Читать книгу Quantitative Portfolio Management - Michael Isichenko - Страница 9

Science is what we understand well enough to explain to a computer. Art is everything else we do.

Donald Knuth

Financial investment is a way of increasing existing wealth by buying and selling assets of fluctuating value and bearing related risk. The value of a bona fide investment is expected to grow on average, or in expectation, albeit without a guarantee. The very fact that such activity, pure gambling aside, exists is rooted in the global accumulation of capital, or, loosely speaking, increase in commercial productivity through rational management and technological innovation. There are also demographic reasons for the stock market to grow—or occasionally crash.

Another important reason for investments is that people differ in their current need for money. Retirees have accumulated assets to spend while younger people need cash to pay for education or housing, entrepreneurs need capital to create new products and services, and so forth. The banking and financial industry serves as an intermediary between lenders and borrowers, facilitating loans, mortgages, and municipal and corporate bonds. In addition to debt, much of the investment is in equity. A major part of the US equity market is held by pension funds, including via mutual funds holdings.¹ Aside from occasional crisis periods, the equity market has outperformed the inflation rate. Stock prices are correlated with the gross domestic product (GDP) in all major economies.² Many index and mutual funds make simple diversified bets on national or global stock markets or industrial sectors, thus providing inexpensive investment vehicles to the public.

In addition to the traditional, long-only investments, many hedge funds utilize long-short and market-neutral strategies by betting on both asset appreciation and depreciation.³ Such strategies require alpha, or the process of continuous generation of specific views of future returns of individual assets, asset groups, and their relative movements. Quantitative alpha-based portfolio management is conceptually the same for long-only, long-short, or market-neutral strategies, which differ only in exposure constraints and resulting risk profiles. For reasons of risk and leverage, however, most quantitative equity portfolios are exactly or approximately market-neutral. Market-neutral quantitative trading strategies are often collectively referred to as statistical arbitrage or statarb. One can think of the long-only market-wide investments as sails relying on a breeze subject to a relatively stable weather forecast and hopefully blowing in the right direction, and market-neutral strategies as feeding on turbulent eddies and waves that are zero-mean disturbances not transferring anything material—other than wealth changing hands. The understanding and utilization of all kinds of pricing waves, however, involves certain complexity and requires a nontrivial data processing, quantitative, and operational effort. In this sense, market-neutral quant strategies are at best a zero-sum game with a natural selection of the fittest. This does not necessarily mean that half of the quants are doomed to fail in the near term: successful quant funds probably feed more on imperfect decisions and execution by retail investors, pension, and mutual funds than on less advanced quant traders. By doing so, quant traders generate needed liquidity for traditional, long-only investors. Trading profits of market-neutral hedge funds, which are ultimately losses (or reduced profits) of other market participants, can be seen as a cost of efficiency and liquidity of financial markets. Whether or not this cost is fair is hard to say.

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1 1 Organization for Economic Co-operation and Development (OECD) presents a detailed analysis of world equity ownership: A. De La Cruz, A. Medina, Y. Tang, Owners of the World's Listed Companies, OECD Capital Market Series, Paris, 2019.

2 2 F. Jareño, A. Escribano, A. Cuenca, Macroeconomic variables and stock markets: an international study, Applied Econometrics and International Development, 19(1), 2019.

3 3 A.W. Lo, Hedge Funds: An Analytic Perspective - Updated Edition, Princeton University Press, 2010.

Historically, statistical arbitrage started as trading pairs of similar stocks using mean-reversion-type alpha signals betting on the 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. Just like it is difficult to make forecasts in efficient markets, it is also difficult, but not impossible, to optimally combine forecasts due to their correlation and what is known as the curse of dimensionality. To break the never ending cycle of quantitative trial and error, it is important to understand fundamental limitations on what can and what can't be done.

