree distribution of price movements is normal, extreme events are exceedingly rare, and derivatives can be properly priced using a “risk-free” rate. In fact, when AIG was on the brink of default in 2008, no counterparty cared about its net position; AIG was about to default on the gross position to each counterparty. Data show that the time series of price moves is distributed along a power curve, not a normal curve. Extreme events are not rare at all; they happen every seven years or so. And the United States, issuer of benchmark “risk-free” bonds, recently suffered a credit downgrade that implied at least a small risk of default. In brief, all four of the assumptions behind VaR are false.

The next day, the Dow Jones Industrial Average fell 777 points, an 8 percent plunge, the largest one-day point drop ever. Two days later, on October 2, The Washington Post published my op-ed “A Mountain, Overlooked: How Risk Models Failed Wall St. and Washington.” This was my first public effort to use complexity theory to explain the ongoing financial collapse. In the op-ed I wrote: Since the 1990s, risk management on Wall Street has been dominated by a model called “value at risk” (VaR). VaR attributes risk factors to every security and aggregates these factors across an entire portfolio, identifying those risks that cancel out. What’s left is “net” risk that is then considered in light of historical patterns. The model predicts with 99 percent probability that institutions cannot lose more than a certain amount of money. Institutions compare this “worst case” with their actual capital and, if the amount of capital is greater, sleep soundly at night.

Both swap trades are off-balance-sheet, invisible to outsiders. The market risk in Goldman’s position boils down to the spread between the fixed rate Goldman pays and the fixed rate it receives. The spread between two-year notes and five-year notes is historically low. As a result, Goldman is required to hold very little capital against this risk. Wall Street banks use a formula called value at risk, or VaR, mentioned earlier, which implies Goldman has almost no risk. Under accounting and regulatory rules applied to swaps, the notes disappear, the accounting disappears, and almost all market risk disappears. It’s all good. Yet it’s not all good. In the real world, when Citibank and Bank of America do these trades with Goldman, they turn around and do trades in the opposite direction to hedge the risk to Goldman.

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Austerity: The History of a Dangerous Idea by Mark Blyth

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.

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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

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.

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

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.

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

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.

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

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.

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

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.

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Hedge Fund Market Wizards by Jack D. Schwager

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.

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.

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

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.

Money and Government: The Past and Future of Economics by Robert Skidelsky

In this way, mark-to-market accounting increases volatility by artificially enlarging and contracting balance sheets. But its doompotential was blithely ignored. Value at risk modelling was used by banks to assess the amount of risk they faced on their portfolios. A VaR measure takes a given portfolio, a time horizon and a probability level p, and spits out a threshold value of loss for that portfolio, representing a ‘realistic’ worst-case scenario. For example, if your portfolio has a one-day 1 per cent VaR of \$1 million, this means that 99 per cent of the time your portfolio will not fall in value by more than \$1 million over a one-day period. VaR measures were popular, as they condensed lots of risk modelling into a single, easily comprehensible figure. VaR modelling is deeply flawed. It overlooks the worst risks by ignoring scenarios that are less likely to happen than some arbitrary threshold, lulling bankers (and regulators) into a false sense of security.

Hyman Minsky, an economist whose work was completely ignored until after the crash, argued that financial stability leads inevitably to financial fragility, as optimism turns to ‘speculative euphoria’ and markets become ‘dominated by speculation about sentiments and movements in the market rather than about fundamental asset values’.18 But these arguments had no place in the neo-classical hegemony and so, despite its glaring theoretical gaps, the EMH became the intellectual underpinning of financial market deregulation. 313 M ac roe c onom ic s i n t h e C r a s h a n d A f t e r , 2 0 0 7 – ‘Mark-to-market (M2M) and value at risk (VaR) frameworks offer accurate measures of value and thus are appropriate ways of managing risk’ Mark-to-market accounting aims to estimate the ‘fair value’ of an asset by reference to its current market price, rather than what it cost the investor to buy. If an investor owns ten shares of a stock bought for \$4 a share and that stock now trades at \$6, its mark-to-market value is 50 per cent more than its book value.

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

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.

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The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot, Richard L. Hudson

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.

