# statistical arbitrage

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pages: 257 words: 13,443

Statistical Arbitrage: Algorithmic Trading Insights and Techniques by Andrew Pole

The language of mathematical models compounds the unfamiliarity of the notions, generating a sense of disquiet, a fear of lack of understanding. In Statistical Arbitrage, Pole has given his audience a didactic tour of the basic principles of statistical arbitrage, eliminating opacity at the Statistical Arbitrage 101 level. In the 1980s and early 1990s, Stat. Arb. 101 was, for the most part, all there was (exceptions such as D.E. Shaw and Renaissance aside). Today, more than a decade later, there is a much more extensive and complex world of statistical arbitrage. Foreword xxi This is not unlike the natural world, which is now populated by incredibly complex biological organisms after four billion years of evolution. Yet the simplest organisms thrive everywhere and still make up by far the largest part of the planet’s biomass. So is it true in statistical arbitrage, where the basics underpin much of contemporary practice.

Foreword reversion in prices, as in much of human activity, is a M ean powerful and fundamental force, driving systems and markets to homeostatic relationships. Starting in the early 1980s, statistical arbitrage was a formal and successful attempt to model this behavior in the pursuit of profit. Understanding the arithmetic of statistical arbitrage (sometimes abbreviated as stat. arb.) is a cornerstone to understanding the development of what has come to be known as complex financial engineering and risk modeling. The trading strategy referred to as statistical arbitrage is generally regarded as an opaque investment discipline. The view is that it is being driven by two complementary forces, both deriving from the core nature of the discipline: the vagueness of practitioners and the lack of quantitative knowledge on the part of investors. Statistical arbitrage exploits mathematical models to generate returns from systematic movements in securities prices.

Chapters 8 and 9 tell of the midlife crisis of statistical arbitrage. The roiling of United States financial markets for many months, beginning with the Enron debacle in 2000 and running through the terrorist attacks of 2001 and what Pole calls ‘‘an appalling litany’’ of corporate misconduct, is dissected for anticipated impact on statistical arbitrage performance. Adding to that mix have been technical changes in the markets, including decimalization and the decline of independent specialists on the floor of the NYSE. Pole draws a clear picture of why statistical arbitrage performance was disrupted. Very clearly the impression is made that the disruption was not terminal. Chapters 10 and 11 speak to the arriving future of statistical arbitrage. Trading algorithms, at first destroyers of classical stat. arb. are now, Pole argues, progenitors of new, systematically exploitable opportunities.

pages: 354 words: 26,550

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

Gatev, Goetzmann, and Rouwenhorst (2006) document that the out-of-sample back tests conducted on the daily equity data from 1967 to 1997 using their stat-arb strategy delivered Sharpe ratios well in excess of 4. High-frequency stat-arb delivers even higher performance numbers. PRACTICAL APPLICATIONS OF STATISTICAL ARBITRAGE General Considerations Most common statistical arbitrage strategies relying solely on statistical relationships with no economic background produce fair results, but these Statistical Arbitrage in High-Frequency Settings 189 relationships often prove to be random or spurious. A classic example of a spurious relationship is the relationship between time as a continuous variable and the return of a particular stock; all publicly listed firms are expected to grow with time, and while the relationship produces a highly significant statistical dependency, it can hardly be used to make meaningful predictions about future values of equities.

CONCLUSION Event arbitrage strategies utilize high-frequency trading since price equilibrium is reached only after market participants have reacted to the news. Short trading windows and estimation of the impact of historical announcements enable profitable trading decisions surrounding market announcements. CHAPTER 13 Statistical Arbitrage in High-Frequency Settings tatistical arbitrage (stat-arb) exploded on the trading scene in the late 1990s, with PhDs in physics and other “hard” sciences reaping double-digit returns using simple statistical phenomena. Since then, statistical arbitrage has been both hailed and derided. The advanced returns generated before 2007 by many stat-arb shops popularized the technique. Yet some blame stat-arb traders for destabilizing the markets in the 2007 and 2008 crises. Stat-arb can lead to a boon in competent hands and a bust in semi-proficient applications.

pages: 505 words: 142,118

A Man for All Markets by Edward O. Thorp

People at Morgan Stanley began leaving the quantitative systems group that was in charge of statistical arbitrage. Among those to depart was David E. Shaw, a former professor of computer science at Columbia University. He had been wooed to Wall Street to use computers to find opportunities in the market. In the spring of 1988, Shaw spent the day in Newport Beach. We discussed his plan to launch an improved statistical arbitrage product. PNP was able to put up the \$10 million he wanted for start-up, and we were impressed by his ideas but decided not to go ahead because we already had a good statistical arbitrage product. He found other backing, creating one of the most successful analytic firms on Wall Street, and later would become a member of the president’s science advisory committee. Using statistical arbitrage as a core profit center, he expanded into related hedging and arbitrage areas (the PNP business plan again), and hired large numbers of smart quantitative types from academia.

For that graph of XYZ’s performance, see Thorp, Edward O., “Statistical Arbitrage, Part VI,” Wilmott, July 2005, pp. 34–36. had ever experienced Reportedly, Simons’s secretive Renaissance Partners had a similar experience in August of 2008, losing 8 percent or so in a few days, then rebounding to make more than 100 percent for the year. employees, only six Since the six people in my office also had other responsibilities, we had only 3.5 “full-time equivalents” on the project. in statistical arbitrage Firms doing statistical arbitrage, such as the hedge fund group Citadel, already had in place most of the technology, talent, and expertise needed later to create and implement high frequency trading (HFT). For an account of HFT, see the book Flash Boys by Michael Lewis; In 2005, three years after we went out of the statistical arbitrage business, Steve and I worked with Jerry Baesel, who was then at Morgan Stanley Asset Management, to see if it was worth restarting.

At \$30 billion in 2014, Bezos was the fifteenth richest American. As PNP began winding down in late 1988, despite the stress we developed yet another approach to statistical arbitrage that was simpler and more powerful. But as PNP phased out, I wanted simplicity. We focused on two areas that could be managed by a small staff, Japanese warrant hedging and investing in other hedge funds. Both went well. I had no immediate plans to use our new statistical arbitrage technique and I expected that continuing innovations by investors using related systems would, as is the way of things, gradually erode its value. Four years passed, and then, my friend and former partner Jerry Baesel came to me with tales of extraordinary returns from statistical arbitrage. Besides D. E. Shaw & Company, the practitioners included former Morgan Stanley quants who were starting their own hedge funds, and some of my past PNP associates.

(In fact, one can become quite poor trading complex mortgage-backed securities, as the financial crisis of 2007–08 and the demise of Bear Stearns have shown.) The kind of quantitative trading I focus on is called statistical arbitrage trading. Statistical arbitrage deals with the simplest financial instruments: stocks, futures, and sometimes currencies. One does not need an advanced degree to become a statistical arbitrage trader. If you have taken a few high school–level courses in math, statistics, computer programming, or economics, you are probably as qualified as anyone to tackle some of the basic statistical arbitrage strategies. P1: JYS c01 JWBK321-Chan September 24, 2008 13:44 Printer: Yet to come The Whats, Whos, and Whys of Quantitative Trading 3 Okay, you say, you don’t need an advanced degree, but surely it gives you an edge in statistical arbitrage trading? Not necessarily. I received a PhD from one of the top physics departments of the world (Cornell’s).

This seemingly innocuous change has had a dramatic impact on the market structure, which is particularly negative for the profitability of statistical arbitrage strategies. The reason for this may be worthy of a book unto itself. In a nutshell, decimalization reduces frictions in the price discovery process, while statistical arbitrageurs mostly act as market makers and derive their profits from frictions and inefficiencies in this process. (This is the explanation given by Dr. Andrew Sterge in a Columbia University financial engineering seminar titled “Where Have All the Stat Arb Profits Gone?” in January 2008. Other industry practitioners have made the same point to me in private conversations.) Hence, we can expect backtest performance of statistical arbitrage strategies prior to 2001 to be far superior to their present-day performance. The other regime shift is relevant if your strategy shorts stocks.

There is one usual caveat, however. All this is based on the Gaussian assumption of return distributions. (See discussions in Chapter 6 on this issue.) Since the actual returns distributions have fat tails, one should be quite wary of using too much leverage on normally low-beta stocks. SUMMARY This book has been largely about a particular type of quantitative trading called statistical arbitrage in the investment industry. Despite this fancy name, statistical arbitrage is actually far simpler than trading derivatives (e.g., options) or fixed-income instruments, both conceptually and mathematically. I have described a large part of the statistical arbitrageur’s standard arsenal: mean reversion and momentum, regime switching, stationarity and cointegration, arbitrage pricing theory or factor model, seasonal trading models, and, finally, high-frequency trading.

pages: 321

Finding Alphas: A Quantitative Approach to Building Trading Strategies by Igor Tulchinsky

But does that mean an alpha can effectively predict stock prices? More specifically, can quants predict the price of a given stock on a given date in the future? Unfortunately, we probably cannot make single predictions with any reasonable confidence. It is the nature of statistical arbitrage that prediction is possible only in a “statistical” sense: only over a large number of predictions do random errors average out to a usable level of accuracy in the aggregate. More interestingly, there are many ways of making such statistical price predictions. STATISTICAL ARBITRAGE The key underlying assumption of statistical arbitrage is that the prices of financial instruments are driven by consistent rules, which can be discovered from their historical behavior and applied to the future. The prices of financial instruments are influenced by multiple factors, including trading microstructures, fundamental valuation, and investor psychology.

The period also demonstrated the flexibility and resilience of the quantitative investment approach, and showed that the quantitative operators developing alpha forecasts were able to adapt to new market environments, innovate, and ultimately stay relevant. In the next section, we will take a closer look at the alphas driving the quantitative strategies described above. 10 Finding Alphas STATISTICAL ARBITRAGE The term “statistical arbitrage” (stat arb) is sometimes used to describe a trading strategy based on the monetization of systematic price forecasts, or alphas. Unlike pure arbitrage, when a risk-free profit can be locked in by simultaneously purchasing and selling a basket of assets, a stat arb strategy aims to exploit relationships among asset prices that are estimated using historical data. Because estimation methods are imperfect, and because the exact relationships among assets are unknown and infinitely complex, the stat arb strategy’s profit is uncertain.

pages: 272 words: 19,172

Hedge Fund Market Wizards by Jack D. Schwager

But Princeton Newport was doing so well on a risk-adjusted basis with the strategies it had already that we put the statistical arbitrage strategy aside. It wasn’t clear that the marginal improvement that could have been obtained by adding statistical arbitrage to the existing strategies warranted diverting the resources that would have been needed for its implementation. When did you turn back to it again? In 1985, we placed an ad in the Wall Street Journal looking for people who had reliable ideas that would produce provable excess returns. One of the calls we received in response to that ad was from Gerry Bamberger, who turned out to be the person who had discovered statistical arbitrage at Morgan Stanley. My recollection is that he developed the strategy around 1982 and was eventually shouldered aside by Nunzio Tartaglia who was his immediate superior.

It was running at about 8 percent annualized, which is not too bad in a 2 percent world, but not good enough to make me want to go back and do it. What was your involvement with David Shaw, who was another relatively early practitioner of statistical arbitrage? In 1988, David Shaw had left Solomon and was looking for someone to fund him in a statistical arbitrage startup. I didn’t know exactly what he wanted when he came out here, but we talked for about six hours, and it seemed that his strategy was redundant with ours. So we parted on friendly terms. So it was basically a matter of you both realizing that you were working on the same thing, and there really wasn’t a match. That is exactly right. What did you do after you shut down the statistical arbitrage fund in 2002? I managed my investments in other people’s hedge funds. Do you have any recommendations on investing in hedge funds? I don’t have any recommendations now because I have run low on hedge fund candidates.

