Abstract
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.
Highlights
Portfolio optimization is one of the best known approaches in financial portfolio selection
We present Conditional Value at Risk (CVaR) robust mean-CVaR portfolio optimization problem that estimation risk in mean return is measured by CVaR
First we will compare the performance of the CVaR robust mean-CVaR model with robust mean-CVaR models using interval and ellipsoidal uncertainty sets by actual data
Summary
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]. Risk and return are uncertain parameters in portfolio optimization models, and estimating them might lead to large error in the final decision. To deal with such situation, one of the widely used and effective approaches is robust optimization technique. We have applied this technique to give the robust counterpart of the mean-CVaR portfolio selection problem under the estimation risk in mean return. We demonstrate that the value of confidence level affects the conservatism level, diversification, and the value of the maximum expected return of the resulting portfolios
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