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Making It Happen: Fred Goodwin, RBS and the Men Who Blew Up the British Economy by Iain Martin

Increasingly complex risk management systems were evolved in banks to monitor the extent of the exposure and flag warnings, particularly in trading. A lot rested on the adoption of something called VaR, Value at Risk, which teams of risk managers and risk committees inside the banks used to assess, according to various formulae, how much a bank might lose on a particular asset in an emergency.7 It was supposed to be an early warning system. It had been developed by a team at J. P. Morgan in the early 1990s and computer-assisted modelling was integral to the process. VaR was pivotal to the expansion of banks, and what was to follow, because it created a sense of reassurance and confidence. The teams of risk professionals that managed the process checked that the traders were acting within the VaR guidelines set for the bank, and if they were then all was probably fine. Risk was being measured, modelled, every day, constantly.

The bigger question of liquidity – was it certain that a bank with such a large balance sheet could safely lay its hands on enough money – was not regarded by the FSA as a central concern. It was referred to at points in speeches by officials and reports, but never pounced on as a potentially fatal weakness. Anyway, there was no expectation that there would suddenly be a shortage of money. Supposedly the Value at Risk (VaR) system also meant that the banks had clearer sight than ever before of what was at risk as their balance sheets expanded. At Tiner’s management meetings participants remember almost no discussion about the safety of the banks, for good reason: it was hardly mentioned. ‘Prudential’ matters were a low priority barely touched on there or at the board. Between January 2006 and July 2007, only one topic out of sixty-one discussed at the FSA board dealt with the risks that banks were taking.

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Radical Uncertainty: Decision-Making for an Unknowable Future by Mervyn King, John Kay

Perhaps the personal flying platforms for which we have waited so long will be available to them, or perhaps our descendants will have reverted to the horse and cart after abandoning the use of fossil fuels. We simply do not know. WebTAG, however, expects that everyone will still be travelling in the same way as now; only their numbers and the value of their time will have changed. Value at risk Value at risk models (VaR), used for risk management in banks, were the technique which lay behind Mr Viniar’s claim to have observed a ‘25 standard deviation’ event. These models were based on the portfolio theory pioneered by Markowitz and were developed at J. P. Morgan in the late 1980s to help the bank cope with the variety of debt instruments which had appeared in that decade. As in the Markowitz model, the starting point is the variance of daily returns on each security and the covariance of returns between securities.

pages: 225 words: 11,355

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

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.

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.

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More Than You Know: Finding Financial Wisdom in Unconventional Places (Updated and Expanded) by Michael J. Mauboussin

The good news is that these assumptions are reasonable for the most part. The bad news, as physicist Phil Anderson notes above, is that the tails of the distribution often control the world. Tell Tail Normal distributions are the bedrock of finance, including the random walk, capital asset pricing, value-at-risk (VaR), and Black-Scholes models. Value-at-risk 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.2 The research, some done as far back as the early 1960s, shows that price changes do not follow a normal distribution.

theory: attribute-based approach; building, steps of; falsifiability Thorp, Ed time horizons timing rules tipping point total return to shareholders (TRS) tracking error transaction costs traveling-salesman problem Treynor, Jack Tupperware parties Tversky, Amos Twain, Mark two-by-two matrix Ulysses uncertainty classifications expectations and U.S. Steel utility Utterback, James valuation, investor evolution and value-at-risk (VaR) models value investors value traps, downturns volatility “Vox Populi” (Galton) Waldrop, Mitchell Watts, Duncan weak signals wealth, isolated components vs. total Welch, Ivo Welch, Jack Wermers, Russ wheel of fortune experiment Why Stock Markets Crash (Sornette) Wiggins, Robert R. wild-hair alternative Wilson, Edward O., v winner’s curse Winters, Sidney Wisdom of the Hive, The (Seeley) Wolfram, Stephen Wolpert, Lewis Woods, Tiger Wright, Orville Zajonc, Robert B.

Jackwerth and Rubinstein note that assuming annualized volatility of 20 percent for the market and a lognormal distribution, the 29 percent drop in the S&P 500 futures was a twenty-seven-standard-deviation event, with a probability of 10−160. 5 Per Bak, How Nature Works (New York: Springer-Verlag, 1996). 6 See chapter 22. 7 Sushil Bikhchandani and Sunil Sharma, “Herd Behavior in Financial Markets,” IMF Staff Papers 47, no. 3 (September 2001); see http://www.imf. org/External/Pubs/FT/staffp/2001/01/pdf/Bikhchan.pdf. 8 Michael S. Gibson, “Incorporating Event Risk into Value-at-Risk,” The Federal Reserve Board Finance and Economics Discussion Series, 2001-17 (February 2001); see http://www.federalreserve.gov/pubs/feds/2001/200117/200117abs.html. 32. Integrating the Outliers 1 Daniel Bernoulli, “Exposition of a New Theory on the Measurement of Risk,” Econometrica, 22 (January 1954): 23-36. Originally published in 1738. Daniel’s cousin, Nicolaus, initially proposed the game. 2 See The Stanford Encyclopedia of Philosophy, s.v.