During 1990 to 1992, he focused primarily on trading Japanese warrants, which he found to be broadly mispriced. He eventually was forced to abandon this strategy when the dealers dramatically widened their bid/ask spreads, wiping out about half the potential profit on each trade. Thorp had successfully traded a statistical arbitrage strategy since the mid-1980s. In 1992, he was asked to run the strategy for a large institutional client. Two years later, he started his second hedge fund, Ridgeline Partners, to open the statistical arbitrage strategy to other investors. Ridgeline traded very actively, averaging about 6 million shares per day and accounting for about ½ percent of total NYSE volume. Thorp ran the strategy over 10 years. He averaged a 21 percent average annual compounded return with only a 7 percent annualized volatility—another remarkable track record.

The benefit of the mean reversion trading approach to economic releases over the trend-following approach is that the latter is less sensitive to latency between economic indicator release and time window within which the trading strategy must initiate a position. Understanding and implementing basic statistical arbitrage trading strategies Statistical arbitrage trading strategies (StatArb) first became popular in the 1980s, delivering many firms double-digit returns. It is a class of strategies that tries to capture relationships between short-term price movements in many correlated products. Then it uses relationships that have been found to be statistically significant in the past research to make predictions in the instrument being traded based on price movements in a large group of correlated products. Basics of StatArb Statistical arbitrage or StatArb is in some way similar to pairs trading that takes offsetting positions in co-linearly related products that we explored in Chapter 4, Classical Trading Strategies Driven by Human Intuition.

With sophisticated trading strategies, such as volatility adjusted trading strategies, economic-release-based trading strategies, pair-trading strategies, and statistical arbitrage strategies, there are more underlying assumptions about the relationship between volatility measures and trading instruments, the relationship between economic releases and impact on economy, and price moves in trading instruments. Pair-trading and statistical arbitrage trading strategies also make assumptions about the relationship between different trading instruments and how it evolves over time. As we discussed when we covered statistical arbitrage trading strategies, when these relationships break down, the strategies no longer continue to be profitable. When we build trading signals and algorithmic trading strategies, it's important to understand and be mindful of the underlying assumptions that the specific trading signals and the specific trading strategies depend on to be profitable.

pages: 297 words: 91,141

Market Sense and Nonsense by Jack D. Schwager

A classic example of this phenomenon was the meltdown of statistical arbitrage funds in August 2007. Statistical arbitrage is a market neutral, mean reversion strategy that uses mathematical models to identify short-term anomalies in stock movements, balancing sales of stocks witnessing upside deviations (as defined by its models) with purchases of stocks witnessing downside deviations. Since the strategy will normally embed multidimensional neutrality (e.g., market, sector, capitalization, region, etc.), significant leverage is typically employed to achieve desired return levels. As a group, statistical arbitrage funds will often have significant overlap in the stocks they are long and short. In August 2007, large liquidations by some statistical arbitrage funds caused other funds in this strategy to suddenly see their portfolios behaving perversely, with longs falling and shorts simultaneously rallying.

If, as occurred in 2008, they need to liquidate at the same time because of a flight-to-safety psychology in the market, the huge imbalance between supply and demand can result in managers being forced to liquidate positions at deeply discounted prices. Statistical arbitrage. The premise underlying statistical arbitrage is that short-term imbalances in buy and sell orders cause temporary price distortions, which provide short-term trading opportunities. Statistical arbitrage is a mean-reversion strategy that seeks to sell excessive strength and buy excessive weakness based on statistical models that define when short-term price moves in individual equities are considered out of line relative to price moves in related equities. The origin of the strategy was a subset of statistical arbitrage called pairs trading. In pairs trading, the price ratios of closely related stocks are tracked (e.g., Ford and General Motors), and when the mathematical model indicates that one stock has gained too much versus the other (either by rising more or by declining less), it is sold and hedged by the purchase of the related equity in the pair.

Pairs trading was successful in its early years, but lost its edge as too many proprietary trading groups and hedge funds employed similar strategies. Today’s statistical arbitrage models are far more complex, simultaneously trading hundreds or thousands of securities based on their relative price movements and correlations, subject to the constraint of maintaining multidimensional market neutrality (e.g., market, sector, etc.). Although mean reversion is typically at the core of this strategy, statistical arbitrage models may also incorporate other types of uncorrelated or even inversely correlated strategies, such as momentum and pattern recognition. Statistical arbitrage involves highly frequent trading activity, with trades lasting between seconds and days. Fixed income arbitrage. This strategy seeks to profit from perceived mispricings between different interest rate instruments.

pages: 407 words: 104,622

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution by Gregory Zuckerman

Kepler Financial, the company launched by former Morgan Stanley math and computer specialist Robert Frey that Simons had backed, was just plodding along. The firm was improving on the statistical-arbitrage strategies Frey and others had employed at Morgan Stanley by identifying a small set of market-wide factors that best explained stock moves. The trajectory of United Airlines shares, for example, is determined by the stock’s sensitivity to the returns of the overall market, changes in the price of oil, the movement of interest rates, and other factors. The direction of another stock, like Walmart, is influenced by the same explanatory factors, though the retail giant likely has a very different sensitivity to each of them. Kepler’s twist was to apply this approach to statistical arbitrage, buying stocks that didn’t rise as much as expected based on the historic returns of these various underlying factors, while simultaneously selling short, or wagering against, shares that underperformed.

Team members didn’t know a thing about the stocks they traded and didn’t need to—their strategy was simply to wager on the re-emergence of historic relationships between shares, an extension of the age-old “buy low, sell high” investment adage, this time using computer programs and lightning-fast trades. New hires, including a former Columbia University computer-science professor named David Shaw and mathematician Robert Frey, improved profits. The Morgan Stanley traders became some of the first to embrace the strategy of statistical arbitrage, or stat arb. This generally means making lots of concurrent trades, most of which aren’t correlated to the overall market but are aimed at taking advantage of statistical anomalies or other market behavior. The team’s software ranked stocks by their gains or losses over the previous weeks, for example. APT would then sell short, or bet against, the top 10 percent of the winners within an industry while buying the bottom 10 percent of the losers on the expectation that these trading patterns would revert.

A handful of investors and academics were mulling factor investing around that same time, but Frey wondered if he could do a better job using computational statistics and other mathematical techniques to isolate the true factors moving shares. Frey and his colleagues couldn’t muster much interest among the Morgan Stanley brass for their innovative factor approach. “They told me not to rock the boat,” Frey recalls. Frey quit, contacting Jim Simons and winning his financial backing to start a new company, Kepler Financial Management. Frey and a few others set up dozens of small computers to bet on his statistical-arbitrage strategy. Almost immediately, he received a threatening letter from Morgan Stanley’s lawyers. Frey hadn’t stolen anything, but his approach had been developed working for Morgan Stanley. Frey was in luck, though. He remembered that Tartaglia hadn’t allowed him or anyone else in his group to sign the bank’s nondisclosure or noncompete agreements. Tartaglia had wanted the option of taking his team to a rival if their bonuses ever disappointed.

pages: 289 words: 113,211

A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation by Richard Bookstaber

And well they 183 ccc_demon_165-206_ch09.qxd 7/13/07 2:44 PM Page 184 A DEMON OF OUR OWN DESIGN should, because someone else is getting saddled with the risk of the position, someone who most likely did not want to take on that position at the existing market price. Thus the demand for liquidity not only is the source of most price movement; it is at the root of most trading strategies. It is this liquidity-oriented, tectonic market shift that has made statistical arbitrage so powerful. Statistical arbitrage originated in the 1980s from the hedging demand of Morgan Stanley’s equity block-trading desk, which at the time was the center of risk taking on the equity trading floor. Like other broker-dealers, Morgan Stanley continually faced the problem of how to execute large block trades efficiently without suffering a price penalty. Often, major institutions discover they can clear a large block trade only at a large discount to the posted price.

But using statistical analysis he could show in the aggregate a clear tendency toward mean reversion— the stocks would get back in line with their history. There was money to be made, but the key was to hold many, many pairs to average out the market effects. The pairwise stock trades that form the elements of statistical arbitrage trading in the equity market are just one more flavor of spread trades. On an individual basis, they’re not very good spread trades. It is the diversification that comes from holding many pairs that makes this strategy a success. But even then, although its name suggests otherwise, statistical arbitrage is a spread trade, not a true arbitrage trade. Bamberger pitched his strategy, and surprisingly, given the politics of the firm, the equity division was willing to let him give it a try. He got a desk just to the side of the futures traders, mounted with monitors that tracked every pair: Ford and GM, American Airlines and United Airlines, International Paper and Georgia-Pacific, and so on.

O’Connor’s Partnership was making hundreds of millions of dollars by applying the Black-Scholes formula to options in the nascent Chicago Board Options Exchange in the late 1970s and early 1980s, with a cadre of young traders grabbing their pricing sheets at the start of the day and taking their posts along the CBOE trading floor to apply delta hedges to mispriced options. By the mid-1980s, the writing was on the wall for margin contractions in the floor marketmaking business, and O’Connor’s sold itself to Swiss Bank. On the heels of the cash-futures and index arbitrage opportunities came statistical arbitrage, which was the first to emerge in a hedge fund structure. In 1985, the first statistical arbitrage strategy was developed at Morgan Stanley, by Gerry Bamberger, a young information technology (IT) person who had been assigned to work on some hedging issues on the equity trading floor. As we discussed earlier, Bamberger developed a pairs trading strategy that resulted in a burgeoning business for Morgan Stanley and spawned D.E. Shaw and a host of other stat arb firms.

pages: 389 words: 109,207

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

By 1987 it was down to 15 percent, no longer competitive with Princeton-Newport’s other opportunities. The problem was apparently competition. Tartaglia continued to expand Morgan Stanley’s statistical arbitrage operation. By 1988 Tartaglia’s team was buying and selling \$900 million worth of stock. Bamberger would often be trying to buy the same temporarily bargain-priced stock as Morgan Stanley, driving up the price. This cut into the profit. Bamberger, who had made a good deal of money, decided to retire. BOSS was closed down. Finally, according to stories, Morgan Stanley’s operation suffered a substantial loss. The bank closed down its statistical arbitrage business too. Thorp continued to tinker with statistical arbitrage. He replaced Bamberger’s division by industry groups with a more flexible “factor analysis” system. The system analyzed stocks by how their price moves correlated with factors such as the market indexes, inflation, the price of gold, and so on.

They are less likely to accept an apparent winning strategy that might be a mere statistical fluke.” Each statistical arbitrage operation competes against the others to scoop up the so-called free money created by market inefficiency. All successful operations revise their software constantly to keep pace with changing markets and the changing nature of their competition. The inexplicable aspect of Thorp’s achievement was his continuing ability to discover new market inefficiencies, year after year, as old ones played out. This is a talent, like discovering new theorems or jazz improvisations. Statistical arbitrage is nonetheless a few degrees easier to understand than the intuitive trading of more conventional portfolio managers. It is an algorithm, the trades churned out by lines of computer code. The success of statistical arbitrage operations makes a case that there are persistent classes of market inefficiencies and that Kelly-criterion-guided money management can use them to achieve higher-than-market return without ruinous risk.

It is based on so many factors that it is hard for an investor, or anyone else, to understand what a fund manager is doing. You are unlikely to convince a skeptic that a manager’s return is not just luck when no one else can understand the logic of his stock picks. Indicators Project ONE OF THE BEST CASES for beating the stock market involves a scheme called statistical arbitrage. To make money in the market, you have to buy low and sell high. Why not use a computer to tell you which stocks are low and which are high? In concept, that is statistical arbitrage. Fundamental analysts look at scores of factors, many of them numerical, in deciding which stocks to buy. If there is any validity to this process, then it ought to be possible to automate it. Ed Thorp began pursuing this idea as early as 1979. It emerged as one of the discoveries of what became known as the “Indicators Project” at Princeton-Newport.

pages: 504 words: 139,137

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

The figure shows the percentage spread between the prices of Unilever NV and Unilever PLC computed as PNV/PPLC – 1, where the adjusted prices are expressed in common currency. In 2008, the liquidity problems spread much more broadly around the economy and, in September 2008 a truly systemic liquidity crisis unfolded around the bankruptcy of Lehman Brothers. Ironically, the value/momentum quant equity strategies performed relatively well during 2008. 9.2. STATISTICAL ARBITRAGE Statistical arbitrage (stat arb) strategies are also quantitative, but they are usually less based on an analysis of economic fundamentals and more based on arbitrage relations and statistical relations. Dual-Listed Shares: Siamese Twin Stocks Some stocks are joined at the hip in the sense that their fundamental values are economically linked. A classic example is when two merging companies in different countries decide to retain separate legal identities but function economically as a single firm through an “equalization agreement.”

