Estimation of the Period Value at Risk of Investments with Multiple Risk Factors

This study is to propose a Monte Carlo simulation based method for estimating the Period Value at Risk (PVaR) of investments with multiple risk factors. There proposed many measures for market risk like variance, value at risk (VaR), however, these measures only reflect the risk at specific point of time. We proposed in 2012 the notion of period value at risk (PVaR) to reflect the risk in a time period, and suggested to estimate the PVaR of an investment using MC simulation. This paper will extend the method to estimate the PVaR of investments where multiple risk factors are involved. After proposing the MC simulation based method, we use this method to estimate the risk of an investment in five stocks assuming that the stock prices are geometric Brownian motion processes. To compare the difference with risk measured by VaR, we calculate one-year PVaR and VaR at the end of one year of the investment. Our computing experiments show that the proposed method can be used to estimate the PVaR of an investment, and there is a significant difference between PVaR and VaR. In our computing experiments, PVaR at confidence level 90% is 0.52560 but VaR at the same confidence level is 0.17974. Hence we conclude that the proposed method is usable in estimating the PVaR of investments with multiple risk factors, and PVaR is a proper measure for market risk in a period of time.