Target risk of portfolios with return constraints: Optimization of conditional value at risk

Abstract

This paper is a study about Conditional Value at Risk (CVaR) concept which is widely known as an efficient instrument for measuring the amount of loss and also constructing an optimal portfolio. Based on the crucial objective which is minimizing the target risk value CVaR with the main constraint including the returns value, this method developed an optimization model which allows us finding the optimal value of the weight of each asset contained in the portfolio while also calculated the minimal value of CVaR. The mathematical theory includes definition, some main properties, optimization model and the application of this concept in practice will be introduced. Using data from Viet Nam Stock Market, a sample portfolio including 16 stocks from 8 different industries selected from VN-Index will be examined to clarify the application of CVaR optimization model in practice. The performance of optimal portfolio constructed by CVaR optimization will also be evaluated and compared with the Mean – Variance Optimization portfolio. Although the algorithm of this model is quite complicated to understand and difficult for many investors to use, the study will try to give a framework and explain the basic characteristics and application of it in portfolio management activity. Despite some limitations of this research, it is hoped to contribute implication for investors in making good investments and building their optimal portfolios.