Portfolio value-at-risk forecasting with GA-based extreme value theory

Value-at-Risk (VaR) has become a popular risk measure since it was adopted by the Bank for International Settlements and US regulatory agencies in 1988. The VaR concept has also been further extended to the portfolio Value-at-Risk (PVaR) measure used for managing risks and returns under a multiple-asset portfolio. Precise prediction of PVaR provides better evaluation criteria in areas such as investment decision-making and risk management. The two issues concerned with portfolio risk are efficient set selection and volatility forecasting. Most of the statistical portfolio selection models are based on linear functions under specific assumptions. Due to the fat-tailed distribution in most real financial time-series data, extreme value theory (EVT) is powerful in determining the VaR of a portfolio by concentrating on estimating the shape of the fat-tailed probability distribution. However, using EVT to evaluate the portfolio's volatility is very difficult, because each individual within the portfolio has its own distinct peak threshold value. This study introduces an evolutionary portfolio volatility forecasting model to optimize portfolios under their maximum expected returns subject to a risk constraint. We use a genetic algorithm (GA) to extract the best portfolio set and most suitable peak threshold in order to estimate the portfolio's VaR by means of EVT.