A Note on Portfolio Selection under Various Risk Measures

Enrico De Giorgi (enrico.degiorgi@unisg.ch)

No 122, IEW - Working Papers from Institute for Empirical Research in Economics - University of Zurich

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.

Keywords: decision under risk; mean-risk models; portfolio optimization; value-at-risk; expected shortfall; efficient frontier (search for similar items in EconPapers)
JEL-codes: G11 (search for similar items in EconPapers)
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Citations: View citations in EconPapers (18)

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