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. Our first finding is the proof of a conjecture of Li and Ng (cf. [LN00]), Leippold, Trojani and Vanini (cf. [LTV04], [LTV03]) about the equivalence of the original non-separable mean-variance problem and its embedding into a higher dimensional separable problem. We further prove 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 show that it is then optimal to mimic the benchmark strategy. We apply the model first to UBS data and show that the myopic models are not acceptable for key rate delta profile management. Then, we calculate present value of a portfolio for 2005. It follows that the optimal dynamic portfolio strategy leads to a return of 3:12% compared to 2:6% of the myopic model.