“This decomposition provides a clear and simple framework for resolving the question of whether hedge-fund investors are paying for alpha and getting beta...”
Where Do Alphas Come From?
As more money pours into hedge fund strategies an increasingly large portion of their returns can be obtained independently of hedge funds and their draw-backs. Dr. Andrew Lo discusses a risk based framework for thinking about the expected returns of hedge funds.
Videos
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Where Do Alphas Come From?
As more money pours into hedge fund strategies an increasingly large portion of their returns can be obtained independently of hedge funds and their draw-backs. Dr. Andrew Lo discusses a risk based framework for thinking about the expected returns of hedge funds.
PLAYThis decomposition provides a clear and simple framework for resolving the question of whether hedge-fund investors are paying for alpha and getting beta...
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Setting Hedge Fund Return Expectations
Hedge fund strategies can be very different from one another making it difficult to identify a common risk model or a single set of risk factors. Dr. Andrew Lo discusses how the use of a simple two-state Markov regime switching model can help investors to understand what is driving their returns and can help to set return expectations.
PLAY...it is going to be harder and harder for managers to be able to produce the kinds of returns they’ve produced historically.
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Portfolio Risk Decomposition
Dr. Andrew Lo discusses risk modeling and provides a framework for thinking about the sources of volatility in a portfolio and how that volatility can be decomposed into systematic risks that can be tailored to an investor's preferences.
PLAY...you can squeeze more expected return per unit of risk out of a portfolio if you know what bets you’re making and how...
Articles by topic
- FEATURED
- Adaptive markets
- Alternative betas
- Risk analytics
and management - Systemic risk
and hedge funds
The Alpha-Beta Divide
by Andrew W. Lo, Canadian Investment Review Fall 2007
FALL 2007
As institutional investors take a more active interest in alternative investments, a significant gap has emerged between the culture and expectations of those investors and hedge fund managers. Pension plan sponsors typically require transparency from their managers and impose a number of restrictions in their investment mandates because of regulatory requirements such as ERISA rules; hedge fund managers rarely provide position-level transparency and bristle at any restrictions on their investment process because restrictions often hurt performance.
SEE ALL articles on: Alternative betas
Where Do Alphas Come From?: A Measure of the Value of Active Investment Management
by Andrew W. Lo
APRIL 27, 2008
The 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 article, I propose a 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 this decomposition.
SEE ALL articles on: Risk analytics and management
The Adaptive Markets Hypothesis
by Andrew W. Lo, The Journal of Portfolio Management 30th Anniversary Issue
2004
In this article, I review the current state of the controversy surrounding the Efficient Markets Hypothesis and Behavioral Economics and propose a new perspective that reconciles the two opposing schools of thought. The proposed reconciliation which I call the Adaptive Markets Hypothesis, is based on an evolutionary approach to economic interactions, as well as some recent research in the cognitive neurosciences that has been transforming and revitalizing the intersection of psychology and management.
SEE ALL articles on: Adaptive markets
What Happened to the Quants in August 2007?
by Amir E. Khandani and Andrew W. Lo, Journal of Investment Management, Vol. 5, No. 4, 2007, 5-54
2007
During the week of August 6, 2007, a number of quantitative long/short equity hedge funds experienced unprecedented losses. Based on TASS hedge-fund data and simulations of a specific long/short equity strategy, we hypothesize that the losses were initiated by the rapid "unwind" of one or more sizable quantitative equity market-neutral portfolios. Given the speed and price impact with which this occurred, it was likely the result of a forced liquidation by a multi-strategy fund or proprietary-trading desk, possibly due to a margin call or a risk reduction. These initial losses then put pressure on a broader set of long/short and long-only equity portfolios, causing further losses by triggering stop/loss and de-leveraging policies. A significant rebound of these strategies occurred on August 10th, which is also consistent with the unwind hypothesis. This dislocation was apparently caused by forces outside the long/short equity sector—in a completely unrelated set of markets and instruments—suggesting that systemic risk in the hedge-fund industry may have increased in recent years.
SEE ALL articles on: Systemic risk and hedge funds
Survival of the Richest
by Andrew W. Lo, Harvard Business Review
MARCH 2006
In financial markets, as in many human endeavors, there's a battle between reason and madness. On one side are the disciples of the efficient-markets hypothesis: the notion that markets fully, accurately, and instantaneously incorporate all relevant information into prices. These adherents assume that market participants are rational, always acting in their own interest and making mathematically optimal decisions. On the other side are the champions of behavioral economics: a younger discipline that points to bubbles, crashes, panics, manias, and other distinctly unreasonable phenomena as evidence of irrationality.