Quants build computer systems that generate trading signals based on these relations, carry out portfolio optimization in light of trading costs, and trade using automated execution schemes that route hundreds of orders every few seconds. In other words, trading is done by feeding data into computers that run various programs with human oversight. Some quants focus on high-frequency trading, where they exit a trade within milliseconds or minutes after it was entered. Others focus on statistical arbitrage, that is, trading at a daily frequency based on statistical patterns. Yet others focus on lower frequency trades called fundamental quant (or equity market neutral) investing. Fundamental quant investing considers many of the same factors as discretionary traders, seeking to buy cheap stocks and short sell expensive ones, but the difference is that fundamental quants do so systematically using computer systems.

Another investment style (as seen in Overview Table III) is liquidity provision, meaning buying securities with high liquidity risk or securities being sold by other investors who demand liquidity. This investment style comes in many shapes and forms, from Griffin buying illiquid convertible bonds to earn a liquidity risk premium, to Paulson buying merger targets being dumped by investors who demand liquidity for fear of event risk, to Soros riding a credit cycle, to Asness providing liquidity through statistical arbitrage trades. Carry trading is the investment style of buying securities with high “carry,” that is, securities that will have a high return if market conditions stay the same (e.g., if prices do not change). For instance, global macro investors are known to pursue the currency carry trade where they invest in currencies with high interest rates, bond traders often prefer high-yielding bonds, equity investors like stocks with high dividend yields, and commodity traders like commodity futures with positive “roll return.”

pages: 318 words: 87,570

Broken Markets: How High Frequency Trading and Predatory Practices on Wall Street Are Destroying Investor Confidence and Your Portfolio by Sal Arnuk, Joseph Saluzzi

With that kind of uncertainty, the programs exit their positions and “liquidity provision.” Spreads widen. And sometimes, such as the May 6, 2010 Flash Crash, there is a “liquidity vacuum.” Andy Haldane, the Executive Director of Financial Stability at the Bank of England, in a July 8, 2011 speech titled “The Race to Zero,” described this as “adding liquidity in a monsoon and absorbing it in a drought.”6 Statistical Arbitrage Statistical Arbitrage (AKA, “stat arb”) has been in operation for decades. The type of example most often given is when IBM is trading “rich” in London and “cheap” on the NYSE, the stat arb guys will simultaneously short it in London and buy it back on the NYSE. Oh, if it were only that simple today. Today, the stat arb guys are trading “rich” versus “cheap” in more than 50 fragmented destinations.

Senator Ted Kaufman Introduction Chapter 1 Broken Markets Why Has Our Stock Market Structure Changed So Drastically? When Did HFT Start? How Did HFT Become So Big? Why Have We Allowed This to Happen? Will There Be Another Market Crash? Where’s the SEC in All This? Endnotes Chapter 2 The Curtain Pulled Back on High Frequency Trading What Is High Frequency Trading, and Who Is Doing It? Market Making Rebate Arbitrage Statistical Arbitrage Market Structure and Latency Arbitrage Momentum Ignition How the World Began to Learn About HFT The SEC’s Round Table on Equity Market Structure—or Sal Goes to Washington 60 Minutes—or Joe Makes It to Primetime Endnotes Chapter 3 Web of Chaos NYSE and the Regionals NASDAQ SOES Instinet Problems for NYSE and NASDAQ Four For-Profit Exchanges Conflicts of Interest Fragmentation The Tale of the Aggregator Endnotes Chapter 4 Regulatory Purgatory Early 1990s Change in Regulations Late 1990s Regulations—Decimalization, Reg NMS, and Demutualization Early 2000s—Reg NMS Endnotes Chapter 5 Regulatory Hangover The Flash Order Controversy The Concept Release on Market Structure...Interrupted The Band-Aid Fixes Endnotes Chapter 6 The Arms Merchants Colocation Private Data Feeds Rebates for Order Flow (The Maker/Taker Model) Not Your Father’s Stock Exchange Endnotes Chapter 7 It’s the Data, Stupid Information for Sale on Hidden Customer Orders Data Theft on Wall Street The Heat Is On Phantom Indexes Machine-Readable News Who Owns the Data?

They get the data from the stock exchanges, too. Then they trade, capitalizing on those patterns. And, in many cases, the exchanges pay them to trade. In our Big Picture Conference presentation, we spoke about a few types of HFT: • “Market making” rebate arbitrage (we use quotations around “market making” because we really don’t see how it even closely resembles real market making) • Statistical arbitrage • Latency arbitrage • Momentum ignition Market Making Rebate Arbitrage This is probably the largest bucket of HFT. It is the style and strategy especially catered to by all the for-profit exchanges. With the exchanges becoming for-profit, and, in many cases, converting to publicly traded companies, such as the NYSE or NASDAQ, they now care very much about how to keep growing revenues.

pages: 374 words: 114,600

The Quants by Scott Patterson

By then, Thorp and Regan were managing about \$130 million, a heady increase from the \$10,000 stake Thorp had received from Manny Kimmel for his first blackjack escapade in 1961. (In 1969, when the fund opened its doors for business, it had a stake of \$1.4 million.) But Thorp wasn’t resting on his laurels. He was always on the lookout for new talent. In 1985, he ran across a hotshot trader named Gerry Bamberger who’d just abandoned a post at Morgan Stanley. Bamberger had created a brilliant stock trading strategy that came to be known as statistical arbitrage, or stat arb—one of the most powerful trading strategies ever devised, a nearly flawless moneymaking system that could post profits no matter what direction the market was moving. It was right up Thorp’s alley. Gerry Bamberger discovered stat arb almost by accident. A tall, quick-witted Orthodox Jew from Long Island, he’d joined Morgan Stanley in 1980 after earning a degree in computer science at Columbia University.

The weekend after the presentation, Shaw decided to quit, informing Tartaglia of his decision the following Monday. Tartaglia, possibly perceiving Shaw as a threat, was happy to see him go. It may have been one of the most significant losses of talent in the history of Morgan Stanley. Shaw landed on his feet, starting up his own investment firm with \$28 million in capital and naming his fund D. E. Shaw. It soon became one of the most successful hedge funds in the world. Its core strategy: statistical arbitrage. Tartaglia, meanwhile, hit a rough patch, and in 1988, Morgan’s higher-ups slashed APT’s capital to \$300 million from \$900 million. Tartaglia amped up the leverage, eventually pushing the leverage-to-capital ratio to 8 to 1 (it invested \$8 for each \$1 it actually had in its coffers). By 1989, APT had started to lose money. The worse things got, the more frantic Tartaglia became. Eventually he was forced out.

By then, Citadel had more than \$1 billion under management. The fund was diving into nearly every trading strategy known to man. In the early 1990s, it had thrived on convertible bonds and a boom in Japanese warrants. In 1994, it launched a “merger arbitrage” group that made bets on the shares of companies in merger deals. The same year, encouraged by Ed Thorp’s success at Ridgeline Partners, the statistical arbitrage fund he’d started up after shutting down Princeton/Newport, it launched its own stat arb fund. Citadel started dabbling in mortgage-backed securities in 1999, and plunged into the reinsurance business a few years later. Griffin created an internal market–making operation for stocks that would let it enter trades that flew below Wall Street’s radar, always a bonus to the secrecy-obsessed fund manager.

Michael Kearns is professor of computer and information science at the University of Pennsylvania, where he holds secondary appointments in the statistics and operations and information management departments of the Wharton School. His research interests include machine learning, algorithmic game theory, quantitative finance and theoretical computer science. Michael also has extensive experience working with quantitative trading and statistical arbitrage groups, including at Lehman Brothers, Bank of America and SAC Capital. David Leinweber was a co-founder of the Center for Innovative Financial Technology at Lawrence Berkeley National Laboratory. Previously, he was visiting fellow at the Hass School of Business and x i i i i i i “Easley” — 2013/10/8 — 11:31 — page xi — #11 i i ABOUT THE AUTHORS at Caltech. He was the founder of Integrated Analytics Corporation, with was acquired by Jefferies Group and spun off as Investment Technology Group (NYSE: ITG).

Albert’s research focuses on securities trading, liquidity, asset pricing and financial econometrics. He has published in the Journal of Finance, Journal of Business and Economic Statistics and Journal of Financial and Quantitative Analysis, among others. He has been a member of the Group of Economic Advisors of the European Securities and Market Authority (ESMA) since 2011. Yuriy Nevmyvaka has extensive experience in quantitative trading and statistical arbitrage, including roles as portfolio manager and head of groups at SAC Capital, Bank of America and Lehman Brothers. He has also published extensively on topics in algorithmic trading and market microstructure, and is a visiting scientist in the computer and information science department at the University of Pennsylvania. Yuriy holds a PhD in computer science from Carnegie Mellon University. xi i i i i i i “Easley” — 2013/10/8 — 11:31 — page xii — #12 i i HIGH-FREQUENCY TRADING Richard B.

CONCLUSION In this chapter we reviewed the evolution of trading algorithms and focused on the event-driven, adaptive generation, as this is more suitable for an HFT ecosystem. We reviewed methods of constructing trading signals and illustrated them with a few examples. Our focus was on execution strategies for large orders of predetermined size and buy/sell direction. The other large class of strategies not discussed here contains the market-making and spread-capturing algorithms of statistical arbitrage. High-frequency trading has established a new normal mode in the equity markets and it is spreading in other asset classes. It is clear that executing orders in this environment requires fast information processing and fast action. Fast information processing leads to development and calibration of trading signals and adaptive algorithms. Fast action requires investment in computer networking and order routing technology.

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

c01.indd 5 1/10/08 11:00:55 AM 6 Getting a Job in Hedge Funds Table 1.3 Instruments and Styles COMMONLY USED INSTRUMENTS HEDGE FUND STYLES Public Equities Long/Short Quantitative Fixed Income Long Bias Event-Driven/Special Situations Currencies Short Only Value Commodities Arbitrage Trading Oriented Derivatives/Futures Market Neutral Global Macro Private Equity Industry Focus Multi-strategy Convertible Bonds Distressed Geographic Focus Arbitrage Strategies There are various types of arbitrage strategies, and all seek to exploit imbalances between different financial markets such as currencies, commodities, and debt. Some of the more popular hedge fund arbitrage strategies are convertible fixed income, risk, and statistical arbitrage. Convertible Arbitrage This strategy is identified by hedge investing in the convertible securities of a company. To do this, a hedge fund manager would buy the convertible bonds of a company while at the same time selling (or shorting) the company’s common stock. Positions are designed to generate profits from the fixed income security as well as the short sale of stock, while protecting principal from market moves.

Risk arbitrageurs invest simultaneously in long and short positions in both companies involved in a merger or acquisition. As such, they are typically long the stock of the company being acquired and short the stock of the acquirer. The principal risk is deal risk, should the deal fail to close. Merger arbitrage may hedge against market risk by purchasing Standard & Poor’s (S&P) 500 put options or put option spreads. Statistical Arbitrage Stat arb funds focus on the statistical mispricing of one or more assets based on the expected value of those assets. This is a very quantitative and systematic trading strategy that uses advanced software programs. Note: These funds typically hire PhDs, mathematicians, and/or programming experts. Emerging Markets This strategy involves equity or fixed income investing in emerging markets around the world.

While most quantitative funds invest in equities, others target fixed-income securities, commodities, currencies, and market indexes. These funds, some of which have billions of dollars in assets, can move the markets in which they invest when an internal buy or sell order is triggered. While quantitative strategies have sometimes produced stellar returns, there have also been some well-known failures of funds using this strategy. Some examples of funds that use quantitative investing strategies are statistical arbitrage, options arbitrage, fixed-income arbitrage, convertible bond arbitrage, mortgagebacked security arbitrage, derivatives arbitrage, equity market neutral, managed futures, and long/short funds. Sector-Specific Funds Some hedge fund managers may use any of the aforementioned strategies, but in doing so would focus investments on a specific sector of the market. Managers of these funds usually have both long and short equity positions.

