Expansion of the investment portfolio performance assessment model based on value-at-risk using a time series approach

Portfolio performance assessment needs to be carried out before or after the investment decision is taken, in order to minimize the possibility of risk loss. This paper discusses the expansion of the investment portfolio performance appraisal model based on Value-at-Risk, where the analyzed stock returns on mean and volatility is non-constant.The aim is to increase the likelihood of achieving investment objectives by investors. In this paper the mean is estimated using autoregressive moving average models, while the non-constant volatility is estimated using generally autoregressive conditional heteroscedastic models. The estimator's ofmean and non-constant volatility are then used for the analysis of investment portfolio optimization. Portfolio optimization issues are followed based on the basic framework of the Mean-Value-at-Risk model. The solution to the investment portfolio optimization problem is done by using the Lagrange multiplier technique and the Kuhn-Tucker method.Assessment of investment portfolio performance is based on Reward to Value-at-Risk, which is then used to compare the two investment portfolios A and B are analyzed. The results of the analysis show that portfolio A has better performance than portfolio B. So it is recommended to investors to choose an investment portfolio A, to achieve a better level of success.