Reconciling Efficient Markets with Behavioral Finance: The Adaptive Markets Hypothesis
by Andrew W. Lo, The Journal of Investment Consulting Vol. 7, No. 2, 21-44
2005
The battle between proponents of the Efficient Markets Hypothesis and champions of behavioral finance has never been more pitched, and little consensus exists as to which side is winning or the implications for investment management and consulting. In this article, I review the case for and against the Efficient Markets Hypothesis and describe a new framework—the Adaptive Markets Hypothesis—in which the traditional models of modern financial economics can coexist alongside behavioral models in an intellectually consistent manner. Based on evolutionary principles, the Adaptive Markets Hypothesis implies that the degree of market efficiency is related to environmental factors characterizing market ecology such as the number of competitors in the market, the magnitude of profit opportunities available, and the adaptability of the market participants. Many of the examples that behavioralists cite as violations of rationality that are inconsistent with market efficiency—loss aversion, overconfidence, overreaction, mental accounting, and other behavioral biases—are, in fact, consistent with an evolutionary model of individuals adapting to a changing environment via simple heuristics. Despite the qualitative nature of this new paradigm, I show that the Adaptive Markets Hypothesis yields a number of surprisingly concrete applications for both investment managers and consultants.
Frontiers of Finance: Evolution and Efficient Markets
by J. Doyne Farmer and Andrew W. Lo, Proceedings of the National Academy of Sciences Vol. 96, pp. 9991-9992
AUGUST 1999
In this review article, we explore several recent advances in the quantitative modeling of financial markets. We begin with the Efficient Markets Hypothesis and describe how this controversial idea has stimulated a number of new directions of research, some focusing on more elaborate mathematical models that are capable of rationalizing the empirical facts, others taking a completely different tack in rejecting rationality altogether. One of the most promising directions is to view financial markets from a biological perspective and, specifically, within an evolutionary framework in which markets, instruments, institutions, and investors interact and evolve dynamically according to the ‘‘law‘‘ of economic selection. Under this view, financial agents compete and adapt, but they do not necessarily do so in an optimal fashion. Evolutionary and ecological models of financial markets are truly a new frontier whose exploration has just begun.
130/30: The New Long-Only
by Andrew W. Lo and Pankaj N. Patel, Journal of Portfolio Management
WINTER 2008
One of the fastest growing areas in institutional investment management is the so-called active extension or 130/30 class of strategies in which the short-sales constraint of a traditional long-only portfolio is relaxed. Fueled both by the historical success of long-short equity hedge funds and the increasing frustration of portfolio managers at the apparent impact of long-only constraints on performance, 130/30 products have grown to over $75 billion in assets and could reach $2 trillion by 2010.
Can Hedge-Fund Returns Be Replicated?: The Linear Case
by Jasmina Hasanhodzic and Andrew W. Lo, Journal of Investment Management Vol. 5, No. 2, 5-45
2007
In 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. By using monthly returns data for 1610 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.
Attack of the Clones
by Jasmina Hasanhodzic and Andrew W. Lo, Institutional Investor's Alpha
JUNE 2006
Hedge funds are considered by many investors to be an attractive investment, thanks in large part to their diversification benefits and distinctive risk profiles. The major drawbacks are their high fees and lack of transparency. Research by Jasmina Hasanhodzic and Andrew W. Lo of the Massachusetts Institute of Technology raises the possibility of creating passive portfolios that provide similar risk exposures to those of hedge funds at lower costs and with greater transparency. Hasanhodzic and Lo find that for certain hedge fund strategies, these hedge fund "clones" perform well enough to warrant serious consideration.
Personal Indexes: One Day, Artificial Intelligence Will Build Them for Each Investor
by Andrew W. Lo, Journal of Indexes
2ND QUARTER 2001
One of the main purposes of an index of any kind is to facilitate the extraction and summary of information through an algorithmic process, e.g., averaging. Now typically done by computers, averaging is a simple example of artificial intelligence! Indeed, an important factor in the early popularity of the Dow Jones Industrial Average, first introduced in May 1896, was the Dow Theory, a collection of heuristics proposed by Charles H. Dow and later expanded by William P. Hamilton in which specific economic meaning is attributed to certain time series patterns in the index. The dream of developing automated processes for making better investment decisions is obviously not unique to our times.
