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Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers

Author

Listed:
  • Kaynar, B.
  • Birbil, S.I.
  • Frenk, J.B.G.

Abstract

In this paper portfolio problems with linear loss functions and multivariate elliptical distributed returns are studied. We consider two risk measures, Value-at-Risk and Conditional-Value-at-Risk, and two types of decision makers, risk neutral and risk averse. For Value-at-Risk, we show that the optimal solution does not change with the type of decision maker. However, this observation is not true for Conditional-Value-at-Risk. We then show for Conditional-Value-at-Risk that the objective function can be approximated by Monte Carlo simulation using only a univariate distribution. To solve the equivalent Markowitz model, we modify and implement a finite step algorithm. Finally, a numerical study is conducted.

Suggested Citation

  • Kaynar, B. & Birbil, S.I. & Frenk, J.B.G., 2007. "Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers," ERIM Report Series Research in Management ERS-2007-032-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    • Handle: RePEc:ems:eureri:10151
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    Citations

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    Cited by:

    1. Krajina, A., 2009. "A Method of Moments Estimator of Tail Dependence in Elliptical Copula Models," Discussion Paper 2009-42, Tilburg University, Center for Economic Research.
    2. Jamie Fairbrother & Amanda Turner & Stein W. Wallace, 2018. "Scenario Generation for Single-Period Portfolio Selection Problems with Tail Risk Measures: Coping with High Dimensions and Integer Variables," INFORMS Journal on Computing, INFORMS, vol. 30(3), pages 472-491, August.
    3. Krajina, A., 2010. "An M-estimator of multivariate tail dependence," Other publications TiSEM 66518e07-db9a-4446-81be-c, Tilburg University, School of Economics and Management.

    More about this item

    Keywords

    Conditional value-at-risk; Disutility; Elliptical distributions; Linear loss functions; Portfolio optimization; Value-at-risk;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G3 - Financial Economics - - Corporate Finance and Governance
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • M11 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Administration - - - Production Management

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