Discover foundational and advanced techniques in quantitative equity trading from a veteran insider
In Quantitative Portfolio Management: The Art and Science of Statistical Arbitrage, distinguished physicist-turned-quant Dr. Michael Isichenko delivers a systematic review of the quantitative trading of equities, or statistical arbitrage. The book teaches you how to source financial data, learn patterns of asset returns from historical data, generate and combine multiple forecasts, manage risk, build a stock portfolio optimized for risk and trading costs, and execute trades.
In this important book, you'll discover:
* Machine learning methods of forecasting stock returns in efficient financial markets
* How to combine multiple forecasts into a single model by using secondary machine learning, dimensionality reduction, and other methods
* Ways of avoiding the pitfalls of overfitting and the curse of dimensionality, including topics of active research such as "benign overfitting" in machine learning
* The theoretical and practical aspects of portfolio construction, including multi-factor risk models, multi-period trading costs, and optimal leverage
Perfect for investment professionals, like quantitative traders and portfolio managers, Quantitative Portfolio Management will also earn a place in the libraries of data scientists and students in a variety of statistical and quantitative disciplines. It is an indispensable guide for anyone who hopes to improve their understanding of how to apply data science, machine learning, and optimization to the stock market.
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MICHAEL ISICHENKO, PhD, is a theoretical physicist and a quantitative portfolio manager who worked at Kurchatov Institute, University of Texas, University of California, SAC Capital Advisors, Societe Generale, and Jefferies. He received his doctorate in physics and mathematics from the Moscow Institute of Physics and Technology and is an expert in plasma physics, nonlinear dynamics, and statistical and chaos theory.
1 Market Data 9
1.1 Tick and bar data 9
1.2 Corporate actions and adjustment factor 10
1.3 Linear vs log returns 11
2 Forecasting 13
2.1 Data for forecasts 14
2.1.1 Point-in-time and lookahead 15
2.1.2 Security master and survival bias 16
2.1.3 Fundamental and accounting data 16
2.1.4 Analyst estimates 17
2.1.5 Supply chain and competition 18
2.1.6 M&A and risk arbitrage 18
2.1.7 Event-based predictors 18
2.1.8 Holdings and flows 19
2.1.9 News and social media 20
2.1.10 Macroeconomic data 21
2.1.11 Alternative data 21
2.1.12 Alpha capture 21
2.2 Technical forecasts 22
2.2.1 Mean reversion 22
2.2.2 Momentum 24
2.2.3 Trading volume 24
2.2.4 Statistical predictors 25
2.2.5 Data from other asset classes 25
2.3 Basic concepts of statistical learning 27
2.3.1 Mutual information and Shannon entropy 28
2.3.2 Likelihood and Bayesian inference 32
2.3.3 Mean square error and correlation 33
2.3.4 Bias-variance tradeoff 35
2.3.5 PAC learnability, VC dimension, and generalization error bounds 36
2.4 Machine learning 40
2.4.1 Types of machine learning 41
2.4.2 Overfitting 43
2.4.3 Ordinary and generalized least squares 44
2.4.4 Deep learning 46
2.4.5 Types of neural networks 48
2.4.6 Nonparametric methods 51
2.4.7 Cross-validation 54
2.4.8 Curse of dimensionality, eigenvalue cleaning, and shrinkage 56
2.4.9 Smoothing and regularization 61
188.8.131.52 Smoothing spline 62
184.108.40.206 Total variation denoising 62
220.127.116.11 Nadaraya-Watson kernel smoother 63
18.104.22.168 Local linear regression 64
22.214.171.124 Gaussian process 64
126.96.36.199 Ridge and kernel ridge regression 67
188.8.131.52 Bandwidth and hypertuning of kernel smoothers 68
184.108.40.206 Lasso regression 69
2.4.10 Generalization puzzle of deep and overparameterized learning 69
2.4.11 Online machine learning 74
2.4.12 Boosting 75
2.4.13 Randomized learning 79
