Managing Interest Rate Risk for Long Liabilities

This paper examines the effectiveness of various investment strategies in immunizing a 50-year level annuity certain. Each investment strategy is analyzed over 100 paths of interest rates generated from the one-factor Cox-Ingersoll-Ross stochastic model. It is found that using Macaulay-type risk indexes, such as duration (first order) and convexity (second order), achieves good immunization. An improvement in immunization effectiveness is obtained by using risk indexes that measure price responses to orthonormal-polynominal-based shocks to the term structure of interest rates. It is shown why these new risk indexes, which are not derived from any particular model of interest rate dynamics, are expected to be particularly useful in managing the interest rate risk for long-term liabilities.