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.

Additional Metadata
Keywords Conditional value-at-risk, Disutility, Elliptical distributions, Linear loss functions, Portfolio optimization, Value-at-risk
JEL Optimization Techniques; Programming Models; Dynamic Analysis (jel C61), Portfolio Choice; Investment Decisions (jel G11), Corporate Finance and Governance (jel G3), Business Administration and Business Economics; Marketing; Accounting (jel M), Production Management (jel M11)
Publisher Erasmus Research Institute of Management (ERIM)
Persistent URL
Series ERIM Report Series Research in Management
Journal ERIM report series research in management Erasmus Research Institute of Management
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 (No. ERS-2007-032-LIS). ERIM report series research in management Erasmus Research Institute of Management. Erasmus Research Institute of Management (ERIM). Retrieved from