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More Money Than God: Hedge Funds and the Making of a New Elite by Sebastian Mallaby

Presented with apparently random data and no further clues, they sift it repeatedly for patterns, exploiting the power of computers to hunt for ghosts that to the human eye would be invisible. Renaissance’s quantitative rivals have reason to avoid ghost hunting. The computer may find fake ghosts—patterns that exist for no reason beyond chance, and that consequently have no predictive value. Eric Wepsic, who runs statistical arbitrage at D. E. Shaw, gives the example of the Super Bowl: It used to be said that if a team from the original National Football League won, the market would head upward. As a matter of statistics, this relationship might hold; but as a matter of common sense, it is a meaningless coincidence. Because of the threat from coincidental correlations masquerading as predictive signals, Wepsic suggests that it is often dangerous to trade on statistical evidence unless it can be intuitively explained.

But once the firm realized that the correlations made intuitive sense—they reflected the technology euphoria that had pushed into all these industries—they seemed more likely to be tradable.27 Moreover, signals based on intuition have a further advantage: If you understand why they work, you probably understand why they might cease to work, so you are less likely to keep trading them beyond their point of usefulness. In short, Wepsic is saying that pure pattern recognition is a small part of what Shaw does, even if the firm does some of it. Again, this presents a contrast with Renaissance. Whereas D. E. Shaw grew out of statistical arbitrage in equities, with strong roots in fundamental intuitions about stocks, Renaissance grew out of technical trading in commodities, a tradition that treats price data as paramount.28 Whereas D. E. Shaw hired quants of all varieties, usually recruiting them in their twenties, the crucial early years at Renaissance were largely shaped by established cryptographers and translation programmers—experts who specialized in distinguishing fake ghosts from real ones.

But by 2005 nobody could argue that hedge funds were exceptional in any way: More than eight thousand had sprouted, and the long track records of the established funds made it hard to dismiss their enviable returns as the products of good fortune. Bit by bit, the old talk of luck and genius faded and the new lingo took its place—at hedge-fund conferences from Phoenix to Monaco, a host of consultants and gurus held forth about the scientific product they called alpha. The great thing about alpha was that it could be explained: Strategies such as Tom Steyer’s merger arbitrage or D. E. Shaw’s statistical arbitrage delivered uncorrelated, market-beating profits in a way that could be understood, replicated, and manufactured by professionals. And so the era of the manufacturer arrived. Innovation and inspiration gave way to a new sort of alpha factory. You could see this transformation all over the hedge-fund industry. By the early 2000s, there was no longer much doubt that long/short equity stock picking, as practiced by Julian Robertson’s Tiger, could deliver market-beating returns.

Stock Market Wizards: Interviews With America's Top Stock Traders by Jack D. Schwager

An example of classic arbitrage would be buying gold in New York at \$290 an ounce and simultaneously selling the same quantity in London at \$291. In our age of computerization and near instantaneous communication, classic arbitrage opportunities are virtually nonexistent. Statistical arbitrage expands the classic arbitrage concept of simultaneously buying and selling identical financial instruments for a locked-in profit to encompass buying and selling closely related financial instruments for a probable profit. In statistical arbitrage, each individual trade is no longer a sure thing, but the odds imply an edge. The trader engaged in statistical arbitrage will lose on a significant percentage of trades but will be profitable over the long run, assuming trade probabilities and transaction costs have been accurately estimated. An appropriate analogy would be roulette (viewed from the casino's perspective): The casino's DAVID SHAW: odds of winning on any particular spin of the wheel are only modestly better than fifty-fifty, but its edge and the laws of probability will assure that it wins over the long run.

An appropriate analogy would be roulette (viewed from the casino's perspective): The casino's DAVID SHAW: odds of winning on any particular spin of the wheel are only modestly better than fifty-fifty, but its edge and the laws of probability will assure that it wins over the long run. There are many different types of statistical arbitrage. We will focus on one example: pairs trading. In addition to providing an easy-to grasp illustration, pairs trading has the advantage of reportedly being one of the prime strategies used by the Morgan Stanley trading group, for which Shaw worked before he left to form his own firm. Pairs trading involves a two-step process. First, past data are used to define pairs of stocks that tend to move together. Second, each of these pairs is monitored for performance divergences. Whenever there is a statistically meaningful performance divergence between two stocks in a defined pair, the stronger of the pair is sold and the weaker is bought.

Pairs Trading: Performance of a Relative Value Arbitrage Rule. National Bureau of Economic Research Working Paper No. 7032; March 1999. f HE Q U A N T I T A T I V E E D G E structure of identifying securities that are underpriced relative to other securities. However, that is where the similarity ends. A partial list of the elements of complexity that differentiate Shaw's trading methodology from a simple statistical arbitrage strategy, such as pairs trading, include some, and possibly all, of the following: Trading signals are based on over twenty different predictive techniques, rather than a single method. Each of these methodologies is probably far more sophisticated than pairs trading. Even if performance divergence between correlated securities is the core of one of these strategies, as it is for pairs trading, the mathematical structure would more likely be one that simultaneously analyzes the interrelationship of large numbers of securities, rather than one that analyzes two stocks at a time.

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Understanding Asset Allocation: An Intuitive Approach to Maximizing Your Portfolio by Victor A. Canto

In fact, one can make the case that for the few strategies with higher monthly returns than the S&P 500, the differences do not appear to be statistically significant. Table 12.2 Average monthly returns and standard deviation for selected hedge-fund strategies: January 1990 to December 2004. Monthly Returns Standard Deviation Sharpe Ratio 0.69% 1.25% 0.95 HFRI Equity Market Neutral Index: 0.71% Statistical Arbitrage 1.14% 1.14 HFRI Equity Market Neutral Index 0.75% 0.92% 1.61 HFRI Fixed Income: High Yield Index 0.80% 1.84% 0.85 HFRI Fixed Income (Total) 0.86% 1.00% 1.79 HFRI Convertible Arbitrage Index 0.86% 0.98% 1.86 S&P 500 0.96% 4.23% 0.51 S&P 500 Equal Weighted 1.11% 4.53% 0.58 HFRI Event-Driven Index 1.19% 1.91% 1.53 HFRI Distressed Securities Index 1.23% 1.77% 1.71 HFRI Emerging Markets (Total) 1.29% 4.31% 0.76 HFRI Macro Index 1.29% 2.44% 1.35 HFRI Fixed Income : Arbitrage Index continues Chapter 12 Keeping the Wheels on the Hedge-Fund ATV 229 Table 12.2 continued Monthly Returns Standard Deviation Sharpe Ratio HFRI Equity Hedge Index 1.39% 2.58% 1.42 HFRI Market Timing Index 1.03% 1.95% 1.23 HFRI Composite Index 1.15% 2.00% 1.40 Source: Hedge Fund Research, Inc.

Looking at the ratio of the hedge-fund strategies’ cumulative returns to the S&P 500, it is apparent there are runs in the data. As a cycle-minded investor can guess, some simple tests reject the hypothesis that the runs in the data are randomly generated. 230 UNDERSTANDING ASSET ALLOCATION Five of the six hedge-fund strategies reported in Figures 12.1a through 12.1f— market neutral (see Figure 12.1a), fixed-income arbitrage (see Figure 12.1b), fixed-income high-yield (see Figure 12.1c), equity market neutral statistical arbitrage (see Figure 12.1e), and fixed-income (total) (see Figure 12.f)— underperformed the S&P 500 during the 1990–2004 period. The sixth strategy, convertible arbitrage (see Figure 12.1d), barely outperformed the S&P 500. The data also show most of the strategies were keeping up with the S&P 500 prior to 1994, as evidenced by the flat or rising relative performance line in Figures 12.1a, b, d, and e.

Chapter 12 Keeping the Wheels on the Hedge-Fund ATV 231 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1990 1992 1994 1996 1998 2000 2002 2004 Figure 12.1c Ratio of the fixed-income, high-yield hedge-fund index to the S&P 500. 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1990 1992 1994 1996 1998 2000 2002 2004 Figure 12.1d Ratio of the convertible arbitrage hedge-fund index to the S&P 500. 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1990 1992 Figure 12.1e 232 1994 1996 1998 2000 2002 2004 Ratio of the equity market neutral statistical arbitrage hedge-fund index to the S&P 500. UNDERSTANDING ASSET ALLOCATION 1.4 1.3 1.2 1.1 1.0 0.9 0.8 0.7 0.6 0.5 1990 1992 1994 1996 1998 2000 2002 2004 Figure 12.1f Ratio of the fixed-income (total) hedge-fund index to the S&P 500. There’s a clear pattern of relative underperformance and outperformance for the hedge-fund strategies. Another six strategies—macro (see Figure 12.2a), distressed securities (see Figure 12.2b), event driven (see Figure 12.2c), emerging markets (see Figure 12.2d), market timing (see Figure 12.2e), and hedgefund composite (see Figure 12.2f)—outperformed the S&P 500 during the 1990–1994 and 1999–2004 time periods. 2.6 2.4 2.2 2.0 1.8 1.6 1.4 1.2 1.0 1990 1992 Figure 12.2a 1994 1996 1998 2000 2002 2004 Ratio of the global macro hedge-fund index to the S&P 500.

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Endless Money: The Moral Hazards of Socialism by William Baker, Addison Wiggin

A town that has 100 traffic cops and no murder detectives probably won’t find any dead bodies, but its police force will be very busy and profitable. Evidence-Based Investing How else could one get the courage to lever up to five-to-one or even 30-to-1 as was the case in some investment banks and statistical arbitrage proprietary trading funds, without “proof ” that certain assets and liabilities would behave in correlation or within bands of normal distribution? One year before the equity market imploded due to the credit crisis, a class of hedge funds known as “statistical arbitrage” funds collapsed, foretelling the effect leverage was having on stability of the market. The premise of this fund category was that excess returns could be harvested from bets on mean reversion, such as spreads between certain categories of debt, or among equity sectors such banks that lend against real estate and REITs, which own property.

But due to the mathematics, its sensitivity to the change in covariance of its positions is magnified fourfold. Probably half of all statistical arbitrage funds that deployed this strategy have moved on to greener pastures. But the use of value-at-risk statistical models to control exposure in hedge funds or even for large pension funds that allocate between different asset types continues, and it is virtually a mandatory exercise for institutional managers. There is hardly a large pension plan that has not developed a PowerPoint presentation that boasts it realigned its investments to increase excess return (alpha) and also reduced risk (variance). So in this sense, statistical arbitrage exists in some diluted form almost everywhere. Nassim Taleb decries the practice of evidence-based investing and value at risk models as conducted in the mainstream of Wall Street in his tome The Black Swan.

., 294–295 Smith, Adam, 264–265 Smyth, Douglas, 252 “Social credit,” 113 Social Investment Fund Network, 181–182 Socialism, and “I.O.U.S.A.,” 335–338. See also Capitalism; Fiat currency; Moral hazard Soros, George, 180–181, 184–185 Sowell, Thomas, 216 Specie, 36. See also Gold; Hard money INDEX Specie Circular, 49 Spitzer, Elliot, 322, 328 “Stamped money,” 113 Stanford, Allen, 330 Stanford Capital, 26 State Children’s Health Insurance Program (SCHIP), 202 Statistical arbitrage funds, 27–28 Stocks for the Long Run (Siegel), 31 Stolo, Licinius, 246 Strong, Benjamin, 64 Study of Administration (Wilson), 288 “Subprime Fiasco Exposes Manipulation by Mortgage Brokers” (Lubove, Taub), 148 Swaps, 125 Swope, Gerard, 317 Tabulae novae, 247 Taleb, Nassim Nicholas, 15, 16, 28, 280 Tallmadge, Benjamin, 3 Taub, Daniel, 148–149 Taxation: and federal budget deficit, 189–197 flat (or fair) tax, 202–204 history of, 197–202 overview, 188–189 Taylor Rule, 75–76 Taylor, John B., 75–76 Temin, Peter, 107–108, 114 Term Securities Lending Facility, 124–125 Theory of Moral Sentiments (Smith), 264 Tiberius, 249, 258 Tides Foundation, 180, 181 Torricelli Principle, 362 Trienans, Howard, 168 Troubled Asset Relief Program (TARP), 122, 128, 130, 139, 141, 143, 152, 214, 220, 235 Truman, Harry, 289 Index Turk, James, 350 Turner, Ted, 175 Turning Point Inc., 320 UBS, 22, 173 U.S.

