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A Note on Portfolio Selection under Various Risk Measures

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Enrico De Giorgi

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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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Paper provided by Institute for Empirical Research in Economics - IEW in its series IEW - Working Papers with number iewwp122.

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Handle: RePEc:zur:iewwpx:122

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

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G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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  1. Ralf Becker & Urs Fischbacher & Thorsten Hens, . "Soft Landing of a Stock Market Bubble, An Experimental Study," IEW - Working Papers iewwp090, Institute for Empirical Research in Economics - IEW. [Downloadable!]
  2. Bruno S. Frey & Stephan Meier, . "Pro-Social Behavior, Reciprocity or Both?," IEW - Working Papers iewwp107, Institute for Empirical Research in Economics - IEW. [Downloadable!]
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  3. Simon Gächter & Armin Falk, . "Work motivation, institutions, and performance," IEW - Working Papers iewwp062, Institute for Empirical Research in Economics - IEW. [Downloadable!]
  4. Alois Stutzer, . "The Role of Income Aspirations in Individual Happiness," IEW - Working Papers iewwp124, Institute for Empirical Research in Economics - IEW. [Downloadable!]
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  5. Lars Feld & Bruno Frey, 2000. "Trust Breeds Trust: How Taxpayers are Treated," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
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  6. Bruno Frey & Stephan Meier, 2005. "Selfish and Indoctrinated Economists?," European Journal of Law and Economics, Springer, vol. 19(2), pages 165-171, April. [Downloadable!] (restricted)
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  7. Rafael Lalive & Jan C. van Ours & Josef Zweimüller, 2005. "The Effect Of Benefit Sanctions On The Duration Of Unemployment," Journal of the European Economic Association, MIT Press, vol. 3(6), pages 1386-1417, December. [Downloadable!] (restricted)
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  8. Fehr, Ernst & Klein, Alexander & Schmidt, Klaus M., 2001. "Fairness, Incentives and Contractual Incompleteness," CEPR Discussion Papers 2790, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  9. Bruno Frey & Alois Stutzer, 2001. "Beyond Bentham -- Measuring Procedural Utility," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  10. Rabah Amir & Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, . "Market Selection and Survival of Investment Strategies," IEW - Working Papers iewwp091, Institute for Empirical Research in Economics - IEW. [Downloadable!]
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  11. Bruno Frey, 2001. "Flexible Citizenship for a Global Society," Berkeley Olin Program in Law & Economics, Working Paper Series 1018, Berkeley Olin Program in Law & Economics. [Downloadable!]
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Cited by:
(explanations, 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.)

  1. Alejandro Reveiz & Carlos León, . "Efficient Portfolio Optimization in the Wealth Creation and Maximum Drawdown Space," Borradores de Economia 520, Banco de la Republica de Colombia. [Downloadable!]
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