Publications
Robust Ranking and Portfolio Optimization
2012The portfolio optimization problem has attracted researchers from many disciplines to resolve the issue of poor out-of-sample performance due to estimation errors in the expected returns. A practical method for portfolio construction is to use assets’ ordering information, expressed in the form of preferences over the stocks, instead of the exact expected returns. Due to the fact that the ranking itself is often described with uncertainty, we introduce a generic robust ranking model and apply it to portfolio optimization. In this problem, there are n objects whose ranking is in a discrete uncertainty set. We want to find a weight vector that maximizes some generic objective function for the worst realization of the ranking. This robust ranking problem is a mixed integer minimax problem and is very difficult to solve in general. To solve this robust ranking problem, we apply the constraint generation method, where constraints are efficiently generated by solving a network flow problem. For empirical tests, we use post-earnings-announcement drifts to obtain ranking uncertainty sets for the stocks in the DJIA index. We demonstrate that our robust portfolios produce smaller risk compared to their non-robust counterparts.
What Happened To The Quants In August 2007?: Evidence from Factors and Transactions Data
2011During the week of August 6, 2007, a number of quantitative long/short equity hedge funds experienced unprecedented losses. It has been hypothesized that a coordinated deleveraging of similarly constructed portfolios caused this temporary dislocation in the market. Using the simulated returns of long/short equity portfolios based on five specific valuation factors, we find evidence that the unwinding of these portfolios began in July 2007 and continued until the end of 2007. Using transactions data, we find that the simulated returns of a simple market-making strategy were significantly negative during the week of August 6, 2007, but positive before and after, suggesting that the Quant Meltdown of August 2007 was the combined effects of portfolio deleveraging throughout July and the first week of August, and a temporary withdrawal of market-making risk capital starting August 8th. Our simulations point to two unwinds—a mini-unwind on August 1st starting at 10:45am and ending at 11:30am, and a more sustained unwind starting at the open on August 6th and ending at 1:00pm—that began with stocks in the financial sector and long Book-to-Market and short Earnings Momentum. These conjectures have significant implications for the systemic risks posed by the hedge-fund industry.
Illiquidity Premia in Asset Returns: An Empirical Analysis of Hedge Funds, Mutual Funds, and US Equity Portfolios
2011We establish a link between illiquidity and positive autocorrelation in asset returns among a sample of hedge funds, mutual funds, and various equity portfolios. For hedge funds, this link can be confirmed by comparing the return autocorrelations of funds with shorter vs. longer redemption-notice periods. We also document significant positive return-autocorrelation in portfolios of securities that are generally considered less liquid, e.g., small-cap stocks, corporate bonds, mortgage-backed securities, and emerging-market investments. Using a sample of 2,927 hedge funds, 15,654 mutual funds, and 100 size- and book-to-market-sorted portfolios of U.S. common stocks, we construct autocorrelation-sorted long/short portfolios and conclude that illiquidity premia are generally positive and significant, ranging from 2.74% to 9.91% per year among the various hedge funds and fixed-income mutual funds. We do not find evidence for this premium among equity and asset-allocation mutual funds, or among the 100 U.S. equity portfolios. The time variation in our aggregated illiquidity premium shows that while 1998 was a difficult year for most funds with large illiquidity exposure, the following four years yielded significantly higher illiquidity premia that led to greater competition in credit markets, contributing to much lower illiquidity premia in the years leading up to the Financial Crisis of 2007–2008.
Hedge Funds: An Analytic Perspective
2010 Revised EditionThe hedge fund industry has grown dramatically over the last two decades, with more than eight thousand funds now controlling close to two trillion dollars. Originally intended for the wealthy, these private investments have now attracted a much broader following that includes pension funds and retail investors. Because hedge funds are largely unregulated and shrouded in secrecy, they have developed a mystique and allure that can beguile even the most experienced investor. In Hedge Funds, Andrew Lo--one of the world's most respected financial economists--addresses the pressing need for a systematic framework for managing hedge fund investments.
