Application of a General Risk Management Model to Portfolio Optimization Problems with Elliptical Distributed Returns for Risk Neutral and Risk Averse Decision Makers
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.
|Keywords||Conditional value-at-risk, Disutility, Elliptical distributions, Linear loss functions, Portfolio optimization, Value-at-risk|
|JEL||C61, Optimization Techniques; Programming Models; Dynamic Analysis (jel), G11, Portfolio Choice; Investment Decisions (jel), G3, Corporate Finance and Governance (jel), M, Business Administration and Business Economics; Marketing; Accounting (jel), M11, Production Management (jel)|
|Publisher||Erasmus Research Institute of Management (ERIM)|
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 http://hdl.handle.net/1765/10151