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Entropic risk measures and their comparative statics in portfolio selection: Coherence vs. convexity

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  • Brandtner, Mario
  • Kürsten, Wolfgang
  • Rischau, Robert

Abstract

We conduct a decision-theoretic analysis of optimal portfolio choices and, in particular, their comparative statics under two types of entropic risk measures, the coherent entropic risk measure (CERM) and the convex entropic risk measure (ERM). Starting with the portfolio selection between a risky and a risk free asset (framework of Arrow (1965) and Pratt (1964)), we find a restrictive all-or-nothing investment decision under the CERM, while the ERM yields diversification. We then address a portfolio problem with two risky assets, and provide comparative statics with respect to the investor’s risk aversion (framework of Ross (1981)). Here, both the CERM and the ERM exhibit closely interrelated inconsistencies with respect to the interpretation of their risk parameters as a measure of risk aversion: for any two investors with different risk parameters, it may happen that the investor with the higher risk parameter invests more in the riskier one of the two assets. Finally, we analyze the portfolio problem “risky vs. risk free” in the presence of an independent background risk, and analyze the effect of changes in this background risk (framework of Gollier and Pratt (1996)). Again, we find questionable predictions: under the CERM, the optimal risky investment is always increasing instead of decreasing when a background risk is introduced, while under the ERM it remains unaffected.

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  • Brandtner, Mario & Kürsten, Wolfgang & Rischau, Robert, 2018. "Entropic risk measures and their comparative statics in portfolio selection: Coherence vs. convexity," European Journal of Operational Research, Elsevier, vol. 264(2), pages 707-716.
    • Handle: RePEc:eee:ejores:v:264:y:2018:i:2:p:707-716
    DOI: 10.1016/j.ejor.2017.07.007
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    4. Brandtner, Mario & Kürsten, Wolfgang & Rischau, Robert, 2020. "Beyond expected utility: Subjective risk aversion and optimal portfolio choice under convex shortfall risk measures," European Journal of Operational Research, Elsevier, vol. 285(3), pages 1114-1126.
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    6. J. Arismendi-Zambrano & R. Azevedo, 2020. "Implicit Entropic Market Risk-Premium from Interest Rate Derivatives," Economics Department Working Paper Series n303-20.pdf, Department of Economics, National University of Ireland - Maynooth.
    7. Kirkby, J. Lars & Mitra, Sovan & Nguyen, Duy, 2020. "An analysis of dollar cost averaging and market timing investment strategies," European Journal of Operational Research, Elsevier, vol. 286(3), pages 1168-1186.

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