The book is structured as follows. Chapter 1 briefly reviews raw and derived market data used by quants. Alpha generation, the central part of the quant process, is discussed in Chapter 2. This chapter starts with additional financial data usable for forecasting future asset returns. Both theoretical and algorithmic aspects of machine learning (ML) are discussed with an emphasis on challenges specific to financial forecasting. Once multiple alphas have been generated, they need to be combined to form the best possible forecast for each asset. Good ways of combining alphas is an alpha in itself. ML approaches to forecast combining are discussed in Chapter 3. A formal view of risk management, as relevant to portfolio construction, is presented in Chapter 4. Trading costs, with an emphasis on their mathematical structure, are reviewed in Chapter 5. There a case is made for a linear impact model that, while approximate, has a strong advantage of making several closed-form multi-period optimization solutions possible. Impact of a net flow of funds at a macro scale is also discussed with implications for stock market elasticity and bubbles. Chapter 6 describes the construction of a portfolio optimized for expected future profits subject to trading costs and risk preferences. This part tends to use the most math and includes previously unpublished results for multi-period portfolio optimization subject to impact and slippage costs. Related questions of portfolio capacity and optimal leverage, including the Kelly criterion, are also discussed. Chapter 7 concerns the purpose and implementation of a trading simulator and its role in quant research. A few auxiliary algorithmic and mathematical details are presented in appendices.

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1 11 X. Gabaix, R.S.J. Koijen, In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis, Swiss Finance Institute Research Paper No. 20-91, Available at SSRN: https://ssrn.com/abstract=3686935, 2021.

2 12 J.-P. Bouchaud, J.D. Farmer, F. Lillo, How markets slowly digest changes in supply and demand, arXiv:0809.0822 [q-fin.TR], 2008.

Computation is a primary tool in most parts of the quantitative trading process and in machine learning. Several aspects of computing, including coding style, efficiency, bugs, and environmental issues are discussed throughout the book. A few important machine learning concepts, such as bias-variance tradeoff (Secs. 2.3.5 and 2.4.12) and the curse of dimensionality (Sec. 2.4.10), are supported by small self-contained pieces of Python code generating meaningful plots. The reader is encouraged to experiment along these lines. It is often easier to do productive experimental mathematics than real math.

Some of the material covering statistics, machine learning, and optimization necessarily involves a fair amount of math and relies on academic and applied research in various, often disjoint, fields. Our exposition does not attempt to be mathematically rigorous and mostly settles for a “physicist's level of rigor” while trying to build a qualitative understanding of what's going on. Accordingly, the book is designed to be reasonably accessible and informative to a less technical reader who can skip over the more scary math and focus on the plain English around it. For example, the fairly technical method of boosting in ML (Sec. 2.4.14) is explained as follows: The idea of boosting is twofold: learning on someone else's errors and voting by majority.

The field of quantitative portfolio management is too broad for a single paper or book to cover. Important topics either omitted here or just mentioned in passing include market microstructure theory, algorithmic execution, big data management, and non-equity asset classes. Several books cover these and related topics.^{13,14,15,16,17} While citing multiple research papers in various fields, the author could not possibly do justice to all relevant or original multidisciplinary contributions. The footnote references include work that seemed useful, stimulating, or just fascinating when developing (or explaining) forecasting and optimization ideas for quantitative portfolio management. Among the many destinations where Google search brings us, the arXiv,¹⁸ is an impressive open source of reasonably high signal-to-noise ratio¹⁹ publications.

A note about footnotes. Citing sources in footnotes seems more user-friendly than at the end of chapters. Footnotes are also used for various reflections or mini stories that could be either meaningful or entertaining but often tangential to the main material.

Finally, in the spirit of the quant problem-solving sportsmanship, and for the reader's entertainment, a number of actual interview questions asked at various quant job interviews are inserted in different sections of the book and indexed at the end, along with the main index, quotes, and the stories.

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1 13 R.C. Grinold, R.N. Kahn, Active Portfolio Management: A Quantitative Approach for Producing Superior Returns and Controlling Risk. McGraw-Hill, New York, 2000.

2 14 R.K. Narang, Inside the Black Box: A Simple Guide to Quantitative and High Frequency Trading, 2nd Edition, Wiley, 2013.

3 15 J.-P. Bouchaud, J. Bonart, J. Donier, M. Gould, Trades, Quotes and Prices. Financial Markets Under the Microscope, Cambridge University Press, 2018.

4 16 Z. Kakushadze, J.A. Serur, 151 Trading Strategies, Available at SSRN: https://ssrn.com/abstract=3247865, 2018.

5 17 Finding Alphas: A Quantitative Approach to Building Trading Strategies, 2nd Edition, Edited by I. Tulchinsky, Wiley, New York, 2019.

6 18 https://arxiv.org.

7 19 A. Jackson, From Preprints to E-prints: The Rise of Electronic Preprint Servers in Mathematics, Notices of the AMS, 49, 2002.