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Skewness in hedge funds returns: classical skewness coefficients vs Azzalini's skewness parameter

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Author Info

  • Martin Eling
  • Simone Farinelli
  • Damiano Rossello
  • Luisa Tibiletti

Abstract

Purpose – Recent literature discusses the persistence of skewness and tail risk in hedge fund returns. The aim of this paper is to suggest an alternative skewness measure, Azzalini's skewness parameter delta, which is derived as the normalized shape parameter from the skew-normal distribution. The paper seeks to analyze the characteristics of this skewness measure compared with other indicators of skewness and to employ it in some typical risk and performance measurements. Design/methodology/approach – The paper first provides an overview of the skew-normal distribution and its mathematical formulation. Then it presents some empirical estimations of the skew-normal distribution for hedge fund returns and discusses the characteristics of using delta with respect to classical skewness coefficients. Finally, it illustrates how delta can be used in risk management and in a performance measurement context. Findings – The results highlight the advantages of Azzalini's skewness parameter delta, especially with regard to its interpretation. Delta has a limpid financial interpretation as a skewness shock on normally distributed returns. The paper also derives some important characteristics of delta, including that it is more stable than other measures of skewness and inversely related to popular risk measures such as the value-at-risk (VaR) and the conditional value-at-risk (CVaR). Originality/value – The contribution of the paper is to apply the skew-normal distribution to a large sample of hedge fund returns. It also illustrates that using Azzalini's skewness parameter delta as a skewness measure has some advantages over classical skewness coefficients. The use of the skew-normal and related distributions is a relatively new, but growing, field in finance and not much has been published on the topic. Skewness itself, however, has been the subject of a great deal of research. Therefore, the results contribute to three fields of research: skewed distributions, risk measurement, and hedge fund performance.

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Bibliographic Info

Article provided by Emerald Group Publishing in its journal International Journal of Managerial Finance.

Volume (Year): 6 (2010)
Issue (Month): 4 (September)
Pages: 290-304

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Handle: RePEc:eme:ijmfpp:v:6:y:2010:i:4:p:290-304

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Related research

Keywords: Hedging; Performance measures; Skewness;

References

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  1. 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.
  2. Vikas Agarwal, 2004. "Risks and Portfolio Decisions Involving Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 17(1), pages 63-98.
  3. Stefan Kassberger & Rüdiger Kiesel, 2006. "A fully parametric approach to return modelling and risk management of hedge funds," Financial Markets and Portfolio Management, Springer, vol. 20(4), pages 472-491, December.
  4. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
  5. 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.
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  7. Adelchi Azzalini, 2005. "The Skew-normal Distribution and Related Multivariate Families," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics & Finnish Statistical Society & Norwegian Statistical Association & Swedish Statistical Association, vol. 32(2), pages 159-188.
  8. Dowd, Kevin, 2000. "Adjusting for risk:: An improved Sharpe ratio," International Review of Economics & Finance, Elsevier, vol. 9(3), pages 209-222, July.
  9. Kim, Tae-Hwan & White, Halbert, 2004. "On more robust estimation of skewness and kurtosis," Finance Research Letters, Elsevier, vol. 1(1), pages 56-73, March.
  10. Dries Darius & Aytac Ilhan & John Mulvey & Koray Simsek & Ronnie Sircar, 2002. "Trend-following hedge funds and multi-period asset allocation," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 354-361.
  11. Fung, William & Hsieh, David A, 1997. "Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 10(2), pages 275-302.
  12. Daniel Capocci, 2002. "An Analysis of Hedge Fund Performance," Finance 0210001, EconWPA.
  13. Mark Mitchell, 2001. "Characteristics of Risk and Return in Risk Arbitrage," Journal of Finance, American Finance Association, vol. 56(6), pages 2135-2175, December.
  14. Capocci, Daniel & Hubner, Georges, 2004. "Analysis of hedge fund performance," Journal of Empirical Finance, Elsevier, vol. 11(1), pages 55-89, January.
  15. Bill Ding & Hany A. Shawky, 2007. "The Performance of Hedge Fund Strategies and the Asymmetry of Return Distributions," European Financial Management, European Financial Management Association, vol. 13(2), pages 309-331.
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