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Performance Measurement

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When evaluating the performance of a mutual fund or other investment, one must somehow adjust it for the relative riskiness inherent therein.  There are three primary means of doing so: the Jensen index, the Treynor index, and the Sharpe Ratio.  More recent, but less well known and used, are the Sortino Ratio and the Upside Potential Ratio.  Also, see the section on Risk Measures and Performance Evaluation.

Aswath Damodoran, "Estimating Risk-Free Rates," NYU Stern School of Business  (22kb).  Nearly all measures of risk-adjusted performance require estimation of a "risk-free" return.  This paper thoroughly discusses issues surrounding estimating such a value.

Michael C. Jensen, “The Performance of Mutual Funds in the Period 1945-1964,” Journal of Finance, May 1968, pp. 389-416 (178kb). Also here.  Introduces "alpha," more commonly known as "Jensen's Alpha."  This is a risk adjusted measure of how much a particular investment's return exceeds that of some benchmark.

Paul D. Kaplan and James A. Knowles, "Kappa: A Generalized Downside Risk Performance Measure," Journal of Performance Measurement, 8(3) (225kb).  Introduces "kappa," a measure of risk-adjusted return.

Con Keating and William F. Shadwick, "A Universal Performance Measure," Journal of Performance Measurement, 6(3) (491kb).  Introduces "gamma," a measure of risk-adjusted return.

Franco Modigliani and Leah Modigliani, "Risk-Adjusted Performance," Journal of Portfolio Management, Winter 1997, pp. 45-54.  This paper introduces the measure popularly known as M2 ("M-square").  M2 is a measure closely related to the Sharpe Ratio.  Its major benefit over the Sharpe ratio is that, rather than being a dimensionless ratio, it states the result in terms of percentage return, which is much more appealing and understandable by most people.  Co-written by a Nobel prize winner.  Also, see the Modigliani article below.

Leah Modigliani, "Yes, You Can Eat Risk-Adjusted Returns," Morgan Stanley U.S. Investment Research, March 17 1997 (36kb).  An excellent discussion of the M2 ("M-square") measure of risk-adjusted performance.  This is a much easier-to-read discussion than the ModiglianiModigliani paper above.

Robert L. Padgette, "Performance Reporting: The Basics and Beyond, Part II," Journal of Financial Planning, October 1995, pp. 172-180.  A pretty good discussion of four major measures of risk-adjusted performance: Jensen, Treynor, Sharpe, and Sortino.

Auke Plantinga, Robert van der Meer, and Frank A. Sortino, "The Impact of Downside Risk on Risk-Adjusted Performance of Mutual Funds in the Euronext Markets," Social Science Research Network working paper number 277352, July 21 2001 (171kb).  This excellent paper concludes that Upside Potential Ratio is a better measure of risk-adjusted performance than the Sharpe Ratio.  However, it goes on to note that this is only the case where return distributions are skewed (i.e., unsymmetrical) and that the mutual funds they analyzed seemed to have symmetrical returns, meaning that the (easier to calculate) Sharpe Ratio should generally give reliable results.

Jeffrey H. Rattiner, "Adjust for Comfort: Keep your Clients Comfortable by Matching Risk-Adjusted Returns with their Risk-Tolerance Profiles — The Quantifiable Way," Financial Planning, May 1 2001, pp. 111-113.  A very readable summary description of the three most popular measures for risk-adjusted performance.

A.D. Roy, "Safety First and the Holding of Assets," Econometrica, July 1952, pp. 431-450.  This may have been the first paper to suggest the idea of a "minimal acceptable return" as part of the measurement of risk-adjusted return.  Roy suggested maximizing the ratio "(m-d)σ", where m is expected gross return, d is some "disaster level" (a.k.a., minimum acceptable return) and σ is standard deviation of returns.  This ratio is just the Sharpe Ratio, only using minimum acceptable return instead of risk-free return in the numerator!

William F. Sharpe, "Mutual Fund Performance," Journal of Business, January 1966, pp. 119-138.  This paper first introduced what would eventually be termed "the Sharpe Ratio."  Written by a Nobel Prize winner.

William F. Sharpe, "The Sharpe Ratio," Journal of Portfolio Management, Fall 1994, pp. 49-58.  An excellent discussion of one of the most popular measures of risk-adjusted investment performance.  Written by a Nobel Prize winner.

Frank A. Sortino, Robert van der Meer, Auke Plantinga, and Hal Forsey, "Upside Potential Ratio," Pension Research Institute, 1998.  This article describes the "Upside Potential Ratio," another means of measuring risk-adjusted return.  In order to perform the calculation, you must define a Minimum Acceptable Return (MAR).  The Upside Potential Ratio assumes that the investment objective is to maximize the expected return above the MAR, subject to the risk of falling below the MAR.  It is calculated by dividing the upside potential by the downside deviation.

Jack L. Treynor, “How to Rate Management Investment Funds,” Harvard Business Review, JanuaryFebruary 1966, pp. 63-74.  While not used as often as the Jensen Index or the Sharpe Ratio, the "Treynor Index" introduced here is sometimes used for evaluating risk-adjusted performance.

Performance Measurement Bibliography.  An excellent bibliography for this subject area.  No downloadable links.

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