Jacobs Levy Home
Firm Profile
Equity Research
Jacobs Levy Center
BF/JL Awards
JLM Simulator
Site Search
Contact Info


Security Selection    

Copyright 1989, Institutional Investor Journals. Reproduced and republished from Journal of Portfolio Management with permission.  All rights reserved.

Copyright 1988, Association for Investment Management and Research. Reproduced and republished from Financial Analysts Journal with permission. All rights reserved.

The Complexity of the Stock Market
by Bruce I. Jacobs and Kenneth N. Levy, The Journal of Portfolio Management, Fall 1989

Disentangling Equity Return Regularities: New Insights and Investment Opportunities
by Bruce I. Jacobs and Kenneth N. Levy, Financial Analysts Journal, May/June 1988

The articles abstracted here address Jacobs Levy Equity Management's view of the market as a complex system and some of the methods that can best be used to “disentangle” this complexity.

U.S. equity market returns are driven by complex combinations of company fundamentals, such as earnings and growth rates; macroeconomic conditions, such as interest rates and inflation; and behavioral factors, such as investors' tendency to overreact to news and events. As a result, the market is permeated by a complex web of interrelated return regularities. Disentangling this web allows potentially profitable investment opportunities to emerge.

“The Complexity of the Stock Market” first appeared in the 15th anniversary issue of the Journal of Portfolio Management and was selected for inclusion in Streetwise: The Best of the Journal of Portfolio Management. This article demonstrates that active quantitative investing (despite the assertions of the efficient market theorists and random walk advocates) is not a futile task; at the same time, it explains why simple investment techniques, such as buying low-P/E stocks, cannot provide consistent outperformance. Identifying the complex web of interrelationships that underlie stock price movements, and exploiting them for profitable investing, requires extensive computer-based statistical modeling.

Robust insights into stock price behavior emerge only from an analysis that carefully considers numerous factors simultaneously. Naïve attempts to relate returns and potential return predictors do not take correlation into account. Quintiling or univariate analysis, for instance, naively assumes that prices are responding only to the variable under consideration. By contrast, simultaneous analysis of all relevant variables takes into account and adjusts for any correlations; the results of such analysis provide a truer picture of real return-predictor relationships.

“Disentangling Equity Return Regularities: New Insights and Investment Opportunities” describes Jacobs Levy's pioneering methodology for “disentangling” and “purifying” return effects via multivariate analysis. Disentangling distinguishes real effects from mere proxies (and real investment opportunities from spurious ones). Disentangling is of the utmost importance because it results in the “pure” returns to a given predictor, uncontaminated by the possible effects of other related variables. These pure returns are less volatile, and more predictable, than the naïve return estimates produced by less rigorous methodologies. “Disentangling” won a Graham & Dodd Award from the Financial Analysts Journal and was subsequently translated into Japanese for the Security Analysts Journal of Japan.

Key Articles:

· “Ten Investment Insights that Matter,” by Bruce I. Jacobs and Kenneth N. Levy, Journal of Portfolio Management, Special 40th Anniversary Issue, September 2014. article
This article discusses the key insights that inform our investment process, developed over 30 years of research and portfolio management. These insights and the resulting rewards to active management stem from the realization that the market is a complex system. Paradoxically, if the market were simpler, and investing easier, the rewards would be smaller, because many would have the skills to succeed. It is the market’s very complexity that offers the opportunity to outperform—to those investors willing and able to grapple with that complexity.

· “Investing in a Multidimensional Market,” by Bruce I. Jacobs and Kenneth N. Levy, Financial Analysts Journal, November/December 2014. article
Many years ago, Bruce Jacobs and Ken Levy demonstrated that there is much greater dimensionality to the stock market than is suggested by the one-factor capital asset pricing model. Investors today continue to underestimate the market’s dimensionality through their recent embrace of “smart beta” strategies. Such strategies assume a market in which a few chosen factors produce persistent returns. In reality, there are numerous factors that produce returns, which vary over time. Those returns can best be captured by a multidimensional approach that emphasizes diversification across many proprietary factors and continuous adjustment of exposures to those factors.