Humble Pi: A Comedy of Maths Errors by Matt Parker

But the chain of mistakes featured some serious spreadsheet abuse, including the calculation of how big the risk was and how losses were being tracked. A Value at Risk (aka VaR) calculation gives traders a sense of how big the current risk is and limits what sorts of trades are allowed within the company’s risk policies. But when that risk is underestimated and the market takes a turn for the worse, a lot of money can be lost. Amazingly, one specific Value at Risk calculation was being done in a series of Excel spreadsheets with values having to be manually copied between them. I get the feeling it was a prototype model for working out the risk that was put into production without being converted over to a real system for doing mathematical modelling calculations. And enough errors accumulated in the spreadsheets to underestimate the VaR. An overestimation of risk would have meant that more money was kept safe than should have been, and because it was limiting trades it would have caused someone to investigate what was going on.

It will mess things up. That very code was used in 2008 to attack the UK government and the United Nations – except some of it had been converted into hexadecimal values to slip by security systems looking for incoming code. Once in the database, it would unzip back into computer code, find the database entries then phone home to download additional malicious programs. This is it when it was camouflaged: script.asp?var=random';DECLARE%20@S%20NVARCHAR(4000);SET%20@S=CAST(0x4400450043004C004100520045002000400054002000760061007200630068006100720028 … [another 1,920 digits] 004F00430041005400450020005400610062006C0065005F0043007500720073006F007200%20AS%20NVARCHAR(4000));EXEC(@S);-- Sneaky, huh? From unfortunate names to malicious attacks, running a database is difficult. And that’s even before you have to deal with any legitimate data-entry mistakes.

An overestimation of risk would have meant that more money was kept safe than should have been, and because it was limiting trades it would have caused someone to investigate what was going on. An underestimation of VaR silently let people keep risking more and more money. But surely these losses would be noticed by someone. The traders regularly gave their portfolio positions ‘marks’ to indicate how well or badly they were doing. As they would be biased to underplay anything that was going wrong, the Valuation Control Group (VCG) was there to keep an eye on the marks and compare them to the rest of the market. Except they did this with spreadsheets featuring some serious mathematical and methodological errors. It got so bad an employee started their own ghost spreadsheet to try and track the actual profits and losses. The JPMorgan Chase & Co.

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Paper Promises by Philip Coggan

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.

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

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.

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The Big Short: Inside the Doomsday Machine by Michael Lewis

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.

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

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?

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.

More overlooked were investments in assets that were liquid in good times but became very illiquid in periods of stress, including external managers who threw up gates, credit derivatives whereby whole tranches became toxic, and even crowded trades such as single stocks chosen according to well-known quantitative screens. As a result, when the liquidity crisis hit, it hit everywhere all at once, creating devastating effects. Finally, 2008 also exposed faults in the traditional methods of calculating risk. No matter how your plan went about calculating value at risk (VaR)—historical, parametric, Monte Carlo, or other—the statisticians claimed that the more data used to calculate the parameters (i.e., the further the look-back in time), the better. But 2008 showed that this is not necessarily correct, especially for the liquid portions of our investments. The result was that almost all real money funds got caught badly off-guard with the ferociousness and comprehensiveness of the market declines.

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

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!

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.

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

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.

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.

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The Quants by Scott Patterson

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.”

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.”

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Conspiracy of Fools: A True Story by Kurt Eichenwald

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.”

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

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

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.

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.

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

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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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

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.

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!

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.