2.4.14 Latent structure 80
2.4.15 No free lunch and AutoML 81
2.4.16 Computer power and machine learning 83
2.5 Dynamical modeling 87
2.6 Alternative reality 89
2.7 Timeliness-significance tradeoff 90
2.8 Grouping 91
2.9 Conditioning 92
2.10 Pairwise predictors 92
2.11 Forecast for securities from their linear combinations 93
2.12 Forecast research vs simulation 95
3 Forecast Combining 97
3.1 Correlation and diversification 98
3.2 Portfolio combining 99
3.3 Mean-variance combination of forecasts 102
3.4 Combining features vs combining forecasts 103
3.5 Dimensionality reduction 104
3.5.1 PCA, PCR, CCA, ICA, LCA, and PLS 105
3.5.2 Clustering 107
3.5.3 Hierarchical combining 108
3.6 Synthetic security view 108
3.7 Collaborative filtering 109
3.8 Alpha pool management 110
3.8.1 Forecast development guidelines 111
220.127.116.11 Point-in-time data 111
18.104.22.168 Horizon and scaling 111
22.214.171.124 Type of target return 112
126.96.36.199 Performance metrics 112
188.8.131.52 Measure of forecast uncertainty 112
184.108.40.206 Correlation with existing forecasts 112
220.127.116.11 Raw feature library 113
18.104.22.168 Overfit handling 113
3.8.2 Pnl attribution 114
22.214.171.124 Marginal attribution 114
126.96.36.199 Regression-based attribution 114
4 Risk 117
4.1 Value at risk and expected shortfall 117
4.2 Factor models 119
4.3 Types of risk factors 120
4.4 Return and risk decomposition 121
4.5 Weighted PCA 122
4.6 PCA transformation 123
4.7 Crowding and liquidation 124
4.8 Liquidity risk and short squeeze 126
4.9 Forecast uncertainty and alpha risk 127
5 Trading Costs 129
5.1 Slippage 130
5.2 Impact 130
5.2.1 Empirical observations 132
5.2.2 Linear impact model 133
5.2.3 Impact arbitrage 135
5.3 Cost of carry 135
6 Portfolio Construction 137
6.1 Hedged allocation 137
6.2 Single-period vs multi-period mean-variance utility 139
6.3 Single-name multi-period optimization 140
6.3.1 Optimization with fast impact decay 141
6.3.2 Optimization with exponentially decaying impact 142
6.3.3 Optimization conditional on a future position 143
6.3.4 Position value and utility leak 145
6.3.5 Optimization with slippage 146
6.4 Multi-period portfolio optimization 148
6.4.1 Unconstrained portfolio optimization with linear impact costs 149
6.4.2 Iterative handling of factor risk 150
6.4.3 Optimizing future EMA positions 151
6.4.4 Portfolio optimization using utility leak rate 151
6.4.5 Notes on portfolio optimization with slippage 152
6.5 Portfolio capacity 152
6.6 Portfolio optimization with forecast revision 153
6.7 Portfolio optimization with forecast uncertainty 156
6.8 Kelly criterion and optimal leverage 157
6.9 Intraday optimization and execution 160
6.9.1 Trade curve 160
6.9.2 Forecast-timed execution 161
6.9.3 Algorithmic trading and HFT 162
6.9.4 HFT controversy 166
7 Simulation 169
7.1 Simulation vs production 170
7.2 Simulation and overfitting 171
7.3 Research and simulation efficiency 172
7.4 Paper trading 173
7.5 Bugs 173
Afterword: Economic and Social Aspects of Quant Trading 179
A1 Secmaster mappings 183
A2 Woodbury matrix identities 184
A3 Toeplitz matrix 185
Questions index 195
Quotes index 197
Stories index 199
Science is what we understand well enough to explain to a computer. Art is everything else we do.
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.
- 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 F. Jareño, A. Escribano, A. Cuenca, Macroeconomic variables and stock markets: an international study, Applied Econometrics and International Development, 19(1), 2019.
- 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.
- 4 M. Avellaneda, J.-H. Lee. Statistical arbitrage in the US equities market, Quantitative Finance, 10(7), pp. 761-782, 2010.
- 5 P. Muller, Proprietary trading: truth and fiction, Quantitative Finance, 1(1), 2001.
- 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...
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