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Portfolio Optimization with Optimal Expected Utility Risk Measures


  • H. Fink
  • S. Geissel
  • J. Herbinger
  • F. T. Seifried


The purpose of this article is to evaluate optimal expected utility risk measures (OEU) in a risk-constrained portfolio optimization context where the expected portfolio return is maximized. Wecompare the portfolio optimization with OEU constraint to a portfolio selection model using valueat risk as constraint. The former is a coherent risk measure for utility functions with constantrelative risk aversion and allows individual specifications to the investor’s risk attitude and timepreference. In a case study with three indices we investigate how these theoretical differences in-fluence the performance of the portfolio selection strategies. A copula approach with univariateARMA-GARCH models is used in a rolling forecast to simulate monthly future returns and cal-culate the derived measures for the optimization. The results of this study illustrate that bothoptimization strategies perform considerably better than an equally weighted portfolio and a buyand hold portfolio. Moreover, our results illustrate that portfolio optimization with OEU con-straint experiences individualized effects, e.g. less risk averse investors lose more portfolio value inthe financial crises but outperform their more risk averse counterparts in bull markets.

Suggested Citation

  • H. Fink & S. Geissel & J. Herbinger & F. T. Seifried, 2019. "Portfolio Optimization with Optimal Expected Utility Risk Measures," Working Paper Series 2019-07, University of Trier, Research Group Quantitative Finance and Risk Analysis.
  • Handle: RePEc:trr:qfrawp:201907

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    References listed on IDEAS

    1. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    2. Adam, Alexandre & Houkari, Mohamed & Laurent, Jean-Paul, 2008. "Spectral risk measures and portfolio selection," Journal of Banking & Finance, Elsevier, vol. 32(9), pages 1870-1882, September.
    3. Yannick Malevergne & Ali Chabaane & Jean-Paul Laurent & Françoise Turpin, 2006. "Alternative Risk Measures for Alternative Investments," Post-Print hal-02311832, HAL.
    4. Holger Fink & Yulia Klimova & Claudia Czado & Jakob Stöber, 2017. "Regime Switching Vine Copula Models for Global Equity and Volatility Indices," Econometrics, MDPI, vol. 5(1), pages 1-38, January.
    5. Priscilla Serwaa Nkyira Gambrah & Traian Adrian Pirvu, 2014. "Risk Measures and Portfolio Optimization," JRFM, MDPI, vol. 7(3), pages 1-17, September.
    6. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2007. "Mean-variance portfolio selection with `at-risk' constraints and discrete distributions," Journal of Banking & Finance, Elsevier, vol. 31(12), pages 3761-3781, December.
    7. Bing Liang & Hyuna Park, 2007. "Risk Measures for Hedge Funds: a Cross‐sectional Approach," European Financial Management, European Financial Management Association, vol. 13(2), pages 333-370, March.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Arzac, Enrique R. & Bawa, Vijay S., 1977. "Portfolio choice and equilibrium in capital markets with safety-first investors," Journal of Financial Economics, Elsevier, vol. 4(3), pages 277-288, May.
    10. Chen, Zhiping & Wang, Yi, 2008. "Two-sided coherent risk measures and their application in realistic portfolio optimization," Journal of Banking & Finance, Elsevier, vol. 32(12), pages 2667-2673, December.
    11. Alexandre Adam & Mohamed Houkari & Jean-Paul Laurent, 2008. "Spectral risk measures and portfolio selection," Post-Print hal-03676385, HAL.
    12. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    13. Donald Meyer & Jack Meyer, 2005. "Relative Risk Aversion: What Do We Know?," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 243-262, December.
    14. David E. Allen & Michael McAleer & Robert J. Powell & Abhay K. Singh, 2016. "Down-Side Risk Metrics as Portfolio Diversification Strategies across the Global Financial Crisis," JRFM, MDPI, vol. 9(2), pages 1-18, June.
    15. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    16. Boubaker, Heni & Sghaier, Nadia, 2013. "Portfolio optimization in the presence of dependent financial returns with long memory: A copula based approach," Journal of Banking & Finance, Elsevier, vol. 37(2), pages 361-377.
    17. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    1. Géraldine Bouveret & Athena Picarelli, 2020. "A Level-Set Approach for Stochastic Optimal Control Problems Under Controlled-Loss Constraints," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 779-805, September.

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    More about this item


    optimal expected utility; portfolio optimization; risk measures; value at risk;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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