The Evolution of Technical Analysis
2010"A movement is over when the news is out," so goes the Wall Street maxim. For thousands of years, technical analysis—marred with common misconceptions likening it to gambling or magic and dismissed by many as "voodoo finance"—has sought methods for spotting trends in what the market's done and what it's going to do. After all, if you don't learn from history, how can you profit from it?
In The Evolution of Technical Analysis, the director of MIT's Laboratory for Financial Engineering, Andrew Lo, and coauthor Jasmina Hasanhodzic present an engaging account of the origins and development of this mysterious "black art," tracing its evolution from ancient Babylon to the rise of Wall Street as the world's financial center. Along the way, the practices of Eastern technical analysts like Munehisa Homma ("the god of the markets") are compared and contrasted with those of their Western counterparts, such as Humphrey Neill, William Gann, and Charles Dow ("the father of technical analysis").
With deep roots in antiquity, technical analysis is part art and part science, seeking to divine trends, reversals, cycles, and other predictable patterns in historical market prices. While the techniques for capturing such regularities have evolved considerably over the centuries, the all-too-human predilection to extrapolate into the future using the past has been a constant driving force throughout history.
The authors chronicle the fascinating and unexpected path of charting that likely began with simple superstitions and coincidences, and has developed into widespread practices in many markets and instruments, involving sophisticated computational algorithms and visualization techniques. The Evolution of Technical Analysis is the story of how some early technicians failed miserably, how others succeeded beyond their wildest dreams, and what it means for traders today.
Stock Market Trading Volume
2010If price and quantity are the fundamental building blocks of any theory of market interactions, the importance of trading volume in understanding the behavior of financial markets is clear. However, while many economic models of financial markets have been developed to explain the behavior of prices – predictability, variability, and information content – far less attention has been devoted to explaining the behavior of trading volume. In this chapter, we hope to expand our understanding of trading volume by developing well-articulated economic models of asset prices and volume and empirically estimating them using recently available daily volume data for individual securities from the University of Chicago’s Center for Research in Securities Prices. Our theoretical contributions include (1) an economic definition of volume that is most consistent with theoretical models of trading activity; (2) the derivation of volume implications of basic portfolio theory; and (3) the development of an intertemporal equilibrium model of asset market in which the trading process is determined endogenously by liquidity needs and risk-sharing motives. Our empirical contributions include (1) the construction of a volume/returns database extract of the CRSP volume data; (2) comprehensive exploratory data analysis of both the time-series and cross-sectional properties of trading volume; (3) estimation and inference for price/volume relations implied by asset pricing models; and (4) a new approach for empirically identifying factors to be included in a linear factor model of asset returns using volume data.
Impossible Frontiers
2010A key result of the Capital Asset Pricing Model (CAPM) is that the market portfolio—the portfolio of all assets in which each asset's weight is proportional to its total market capitalization—lies on the mean-variance-efficient frontier, the set of portfolios having mean-variance characteristics that cannot be improved upon. Therefore, the CAPM cannot be consistent with efficient frontiers for which every frontier portfolio has at least one negative weight or short position. We call such efficient frontiers 'impossible', and show that impossible frontiers are difficult to avoid. In particular, as the number of assets, n, grows, we prove that the probability that a generically chosen frontier is impossible tends to one at a geometric rate. In fact, for one natural class of distributions, nearly one-eighth of all assets on a frontier is expected to have negative weights for every portfolio on the frontier. We also show that the expected minimum amount of shortselling across frontier portfolios grows linearly with n, and even when shortsales are constrained to some finite level, an impossible frontier remains impossible. Using daily and monthly U.S. stock returns, we document the impossibility of efficient frontiers in the data.
