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A Note on Portfolio Selection under Various Risk Measures

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  • Enrico De Giorgi

Abstract

This work gives a brief overview of the portfolio selection problem following the mean-risk approach first proposed by Markowitz (1952). We consider various risk measures, i.e. variance, value-at-risk and expected-shortfall and we study the efficient frontiers obtained by solving the portfolio selection problem under these measures. We show that under the assumption that returns are normally distributed, the efficient frontiers obtained by taking value-at-risk or expected-shortfall are subsets of the mean-variance efficient frontier. We generalize this result for all risk measures that can be written as a particular combination of mean and variance and we show that for these measures Tobin separation holds under some restrictions.

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Bibliographic Info

Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 122.

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Handle: RePEc:zur:iewwpx:122

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Keywords: decision under risk; mean-risk models; portfolio optimization; value-at-risk; expected shortfall; efficient frontier;

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  1. Enrico De Giorgi, . "Reward-Risk Portfolio Selection and Stochastic Dominance," IEW - Working Papers 121, Institute for Empirical Research in Economics - University of Zurich.
  2. 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.
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Cited by:
  1. Solange Berstein & Rómulo Chumacero, 2008. "VaR Limits for Pension Funds: An Evaluation," Working Papers 26, Superintendencia de Pensiones, revised May 2008.
  2. Bruno S. Frey & Alois Stutzer, . "Direct Democracy: Designing a Living Constitution," IEW - Working Papers 167, Institute for Empirical Research in Economics - University of Zurich.
  3. Alejandro Reveiz & Carlos Eduardo León, 2008. "Efficient Portfolio Optimization in the Wealth Creation and Maximum Drawdown Space," BORRADORES DE ECONOMIA 004732, BANCO DE LA REPÚBLICA.
  4. De Giorgi, Enrico, 2005. "Reward-risk portfolio selection and stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 895-926, April.
  5. Enrico De Giorgi & Stefan Reimann, . "The ?-Beauty Contest: Choosing Numbers, Thinking Intervals," IEW - Working Papers 183, Institute for Empirical Research in Economics - University of Zurich.
  6. Winker, Peter & Maringer, Dietmar, 2004. "The Hidden Risks of Optimizing Bond Portfolios under VaR," Research Notes 13, Deutsche Bank Research.
  7. Wozabal, Nancy, 2009. "Uniform limit theorems for functions of order statistics," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1450-1455, June.

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