B. Kaynar, “Application of a General Risk Management Model to... ”
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Faculty of Engineering and Natural Sciences
IE 551 - Graduate Seminar

“Application of a General Risk Management Model to Portfolio Problems with Elliptic Distributions”


Bahar Kaynar
Sabanci University
Istanbul, Turkey

Abstract:  In this study, we discuss a class of risk measures for portfolio optimization with linear loss functions, where the random return variables of financial instruments are assumed to be distributed by multivariate elliptic distributions. We consider recent risk measures, Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR) under this setting. The optimal solution of the mathematical models with objective functions formed by VaR and CVaR measures, is equivalent to the solution of the corresponding Markowitz model. To solve the Markowitz model, we have modified and implemented a finite step algorithm proposed in the literature. Finally, we introduce the CVaR model with convex increasing utility functions reflecting the behavior of risk averse investors. Although, we have a convex objective function in this case, an analytic form cannot be defined. However, unlike generating scenarios from multivariate distributions as suggested in the literature, we show that the objective function can be closely estimated by simulating realizations only from univariate distributions.

May 3, 2006, 13:40, FENS, L048