Asset Allocation and Derivatives
by Martin B. Haugh and Andrew W. Lo, Quantitative Finance Vol. 1, 45-72
2001
The fact that derivative securities are equivalent to specific dynamic trading strategies in complete markets suggests the possibility of constructing buy-and-hold portfolios of options that mimic certain dynamic investment policies, e.g. asset-allocation rules. We explore this possibility by solving the following problem: given an optimal dynamic investment policy, find a set of options at the start of the investment horizon which will come closest to the optimal dynamic investment policy. We solve this problem for several combinations of preferences, return dynamics and optimality criteria, and show that under certain conditions, a portfolio consisting of just a few options is an excellent substitute for considerably more complex dynamic investment policies
An Econometric Model of Serial Correlation and Illiquidity in Hedge Fund Returns
by Mila Getmansky, Andrew W. Lo and Igor Makarov, Journal of Financial Economics Vol. 74, 529—609
2004
The returns to hedge funds and other alternative investments are often highly serially correlated. In this paper, we explore several sources of such serial correlation and show that the most likely explanation is illiquidity exposure and smoothed returns. We propose an econometric model of return smoothing and develop estimators for the smoothing profile as well as a smoothing-adjusted Sharpe ratio. For a sample of 908 hedge funds drawn from the TASS database, we show that our estimated smoothing coefficients vary considerably across hedge-fund style categories and may be a useful proxy for quantifying illiquidity exposure.
It's 11pm - Do You Know Where Your Liquidity Is? The Mean-Variance-Liquidity Frontier
by Andrew W. Lo, Constantin Petrov and Martin Wierzbick, Journal of Investment Management Vol. 1, No. 1, 55-93
2003
We introduce liquidity into the standard mean-variance portfolio optimization framework by defining several measures of liquidity and then constructing three-dimensional mean-variance-liquidity frontiers in three ways: liquidity filtering, liquidity constraints, and a mean-variance-liquidity objective function. We show that portfolios close to each other on the traditional mean-variance efficient frontier can differ substantially in their liquidity characteristics. In a simple empirical example, the liquidity exposure of mean-variance efficient portfolios changes dramatically from month to month, and even simple forms of liquidity optimization can yield significant benefits in reducing a portfolio's liquidity-risk exposure without sacrificing a great deal of expected return per unit risk.
The Statistics of Sharpe Ratios
by Andrew W. Lo, Financial Analysts Journal, 36-52
JULY/AUG 2002
The building blocks of the Sharpe ratio—expected returns and volatilities—are unknown quantities that must be estimated statistically and are, therefore, subject to estimation error. This raises the natural question: How accurately are Sharpe ratios measured? To address this question, I derive explicit expressions for the statistical distribution of the Sharpe ratio using standard asymptotic theory under several sets of assumptions for the return-generating process—independently and identically distributed returns, stationary returns, and with time aggregation. I show that monthly Sharpe ratios cannot be annualized by multiplying by sqrt(12) except under very special circumstances, and I derive the correct method of conversion in the general case of stationary returns. In an illustrative empirical example of mutual funds and hedge funds, I find that the annual Sharpe ratio for a hedge fund can be overstated by as much as 65 percent because of the presence of serial correlation in monthly returns, and once this serial correlation is properly taken into account, the rankings of hedge funds based on Sharpe ratios can change dramatically.
Risk Management for Hedge Funds: Introduction and Overview
by Andrew W. Lo, Financial Analysts Journal, 16-33
NOV/DEC 2001
Although risk management has been a well-plowed field in financial modeling for more than two decades, traditional risk management tools such as mean—variance analysis, beta, and Value-at-Risk do not capture many of the risk exposures of hedge-fund investments. In this article, I review several unique aspects of risk management for hedge funds—survivorship bias, dynamic risk analytics, liquidity, and nonlinearities—and provide examples that illustrate their potential importance to hedge-fund managers and investors. I propose a research agenda for developing a new set of risk analytics specifically designed for hedge-fund investments, with the ultimate goal of creating risk transparency without compromising the proprietary nature of hedge-fund investment strategies.
Nonparametric Risk Management and Implied Risk Aversion
by Yacine Aït-Sahalia and Andrew W. Lo, Journal of Econometrics Vol. 94, 9-51
2000
Typical value-at-risk (VaR) calculations involve the probabilities of extreme dollar losses, based on the statistical distributions of market prices. Such quantities do not account for the fact that the same dollar loss can have two very different economic valuations, depending on business conditions. We propose a non-parametric VaR measure that incorporates economic valuation according to the state-price density associated with the underlying price processes. The state-price density yields VaR values that are adjusted for risk aversion, time preferences, and other variations in economic valuation. In the context of a representative agent equilibrium model, we construct an estimator of the risk-aversion coefficient that is implied by the joint observations on the cross-section of option prices and time-series of underlying asset values.
