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Beyond Sharpe ratio: Optimal asset allocation using different performance ratios

  • Farinelli, Simone
  • Ferreira, Manuel
  • Rossello, Damiano
  • Thoeny, Markus
  • Tibiletti, Luisa

As the assumption of normality in return distributions is relaxed, classic Sharpe ratio and its descendants become questionable tools for constructing optimal portfolios. In order to overcome the problem, asymmetrical parameter-dependent performance ratios have been recently proposed in the literature. The aim of this note is to develop an integrated decision aid system for asset allocation based on a toolkit of eleven performance ratios. A multi-period portfolio optimization up covering a fixed horizon is set up: at first, bootstrapping of asset return distributions is assessed to recover all ratios calculations; at second, optimal rebalanced-weights are achieved; at third, optimal final wealth is simulated for each ratios. Eventually, we make a robustness test on the best performance ratios. Empirical simulations confirm the weakness in forecasting of Sharpe ratio, whereas asymmetrical parameter-dependent ratios, such as the Generalized Rachev, Sortino-Satchell and Farinelli-Tibiletti ratios show satisfactorily robustness.

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Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 32 (2008)
Issue (Month): 10 (October)
Pages: 2057-2063

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Handle: RePEc:eee:jbfina:v:32:y:2008:i:10:p:2057-2063
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  1. Farinelli, Simone & Ferreira, Manuel & Rossello, Damiano & Thoeny, Markus & Tibiletti, Luisa, 2009. "Optimal asset allocation aid system: From "one-size" vs "tailor-made" performance ratio," European Journal of Operational Research, Elsevier, vol. 192(1), pages 209-215, January.
  2. Anders Ekholm & Daniel Pasternack, 2005. "The negative news threshold—An explanation for negative skewness in stock returns," The European Journal of Finance, Taylor & Francis Journals, vol. 11(6), pages 511-529.
  3. Farinelli, Simone & Tibiletti, Luisa, 2008. "Sharpe thinking in asset ranking with one-sided measures," European Journal of Operational Research, Elsevier, vol. 185(3), pages 1542-1547, March.
  4. Shalit, Haim & Yitzhaki, Shlomo, 1984. " Mean-Gini, Portfolio Theory, and the Pricing of Risky Assets," Journal of Finance, American Finance Association, vol. 39(5), pages 1449-68, December.
  5. Martin R. Young, 1998. "A Minimax Portfolio Selection Rule with Linear Programming Solution," Management Science, INFORMS, vol. 44(5), pages 673-683, May.
  6. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
  7. Hiroshi Konno & Hiroaki Yamazaki, 1991. "Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market," Management Science, INFORMS, vol. 37(5), pages 519-531, May.
  8. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
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