The Heretics of Finance
2009The Heretics of Finance provides extraordinary insight into both the art of technical analysis and the character of the successful trader. Distinguished MIT professor Andrew W. Lo and researcher Jasmina Hasanhodzic interviewed thirteen highly successful, award-winning market professionals who credit their substantial achievements to technical analysis. The result is the story of technical analysis in the words of the people who know it best; the lively and candid interviews with these gurus of technical analysis.
The first half of the book focuses on the technicians' careers:
- How and why they learned technical analysis
- What market conditions increase their chances of making mistakes
- What their average workday is like
- To what extent trading controls their lives
- Whether they work on their own or with a team
- How their style of technical analysis is unique
The second half concentrates on technical analysis and addresses questions such as these:
- Did the lack of validation by academics ever cause you to doubt technical analysis?
- Can technical analysis be applied to other disciplines?
- How do you prove the validity of the method?
- How has computer software influenced the craft?
- What is the role of luck in technical analysis?
- Are there laws that underlie market action?
- What traits characterize a highly successful trader?
- How you test patterns before you start using them with real money?
Interviewees include:
Ralph J. Acampora, Laszlo Birinyi, Walter Deemer, Paul Desmond, Gail Dudack, Robert J. Farrell, Ian McAvity, John Murphy, Robert Prechter, Linda Raschke, Alan R. Shaw, Anthony Tabell, Stan Weinstein.
Regulatory Reform in the Wake of the Financial Crisis of 2007‐2008
2009PURPOSE: The purpose of this paper is to analyse regulatory reform in the wake of the financial crisis of 2007-2008.
DESIGN/METHODOLOGY/APPROACH: The paper proposes a framework for regulatory reform that begins with the observation that financial manias and panics cannot be legislated away, and may bean unavoidable aspect of modern capitalism.
FINDINGS: Financial crises are unavoidable when hardwired human behavior—fear and greed, or“animal spirits”—is combined with free enterprise, and cannot be legislated or regulated away. Like hurricanes and other forces of nature, market bubbles, and crashes cannot be entirely eliminated, but their most destructive consequences can be greatly mitigated with proper preparation. In fact, the most damaging effects of financial crisis come not from loss of wealth, but rather from those who are unprepared for such losses and panic in response. This perspective has several implications for the types of regulatory reform needed in the wake of the financial crisis of 2007-2008, all centered around the need for greater transparency, improved measures of systemic risk, more adaptive regulations,including counter-cyclical leverage constraints, and more emphasis on financial literacy starting in high school, including certifications for expertise in financial engineering for the senior management and directors of all financial institutions.
ORIGINALITY/VALUE: The paper stresses how we must resist the temptation to react too hastily to market events, and deliberate thoughtfully and broadly, instead, craft new regulations for the financial system of the twenty-first century. Financial markets do not need more regulation; they need smarter and more effective regulation
Jumping the Gates: Using Beta-Overlay Strategies to Hedge Liquidity Constraints
2009In response to the current financial crisis, a number of hedge funds have implemented "gates" on their funds that restrict withdrawals when the sum of redemption requests exceeds a certain percentage of the fund's total assets. To reduce the investor's risk exposures during these periods, we propose a futures overlay strategy designed to hedge out or control the common factor exposures of gated assets. By taking countervailing positions in stock, bond, currency, and commodity exposures, an investor can greatly reduce the systematic risks of their gated assets while still enjoying the benefits of manager-specific alpha. Such overlay strategies can also be used to reposition the betas of an investor's entire portfolio, effectively rebalancing asset-class exposures without having to trade the less liquid underlying assets during periods of market dislocation. To illustrate the costs and benefits of such overlay, we simulate the impact of a simple beta-hedging strategy applied to long/short equity hedge funds in the TASS database.