The Three P's of Total Risk Management
by Andrew W. Lo, Financial Analysts Journal Vol. 55, 13-26
1999
Current risk-management practices are based on probabilities of extreme dollar losses (e.g., measures like Value at Risk), but these measures capture only part of the story. Any complete risk-management system must address two other important factors: prices and preferences. Together with probabilities, these comprise the three P's of Total Risk Management. This article describes how the three Ps interact to determine sensible risk profiles for corporations and for individuals, guidelines for how much risk to bear and how much to hedge. By synthesizing existing research in economics, psychology, and decision sciences, and through an ambitious research agenda to extend this synthesis into other disciplines, a complete and systematic approach to rational decision making in an uncertain world is within reach.
Systemic Risk and Hedge Funds
by Nicholas Chan, Mila Getmansky, Shane M. Haas and Andrew W. Lo, in Carey and Stulz, eds., The Risks of Financial Institutions. Chicago, IL: University of Chicago Press
2007
Systemic 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 ndings 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.
Do Hedge Funds Increase Systemic Risk?
by Nicholas Chan, Mila Getmansky, Shane M. Haas and Andrew W. Lo, Economic Review, 49-80
4th QUARTER 2006
The term "systemic risk" is commonly used to describe the possibility of a series of correlated defaults among financial institutions—typically banks—that occurs over a short period of time, often caused by a single major event. A classic example is a banking panic in which large groups of depositors decide to withdraw their funds simultaneously, creating a run on bank assets that can ultimately lead to multiple bank failures. Banking panics were not uncommon in the United States during the nineteenth and early twentieth centuries, culminating with an average of 2,000 bank failures per year during the 1930—33 period (according to Mishkin 1997) and which in turn prompted the passing of the Glass-Steagall Act of 1933 and the establishment of the Federal Deposit Insurance Corporation (FDIC) in 1934.
Trading Volume: Implications of an Intertemporal Capital Asset Pricing Model
by Andrew W. Lo and Jiang Wang, Journal of Finance Vol. LXI, No. 6, 2805-2840
DECEMBER 2006
We derive an intertemporal asset pricing model and explore its implications for trading volume and asset returns. We show that investors trade in only two portfolios: the market portfolio, and a hedging portfolio that is used to hedge the risk of changing market conditions. We empirically identify the hedging portfolio using weekly volume and returns data for U.S. stocks, and then test two of its properties implied by the theory: Its return should be an additional risk factor in explaining the cross section of asset returns, and should also be the best predictor of future market returns.
Fear and Greed in Financial Markets: A Clinical Study of Day-Traders
by Andrew W. Lo, Dmitry V. Repin and Brett N. Steenbarger, AEA Papers and Proceedings Vol. 95, No. 2, 352-359
2005
The rationality of financial markets has been one of the most hotly contested issues in the history of modern financial economics. Recent critics of the Efficient Markets Hypothesis argue that investors are generally irrational, exhibiting a number of predictable and financially ruinous biases, often attributed to psychological factors—fear, greed, and other emotional responses to price fluctuations and dramatic changes in an investor’s wealth. However, recent research in the cognitive sciences and financial economics suggest an important link between rationality in decision-making and emotion (S. Grossberg and W. Gutowski, 1987; A. Damasio, 1994; Jon Elster, 1998; Lo, 1999; George Loewenstein, 2000; E. Peters and P. Slovic, 2000), implying that the two notions are not antithetical, but in fact complementary. For example, in a pilot study of 10 professional securities traders during live trading sessions, Lo and Repin (2002) present psychophysiological evidence that even the most seasoned trader exhibits significant emotional response, as measured by elevated levels of skin conductance and cardiovascular variables, during certain transient market events such as increased price volatility or intra-day breaks in trend. In a series of case studies, B. Steenbarger (2002) also presents evidence linking emotion with trading performance.
Sifting Through the Wreckage: Lessons from Recent Hedge Fund Liquidations
by Mila Getmansky, Andrew W. Lo and Shauna X. Mei, Journal of Investment Management Vol. 2, No. 4, 6-38
2004
We document the empirical properties of a sample of 1,765 funds in the TASS Hedge Fund database from 1977 to 2004 that are no longer active. The TASS sample shows that attrition rates differ significantly across investment styles, from a low of 5.2% per year on average for convertible arbitrage funds to a high of 14.4% per year on average for managed futures funds. We relate a number of factors to these attrition rates, including past performance, volatility, and investment style, and also document differences in illiquidity risk between active and liquidated funds. We conclude with a proposal for the US Securities and Exchange Commission to play a new role in promoting greater transparency and stability in the hedge-fund industry.
