Risk measures and their applications in asset management

Ilker Birbil, Hans Frenk, B. Kaynar and Nilay N. Nilay

No EI 2008-14, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), 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.

Keywords: conditional value-at-risk; elliptical distributions; mean-risk; portfolio optimization; value-at-risk (search for similar items in EconPapers)
Date: 2008-08-21
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Citations: View citations in EconPapers (2)

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