Portfolio Optimization Using Period Value at Risk Based on Historical Simulation Method

We consider market risk over a period of time that is more applicable in real world investment scenarios. This paper aims at solving technical issues related to the application of period value at risk (PVaR) in investment decision, a recently developed tool for measuring market risk over a period of time. An investment decision model with the objective of minimizing PVaR as the indicator of market risk and the constraint of satisfying investors' expected return is established. We consider portfolio selection problems with PVaR that is calculated applying historical simulation method. The PVaR minimization model becomes a complicated nonlinear programming and we suggested to solve the model by changing it to an equivalent mixed programming model. According to numerical analysis, we conclude that PVaR can provide a more conservative investment strategy for risk aversion investors compared with value at risk (VaR). Finally, we conduct a concise analysis of PVaR that is solved using historical simulation and Monte Carlo simulation.