· “The Complexity of the Stock Market,” by Bruce I. Jacobs and Kenneth N. Levy, The Journal of Portfolio Management, Fall 1989; and abstracted in The CFA Digest, Spring 1990. Also in Peter L. Bernstein and Frank J. Fabozzi, Eds. Streetwise: The Best of The Journal of Portfolio Management. Princeton, NJ: Princeton University Press, 1998.(1) article
The stock market is a complex system, somewhere between the domains of order and randomness. Ordered systems are simple and predictable, and random systems are inherently unpredictable. Simple theories do not adequately describe security pricing, nor is pricing random. Rather, the market is permeated by a web of interrelated return effects. Substantial computational power is needed to disentangle, model, and exploit these return regularities.

· “Disentangling Equity Return Regularities: New Insights and Investment Opportunities,” by Bruce I. Jacobs and Kenneth N. Levy, Financial Analysts Journal, May/June 1988; abstracted in The CFA Digest, Fall 1988; also translated in The Security Analysts Journal of Japan, March and April 1990.(2) article
Stock market phenomena such as the January and low-P/E effects entice investors with prospects of extraordinary returns. Most previous stock market anomaly research has focused on one or two return regularities at a time. This seminal article demonstrates that multivariate regression can provide a unified framework for “disentangling” and analyzing numerous return effects simultaneously. Disentangling purifies the effect of each anomaly, affording a clearer picture of which anomalies are “real” and which are merely proxies for other effects.

While pure payoffs may be smaller than the naïve payoffs of univariate analyses (given the independent nature of the pure effects and the proxying behavior of the naïve effects), their statistical significance is often greater. The residual reversal effect is an exception, emerging stronger in magnitude in its pure form than its naïve form, primarily because the pure measure separates out related effects such as earnings surprise. Some effects, including cash flow/price, disappear completely in their pure form. And both naïve and pure returns to beta prove inconsequential in explaining cumulative returns.

The strength and persistence of returns to such anomaly measures as trends in analysts' earnings estimates represent evidence against semi-strong market efficiency. The significant payoffs to measures such as residual reversal suggest that past prices alone do matter—that is, the market is not even weak—form efficient.

Controlling for tax-loss selling and other attributes in a multivariate framework mitigates the January seasonals exhibited by many of the naïve anomaly measures. For instance, the small size effect's January seasonal vanishes. The yield effect's January seasonal remains strong, however. Also, because long-term tax-loss selling is more powerful than short-term, investor behavior appears suboptimal. A negative January seasonal in pure returns to the relative-strength measure appears to arise from profit-taking associated with tax-gain deferral.

Returns to many attributes appear to have market-related components. For example, naïve returns to low P/E behave defensively, while pure returns to low P/E are not market-related at all. Apparently naïve returns to low P/E are proxies for related defensive effects such as the yield effect. Returns to beta, however, are strongly procyclical in both their naïve and pure forms.

Other Articles:

· “Earnings Estimates, Predictor Specification, and Measurement Error,” by Bruce I. Jacobs, Kenneth N. Levy and Mitchell C. Krask, The Journal of Investing, Summer 1997.(3) article
Increased use of expectational data for modeling stock returns places a spotlight on the specification of predictor variables. Choices between alternative specifications of a given predictor such as E/P or earnings trend, or between different treatments of missing variables, can have wide-ranging effects on portfolio selection and quantitative modeling. The importance of predictor specification may vary depending upon the predictor, the investment strategy, and the estimation procedure used. The relationship between predictors and returns may also vary across types of stocks; for instance, the relationship may be distributed differentially across stocks by the degree of analyst coverage.

· “High-Definition Style Rotation,” by Bruce I. Jacobs and Kenneth N. Levy, The Journal of Investing, Fall 1996; and abstracted in The CFA Digest, Spring 1997.(4) article
Price behavior varies across different types of stock. This suggests a strategy of rotating a portfolio's allocations across styles—growth, value, large-cap, and small—to take advantage of differential performance across different economic environments. The issue then is how to define style. A “high-definition” approach looks at many stock attributes and disentangles the effects of each. This results in a detailed map of returns to stock attributes, with the potential to provide better returns than rotation strategies based on more naïve definitions of style.

· “Forecasting the Size Effect,” by Bruce I. Jacobs and Kenneth N. Levy, Financial Analysts Journal, May/June 1989. article
Small-capitalization stocks have provided higher average returns than large-capitalization stocks, and the outperformance has been strongest in the month of January. A multifactor analysis “disentangles” the effect of firm size from related factors that may influence return, including analyst neglect, low P/E, and tax-loss selling. Disentangling reveals the January small-firm seasonal to be a mere surrogate for the rebound that follows the abatement of tax-loss selling. An analysis of the pure returns to size shows that small stocks outperform the market at some times and lag at others. The payoffs to the size effect are predictable in a broader empirical framework that incorporates macroeconomic drivers such as interest rates and industrial production.

