Portfolio performance evaluation with generalized Sharpe ratios: Beyond the mean and variance
This paper presents a theoretically sound portfolio performance measure that takes into account higher moments of distribution. This measure is motivated by a study of the investor's preferences to higher moments of distribution within Expected Utility Theory and an approximation analysis of the optimal capital allocation problem. We show that this performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges (1998). We present two methods of practical estimation of the GSR: nonparametric and parametric. For the implementation of the parametric method we derive a closed-form solution for the GSR where the higher moments are calibrated to the normal inverse Gaussian distribution. We illustrate how the GSR can mitigate the shortcomings of the Sharpe ratio in resolution of Sharpe ratio paradoxes and reveal the real performance of portfolios with manipulated Sharpe ratios. We also demonstrate the use of this measure in the performance evaluation of hedge funds.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Karlis, Dimitris, 2002. "An EM type algorithm for maximum likelihood estimation of the normal-inverse Gaussian distribution," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 43-52, March.
- Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(02), pages 255-271, June.
- Rachev, Svetlozar & Jasic, Teo & Stoyanov, Stoyan & Fabozzi, Frank J., 2007. "Momentum strategies based on reward-risk stock selection criteria," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2325-2346, August.
- G. Constantinides, 1990.
"Habit formation: a resolution of the equity premium puzzle,"
Levine's Working Paper Archive
1397, David K. Levine.
- Constantinides, George M, 1990. "Habit Formation: A Resolution of the Equity Premium Puzzle," Journal of Political Economy, University of Chicago Press, vol. 98(3), pages 519-543, June.
- Dowd, Kevin, 2000. "Adjusting for risk:: An improved Sharpe ratio," International Review of Economics & Finance, Elsevier, vol. 9(3), pages 209-222, July.
- Cass, David & Stiglitz, Joseph E., 1970. "The structure of investor preferences and asset returns, and separability in portfolio allocation: A contribution to the pure theory of mutual funds," Journal of Economic Theory, Elsevier, vol. 2(2), pages 122-160, June.
- William Goetzmann & Jonathan Ingersoll & Matthew Spiegel & Ivo Welch, 2002.
"Portfolio Performance Manipulation and Manipulation-Proof Performance Measures,"
Yale School of Management Working Papers
amz2471, Yale School of Management, revised 01 Apr 2006.
- Jonathan Ingersoll & Ivo Welch, 2007. "Portfolio Performance Manipulation and Manipulation-proof Performance Measures," Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1503-1546, 2007 17.
- Haley, M. Ryan & McGee, M. Kevin, 2006. "Tilting safety first and the Sharpe portfolio," Finance Research Letters, Elsevier, vol. 3(3), pages 173-180, September.
- Kydland, Finn E & Prescott, Edward C, 1982.
"Time to Build and Aggregate Fluctuations,"
Econometric Society, vol. 50(6), pages 1345-1370, November.
- Finn E. Kydland & Edward C. Prescott, 1982. "Executable program for "Time to Build and Aggregate Fluctuations"," QM&RBC Codes 4, Quantitative Macroeconomics & Real Business Cycles.
- Finn E. Kydland & Edward C. Prescott, 1982. "Web interface for "Time to Build and Aggregate Fluctuations"," QM&RBC Codes 4a, Quantitative Macroeconomics & Real Business Cycles.
- Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2008. "Beyond Sharpe ratio: Optimal asset allocation using different performance ratios," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2057-2063, October.
- Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
- Vikas Agarwal, 2004. "Risks and Portfolio Decisions Involving Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 17(1), pages 63-98.
- R. Mehra & E. Prescott, 2010.
"The equity premium: a puzzle,"
Levine's Working Paper Archive
1401, David K. Levine.
- Merton, Robert C., 1980.
"On estimating the expected return on the market : An exploratory investigation,"
Journal of Financial Economics,
Elsevier, vol. 8(4), pages 323-361, December.
- Robert C. Merton, 1980. "On Estimating the Expected Return on the Market: An Exploratory Investigation," NBER Working Papers 0444, National Bureau of Economic Research, Inc.
- Treynor, Jack L & Black, Fischer, 1973. "How to Use Security Analysis to Improve Portfolio Selection," The Journal of Business, University of Chicago Press, vol. 46(1), pages 66-86, January.
- William N. Goetzmann & Jonathan E. Ingersoll, Jr. & Matthew I. Spiegel & Ivo Welch, 2002.
"Sharpening Sharpe Ratios,"
Yale School of Management Working Papers
ysm29, Yale School of Management.
- William Goetzmann & Jonathan Ingersoll & Matthew I. Spiegel & Ivo Welch, 2002. "Sharpening Sharpe Ratios," NBER Working Papers 9116, National Bureau of Economic Research, Inc.
- William N. Goetzmann & Jonathan E. Ingersoll Jr. & Matthew I. Spiegel & Ivo Welch, 2002. "Sharpening Sharpe Ratios," Yale School of Management Working Papers ysm273, Yale School of Management.
- Kraus, Alan & Litzenberger, Robert H, 1976. "Skewness Preference and the Valuation of Risk Assets," Journal of Finance, American Finance Association, vol. 31(4), pages 1085-1100, September.
- De Giorgi, Enrico, 2005.
"Reward-risk portfolio selection and stochastic dominance,"
Journal of Banking & Finance,
Elsevier, vol. 29(4), pages 895-926, April.
- Enrico De Giorgi, "undated". "Reward-Risk Portfolio Selection and Stochastic Dominance," IEW - Working Papers 121, Institute for Empirical Research in Economics - University of Zurich.
- Eling, Martin & Schuhmacher, Frank, 2007. "Does the choice of performance measure influence the evaluation of hedge funds?," Journal of Banking & Finance, Elsevier, vol. 31(9), pages 2632-2647, September.
- Post, Thierry & van Vliet, Pim & Levy, Haim, 2008. "Risk aversion and skewness preference," Journal of Banking & Finance, Elsevier, vol. 32(7), pages 1178-1187, July.
- He, Hua & Leland, Hayne, 1993. "On Equilibrium Asset Price Processes," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 593-617.
- Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
- Friend, Irwin & Blume, Marshall E, 1975. "The Demand for Risky Assets," American Economic Review, American Economic Association, vol. 65(5), pages 900-922, December.
When requesting a correction, please mention this item's handle: RePEc:eee:jbfina:v:33:y:2009:i:7:p:1242-1254. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Shamier, Wendy)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.