Where Do Alphas Come From?: A New Measure of the Value of Active Investment Management
2008The value of active investment management is traditionally measured by alpha, beta, tracking error, and the Sharpe and information ratios. These are essentially static characteristics of the marginal distributions of returns at a single point in time, and do not incorporate dynamic aspects of a manager's investment process. In this paper, I propose a new measure of the value of active investment management that captures both static and dynamic contributions of a portfolio manager's decisions. The measure is based on a decomposition of a portfolio's expected return into two distinct components: a static weighted-average of the individual securities' expected returns, and the sum of covariances between returns and portfolio weights. The former component measures the portion of the manager's expected return due to static investments in the underlying securities, while the latter component captures the forecast power implicit in the manager's dynamic investment choices. This measure can be computed for long-only investments, long/short portfolios, and asset allocation rules, and is particularly relevant for hedge-fund strategies where both components are significant contributors to their expected returns, but only one should garner the high fees that hedge funds typically charge. Several analytical and empirical examples are provided to illustrate the practical relevance of these new measures.
130/30: The New Long-Only
2008Long-only portfolio managers and investors have acknowledged that the long-only constraint is a potentially costly drag on performance, and loosening this constraint can add value. However, the magnitude of the performance drag is difficult to measure without a proper benchmark for a 130/30 portfolio. In this paper, we provide a passive but dynamic benchmark consisting of a 'plain-vanilla' 130/30 strategy using simple factors to rank stocks and standard methods for constructing portfolios based on these rankings. Based on this strategy, we produce two types of indexes: investable and 'look ahead' indexes, in which the former uses only prior information and the latter uses realized returns to produce an upper bound on performance. We provide historical simulations of our 130/30 benchmarks that illustrate their advantages and disadvantages under various market conditions.
International Library of Financial Econometrics, Volumes I – V
2007This major collection presents a careful selection of the most important published articles in the field of financial econometrics. Starting with a review of the philosophical background, the collection covers such topics as the random walk hypothesis, long-memory processes, asset pricing, arbitrage pricing theory, variance bounds tests, term structure models, market microstructure, Bayesian methods and other statistical tools.
Read Andrew Lo's Introduction to the International Library of Financial Econometrics
Systemic Risk and Hedge Funds
2007Systemic risk is commonly used to describe the possibility of a series of correlated defaults among financial institutions—typically banks—that occur over a short period of time, often caused by a single major event. However, since the collapse of Long Term Capital Management in 1998, it has become clear that hedge funds are also involved in systemic risk exposures. The hedge-fund industry has a symbiotic relationship with the banking sector, and many banks now operate proprietary trading units that are organized much like hedge funds. As a result, the risk exposures of the hedge-fund industry may have a material impact on the banking sector, resulting in new sources of systemic risks. In this paper, we attempt to quantify the potential impact of hedge funds on systemic risk by developing a number of new risk measures for hedge funds and applying them to individual and aggregate hedge-fund returns data. These measures include: illiquidity risk exposure, nonlinear factor models for hedge-fund and banking-sector indexes, logistic regression analysis of hedge-fund liquidation probabilities, and aggregate measures of volatility and distress based on regime-switching models. Our preliminary findings suggest that the hedge-fund industry may be heading into a challenging period of lower expected returns, and that systemic risk is currently on the rise.
Can Hedge-Fund Returns Be Replicated?: The Linear Case
2007In contrast to traditional investments such as stocks and bonds, hedge-fund returns have more complex risk exposures that yield additional and complementary sources of risk premia. This raises the possibility of creating passive replicating portfolios or "clones" using liquid exchange-traded instruments that provide similar risk exposures at lower cost and with greater transparency. Using monthly returns data for 1,610 hedge funds in the TASS database from 1986 to 2005, we estimate linear factor models for individual hedge funds using six common factors, and measure the proportion of the funds' expected returns and volatility that are attributable to such factors. For certain hedge-fund style categories, we find that a significant fraction of both can be captured by common factors corresponding to liquid exchange-traded instruments. While the performance of linear clones is often inferior to their hedge-fund counterparts, they perform well enough to warrant serious consideration as passive, transparent, scalable, and lower-cost alternatives to hedge funds.