Value-at-Risk (VaR) and Dynamic Portfolio Selection.

Abstract

In this study, we analyze the combination of VaR and dynamic portfolio selection strategy. First, we notice the unrealistic assumption of no adjustment in the portfolio during the VaR horizon. This assumption is unrealistic and does not reflect the true risk of the underlying portfolio when the VaR horizon is long. We develop the new VaR incorporating portfolio selection strategies and compare it with the old VaR. The analysis reveals that any adjustment during the VaR horizon could have significant impact on the risk of the portfolio. Second, under Basel's regulation, the VaR needs to be estimated daily and the bank needs to adjust the capital reserve according to the updated VaR. The process of finding the optimal selection strategy can be divided into two parts. The first one is the allocation between risk-free capital and risky portfolio. The second one is the allocation within the risky portfolio. Each part itself is also an optimization problem. We provide a tractable solution to the dynamic portfolio selection strategy under the Basel's VaR-capital requirement.