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Big Debt Crises by Ray Dalio

Based on our calculations, we saw it differently and wrote: “the day of reckoning will be pushed forward, probably to when there is a big tightening by the Fed or a big turndown in the economy.” Why Banks and Investors Were So Exposed to Risky Mortgage Securities Why were investors, banks, rating agencies and policy makers misled into thinking mortgage securities were less risky than they actually were? A key reason is the way risk is analyzed. Consider the conventional way investors think about risk. At the time, Value at Risk (VAR), which is a measure of recent volatility in markets and portfolios, was commonly used by investment firms and commercial banks to determine the likely magnitude and occurrence of losses. It typically uses recent volatility as the main input to how much risk (i.e., what size positions) one could comfortably take. As a simplifying illustration, imagine an investor that never wants to lose more than 20 percent.

If anything, I believe that one should bet on the opposite of what happened lately, because boring years tend to sow the seeds of future instability, as well as making the next downturn worse. That’s because low volatility and benign VAR estimates encourage increased leverage. At the time, some leverage ratios were nearing 100:1. To me, leverage is a much better indicator of future volatility than VAR. In 2007, many banks and investors were heavily exposed to subprime mortgages, since the instruments had not yet had a loss cycle or experienced much volatility. VAR was also self-reinforcing on the down side, because increased market volatility at the peak of the crisis in 2008 made their statistical riskiness look even higher, causing even more selling. The Fall of 2007 With stocks on the rebound after the bumpy summer, policy makers started to consider how they should approach the problems emanating from the mortgage market over the longer term.

If the most that a subprime mortgage has ever lost in a month is 5 percent, then investors might plug that 5 percent number into a model that then says its “safe” for them to borrow until they own three times leveraged subprime. This way of thinking about risk caused many investors to increase their exposures beyond what would normally be seen as prudent. They looked at the recent volatility in their VAR calculations, and by and large expected it to continue moving forward. This is human nature and it was dumb because past volatility and past correlations aren’t reliable forecasts of future risks. But it was very profitable. In fact, when we were cutting back on our positions, our clients urged us to increase them because our VAR was low. We explained why we didn’t do that. Extrapolating current conditions forward and imagining that they will be just a slightly different version of today is to us bad relative to considering the true range of possibilities going forward.

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

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.

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.

–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.

Digital Accounting: The Effects of the Internet and Erp on Accounting by Ashutosh Deshmukh

Copying or distributing in print or electronic forms without written permission of Idea Group Inc. is prohibited. 302 Deshmukh • Supporting portfolio hierarchies • Handling portfolio audits Market risk analyzer manages risks associated with the stock market, foreign currency holdings and fluctuations in interest rates. Stock market positions such as mark-tomarket valuations can be evaluated using the built-in tools. Different calculations, such as risk and return, exposure, future values and value at risk, can be calculated using this analyzer. Accounting standards such as FAS 133 are supported. Simulation tools can be used to run valuation scenarios based on actual and simulated market prices. These tools can also be used to simulate changes in interest and currency exchange rates and run hypothetical valuation scenarios. Market risk analyzer also accesses payment information from the transaction manager, and calculates amount and due dates for payments in different currencies.

Accounting software that serves the mid-size market can provide a full financial suite and advanced industry-specific modules, and offer e-commerce solutions. This software can support multiple users, operate on multiple operating systems and come with an embedded database or work with any existing relational database products. The software is expensive and is generally sold by Value Added Resellers (VARs). VARs specialize in a particular software package and serve as consultants during installation and operation of the system. The ERP packages at the high end are extremely expensive — a software cost of millions of dollars being merely a drop in the bucket compared to extensive consulting, training, reengineering of workflows and restructuring of organizations costs — and require armies of consultants and multiple years to install and make operational.

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Big Mistakes: The Best Investors and Their Worst Investments by Michael Batnick

Russia was at the epicenter of Long‐Term's downward spiral, and in August 1998, as oil – their main export – fell by one‐third and Russian stocks were down by 75% for the year, short‐term interest rates skyrocketed to 200%. And then the wheels fell off for Meriwether and his colleagues. All the brains in the world couldn't save them from what was coming. LTCM took financial science to its extreme – to the outer limits of sanity. They coldly calculated the odds of every wiggle for every position in their portfolio. In August 1998, they calculated that their daily VAR, or value at risk (how much they could lose), was \$35 million. August 21, 1998, is the day when their faith should have evaporated, along with the \$550 million that they lost.19 It was the beginning of the end. By the end of the month, they had lost \$1.9 billion, putting the fund down 52% year‐to‐date. The death spiral was in full effect. “On Thursday September 10, the firm had lost \$530 million; on Friday, \$120 million.