· “Calendar Anomalies: Abnormal Returns at Calendar Turning Points,” by Bruce I. Jacobs and Kenneth N. Levy, Financial Analysts Journal, November/December 1988; and abstracted in The CFA Digest, Summer 1989. article
Abnormal equity returns are associated with the turn of the year, the week and the month, as well as with holidays and the time of day. Tax-loss selling at year-end, cash flows at month-end, and negative news releases over the weekend may explain some of these return abnormalities, but human psychology offers a more promising explanation. Calendar anomalies are difficult to exploit on a stand-alone basis, because of the transactions costs that would be involved. However, an investor can schedule planned trades to take advantage of calendar-based return patterns.

· “On the Value of 'Value',” by Bruce I. Jacobs and Kenneth N. Levy, Financial Analysts Journal, July/August 1988; and abstracted in The CFA Digest, Spring 1989. article
Psychological factors, “noise” trading, and fads in investment styles can cause stock prices to deviate from “fair” value, and such departures can be significant and long-lasting. In a market that is not strictly price-efficient, value as measured by a dividend discount model (DDM) is but a small part of the security pricing story. An examination of security returns over the 1982-87 period shows that a DDM strategy would have produced positive but insignificant returns. When pitted against low P/E, a DDM strategy provided a lower payoff and was significant in fewer quarters. And in a multivariate regression considering DDM simultaneously with 25 equity attributes, DDM was insignificant, while many equity attributes, including sales/price, neglect, relative strength, residual-return reversal, trends in analysts' estimates and earnings surprise, provided positive, statistically significant returns.


Copyright © 2017

Copyright © 2000

Chinese Translation

Copyright © 2006

· Equity Management: The Art and Science of Modern Quantitative Investing, Second Edition, by Bruce I. Jacobs and Kenneth N. Levy, forewords by Harry M. Markowitz, Nobel Laureate, McGraw-Hill, New York, 2017.

· Equity Management: Quantitative Analysis for Stock Selection, by Bruce I. Jacobs and Kenneth N. Levy. McGraw-Hill, New York, NY, 2000. Authorized Chinese translation from English language edition, McGraw-Hill, China Machine Press, 2006.

This new edition of Equity Management reflects 30 years of research and investment practice by two pioneers of quantitative equity investing. In the 1980s, Bruce Jacobs and Ken Levy published in peer-reviewed journals a series of articles on detecting and exploiting the factors that significantly influence stock returns. Since then, they have examined short selling in the context of long-short portfolios, optimization of portfolios with short sales or other leveraged positions, markets in crisis, and models that can simulate realistic market behavior.

Equity Management: The Art and Science of Modern Quantitative Investing includes the classic 15 articles from the original edition plus 24 articles that were published since the first edition appeared. Together, they present a compelling argument for the benefits of a quantitative approach in a complex, multidimensional, and dynamic factor world.

The chapters are grouped into eight parts, with introductory material that places each section within the broader context of the investment body of knowledge. Part 1 examines the intricacies of stock price behavior and focuses on detecting the characteristics, or factors, behind them. Security prices are neither efficient nor random and unpredictable. Rather, the market is a complex system, permeated by a web of return regularities. These regularities must be "disentangled" to arrive at the real sources of return. This requires analyzing numerous promising return-predictor relationships simultaneously.

Part 2 looks at how best to exploit the investment opportunities detected. The chapters outline a holistic approach that is multidimensional and dynamic. Viewing the market as integrated allows for greater breadth of investigation and greater depth of analysis, hence enhances the potential for more and better insights. A dynamic, multidimensional, proprietary approach that can adapt to changes in the underlying environment is better poised to capture opportunities than an approach that restricts itself to a small number of well-known and static factors.

Part 3 examines how short sales can expand investment opportunities and improve performance. Balancing long and short positions within a portfolio creates a market-neutral portfolio whose performance should reflect the returns and risks of the constituent securities, but not the performance of the overall market. The return from security selection can be transported to virtually any asset class via derivatives, allowing the investor to take advantage of manager skill, wherever it lies, while maintaining any desired asset allocation.

Part 4 focuses on another long-short approach—enhanced active equity, or 130-30 type portfolios. These portfolios retain full exposure to the market return, while pursuing excess returns via short positions and leveraged long positions. The development of 130-30 type portfolios was motivated by Jacobs and Levy’s research into optimization of long-short portfolios, which showed that the optimization process should consider long positions, short positions, and any benchmark holding simultaneously.

