Joint Interest Rate Risk Management of Balance Sheet and Hedge Portfolio

We present a multi-period mean-variance optimization program which allows for a joint optimization of the balance and off-balance sheet. We first prove a conjecture of Li and Ng (2000), Leippold et al. (2004, 2003) about the equivalence of the original non-separable mean-variance problem and its embedding into a higher dimensional separable problem. We then show that given a time independent term structure, the one-period and the multi-period problem are equivalent. If the best forecast of the interest rates is the forward rate, we prove that it is then optimal to mimic the benchmark strategy. We apply the model to UBS data and show that the myopic models are not acceptable for key rate delta profile management. We further calculate present values of a portfolio for different strategies. It follows that the optimal dynamic portfolio strategy leads to a return of 3.12% compared to 2.6% for the myopic model