., 48 Time horizons, 120 Time Warner, AOL merger, 49 Tim Ferriss Show, The, (podcast), 150 Tim Hortons, spinoff, 89 Tract on Monetary Reform, A, (Keynes), 125–126 Trader (Jones), 119 Trustees Equity Fund, decline, 50 Tsai, Jerry, 65, 68 stocks, trading, 69 ten good games, 71 Tsai Management Research, sale, 70 Tversky, Amos, 81 Twain, Mark (Samuel Clemens), 25, 27, 75 bankruptcy filings, 32 money, losses, 27–32 public opinion, hypersensitivity, 31 Twilio, Sacca investment, 149 Twitter, Sacca investment, 149–150 Uber, Sacca investment, 149 Undervalued issues, selection, 10 Union Pacific, shares (sale), 18 United Copper, cornering, 19 United States housing bubble, 132 University Computing, trading level, 70 US bonds international bonds, spreads, 41 value, decline, 61 U.S. housing bubble, impact, 132 U.S. Steel, shares orders, 17 US stock portfolio, diversification, 109 U.S. stocks, intra‐year decline, 147 Valeant Pharmaceuticals, 113 Ackman targeting, 90 performance, S&P500 comparison, 113 shares, decline, 114 Valuation metrics, 160 Value at risk (VAR), 41–42 Value investing, function, 10 Value investors, problems, 58 Vanguard 500 Index returns, 52 size, 47 Vanguard Group, Inc., 51 VeriSign, Druckenmiller purchase, 104 Vranos, 133 Washington Post stocks, problems, 58 Wayne, Ronald, 148 Webster & Company bankruptcy, 31 problems, 30 Webster, Samuel Charles, 29 Wellington Fund, 48 merger, 49 operation, at‐cost basis, 51 Wellington Management, Bogle firing, 51 Wendy's, stock appreciation, 89 Wesco Financial, purchase, 142 Wheeler, Munger & Company, 141 Whiz Kids Take Over, The, 49 “Who Wants to Be a Millionaire” (Ackman), 90–91 Winning the Loser's Game (Ellis), 99 Woodman, Nick, 150 WordPress, 149 World War I, global monetary system, 122 Wozniak, Steve, 148 Wright Aeronautical, business demonstration, 3 Xerox, trading level, 70 Yahoo!

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

One important implication for long-horizon institutional investors is that when they delegate asset management, external managers may not inherit the ultimate investor’s long horizon. 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.

They blamed widespread belief in the EMH, and more loosely “market fundamentalism”, for the laissez faire attitude of policymakers and regulators: letting leverage and asset booms grow unchecked and allowing ever more complex financial instruments and questionable sales practices flourish without restraint, under the cover that the market would inevitably get the prices of these securities right. Other criticisms come as though out of a scattergun: some attack the classical notion that competitive markets are inherently self-stabilizing, others blame the Fed’s asymmetric policy responses, while others fault the use of normal distribution and VaR-based risk management in a world where fat tails dominate. All of these criticisms are only tangentially related to the EMH, yet some of the critics do not seem to realize that. To me, a fair conclusion is that recent events have undermined the validity of the EMH’s main idea—that market prices are always “right” (near the fair value)—but have underlined the validity of its main implication for most investors—that beating the markets is extremely difficult (no free lunches).

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

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 VaRvalue-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 Global Money Markets by Frank J. Fabozzi, Steven V. Mann, Moorad Choudhry

Developments in ALM A greater number of ﬁnancial institutions are enhancing their risk management function by adding to the responsibilities of the ALM function. These have included enhancing the role of the head of Treasury and the asset and liability committee (ALCO), using other risk exposure measures such as option-adjusted spread and value-at-risk (VaR), and integrating the traditional interest-rate risk management with credit risk and operational risk. The increasing use of credit derivatives has facilitated this integrated approach to risk management. The additional roles of the ALM desk may include: ■ using the VaR tool to assess risk exposure; ■ integrating market risk and credit risk; ■ using new risk-adjusted measures of return; Asset and Liability Management 285 ■ optimizing portfolio return; ■ proactively managing the balance sheet; this includes giving direction on securitization of assets (removing them from the balance sheet), hedging credit exposure using credit derivatives, and actively enhancing returns from the liquidity book, such as entering into security lending and repo.