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

If an investment’s expected return is higher than the borrowing rate, a trader can amplify the return as a percentage of capital by borrowing at the lower rate and investing at the higher rate. Just as leverage amplifies gains, it also amplifies losses. LTCM had identified very high Sharpe ratio trades with very low volatility. To give investors meaningful returns, the fund leveraged its portfolio. Although most of LTCM’s trades were not pure arbitrages, but rather statistical arbitrages or quasi-arbitrages, it is helpful to illustrate this concept with a pure arbitrage. Suppose LTCM had identified a bond that would pay \$100 in one year with certainty. It bought the bond at \$90, giving an unlevered return of 10%. The risk for the one-year holding period was zero. With no leverage, LTCM could just wait, even if the bond’s price fell as low as \$0.01 in the interim. With leverage, this becomes difficult or impossible.

HighBridge Statistical Opportunities Fund was down 18% for the month; Tykhe Capital LLC, a New York-based quantitative fund, was down 20% for the month; AQR’s flagship fund was down 13% by August 10; by August 14, 2007, Goldman Sachs Global Equity Opportunities Fund had lost more than 30% in one week.10 What Was the Quant Crisis? A quant crisis is one that affects quantitative money managers, vaguely defined as any portfolio managers that use a quantitative system to manage trades, rather than a human-based security-picking system. The quant world includes various types of managers, including those in charge of statistical arbitrage hedge funds, many managed futures funds, and a large class of long-short or market-neutral equity funds. This quant crisis mainly affected funds using quantitative equity strategies. In 2007, the leading quant portfolio companies were Barclays Global Investors (BGI), Goldman Sachs Asset Management (GSAM), State Street, Morgan Stanley’s Process Driven Trading (PDT) group, AQR, First Quadrant, Analytic Investors, AXA Rosenberg, Panagora, Mellon Capital, Acadian, Analytic, and Numeric.

In 2007, the leading quant portfolio companies were Barclays Global Investors (BGI), Goldman Sachs Asset Management (GSAM), State Street, Morgan Stanley’s Process Driven Trading (PDT) group, AQR, First Quadrant, Analytic Investors, AXA Rosenberg, Panagora, Mellon Capital, Acadian, Analytic, and Numeric. The largest of these were BGI, GSAM, and State Street. The leaders and traders in many of these quant funds earned PhDs from leading schools in finance, economics, and mathematics. In this crisis, the large negative returns seemed to disproportionately affect quantitative hedge funds, in particular quantitative equity hedge funds and statistical arbitrage funds.11 The value of common equity factors used to construct quantitative equity portfolios decreased in concert during this period, while their (typically low) correlations increased. Liquidity—especially in typical quant factors—completely dried up, especially during the week of August 6 to 13, 2007. Quantitative funds have a number of common attributes.12 Quantitative equity funds are usually market-neutral or enhanced index hedge funds or mutual funds that use computers to sort stocks by desirable and less desirable factors.

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

Fixed-income trading requires a better grasp of technology and quantitative methods than equities trading. A trader friend of mine summed it up succinctly when, after I commented to him that the fixed-income traders I knew seemed smarter than the equity traders, he replied that "that's because there's no competitive edge to being smart in the equities business" I don't mean to suggest that all quants work on the Black-Scholes model. Increasingly, some of them work on statistical arbitrage, the attempt to seek order and predictability in the patterns of past stock price movements and then exploit them-that is, to divine the future from the past. Hedge funds, private pools of capital that seek out subtle price discrepancies in odd and unexplored corners of markets, have become major employers of quants during the past five years, and continue to hire them to do "stat-arb" Risk management is also in mode, and for good reason.

Nevertheless, in the twenty-first century, as universities have initiated financial engineering programs and financial institutions have embraced risk management, being a quant has slowly become a more legitimate profession. The overheated tech-stock market of the late 1990s cast a warm, reflected glow on geeks of all types, as did the droves of hedge funds trying to use mathematical models to squeeze dollars out of subtleties. The guts to lose a lot of money carries its own aura. D.E. Shaw & Co., a NewYork trading house that was rumored to be making substantial profits doing "black box" computerized statistical arbitrage before their billion-dollar losses in 1998, and Long Term Capital Management, the quant-driven Connecticut hedge fund that ultimately needed a multibillion-dollar bailout, have both contributed to this more glamorous view of quantization. And indeed, many of the Long Term Capital protagonists are back in business again at new firms. The capacity to wreak destruction with your models provides the ultimate respectability.

'Pairs trading is the search for statistically significant oscillatory patterns in the spread between pairs of similar stocks. If you believe you have detected such a phenomenon, you short the expensive stock and buy the cheap one when the spread is large, and then reverse the trade when/if the spread narrows. Since Tartaglia's renowned but temporary successes at Morgan Stanley, trading houses, hedge funds, and the scientists they employ have regularly and hopefully attempted to build model-driven, so-called "statistical arbitrage" money machines of this type. 'At this time I also began attending various computer science research seminars and conferences, where I was always struck by the difference in quality between computer science research and physics research. In physics, seminar speakers described completed achievements. In computer science, however, the majority of the talks were about plans for systems, sketches of new languages, and unimplemented ideas.The hurdle for declaring accomplishment seemed much lower.

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The Physics of Wall Street: A Brief History of Predicting the Unpredictable by James Owen Weatherall

.”: This section in particular is based on an interview with Farmer. The closest thing from Farmer’s and Packard’s days as physicists that was helpful in their early days with the Prediction Company was the work in Farmer and Sidorowich (1987), where they present a method for making short-term predictions based on a particular algorithmic approximation. “One strategy they used was something called statistical arbitrage . . .”: For more on the history of statistical arbitrage, see Bookstaber (2007). Ed Thorp also played a significant role in the early development of the idea; for more on his contribution, see Thorp (2004). “. . . a variety of computer programs known as genetic algorithms”: For more on genetic algorithms, see, for instance, Mitchell (1998). For Packard’s early contributions, see Packard (1988, 1990). “. . . over the firm’s first fifteen years . . .”: More specifically, this person told me that the company had a Sharpe ratio of 3. 7.

What the Predictors were doing, rather, was trying to extract small amounts of information from a great deal of noise. It was a search for regularities of the same sort that lots of investors look for: how markets react to economic news like interest rates or employment numbers, how changes in one market manifest themselves in others, how the performances of different industries are intertwined. One strategy they used was something called statistical arbitrage, which works by betting that certain statistical properties of stocks will tend to return even if they disappear briefly. The classic example is pairs trading. Pairs trading works by observing that some companies’ stock prices are usually closely correlated. Consider Pepsi and Coca-Cola. Virtually any news that isn’t company-specific is likely to affect Pepsi’s products in just the same way as Coca-Cola’s, which means that the two stock prices usually track one another.

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Electronic and Algorithmic Trading Technology: The Complete Guide by Kendall Kim

A pure alpha-seeking strategy is very underdeveloped in algorithmic trading because it is very difficult to accomplish. In this regard, human traders making the final execution decisions still have a decided advantage over pure algorithmic or program trading. The FIX Protocol has allowed different proprietary systems to plug into a common standard and communicate with one another. Some trading programs are designed to decide which shares to buy and sell. These are used for statistical arbitrage, the practice of monitoring and comparing share prices to identify patterns that can be exploited to make a profit. Some exchanges now regulate the use of electronic and algorithmic trading, preventing their systems from being overloaded or to avoid repeating the crash of 1987. On July 7, 2005, the London Stock Exchange asked for algorithmic trading to be suspended after the London bombings.

It has a flexible data model to handle multiple instrument data feeds in a consistent manner and rapidly support any new products that can be integrated into existing legacy systems and traditional relational databases using TimeScape XDK. This product can also be fully compatible with XML Web services based on SOAP and .NET. Xenomorph begins its second decade of growth. Xenomorph’s TimeScape is the current product enhanced and refined over the last 10 years. They currently have 30 clients globally, with investment banks accounting for 50% of their client base, and hedge funds specializing in convertible bond and statistical arbitrage along with asset management firms comprising the remainder. Apama Apama is an independent financial technology firm, founded in 2000, which provides outsourced trading strategies. Apama is designed to reduce the time taken to deploy and maintain an algorithmic trading solution. Apama currently has clients on both the buy and the sell side, with major clients including JP Morgan, ABN Amro, and Deutsche Bank.

The Handbook of Personal Wealth Management by Reuvid, Jonathan.

For more information about our Wealth Management Service contact 020 7189 9901, email Julian.Hall@bestinvest.co.uk julian.hall@bestinvest.co.uk bestinvest.co.uk ________________________________________________ HEDGE FUND STRATEGIES 27 ឣ Market neutral This is an extension to long/short equity where an attempt is made to eliminate market or idiosyncratic risk. Some funds negate exposure to market capitalization and sector exposures and may invest an equal number of stocks on both the long and short sides. Market neutral funds are further broken down into fundamental stock pickers, quantitative based (where the portfolios can be re-balanced by an optimizer ranging in frequency from once a week to quarterly) and statistical arbitrage where more frequent intra-day optimization is achieved. The goal is to derive returns (if all idiosyncratic risks are removed) through stock-picking and efficient execution. Global macro Macro funds may invest in any market, and frequently use leverage and derivatives, futures and swaps to make directional trades in equities, interest rates, currencies and commodities. Macro funds also tend to be very concentrated in their bets.

The outlook for strategic M&A deals remains positive but the potential for leveraged buy-outs has reduced significantly. Fixed income arbitrage This strategy requires leverage, which is now scarce, in order to generate positive returns when credit spreads are narrowing. During 2008 credit spreads widened and leverage was removed. There were large redemptions from this strategy throughout the year and many hedge funds operating this strategy have been forced to close. Statistical arbitrage This market-neutral strategy profits from high-frequency trading with stock holding periods ranging from seconds to months. The volatile trading environment of 2008 has meant that some of the shorter-term positions were able to produce positive ឣ 34 PORTFOLIO INVESTMENT _________________________________________________ returns. Many funds’ computer models were re-calibrated following the restrictions on shorting financials. 2009 outlook Those hedge funds that have preserved capital through 2008 will have the financial fire power to take advantage of the opportunities now arising.

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Crapshoot Investing: How Tech-Savvy Traders and Clueless Regulators Turned the Stock Market Into a Casino by Jim McTague

Narang was dark, slim, and handsome and spoke in a rich baritone. His hair and goatee were jet black, with traces of silver. He was friendly, patient, and forceful, and he had a gift for lecture. He had hung a white board in his office to illustrate his arguments. After graduating from MIT in 1991 with a degree in mathematics and computer science, Narang began working on the proprietary trading desk at First Boston, engaging in statistical arbitrage. He expected the job to be temporary. His plan was to return to academia in a year or so to obtain a Ph.D. in mathematics, but he was bitten by the Wall Street bug. Narang discovered that he enjoyed trading, so he traded virtually everything, from Treasury bonds to equities. Over the next eight years, he worked for a number of Wall Street’s largest firms, including Goldman Sachs. While at Goldman Sachs, he decided to launch his own business.

