CVaR Robust Mean-CVaR Portfolio Optimization

One of the most important problems faced by every investor is asset allocation. An investor during making investment decisions has to search for equilibrium between risk and returns. Risk and return are uncertain parameters in the suggested portfolio optimization models and should be estimated to solve the problem. However, the estimation might lead to large error in the final decision. One of the widely used and effective approaches for optimization with data uncertainty is robust optimization. In this paper, we present a new robust portfolio optimization technique for mean-CVaR portfolio selection problem under the estimation risk in mean return. We additionally use CVaR as risk measure, to measure the estimation risk in mean return. To solve the model efficiently, we use the smoothing technique of Alexander et al. (2006). We compare the performance of the CVaR robust mean-CVaR model with robust mean-CVaR models using interval and ellipsoidal uncertainty sets. It is observed that the CVaR robust mean-CVaR portfolios are more diversified. Moreover, we study the impact of the value of confidence level on the conservatism level of a portfolio and also on the value of the maximum expected return of the portfolio. 1. Introduction Portfolio optimization is one of the best known approaches in financial portfolio selection. The earliest technique to solve the portfolio selection problem is developed by Harry Markowitz in the 1952. In his so-called mean-variance (MV) portfolio optimization model, the portfolio return is measured by the expected return of the portfolio, and the associated risk is measured by the variance of portfolio returns [1]. Variance as the risk measure has its weaknesses. Controlling the variance does not only lead to low deviation from the expected return on the downside, but also on the upside [2]. Hence, alternative risk measures have been suggested to replace the variance such as Value at Risk ( ) that manage and control risk in terms of percentiles of loss distribution. Instead of regarding both upside and downside of the expected return, considers only the downside of the expected return as risk and represents the predicted maximum loss with a specified confidence level (e.g., 95%) over a certain period of time (e.g., one day) [3–5]. is a popular risk measure. However, may have drawbacks and undesirable properties that limit its use [6–8], such as lack of subadditivity; that is, of two different investment portfolios may be greater than the sum of the individual s. Also, is nonconvex and nonsmooth and has multiple local minimum,