Treasury bills, 4, 16, 23, 54, 278 2-week, 132 auction, 27–28 bids/offers, 29 curve, 51 futures, 212–215 contract, 212 LIBOR, comparison, 35–39 liquidity, 23 maturing, 51 price, 73 quotes, 29–32 purchase, 35 sale, 26, 35 tax exemption, 75 types, 23–24 usage, 17 value, 42–43 yields, 12, 74, 102 behavior, 35–39 idiosyncratic variability, 35 LIBOR, relationship, 36 U.S. Treasury bonds, 16, 31 U.S. Treasury coupon securities, 155 U.S. Treasury dealers, 33–35 U.S. Treasury notes, 16, 31, 119– 121 10-year, 133 U.S. Treasury rates, 98 U.S. Treasury securities, 24. See also Maturity supply, decrease, 265 U.S. Treasury yield curve. See On-the-run U.S. Treasury yield curve USSPS Index GP, 254 Valuation model, 117 Value-at-risk (VaR), 284, 302. See also Credit limits, 282 Vanilla swap, 261 Variable-rate closed-end HELs, 198 Variable-rate gap, 293 Variable-rate SBA loans, 207 Variable-rate securities, 102 Variation margin, 211 Vaughan, Mark D., 71 Veterans Administration (VA), 155, 202 Visa, 192, 193 Volatility characteristics. See Floatingrate securities estimate, 272 increase. See Interest rate level, 91 Washington Metropolitan Area Transit Authority, 45 Weak link test, 181 Weighted average, 91 rate, 109–110 Weighted average coupon (WAC) rate, 154, 158–159, 163.

The credit risk of a swap is separate from its interestrate risk or market risk, and arises from the possibility of the counterparty to the swap defaulting on its obligations. If the present value of the swap at the time of default is net positive, then a bank is at risk of loss of this amount. While market risk can be hedged, it is more problematic to hedge credit risk. The common measures taken include limits on lending lines, collateral, and diversiﬁcation across counterparty sectors, as well as a form of credit value-at-risk to monitor credit exposures. A bank therefore is at risk of loss due to counterparty default for all its swap transactions. If at the time of default, the net present value of the swap is positive, this amount is potentially at risk and will probably be written off. If the value of the swap is negative at the time of default, in Swaps and Caps/Floors 263 theory this amount is a potential gain to the bank, although in practice the counterparty’s administrators will try to recover the value for their client.

Principles of Corporate Finance by Richard A. Brealey, Stewart C. Myers, Franklin Allen

In other words, there is more than a 5% chance that the value of your investment will fall 7% or more over the coming year. Bankers refer to this as the value at risk (or VAR) on the Starbucks bonds. There are a number of ways to improve this back-of-the-envelope estimate of the value at risk. For example, we assumed that the yield spreads on corporate bonds are constant. But, if investors become more reluctant to take on credit risk, you could lose much more than 7% on your investment. Notice also that when we calculated the risk from investing in Starbucks debt, we looked only at how the price of the bonds would be affected by a change in credit rating. If we wanted a comprehensive measure of value at risk, we would need to recognize that risk-free interest rates, too, may change over the year. TABLE 23.3 Global average one-year transition rates, 1981–2010, showing the percentage of bonds changing from one rating to another.

Unique risk Specific risk. Unseasoned issue Issue of a security for which there is no existing market (cf. seasoned issue). Unsystematic risk Specific risk. V Value additivity Rule that the value of the whole must equal the sum of the values of the parts. Value at risk (VAR) The probability of portfolio losses exceeding some specified proportion. Value stock A stock that is expected to provide steady income but relatively low growth (often refers to stocks with a low ratio of market-to-book value). Vanilla issue Issue without unusual features. VAR Value at risk. Variable-rate demand bond (VRDB) Floating-rate bond that can be sold back periodically to the issuer. Variance Mean squared deviation from the expected value; a measure of variability. Variation margin The daily gains or losses on a futures contract credited to the investor’s margin account.