The authors also tackled a problem that arises when optimizing portfolios that contain both long and short positions. As the chapters in Part 5 explain, the factor or scenario models of covariance that simplify the optimization process for long-only portfolios do not necessarily apply to long-short portfolios. Jacobs and Levy, working with Harry Markowitz, provide a solution they call “trimability.”

Part 6 addresses the unique risks of leverage, which are distinct from the risk captured by standard deviation, or volatility; most notable is the risk that a margin call can force the unwinding of positions. The mean-variance model central to modern portfolio theory does not consider these unique risks and can thus lead to “optimal” portfolios with very high leverage. The authors present an alternative model—mean-variance-leverage optimization—that allows an investor who is both volatility-averse and leverage-averse to assess the utility of a portfolio.

High levels of leverage almost led to the demise of hedge fund Long-Term Capital Management in 1998 and to the disruption of the entire financial system in 2008-2009. Part 7 examines these episodes and other periods of market crisis, including the 1987 stock market crash. One conclusion is that products and strategies that promise increased returns at reduced risk have attracted investors, encouraged leverage, and too often precipitated not only their own demise, but also the near-collapse of the global economy.

Part 8 presents work undertaken with Harry Markowitz on a model for simulating market behavior. The Jacobs Levy Markowitz Market Simulator (JLMSim) allows users to create their own market models from the bottom up by specifying the numbers and types of market entities, including portfolio analysts, traders, and investors, as well as their decision rules. The results so far suggest that types of investors (value versus momentum), as well as trading rules, can have significant impacts on market stability.

Book Chapters:

“Equity Analysis in a Complex Market,” by Bruce I. Jacobs and Kenneth N. Levy, in Frank J. Fabozzi, Ed. Encyclopedia of Financial Models,Volume II. John Wiley & Sons, Hoboken, NJ, November 2012, and Frank J. Fabozzi and Harry M. Markowitz, Eds. Equity Valuation and Portfolio Management. John Wiley & Sons, Hoboken, NJ, September 2011. Earlier versions appeared as “Investment Analysis: Profiting from a Complex Equity Market” in Frank J. Fabozzi, Ed. Handbook of Finance, Volume II: Investment Management and Financial Management. John Wiley & Sons, Hoboken, NJ, 2008; in Frank J. Fabozzi, Ed. Active Equity Portfolio Management. Frank J. Fabozzi Associates, New Hope, PA, 1998; and in Frank J. Fabozzi, Ed. Handbook of Portfolio Management. Frank J. Fabozzi Associates, New Hope, PA, 1998.
An investment approach that begins with a broad equity universe provides a coherent evaluation framework that benefits from all the insights to be garnered from a wide and diverse range of securities, including variations in price behavior across different types of stocks, and is poised to take advantage of more profit opportunities than a more segmented approach can offer. Because the effects of different sources of stock return can overlap, it is also important to disentangle the connections by examining all variables of interest simultaneously. Disentangling reduces the noise in return estimates, reveals opportunities that might otherwise remain hidden, and improves predictability.

“Security Valuation in a Complex Market,” by Bruce I. Jacobs and Kenneth N. Levy, Chapter 1 in T. Daniel Coggin and Frank J. Fabozzi, Eds. Applied Equity Valuation. Frank J. Fabozzi Associates, New Hope, PA, 1999.
The stock market is characterized by a complex web of interrelated return effects that form predictable patterns of mispricing across stocks and over time. Detecting these patterns requires breadth of analysis and depth of inquiry; disentangling the patterns, separating each from the effects of the others, results in more robust and predictable return-predictor relationships.

· “Stock Market Complexity and Investment Opportunity,” by Bruce I. Jacobs and Kenneth N. Levy, in Frank J. Fabozzi, Ed. Managing Institutional Assets. Harper Row, New York, NY, 1990.(5)
The Efficient Market Hypothesis and the Capital Asset Pricing Model cannot represent the true complexity of security pricing. The market is not totally efficient; it is permeated by numerous price patterns that can be exploited to offer excess returns to active managers. However, these patterns are not detectable or exploitable by the CAPM, low P/E, high B/P or other simple tools. Rather, a complex market calls for the judicious application of computer power to disentangle the market's cross-currents of returns.

