Conditional Value at Risk as a Criterion for Optimal Portfolio Selection

Abstract

<p> The focus of my master's project involves research Conditional Value at Risk (or Expected Shortfall) as a risk measure for optimal portfolio selection. The project is organized as follows. In the first chapter, we introduce and discuss the quantile based risk measures, Vale at Risk (VaR) and Conditional Vale at Risk (CVaR), with respect to axiomatic characterization of coherent measure. The properties and advantages of CVaR are analyzed. The second chapter deals with mean-risk models of portfolio optimization. The common idea in all asset allocation models is the minimization of some measure of risk while simultaneously maximizing portfolio expected return. Portfolio optimization in a mean-CVaR framework has been actively discussed recently. CVaR is a numerically tractable measure, allowing optimal portfolios to be computed by means of covex programming. Most importantly for applications, however, a mean CVaR model can be used with scenario simulation of loss distributions. We investigate the convergence of the Monte-Carlo based CVaR optimal portfolio algorithm when an analytical solution of the optimization problem can be obtained. The last chapter considers the benchmark (or relative) portfolio selection problem in terms of a multiobjective problem. Tracking error optimization in a mean-multirisk framework allows implementation of an interactive decision making and taking into account of the investor's preferences.</p>