Portfolio optimization of risky assets using mean-variance and mean-cvar / Hannah Nadiah Abdul Razak, Ernie Syufina Chun Lee @ Mohd Fadzlee and Nur Hafidzah Hafidzuddin

The aim of this research is to apply the variance and conditional value-at¬ risk (CVaR) as risk measures in portfolio selection problem. To obtain an optimum portfolio of the assets, we minimize the risks using mean-variance and mean-CVaR models. Dataset with stocks from FBMKLCI is used to generate our scenario returns. Both models and dataset are coded and im¬ plemented in AMPL software. Then, we analyzed the numerical results in Microsoft Excel. We compared the performance of both optimized port¬ folios constructed from the models in term of risk measure and realized returns. The optimal portfolios are evaluated across three different target returns that represent the low risk-low returns, medium risk-medium re¬ turns and high risk-high returns portfolios. Numerical results show that the composition of portfolios for mean-variance are generally more diversi¬ fied compared to mean-CVaR portfolios. The in-sample results show that the seven optimal mean-CVaRo.05 portfolios have lower CVaRo.05 values as compared to their optimal mean-variance counterparts. Consequently, the standard deviation for mean-variance optimal portfolios are lower than the standard deviation of its mean-CVaRo.05 counterparts. For the out¬ of sample analysis, we can conclude that mean-variance portfolios only minimize standard deviation at low target return. While, mean-CVaR portfolios are favourable in minimizing risks at high target return.