If on a given day a stock rose in value by X dollars, for instance, the traders might judge the move to be extreme, based on 20 years’ worth of pricing, volume, and related data, and short the stock, expecting it to correct back down. If the underlying company was a big food producer, the stock’s fall might affect the prices of agricultural futures on the commodities exchange. The super-fast computers would exploit such correlations. Statistical arbitrage was a variation on the age-old theme of buy low and sell high, but with some twists. For instance, a trader did not always buy and sell exactly the same stock. The trader could buy a high-tech stock such as Microsoft when it was trending lower and immediately sell an index or exchange-traded fund (ETF) of high-tech stocks such as the QQQ, which has Microsoft as a component and would adjust downward to reflect Microsoft’s lower market value.

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

But if interest rates went up, few people would refinance, and the security holders would get back less than the expected cash flows, at a time when they wanted to take advantage of the higher rates. Prepayment risk was much too small to justify the yield difference. It was possible to trade GNMAs actively, along with bond futures and options, to lock in highly predictable profits. At the time we called this a statistical arbitrage. An arbitrage is a trade with no risk and positive profit. A statistical arbitrage is a trade with controllable risk that is much smaller than the expected positive profit. A good example is a roulette wheel from the standpoint of a casino. Today, however, the term stat arb has been taken over by a group of strategies descended from pairs trading. One of the things I was doing at the time was running such an active GNMA portfolio.

See Securities and Exchange Commission (SEC) Secret history of Wall Street: 1654–1982 period 1983–1987 period 1988–1992 period 1993–2007 period Securities and Exchange Commission (SEC) Securitization Seven principles of risk management: I: risk duality II: valuable boundary III: risk ignition IV: money V: evolution VI: superposition VII: game theory Sharpe ratio Shiller, Robert Smile and skew option Soros, George Sports betting/bettors Spread trade Squam Lake Report, The (French, et. al.) 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).

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

Second, it will bring an increasing number of extremely quantitative people into traditional areas of portfolio management. Their approach will most likely be more analytical and closer to “quantitative” than traditional managers, thus blurring the lines between quant and nonquant. Finally, I think that quantitative asset management’s range is going to increase dramatically over the next 10 years. Today when people think about quantitative asset management they usually think about statistical arbitrage or global tactical asset allocation. Over time, I see quantitative methods being applied to an increasing range of products. Driving this will be increased liquidity in new markets, the availability of data to analyze and the availability of electronic access to those markets. JWPR007-Lindsey May 7, 2007 16:55 136 JWPR007-Lindsey April 30, 2007 19:47 Chapter 8 Peter Carr Head of Quantitative Financial Research, Bloomberg I ’m thrilled to be asked to describe how I became a quant.

Being blind to the heterogeneous process of option decay makes you believe option implied volatilities are more volatile than they really are. Active Portfolio Strategies Cooper Neff had two incarnations: first as an options market maker on exchanges around the world, next as a technology-driven, quantitative modeling firm trading equities at unheard-of high frequencies. The inflection point was in 1995, the year Cooper Neff was acquired by French bank BNP. Active Portfolio Strategies, or APS, was our version of equity statistical arbitrage, but no one ever used those terms at the firm. To us, equity stat arb meant pairs trading or exploiting the residuals of an equity factor model, and nothing we were doing had anything in common with these strategies. So we made up our own name. The genesis of APS came, oddly enough, while I was working at CoreStates in 1987. I came upon a barnburner of a book called The Microstructure of Securities Markets.7 This out-of-print work is a thin but dense and abstruse book that to me was a veritable gold mine.

I’d like to thank Brad Asness, Kent Clark, David Kabiller, Robert Krail, and John Liew for helpful comments on this draft. 3. At AQR our IT department gets a kick out of this as I often yell for help because I’ve lost the ability to display “Helvetica font.” 4. One of these “other things” in my dissertation was a simulation study I never published that I still think is neat and an early study of what is now known as statistical arbitrage, where I concluded that it’s interesting, but doesn’t cover transactions costs, and then ignored several easy improvements, thereby not participating in one of the great hedge fund strategies of the late twentieth century. 5. It didn’t hurt that I’d be working with my best friend Jonathan Beinner (Jon is now a Goldman partner co-running the fixed income group). It also didn’t hurt that Fischer Black was then at GSAM.

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Frequently Asked Questions in Quantitative Finance by Paul Wilmott

However, when deriving the famous option-pricing models we rely on a dynamic strategy, called delta hedging, in which a portfolio consisting of an option and stock is constantly adjusted by purchase or sale of stock in a very specific manner. Now we can see that there are several types of arbitrage that we can think of. Here is a list and description of the most important.• A static arbitrage is an arbitrage that does not require rebalancing of positions • A dynamic arbitrage is an arbitrage that requires trading instruments in the future, generally contingent on market states • A statistical arbitrage is not an arbitrage but simply a likely profit in excess of the risk-free return (perhaps even suitably adjusted for risk taken) as predicted by past statistics • Model-independent arbitrage is an arbitrage which does not depend on any mathematical model of financial instruments to work. For example, an exploitable violation of put-call parity or a violation of the relationship between spot and forward prices, or between bonds and swaps • Model-dependent arbitrage does require a model.

Cointegration is a useful technique for studying relationships in multivariate time series, and provides a sound methodology for modelling both long-run and short-run dynamics in a financial system. Example Suppose you have two stocks S1 and S2 and you find that S1 − 3 S2 is stationary, so that this combination never strays too far from its mean. If one day this ‘spread’ is particularly large then you would have sound statistical reasons for thinking the spread might shortly reduce, giving you a possible source of statistical arbitrage profit. This can be the basis for pairs trading. Long Answer The correlations between financial quantities are notoriously unstable. Nevertheless correlations are regularly used in almost all multivariate financial problems. An alternative statistical measure to correlation is cointegration. This is probably a more robust measure of the linkage between two financial quantities but as yet there is little derivatives theory based on the concept.

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The Enigma of Capital: And the Crises of Capitalism by David Harvey

The ‘shadow banking system’ emerges 1980 Currency swaps 1981 Portfolio insurance introduced; interest rate swaps; futures markets in Eurodollars, in Certificates of Deposit and in Treasury instruments 1983 Options markets on currency, equity values and Treasury instruments; collateralised mortgage obligation introduced 1985 Deepening and widening of options and futures markets; computerised trading and modelling of markets begins in earnest; statistical arbitrage strategies introduced 1986 Big Bang unification of global stock, options and currency trading markets 1987–8 Collateralised Debt Obligations (CDOs) introduced along with Collateralised Bond Obligations (CBOs) and Collateralised Mortgage Obligations (CMOs) 1989 Futures on interest rate swaps 1990 Credit default swaps introduced along with equity index swaps 1991 ‘Off balance sheet’ vehicles known as special purpose entities or special investment vehicles sanctioned 1992–2009 Rapid evolution in volume of trading across all of these instruments.

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

The consistency of the results is impressive: all strategies have positive Sharpe ratios, ranging between 0.1 and 0.9. Value strategies worked especially well for stock selection in Japan and for equity country allocation. Other studies document the success of value strategies among emerging equity markets and among corporate bonds. Many fixed income arbitrage strategies employed in hedge funds and bank proprietary trading desks are based on mean-reverting spreads or related value anchors. Statistical arbitrage in equity markets—pairs trading and more complex variants—is also based on relative value (i.e., mean reversion in the pricing relationship between two assets). The profitability of such “arbitrage” (really: relative value trading) strategies waned significantly in the past decade as the technologies to exploit them became widely available. Low-hanging fruit were eliminated years ago. In country allocation, weighting countries by GDP rather than by market cap in a global index is one way to infuse a value bias.

Another strand of literature analyzes gains of short-term liquidity providers over time. Instead of holding illiquid or high-liquidity-beta assets, these liquidity providers supply liquidity to the marketplace by trading a short-term reversal strategy. My intuition is that recent laggard stocks may have underperformed because of selling pressure, while recent winners may have benefited from buying pressure. Thus a classic “stat arb” (statistical arbitrage) strategy of buying recent laggards and selling recent outperformers attenuates the temporary supply–demand imbalance and should be rewarded. Technological progress has changed market structures and liquidity sources. For example, the New York Stock Exchange has lost market share in U.S. equity turnover to various electronic platforms and dark pools. Market-makers used to be the only explicit liquidity providers but they have increasingly been superseded by hedge funds and other stat arb traders.

Treasuries were often the only asset class to benefit in flight-to-quality episodes, and this safe haven feature partly justifies Treasuries’ low required returns. Interestingly, Figure 19.6 suggests that this feature was not strong for Treasuries over the 20-year window (Treasuries became negatively correlated with VIX changes only around 1998), whereas both momentum and value strategies served such a safe haven role (although value worked as a safe haven mainly in the early 2000s, but not in the late 2000s). Statistical arbitrage strategies (pairs trading or exploiting short-term return reversals) may work even better in high-volatility regimes. Figure 19.6. Average monthly returns when the volatility factor is above or below its median, 1990–2009. Sources: Bloomberg, LPX, MSCI Barra, FTSE, Bank of America Merrill Lynch, Hedge Fund Research, Barclays Capital, S&P GSCI, Ken French’s website, Brevan Howard, own calculations.

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

Jean-Philippe Bouchaud and some colleagues at Capital Fund Management were running two hedge funds with combined capital of \$725 million as of the end of 2003. The funds engage in statistical arbitrage: They use mathematical models and computer horse-power to find what they think is incorrect pricing in the market, or other unstable patterns on which they can bet. The individual bets are small; but it is, for them, a game of large numbers. Many small profits can mount. In 2002, their biggest fund, Ventus, reported a stock-market gain of 28.1 percent, this, in a year when the market overall had fallen by a third. But it is also a game of chance: In 2003, they were less lucky with gains of just 3.32 percent. Their other fund, Discus, in the futures market, reported a 14.1 percent profit that year. “With statistical arbitrage, there are ups and downs,” Bouchaud says with a shrug. Their strategy is part multifractal, part many other things.

Risk Management in Trading by Davis Edwards

Angela Edwards William Fellows Colin Edwards Matt Davis Barbara Sapienza Haseeb Khawaja Dan Gustafson Andrew Coleman Clint Carlin Alexander Abraham John Vickers Varun Chavali Andrew Dunn Kirat Dhillon Ken Parrish Iordanis Karagiannidis Contents Preface ix CHAPTER 1 Trading and Hedge Funds 1 CHAPTER 2 Financial Markets 33 CHAPTER 3 Financial Mathematics 61 CHAPTER 4 Backtesting and Trade Forensics 95 CHAPTER 5 Mark to Market 121 CHAPTER 6 Value-at-Risk 141 CHAPTER 7 Hedging 177 CHAPTER 8 Options, Greeks, and Non-Linear Risks 199 CHAPTER 9 Credit Value Adjustments (CVA) 237 vii viii CONTENTS Afterword 267 Answer Key 269 About the Author 299 Index 301 Preface I started learning about trading strategies and managing trading risk while working on statistical arbitrage trading desks at two investment banks— first at JP Morgan and later Bear Stearns. The core of the job was converting some type of analysis into an action. In other words, I had to use data to make a decision and think through the effects of those decisions. Over time, that most risk management is focused on analysis rather than making decisions. In most risk management texts, there is very little discussion on what decisions are made as the result of analysis.

This result is counter‐intuitive to most risk managers where greater risk will only increase the potential exposures and never decrease them. About the Author DAVIS W. EDWARDS, FRM, ERP, is a senior manager in Deloitte & Touche’s National Securities Pricing Center managing energy derivatives valuation. Prior to joining Deloitte, he was division director of credit risk at Macquarie Bank and senior managing director on the statistical arbitrage trading desk at Bear Stearns. He is a regular speaker on the topic of financial modeling and mathematics applied to real world problems. He is the author of the books Energy Trading and Investingg and Energy Investing Demystified. d Davis is director of the Houston chapter of the Global Association of Risk Professionals. 299 Index A ABS. See asset-backed securities acceptance, risk, 29, 267–268 accredited investor, 5 accuracy of simulations, 98 accurate data, 112–115 ADR.

