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Conditional Value-at-Risk, spectral risk measures and (non-)diversification in portfolio selection problems – A comparison with mean–variance analysis

Mario Brandtner

Journal of Banking & Finance, 2013, vol. 37, issue 12, 5526-5537

Abstract: We study portfolio selection under Conditional Value-at-Risk and, as its natural extension, spectral risk measures, and compare it with traditional mean–variance analysis. Unlike the previous literature that considers an investor’s mean-spectral risk preferences for the choice of optimal portfolios only implicitly, we explicitly model these preferences in the form of a so-called spectral utility function. Within this more general framework, spectral risk measures tend towards corner solutions. If a risk free asset exists, diversification is never optimal. Similarly, without a risk free asset, only limited diversification is obtained. The reason is that spectral risk measures are based on a regulatory concept of diversification that differs fundamentally from the reward-risk tradeoff underlying the mean–variance framework.

Keywords: Portfolio selection; Spectral risk measures; Conditional Value-at-Risk; Comonotonicity; Efficient frontier; Optimal portfolio (search for similar items in EconPapers)
JEL-codes: G11 G21 D81 (search for similar items in EconPapers)
Date: 2013
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