A Note on Portfolio Selection under Various Risk Measures

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A Note on Portfolio Selection under Various Risk Measures

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Enrico De Giorgi

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Enrico Giovanni 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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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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Find related papers by JEL classification:
G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

This paper has been announced in the following NEP Reports:

NEP-ALL-2002-08-29 (All new papers)

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