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Baykan (2011): “Predicting direction of stock price index movement using artificial neural networks and support vector machines: The sample of the Istanbul Stock Exchange.” Expert Systems with Applications, Vol. 38, No. 5, pp. 5311–5319. Kim, K. (2003): “Financial time series forecasting using support vector machines.” Neurocomputing, Vol. 55, No. 1, pp. 307–319. Krauss, C., X. Do, and N. Huck (2017): “Deep neural networks, gradient-boosted trees, random forests: Statistical arbitrage on the S&P 500.” European Journal of Operational Research, Vol. 259, No. 2, pp. 689–702. Laborda, R. and J. Laborda (2017): “Can tree-structured classifiers add value to the investor?” Finance Research Letters, Vol. 22 (August), pp. 211–226. Nakamura, E. (2005): “Inflation forecasting using a neural network.” Economics Letters, Vol. 86, No. 3, pp. 373–378. Olson, D. and C. Mossman (2003): “Neural network forecasts of Canadian stock returns using accounting ratios.”

Zhu (2014): “Pseudo-mathematics and financial charlatanism: The effects of backtest overfitting on out-of-sample performance.” Notices of the American Mathematical Society, 61(5), pp. 458–471. Available at http://ssrn.com/ abstract=2308659. Bailey, D., J. Borwein, M. López de Prado, and J. Zhu (2017): “The probability of backtest overfitting.” Journal of Computational Finance, Vol. 20, No. 4, pp. 39–70. Available at http://ssrn.com/abstract=2326253. Bertram, W. (2009): “Analytic solutions for optimal statistical arbitrage trading.” Working paper. Available at http://ssrn.com/abstract=1505073. Easley, D., M. Lopez de Prado, and M. O'Hara (2011): “The exchange of flow-toxicity.” Journal of Trading, Vol. 6, No. 2, pp. 8–13. Available at http://ssrn.com/abstract=1748633. Notes 1 I would like to thank Professor Peter Carr (New York University) for his contributions to this chapter. 2 The strategy may still be the result of backtest overfitting, but at least the trading rule would not have contributed to that problem. 3 The trading rule R could be characterized as a function of the three barriers, instead of the horizontal ones.

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Adaptive Markets: Financial Evolution at the Speed of Thought by Andrew W. Lo

They began their conversations in almost exactly the same way: “Have you heard of anything unusual going on with other hedge funds . . . ?” After the third call, I realized that something significant was occurring on Wall Street, something that was off the radar of academic theory or hedge fund practice. 284 • Chapter 8 I knew all three alumni were working at hedge funds engaged in the same broad category of strategies known as “statistical arbitrage,” or “statarb” for short—highly sophisticated quantitative algorithms and computerized trading platforms involving long and short positions in hundreds of stocks. These were the same kinds of strategies used by Morgan Stanley and D. E. Shaw in the 1980s (see chapter 7). This seemed like too much of a coincidence. And the fact that these three were calling up their former finance professor to ask about what’s going on in the industry suggested that they must have been really desperate for information!

Also, weight these positions in proportion to the amount the stocks deviate from that index, that 286 • Chapter 8 is, the bigger the deviation, the more weight you give them in your portfolio. This is a more sophisticated version of chapter 7’s hedge fund example of buying Apricot Computers and simultaneously selling BlueBerry Devices, which is known as a “pairs strategy” (apologies for the pun). Since having been introduced at Morgan Stanley in the early 1980s, pairs strategies have radiated into hundreds of different varieties of statistical arbitrage, the strategies growing more elaborate and refined with each iteration, like the radiation of new species that populate unoccupied ecological niches. The motivation for these strategies is often mean reversion—the idea that what goes up must eventually come down, and vice versa. If stock prices revert to the mean, then past “losers” should appreciate and past “winners” should depreciate.

., 100 Sobel, Russell, 206 social Darwinism, 215 social exclusion, 85–86 social media, 55, 270, 405 Société Générale, 60–61 Society of Mind, The (Minsky), 132–133 sociobiology, 170–174, 216–217 Sociobiology (Wilson), 170–171 Solow, Herbert, 395 Soros, George, 6, 219, 222–223, 224, 227, 234, 244, 277 sovereign wealth funds, 230, 299, 409–410 Soviet Union, 411 Space Shut tle Challenger, 12–16, 24, 38 specialization, 217 speech synthesis, 132 Sperry, Roger, 113–114 “spoofi ng,” 360 Springer, James, 159 SR-52 programmable calculator, 357 stagflation, 37 Standard Portfolio Analysis of Risk (SPAN), 369–370 Stanton, Angela, 338 starfish, 192, 242 Star Trek, 395–397, 411, 414 stationarity, 253–255, 279, 282 statistical arbitrage (“statarb”), 284, 286, 288–291, 292–293, 362 statistical tests, 47 Steenbarger, Brett, 94 Stein, Carolyn, 69 sterilization, 171, 174 Stiglitz, Joseph, 224, 278, 310 Stocks for the Long Run (Siegel), 253 stock splits, 24, 47 Stone, Oliver, 346 Stone Age, 150, 163, 165 stone tools, 150–151, 153 stop-loss orders, 359 Strasberg, Lee, 105 stress, 3, 75, 93, 101, 122, 160–161, 346, 413–415 strong connectedness, 374 Strong Story Hypothesis, 133 Strumpf, Koleman, 39 “stub quotes,” 360 subjective value, 100 sublenticular extended amygdala, 89 subprime mortgages, 290, 292, 293, 297, 321, 327, 376, 377, 410 482 • Index Sugihara, George, 366 suicide, 160 Sullenberger, Chesley, 381 Summers, Lawrence (Larry), 50, 315–316, 319–320, 379 sunlight, 108 SuperDot (trading system), 236 supply and demand curves, 29, 30, 31–33, 34 Surowiecki, James, 5, 16 survey research, 40 Sussman, Donald, 237–238 swaps, 243, 298, 300 Swedish Twin Registry, 161 systematic bias, 56 systematic risk, 194, 199–203, 204, 205, 250–251, 348, 389 systemic risk, 319; Bank of England’s measurement of, 366–367; government as source of, 361; in hedge fund industry, 291, 317; of large vs. small shocks, 315; managing, 370–371, 376–378, 387; transparency of, 384–385; trust linked to, 344 Takahashi, Hidehiko, 86 Tanner, Carmen, 353 Tanzania, 150 Tartaglia, Nunzio, 236 Tattersall, Ian, 150, 154 Tech Bubble, 40 telegraphy, 356 Tennyson, Alfred, Baron, 144 testosterone, 108, 337–338 Texas hold ’em, 59–60 Texas Instruments, 357, 384 Thackray, John, 234 Thales, 16 Théorie de la Spéculation (Bachelier), 19 theory of mind, 109–111 thermal homeostasis, 367–368, 370 This Time Is Different (Reinhart and Rogoff ), 310 Thompson, Robert, 1, 81–82, 83, 103–104 three-body problem, 214 ticker tape machine, 356 tight coupling, 321, 322, 361, 372Tiger Fund, 234 Tinker, Grant, 395 Tobin tax, 245 Tokugawa era, 17 Tooby, John, 173, 174 tool use, 150–151, 153, 162, 165 “toxic assets,” 299 trade execution, 257, 356 trade secrets, 284–285, 384 trading volume, 257, 359 transactions tax, 245 Treynor, Jack, 263 trial and error, 133, 141, 142, 182, 183, 188, 198, 265 Triangle Shirtwaist Fire, 378–379 tribbles, 190–205, 216 Trivers, Robert, 172 trolley dilemma, 339 Trusty, Jessica, 120 Tversky, Amos, 55, 58, 66–67, 68–69, 70–71, 90, 106, 113, 388 TWA Flight 800, 84–85 twins, 159, 161, 348 “two-legged goat effect,” 155 UBS, 61 Ultimatum Game, 336–338 uncertainty, 212, 218; risk vs., 53–55, 415 unemployment, 36–37 unintended consequences, 7, 248, 269, 330, 358, 375 United Kingdom, 222–223, 242, 377 University of Chicago, 22 uptick rule, 233 Urbach-Wiethe disease, 82–83 U.S.

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Market Risk Analysis, Quantitative Methods in Finance by Carol Alexander

In Section II.5.4.6 we describe how to track an index using only a relatively small subset of assets. The index tracking regression model has the index return as the dependent variable, and the explanatory variables are the returns on the assets used to track the index. This can be extended to a regression model for enhanced indexation by replacing the dependent variable by the index return plus a fixed outperformance. A further extension is to statistical arbitrage Introduction to Linear Regression 183 strategies which take a long position on an enhanced indexation portfolio and a short position on the index futures. A case study on index tracking of the Dow Jones Industrial Average index is presented in Section II.5.4.7 where we use that fact that the tracking portfolio must be cointegrated with the index if the tracking error is to be stationary.

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

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No One Would Listen: A True Financial Thriller by Harry Markopolos

Then I began putting things in, taking things out, testing and retesting and back-testing to see how each package would perform in various market environments. I did this knowing full well that Bernie hadn’t bothered to do any of this. He just sat down and made it up. It’s considerably easier that way—and you always get the results you want! Eventually I developed a product we named the Rampart Options Statistical Arbitrage. It was a product that would do extremely well in a market environment with low to moderately high volatility. As long as the market didn’t move more than 8 to 10 percent over a 10- to 15-day trading period, it would perform very well. Of course, if there was extremely high volatility or if the market did make a substantial move in either direction over that period, it was possible to lose about 50 percent of its value.

I’m president of the four-thousand-member Boston Security Analysts Society, and I have evidence here of the largest fraud in history,” and handed the envelope to him, he might have taken it seriously. But I did what seemed safest at that time. Slightly more than three years had passed since we had discovered Madoff. We had compiled a strong case against him. Our original reason for trying to bring him down—that he was competition we couldn’t compete against—had ended with the failure of the Rampart Options Statistical Arbitrage strategy. But we were so deeply into this thing that it became impossible to put it down. We had actually developed into a pretty good team. We had two investigators in the field, Frank and Mike, and two quants in Neil and me able to find the defects in the materials they collected. And they did continue to add to our growing pile of evidence. Frank’s new job at Benchmark Plus caused him to spend most of his time with hedge fund and risk managers, and at some point in each conversation he never failed to ask them, “What do you know about Bernie?”

Investment: A History by Norton Reamer, Jesse Downing

Indeed, it is no surprise that managing a macro-oriented portfolio and having consistent success is More New Investment Forms 267 no easy task: the identiﬁcation of a string of exceptional shifts is what separates the one-hit wonders from the macro titans. Relative value funds can encapsulate several different strategies. Some are engaged in what has been termed pairs trading, or the purchase of one security that has been deemed “cheap” on a relative basis and the sale of another that seems correspondingly “expensive.” Relative value funds proﬁt when the prices of the pair of securities readjust. Some funds use statistical arbitrage, often examining the behavior of the time series and making judgments as to relative value based on historical valuations. Others are more fundamentally oriented, believing that one well-positioned ﬁrm will outperform a competitor. The other common strategy employed by relative value funds is seeking value across the capital structure of a publicly traded ﬁrm. By way of example, a relative value fund may believe a publicly traded company will experience severe distress in the next six months.

See Standard & Poor’s 500 speculation: art, stamps, coins, and wine, 283; in derivatives, 221; excesses, 197; impacts of, 232; value and, 4–5 spinning jenny, 71 split-strike conversion, 151–52 sponsor, 286–87 Stabilizing an Unstable Economy (Minsky), 214 Stagecoach Corporate Stock Fund, 284–85 Standard & Poor’s 500 (S&P 500), 187, 228, 285, 305–6, 309 Stanford, Allen, 153–56 Stanford, Leland, 155 Stanford Financial Group, 154 Starbucks, 277 State Street Corporation, 299 State Street Global Advisors, 299 State Street Investment Trust, 141 statistical arbitrage, 267 steam engine, 71 steamships, 90 Stefanadis, Chris, 94 sterling, 65 stock company, 134 stock exchanges: national or international, 94; new, 96; regional, 94–95 stock market: dislocations, 205; in England, 86–87; in Paris, 85 stock ownership: age and, 93–94; direct and indirect, 91, 93; gender and, 93–94; regulations prohibiting too much, 123; study of, 96; in United States, 90–94, 97 stock ticker, 89–90; network, 95 stones (horoi), 27, 60 Strong, Benjamin, 200–203, 206, 226 strong-form efficiency, 249 Studebaker-Packard Corporation, 111 sub hasta (public auction), 50 subprime, 39 subprime-mortgage lending, 223 Suetonius, 59 sugar consumption, in England, 75, 77 Sumerian city-states, 15–16 supply curve, 229 Supreme Court, 108 survivorship bias, 252 swap spread, 266 Swensen, David, 296, 328 SWFs.

