Birbil, S.I. Frenk, J.B.G. Kaynar, B. Noyan, N. (Erasmus Econometric Institute)
Abstract
Several approaches exist to model decision making under risk, where risk can be broadly defined as the effect of variability of random outcomes. One of the main approaches in the practice of decision making under risk uses mean-risk models; one such well-known is the classical Markowitz model, where variance is used as risk measure. Along this line, we consider a portfolio selection problem, where the asset returns have an elliptical distribution. We mainly focus on portfolio optimization models constructing portfolios with minimal risk, provided that a prescribed expected return level is attained. In particular, we model the risk by using Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). After reviewing the main properties of VaR and CVaR, we present short proofs to some of the well-known results. Finally, we describe a computationally efficient solution algorithm and present numerical results.
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Publisher Info
Paper provided by Erasmus University Rotterdam, Econometric Institute in its series Econometric Institute Report with number
EI 2008-14 Revision_Date: 2009-11-06.