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Different risk-adjusted fund performance measures: a comparison

Author

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  • Grau-Carles, Pilar
  • Sainz, Jorge
  • Otamendi, Javier
  • Doncel, Luis Miguel

Abstract

Traditional risk-adjusted performance measures, such as the Sharpe ratio, the Treynor index or Jensen's alpha, based on the mean-variance framework, are widely used to rank mutual funds. However, performance measures that consider risk by taking into account only losses, such as Value-at-Risk (VaR), would be more appropriate. Standard VaR assumes that returns are normally distributed, though they usually present skewness and kurtosis. In this paper we compare these different measures of risk: traditional ones vs. ones that take into account fat tails and asymmetry, such as those based on the Cornish-Fisher expansion and on the extreme value theory. Moreover, we construct a performance index similar to the Sharpe ratio using these VaR-based risk measures. We then use these measures to compare the rating of a set of mutual funds, assessing the different measures' usefulness under the Basel II risk management framework.

Suggested Citation

  • Grau-Carles, Pilar & Sainz, Jorge & Otamendi, Javier & Doncel, Luis Miguel, 2009. "Different risk-adjusted fund performance measures: a comparison," Economics Discussion Papers 2009-54, Kiel Institute for the World Economy (IfW).
  • Handle: RePEc:zbw:ifwedp:200954
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    References listed on IDEAS

    as
    1. Roger Otten & Dennis Bams, 2002. "European Mutual Fund Performance," European Financial Management, European Financial Management Association, vol. 8(1), pages 75-101.
    2. William F. Sharpe, 1965. "Mutual Fund Performance," The Journal of Business, University of Chicago Press, vol. 39, pages 119-119.
    3. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
    4. Mark M. Carhart & Jennifer N. Carpenter & Anthony W. Lynch & David K. Musto, 2002. "Mutual Fund Survivorship," Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1439-1463.
    5. Sentana, Enrique, 2001. "Mean Variance Portfolio Allocation with a Value at Risk Constraint," CEPR Discussion Papers 2997, C.E.P.R. Discussion Papers.
    6. Bing Liang & Hyuna Park, 2007. "Risk Measures for Hedge Funds: a Cross-sectional Approach," European Financial Management, European Financial Management Association, vol. 13(2), pages 333-370.
    7. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    8. Gupta, Anurag & Liang, Bing, 2005. "Do hedge funds have enough capital? A value-at-risk approach," Journal of Financial Economics, Elsevier, vol. 77(1), pages 219-253, July.
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    More about this item

    Keywords

    Mutual funds; performance measures; Value-at-Risk; extreme value theory;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G20 - Financial Economics - - Financial Institutions and Services - - - General

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