., 573n Cram-down, 852 Credit analysis, 783 Credit cards, 788 Credit decision, 783–786 Credit default swaps, 588–589 Credit insurance, 786 Credit management, 781–787 collection policy in, 786–787 credit analysis in, 783 credit decision in, 783–786 promise to pay and, 782 terms of sale in, 781–782 CreditMetrics, 601, 601n Credit risk, 585–603 bank loan, 626 bond ratings, 65–66, 67, 595–597, 601–602, 609, 623, 628n option to default, 590–602 value at risk (VAR), 601–602 yields on corporate debt, 585–589 Credit scoring, 597–599 Credit Suisse, 379, 623 Credit transfer, 788 Cross-border leasing, 652 C&S Sovran, 812 CSX, 224 Cum dividend (with dividend), 402 Cumulative capital requirements, 748–751 Cumulative preferred stock, 356 Cumulative voting, 353 Currency futures market, 695 Currency risk. See Foreign exchange risk Currency swaps, 675–676 Current assets, 722, 750 Current liabilities, 489, 723 Current ratio, 735–736 Current yield, 47 Cusatis, P.

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

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.

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.’

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

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.

“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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How to Kick Ass on Wall Street by Andy Kessler

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Profiting Without Producing: How Finance Exploits Us All by Costas Lapavitsas

Heavy involvement of banks in financial transactions meant new dangers of losses due to changes in asset prices; these gave rise to ‘market risk’. A key step in the development of the Basel Accords, therefore, was the introduction of the Amendment of 1996 which made provision for market risk.22 For the largest banks this meant the introduction of advanced models of calculating risk based on value at risk (VaR). The VaR approach simulates changes in the market value of a bank’s portfolio and calculates a capital requirement based upon possible mark-to-market losses.23 Bank balance sheets thus began continually to reflect the movement of securities prices in the open markets, a factor that proved important in the unfolding of the crisis of 2007. As banks continued to grow and to become increasingly involved in trading in open markets, a still further risk emerged – operational risk.

Arm’s-length assessment of borrowers, for instance, has been deployed in judging the risk of mortgages in the US, including ‘credit scoring’ of individuals based on numerical information (income, age, assets, etc) that could be manipulated statistically.31 The risk of default on assets has been more generally assessed via quantitative models that utilize historical rates of default; estimates were largely extrapolations from past trends, stress-tested within limits indicated by data. Banks, as was discussed in the previous section, have also deployed value-at-risk methods to assess the probability that the value of their assets would decline below a certain level, relying on correlations between asset prices and volatility. VaR methods have made it imperative to adopt the accounting practice of ‘marking to market’ – to use current market valuations rather than historic prices. These practices have become officially incorporated in market-conforming regulation, thus gaining further influence among banks. Historically, banks were able to arrive at a socially valid assessment of borrower creditworthiness partly through ‘relational’ interactions with other agents in the financial system.32 It appears that the adoption of ‘hard’ and computationally intensive techniques has led to loss of capacity by banks to collect information and assess risk on a ‘relational’ basis.

.’, EDS Innovation Research Programme, Discussion Paper No. 002, London School of Economics, October 2005. Saez, Emmanuel, ‘Income and Wealth Concentration in a Historical and International Perspective’, in Public Policy and the Income Distribution, ed. Alan Auerbach, David Card, and John M. Quigley, NY: Russell Sage Foundation, 2006, pp. 221–58. Saunders, Anthony, and Linda Allen, Credit Risk Measurement: New Approaches to Value at Risk and Other Paradigms, 2nd ed., New York: John Wiley and Sons, 2002. Savage, Mike, and Karel Williams (eds), Remembering Elites, London: John Wiley and Sons, 2008. Sawyer, Malcolm, ‘The NAIRU: A Critical Appraisal’, International Papers in Political Economy 6:2, 1999, pp. 1–40; reprinted in Money, Finance and Capitalist Development, ed. Philip Arestis and Malcolm Sawyer, Aldershot: Edward Elgar, 2001, pp. 220–54.

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

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.

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?

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

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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The ensuing reforms comprised an emergency fix followed by a new framework. The awkwardly named Basel 2.5 system was an emergency fix that shored up capital charges for market risk. One reason that the internal risk models used in Basel 2 had generated inadequate capital buffers was that they used historical patterns of shocks and correlations across asset prices. Basel 2.5 moved the system from these value-at-risk models (VaRs) to stressed value-at-risk models (SVaRs) which incorporate the larger financial shocks, higher correlations across asset prices, wider margins between the buy and sell prices of assets, and the higher default risks seen in times of market panic. Some specific provisions for securitized assets, whose markets had largely seized up in the immediate aftermath of the Lehman Brothers bankruptcy, topped off this emergency revamp of capital buffers for market risk.

