Managing Risk using Multi-Stage Stochastic Optimization

The paper discusses the application of multi-stage stochastic optimization for managing and optimizing expected returns versus risk, and contrasts static (single-stage) versus dynamic (multi-stage) portfolio optimization. We present how to best fund a pool of similar fixed rate mortgages through issuing bonds, callable and non-callable, of various maturities using stochastic optimization. We discuss the estimation of expected net present value and risk for different funding instruments using Monte Carlo sampling techniques, and the optimization of the funding using singleand multi-stage stochastic optimization. Using practical data we computed efficient frontiers of expected net present value versus risk for the singleand the multi-stage model, and studied the underlying funding strategies. Constraining the duration and convexity of the mortgage pool and the funding portfolios to match at any decision point, we computed delta and gamma hedged funding strategies and compared them to the ones from the multi-stage stochastic optimization model. The results for the different data assumptions demonstrate that multi-stage stochastic optimization yields significantly larger net present values at the same or at a lower level of risk, compared to single-stage optimization and delta and gamma hedging. We found that the funding strategies obtained from the multi-stage model differed significantly from those from the single-stage model and were again significantly different to funding strategies obtained from delta and gamma hedging. Using multi-stage stochastic optimization for determining the best funding of mortgage pools will lead in the average to significant profits, compared to using single-stage funding strategies, or using delta and gamma hedging. ∗Infanger Investmant Technology, L.L.C., 2680 Bayshore Parkway, Suite 206, Mountain View, CA 94043 and Department of Engineering-Economic Systems and Operations Research, Stanford University, Stanford, CA 94305