Day One Trader: A Liffe Story by John Sussex

Rapid-fire deci- D AY O N E T R A D E R : A L I F F E S T O R Y | 169 sions of the type taken in the pits are made by machines now. Screen traders are finding themselves unable to pull off trades that were possible just three years ago. For example, traders are no longer using calculators in dealing rooms to work out the differential in the price on the bid offer spread of contracts. So-called statistical arbitrage programmes are cleaning these types of transactions up in milliseconds. An unexpected consequence of the emergence of IT specialist traders has been that the trading floor has made a comeback. Only this time it is the racks of computer servers at exchanges and not a crowd of coloured-jacketed dealers that are driving trading volumes. The CME’s floor may now be just sparsely populated with a few options dealers.

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Money Mavericks: Confessions of a Hedge Fund Manager by Lars Kroijer

The general feedback from the guys (there were virtually no women in the crowd) was similar: their jobs were not very structured, there was little hierarchy, skill was enthusiastically acknowledged by superiors and lack of it punished mercilessly. The job was entrepreneurial, in that you were encouraged to pursue what you thought were interesting angles, and if you were good the money was great. It was also clear that the type of work varied quite a bit from fund to fund. While the fixed-income or statistical arbitrage funds could be very mathematical in nature, the work at some of the long or short funds largely resembled that of more traditional stock-picking. Joining the clan I eventually joined a value fund in New York called SC Fundamental. During the interview process, the firm’s founder, Peter Collery, had thoroughly impressed me and I still consider him one of the smartest people I have ever met.

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Traders at Work: How the World's Most Successful Traders Make Their Living in the Markets by Tim Bourquin, Nicholas Mango

When I found pairs trading in equities, however, that was an eye-opening event for me. It gave me the opportunity to be a little more patient with my trades, because I was focused on relative value, not on whether KLA-Tencor [KLAC] stock was going to go up today or Novellus Systems stock was going to go down. Instead, I could trade the relative value in between the KLAC–Novellus pair. Those early days of equity statistical arbitrage pairs trading has really defined my career up to this point. Bourquin: What made agricultural pairs trading more attractive to you than just straight equity pairs trading? Hemminger: I enjoy the research process and looking through data, which are skills that I have continued to build upon as my career in the financial markets has developed and I have gained more confidence. I would say that process really started in 2006.

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The greatest trade ever: the behind-the-scenes story of how John Paulson defied Wall Street and made financial history by Gregory Zuckerman

Pellegrini moved out of their Gracie Square home to an apartment in Westchester, receiving \$300,000 from DeWoody in a divorce settlement, a pretax payout that he figured might have to last him through retirement. Being financially successful was at the top of Pellegrini’'s life goals, right up there with having a happy family life. He had failed miserably at both. “"I was forty-five and had zero net worth,”" Pellegrini recalls. “"And from my perspective, I had no prospects.”" Pellegrini’'s bright ideas kept coming, though. He developed a new method to use “"statistical arbitrage”" to trade stocks, though he couldn’'t make much money with it. A stint at Tricadia Capital, a hedge fund founded by Michaelcheck’'s Mariner Investment Group, Inc., gave Pellegrini an education in the world of securitized debt and credit-default swaps (CDS), which the firm was heavily involved in. But Pellegrini didn’'t make many friends at Tricadia when he suggested that the firm find ways to short collateralized-debt obligations, even as others at the firm were buying and creating versions of these debts.

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The Clash of the Cultures by John C. Bogle

The high demand for the services of HFTs comes not only from “punters”—sheer gamblers who thrive (or hope to thrive) by betting against the bookmakers—but from other diverse sources, as well. These traders may range from longer-term investors who value the liquidity and efficiency of HFTs to hedge fund managers who act with great speed based on perceived stock mispricing that may last only momentarily. This aspect of “price discovery,” namely statistical arbitrage that often relies on complex algorithms, clearly enhances market efficiency, which is definitely a goal of short-term trading, but also benefits investors with a long-term focus. Yes, HFTs add to the efficiency of stock market prices, and have slashed unit trading costs to almost unimaginably low levels. But these gains often come at the expense of deliberate investors, and expose the market to the risks of inside manipulation by traders with knowledge of future order flows.

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

Shaw & Company in 1988 with \$28 million (it now has current assets exceeding \$30 billion).7 What is likely Shaw’s last publication on trading dealt with the mechanics of interfacing Unix systems with the Gr eatest Hits of Computation in Finance 41 current generation of electronic trading systems. He apparently realized that, despite his instincts as a former academic, some things are more valuable unpublished. Subsequent in-house developments made D.E. Shaw a leader (reportedly) in electronic market making, statistical arbitrage, and other fast electronic trading strategies. David Whitcomb, a market microstructure economist at Rutgers University and coauthor of a 1988 book on electronic trading strategies,8 faced the same sort of skepticism selling his ideas to Wall Street. Finding no institutional backing, he joined forces with a computer scientist colleague to found Automated Trading Desk (ATD) in the proverbial garage in Charleston, South Carolina.

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The Everything Store: Jeff Bezos and the Age of Amazon by Brad Stone

Shaw tentatively accepted the job and then changed his mind, telling Hillis he wanted to do something more lucrative and could always return to the supercomputer field after he got wealthy. Hillis argued that even if Shaw did get rich—which seemed unlikely—he’d never return to computer science. (Shaw did, after he became a billionaire and passed on the day-to-day management of D. E. Shaw to others.) “I was spectacularly wrong on both counts,” Hillis says. Morgan Stanley finally pried Shaw loose from academia in 1986, adding him to a famed group working on statistical arbitrage software for the new wave of automated trading. But Shaw had an urge to set off on his own. He left Morgan Stanley in 1988, and with a \$28 million seed investment from investor Donald Sussman, he set up shop over a Communist bookstore in Manhattan’s West Village. By design, D. E. Shaw would be a different kind of Wall Street firm. Shaw recruited not financiers but scientists and mathematicians—big brains with unusual backgrounds, lofty academic credentials, and more than a touch of social cluelessness.

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

This story opens Michael Lewis, Flash Boys (New York: W.W. Norton, 2014), 15. Economic sociologists have also studied Spread Networks. Donald Mackenzie et al., “Drilling Through the Allegheny Mountains: Liquidity, Materiality and High-Frequency Trading” ( Jan., 2012), at http://www.sps.ed .ac.uk /__data /assets/pdf_file/0003/78186/LiquidityResub8.pdf. 131. Ibid. A. D. Wissner- Gross and C. E. Freer, “Relativistic Statistical Arbitrage,” Physical Review E 056104-1 82 (2010): 1– 7. Available at http://www .alexwg.org/publications/PhysRevE _82-056104.pdf. 132. Keller, “Robocops,” 1468. NOTES TO PAGES 131–132 277 133. Ibid. 134. Ibid. 135. See Matt Prewitt, “High-Frequency Trading: Should Regulators Do More?,” Michigan Telecommunications and Technology Law Review 19 (2012): 148 (discussing “spoofi ng” and other deceptive HFT tactics). 136.

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

Well, traders have to be moneymakers—especially so after they are hired. After that I would look at their trading style, the instruments they have traded, and how that fits into what we already have. There are many issues involved with hiring traders, and different characteristics are required for different kinds of trading. A macro trader does not have the same characteristics as a relative value trader, a long/short equity trader, or a statistical arbitrage trader. You need to look at the characteristics that are appropriate for a given strategy. In addition to track record, how do you determine how much capital to allocate to your traders? It depends on the market they are trading—what the level of the market is and if there is an opportunity in that market. It depends how they have been doing over the past few years and also how long they have been with us.

Mastering Private Equity by Zeisberger, Claudia,Prahl, Michael,White, Bowen, Michael Prahl, Bowen White

As Centre Director, he leads its research and outreach activities and has published on topics including operational value creation, responsible investment, LP portfolio construction and minority investment in family businesses. Bowen has spent his career working in and conducting research on the global alternative asset management industry. In the New York hedge fund industry, he researched topics from statistical arbitrage investment strategies in commodities markets to macroeconomic trends and global hedge fund performance. Having worked for both a proprietary trading firm and a fund of funds, he has seen first-hand the challenges faced by investors and allocators of capital to the hedge fund industry. An INSEAD alumnus, Bowen has also advised on a range of VC and growth equity fundraising opportunities across Southeast Asia.

The Outlaw Ocean: Journeys Across the Last Untamed Frontier by Ian Urbina

The police then raided three: “Sealand y el tráfico de armas [Sealand and arms trafficking],” El Mercurio (Santiago), June 17, 2000; José María Irujo, “Sealand, un falso principado en el mar [Sealand, a false principality at sea],” El País (Madrid), March 26, 2000; “Owner of Fort off Britain Issues His Own Passports,” New York Times, March 30, 1969. Nearly four thousand were sold in Hong Kong: Gooch, “Storm Warning.” The Panama Papers included evidence: Langhans, “Newer Sealand.” Each of Sealand’s two legs: Garfinkel, “Welcome to Sealand. Now Bugger Off.” In 2010, a team of researchers: A. D. Wissner-Gross and C. E. Freer, “Relativistic Statistical Arbitrage,” Physical Review, Nov. 5, 2010. One of the companies that HavenCo: Ryan Lackey, “HavenCo: What Really Happened” (presentation at DEF CON 11, Aug. 3, 2003). Within the video, see 30:15. “Almost all time was spent”: Thomas Stackpole, “The World’s Most Notorious Micronation Has the Secret to Protecting Your Data from the NSA,” Mother Jones, Aug. 21, 2013. After Lackey quit HavenCo: Ryan Lackey, “HavenCo: One Year Later” (presentation at DEF CON 9, n.d.).

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The Stack: On Software and Sovereignty by Benjamin H. Bratton

Hugh Tomlinson and Graham Burchell (New York: Columbia University Press, 1994), 214. 14.  Chris C. Demchak and Peter J. Dombrowski, “Rise of a Cybered Westphalian Age: The Coming Age,” Strategic Studies Quarterly 5, no. 1 (2011): 31–62. 15.  Stuart Elden, “Secure the Volume: Vertical Geopolitics and the Depth of Power,” Political Geography 34 (2013): 35–51. 16.  A. Wissner-Gross and C. Freer, “Relativistic Statistical Arbitrage,” Physical Review E 82, no. 5 (2010). On this topic in relation to geodesign, see also Geoff Manaugh, “Islands and the Speed of Light,” March 2011. http://bldgblog.blogspot.com/2011/03/islands-at-speed-of-light.html. 17.  Here I am departing from Catherine Malabou's use of the term plasticity, and toward the mutable future I refer more directly to the chemical qualities of what we commonly call “plastic.”

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Trading and Exchanges: Market Microstructure for Practitioners by Larry Harris

Since pairs traders generally do not know whether other traders are well informed, they often make mistakes when trading. Pairs traders also pay close attention to how quickly and how efficiently markets respond, on average, to new information about common fundamental factors. Arbitrageurs generally should be reluctant to trade against markets that quickly and efficiently aggregate new information because the prices in such markets tend to accurately reflect fundamental values. 17.3.2.3 Statistical Arbitrage Statistical arbitrageurs use factor models to generalize the pairs trading strategy to many instruments. Factor models are statistical models that represent instrument returns by a weighted sum of common factors plus an instrument-specific factor. The weights, called factor loadings, are unique for each instrument. The arbitrageur must estimate them. Either statistical arbitrageurs specify the factors, or they use statistical methods to identify the factors from returns data for many instruments.