By contrast, securities held in the trading book would be subject to new weights based on market risk. Securities would be classified on standardized measures of the risk of large changes in prices—basically the same “bucket” approach that already applied to credit risk. To the surprise of the Committee, this proposal ran into strong criticism. This came mainly from the large banks, who argued that the proposed buckets were much less sophisticated than their own rapidly evolving “value-at-risk” models that calculated the risk to the value of an entire portfolio by taking into account not simply the volatility of individual asset prices but also the correlations across such prices. They noted that adopting the Committee’s proposal would lessen incentives to continue to develop their own internal risk models. Instead, the large banks asked to be allowed to use their own models to calculate the capital buffers needed for the trading book.

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Planet Ponzi by Mitch Feierstein

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.

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A Man for All Markets by Edward O. Thorp

We also offset the danger to the portfolio from sudden large shifts in overall stock market prices and in the volatility level of the market. From the 1980s on, some of these techniques came into usage by modern investment banks and hedge funds. They also adopted a notion we rejected, called VaR or “value at risk,” where they estimated the damage to their portfolio for, say, the worst events among the most likely 95 percent of future outcomes, neglecting the extreme 5 percent “tails,” then acted to reduce any unacceptably large risks. The defect of VaR alone is that it doesn’t fully account for the worst 5 percent of expected cases. But these extreme events are where ruin is to be found. It’s also true that extreme changes in securities prices may be much greater than you would expect from the Gaussian or normal statistics commonly used.

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Stigum's Money Market, 4E by Marcia Stigum, Anthony Crescenzi

For example, if the bank’s foreign-exchange trading operation is exceeding its risk limit, that added risk reduces the amount of risk that other areas of the bank can take—that is, if the bank wants to allow the foreign-exchange department to take the added risk in this instance and for overall risks to stay within the confines of the risks that the bank previously dictated it should take. Value at risk (VAR) is an example of a risk metric that banks use as a means of determining the amount of risk it is exposed to. VAR takes a probabilistic approach to measuring the risks to a portfolio associated with market volatility. One of the metrics that can be deployed in a VAR model is historical volatility, which basically looks at the typical percentage changes that occur in a financial instrument over a period of time. The Basel Committee on Banking Supervision implemented market-capital risk requirements on banks based on VAR analyses, giving banks the option of using their own VAR systems under certain conditions. A key objective was to address systemic risks that might be posed from the growing use of derivatives.

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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

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. Could the financial crisis have been avoided? That is the \$1.1 trillion question—the price tag of the bailout thus far.

New York, July 26, 2009. “great vampire squid wrapped”: Matt Taibbi, “The Great American Bubble Machine,” Rolling Stone, July 13, 2009. Goldman reported a profit of \$5.2 billion: On April 13, Goldman reported net earnings of \$1.81 billion for its first quarter. Three months later, its second-quarter earnings soared to \$3.44 billion. See http://www2.goldmansachs.com. Goldman’s VaR rising to record high: Christine Harper, “Goldman Sachs VaR Reaches Record on Risks Led by Equity Trading,” Bloomberg, July 15, 2009. “emergency actions meant to provide confidence”: Department of the Treasury press release, “Secretary Geithner Introduces Financial Stability Plan,” February 10, 2009. See http://www.treasury.gov/press/releases/tg18.htm. Alan Blinder: “After the fact, it is extremely clear that everything fell apart on the day Lehman went under.”

Hedgehogging by Barton Biggs

A fund of funds typically selects and manages a diversified portfolio of hedge funds that it sells to individuals or institutions that don’t feel capable of making the choices and then monitoring the funds themselves.They run all kinds of analytics on the individual hedge funds and on their overall portfolio to monitor risk and exposures.A couple of years ago, LTCM, a big hedge fund run by a bunch of pointy-headed Nobel Prize economists, blew up when a series of three standard-deviation events occurred simultaneously. The media loved it and published the names of all the supposedly smart, sophisticated individuals and institutions who had lost their money. Everybody was deeply embarrassed, and ever since the big institutions have been obsessed with risk analytics and throw around terms like stress-testing portfolios, value at risk (VAR), and Sharpe ratios. The funds of funds employ sophisticated quantitative analytics to add value by strategically allocating among the different hedge-fund classes.The hedge-fund universe is usually broken down into seven broad investment style classifications.These are event driven, fixed-income arbitrage, global convertible bond arbitrage, equity market-neutral, long/short equity, global macro, and commodity trading funds.

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

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.