Beyond Mean–Variance: Performance Measurement in a Nonsymmetrical World (corrected)

Most practitioners use the capital asset pricing model to measure investment performance. The CAPM, however, assumes either that all asset returns are normally distributed (and thus symmetrical) or that investors have mean–variance preferences (and thus ignore skewness). Both assumptions are suspect. Assuming only that the rate of return on the market portfolio is independently and identically distributed and that markets are “perfect,” this article shows that the CAPM and its risk measures are invalid: The market portfolio is mean–variance inefficient, and the CAPM alpha mismeasures the value added by investment managers. Strategies with positively skewed returns, such as strategies limiting downside risk, will be incorrectly underrated. A simple modification of the CAPM beta, however, will produce correct risk measurement for portfolios with arbitrary return distributions, and the resulting alphas of all fairly priced options and/or dynamic strategies will be zero. The risk measure requires no more info...

[1]  Hayne E. Leland,et al.  On Equilibrium Asset Price Processes , 1993 .

[2]  M. Rubinstein..  The Fundamental Theorem of Parameter-Preference Security Valuation , 1973, Journal of Financial and Quantitative Analysis.

[3]  Sheridan Titman,et al.  A Study of Monthly Mutual Fund Returns and Performance Evaluation Techniques , 1994, Journal of Financial and Quantitative Analysis.

[4]  Stephen A. Ross,et al.  Differential Information and Performance Measurement Using a Security Market Line , 1985 .

[5]  Ravi Jagannathan,et al.  A contingent claim approach to performance evaluation , 1993 .

[6]  M. C. Jensen,et al.  Risk, the Pricing of Capital Assets, and the Evaluation of Investment Portfolios , 1969 .

[7]  Douglas T. Breeden,et al.  Prices of State-Contingent Claims Implicit in Option Prices , 1978 .

[8]  David M. Kreps,et al.  Martingales and arbitrage in multiperiod securities markets , 1979 .

[9]  Richard Bookstaber,et al.  Problems in Evaluating the Performance of Portfolios with Options , 1985 .

[10]  R. Geske,et al.  Option performance measurement* , 1984 .

[11]  R. Litzenberger,et al.  SKEWNESS PREFERENCE AND THE VALUATION OF RISK ASSETS , 1976 .

[12]  Wayne E. Ferson,et al.  Measuring Fund Strategy and Performance in Changing Economic Conditions , 1996 .

[13]  R. C. Merton,et al.  AN INTERTEMPORAL CAPITAL ASSET PRICING MODEL , 1973 .

[14]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[15]  Michael J. Brennan,et al.  The Pricing of Contingent Claims in Discrete Time Models , 1979 .

[16]  Michael J. Brennan,et al.  Optimal Portfolio Insurance , 1981, Journal of Financial and Quantitative Analysis.

[17]  K. Arrow,et al.  Comments on Duesenberry's The Portfolio Approach to the Demand for Money and Other Assets , 1963 .

[18]  F. Sortino,et al.  DOWNSIDE RISK - CAPTURING WHATS AT STAKE IN INVESTMENT SITUATIONS , 1991 .

[19]  Mark Rubinstein,et al.  The Valuation of Uncertain Income Streams and the Pricing of Options , 1976 .

[20]  George M. Constantinides,et al.  Intertemporal Asset Pricing with Heterogeneous Consumers and without Demand Aggregation , 1982 .

[21]  David P. Brown,et al.  A Simple Econometric Approach for Utility‐Based Asset Pricing Models , 1985 .

[22]  Jonathan E. Ingersoll,et al.  Mean-Variance Theory in Complete Markets , 1982 .

[23]  Hayne E. Leland,et al.  Who Should Buy Portfolio Insurance , 1980 .

[24]  Richard Roll,et al.  AMBIGUITY WHEN PERFORMANCE IS MEASURED BY THE SECURITIES MARKET LINE , 1978 .

[25]  Hayne E. Leland,et al.  Replicating Options with Positions in Stock and Cash , 1981 .

[26]  Sheridan Titman,et al.  Portfolio Performance Evaluation: Old Issues and New Insights , 1989 .

[27]  J. Pratt.  RISK AVERSION IN THE SMALL AND IN THE LARGE11This research was supported by the National Science Foundation (grant NSF-G24035). Reproduction in whole or in part is permitted for any purpose of the United States Government. , 1964 .