· “Trading Tactics in an Inefficient Market,” by Bruce I. Jacobs and Kenneth N. Levy, in Wayne H. Wagner, Ed. The Complete Guide to Securities Transactions: Enhancing Investment Performance and Controlling Costs. John Wiley & Sons, New York, NY, 1989.
Multivariate analyses of stock price behavior detect numerous patterns that may be exploitable by investment portfolios. Among these are so-called “calendar effects”—the tendency of stock prices in general to vary in systematic ways according to the time of day, day of week, month of year, etc. These calendar anomalies are difficult to exploit because of the transaction costs involved. However, investors may be able to benefit by using calendar effects to time preconceived trades.

Conference Proceedings:

· “How Dividend Discount Models Can Be Used to Add Value,” by Bruce I. Jacobs and Kenneth N. Levy, in H. Russell Fogler and Darwin M. Bayston, Eds. ICFA Continuing Education: Improving Portfolio Performance With Quantitative Models. Association for Investment Management and Research (today the CFA Institute), Charlottesville, VA, 1989.
The dividend discount model (DDM) appeals to investors because it is a forward-looking model grounded in fundamental analysis. The DDM, however, tends to pick up effects from related factors, such as low P/E, yield, beta, and risk. Multivariate regression including all these factors reveals that DDM's predictive power is often dwarfed by other value attributes.

· “Disentangling Equity Return Regularities,” by Bruce I. Jacobs and Kenneth N. Levy, in Katrina F. Sherrerd, Ed. ICFA Continuing Education: Equity Markets and Valuation Methods. Association for Investment Management and Research (today the CFA Institute), Charlottesville, VA, 1988.(6)
Research reveals a web of cross-sectional and time-dependent return regularities. Some are related to value attributes, some to earnings, some to stock price, and some to time. These regularities tend to be interrelated; it is important to unravel them to determine the real effect of each, independent of the “noise” created by the other effects. The resulting “pure” effects can be exploited by active management. For example, a multidimensional approach places “bets” on several anomalies simultaneously, with the strength of each bet a function of the historical strength and consistency of the anomaly. This approach can be refined by considering variations over time and/or macroeconomic drivers.

Industry Press Publications:

· “The Case for Quantitative Equity Management,” by Bruce I. Jacobs and Kenneth N. Levy, European Pension News, September 20, 1999. article
Quantitative equity management allows for the breadth, discipline and portfolio integrity needed to detect potential profit opportunities and to exploit them in portfolios that can offer superior returns at controlled levels of risk.

· “Web of 'Regularities' Leads to Opportunity,” by Bruce I. Jacobs and Kenneth N. Levy, Pensions & Investments, March 7, 1988.
Some return regularities are linked to macroeconomic drivers such as inflation or exchange rates, others to the institutional structure of the market, including the tax code. Still others have psychological underpinnings. For example, the return reversal effect may be attributable to the human tendency to overreact to unexpected events. Even the dividend discount model is hostage to market psychology, with the model's effectiveness differing between up and down markets. Understanding the sources of these regularities can open the door to opportunities for investors. article

· “Investment Management: Opportunities in Anomalies?” by Bruce I. Jacobs and Kenneth N. Levy, Pension World, February 1987.(7)
The small-stock effect, the low-P/E effect, the day-of-the-week effect and other systematic patterns of stock price behavior seem anomalous in the context of the Efficient Market Hypothesis. Many seem to offer opportunities for profitable active investment. It is important to realize, however, that many of these effects are interrelated; almost all of the excess return to small firms, for example, comes in the month of January. It is necessary to control for these interrelationships in order to understand and exploit the true sources of excess expected return.

Other Research Categories:

Plan Architecture and Portfolio Engineering

Long-Short Investing

Portfolio Optimization, Short Sales, and Leverage Aversion

Market Simulation

Market Crises

(1)The Journal of Portfolio Management 15th Anniversary Issue.
(2)1988 Financial Analysts Journal Graham & Dodd Award winner.
(3)Presented at Corporate Earnings Analysis Seminar, April 1996.
(4)Presented at Rutgers University Colloquium, April 1995.
(5)Presented at the Institute for Quantitative Research in Finance (Q-Group) Seminar on “New Perspectives on Equity Valuation,” Spring 1990.
(6)Required CFA reading.
(7)Presented at the Berkeley Program in Finance Seminar on “The Behavior of Security Prices: Market Efficiency, Anomalies and Trading Strategies,” September 1986. 

Back to top

© Jacobs Levy Equity Management. All rights reserved.