similarity.4 The strategy appears to be first used for proprietary trading at Morgan Stanley in the 1980s. The names often mentioned among the statarb pioneers include Gerry Bamberger, Nunzio Tartaglia, David E. Shaw, Peter Muller, and Jim Simons. The early success of statistical arbitrage started in top secrecy. In a rare confession, Peter Muller, the head of the Process Driven Trading (PDT) group at Morgan Stanley in the 1990s, wrote: Unfortunately, the mere knowledge that it is possible to beat the market consistently may increase competition and make our type of trading more difficult. So why did I write this article? Well, one of the editors is a friend of mine and asked nicely. Plus, chances are you won't believe everything I'm telling you.5 The pair trading approach soon developed into a more general portfolio trading using mean reversion, momentum, fundamentals, and any other types of forecast quants can possibly generate. The secrets proliferated, and multiple quantitative funds were started. Quantitative trading has been a growing and an increasingly competitive part of the financial landscape since early 1990s.
On many occasions within this book, it will be emphasized that it is difficult to build successful trading models and systems. Indeed, quants betting on their complex but often ephemeral models are not unlike behavioral speculators, albeit at a more technical level. John Maynard Keynes once offered an opinion of a British economist on American finance:6 Even outside the field of finance, Americans are apt to be unduly interested in discovering what average opinion believes average opinion to be; and this national weakness finds its nemesis in the stock market... It is usually agreed that casinos should, in the public interest, be inaccessible and expensive. And perhaps the same is true of stock exchanges.
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1 4 M. Avellaneda, J.-H. Lee. Statistical arbitrage in the US equities market, Quantitative Finance, 10(7), pp. 761–782, 2010.
2 5 P. Muller, Proprietary trading: truth and fiction, Quantitative Finance, 1(1), 2001.
3 6 J.M. Kaynes, The General Theory of Employment, Interest, and Money, Macmillan, 1936.
This book touches upon several theoretical and applied disciplines including statistical forecasting, machine learning, and optimization, each being a vast body of knowledge covered by many dedicated in-depth books and reviews. Financial forecasting, a poor man's time machine giving a glimpse of future asset prices, is based on big data research, statistical models, and machine learning. This activity is not pure math and is not specific to finance. There has been a stream of statistical ideas across applied fields, including statements that most research findings are false for most research designs and for most fields.7 Perhaps quants keep up the tradition when modeling financial markets. Portfolio optimization is a more mathematical subject logically decoupled from forecasting, which has to do with extracting maximum utility from whatever forecasts are available.
Our coverage is limited to topics more relevant to the quant research process and based on the author's experience and interests. Out of several asset classes available to quants, this book focuses primarily on equities, but the general mathematical approach makes some of the material applicable to futures, options, and other asset classes. Although being a part of the broader field of quantitative finance, the topics of this book do not include financial derivatives and their valuation, which may appear to be main theme of quantitative finance, at least when judged by academic literature.8 Most of the academic approaches to finance are based on the premise of efficient markets,9 precluding profitable arbitrage. Acknowledging market efficiency as a pretty accurate, if pessimistic, zeroth-order approximation, our emphasis is on quantitative approaches to trading financial instruments for profit while controlling for risks. This activity constitutes statistical arbitrage.
When thinking about ways of profitable trading, the reader and the author would necessarily ask the more general question: what makes asset prices move, predictably or otherwise? Financial economics has long preached theories involving concepts such as fundamental information, noise and informed traders, supply and demand, adaptivity,10 and, more recently, inelasticity,11 which is a form of market impact (Sec. 5.4). In contrast to somewhat axiomatic economists' method, physicists, who got interested in finance, have used their field's bottom-up approach involving market microstructure and ample market data.12 It is definitely supply and demand forces, and the details of market organization, that determine the price dynamics. The dynamics are complicated, in part due to being affected by how market participants learn/understand these dynamics and keep adjusting their trading strategies. From the standpoint of a portfolio manager, price changes are made of two parts: the impact of his own portfolio and the impact of others. If the former can be treated as trading costs, which are partially under the PM's control, the latter is subject to statistical or dynamical modeling and forecasting.
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1 7 J.P.A. Ioannidis, Why Most Published Research Findings Are False, PLoS Med 2(8): e124, 2005.
2 8 P. Wilmott, Frequently Asked Questions in Quantitative Finance, Wiley, 2009.
3 9 P.A. Samuelson, Proof That Properly Anticipated Prices Fluctuate Randomly, Industrial Management Review, 6, pp. 41–49, 1965.
4 10 A.W. Lo, The Adaptive Markets Hypothesis: Market Efficiency from an Evolutionary Perspective, Journal of Portfolio Management, 30(5), pp. 15–29, 2004.
Among other things, this book gives a fair amount of attention to the combination of multiple financial forecasts, an important question not well covered in the literature. Forecast combination is a more advanced version of the well-discussed theme of investment diversification.
