The Duration of Liabilities with Interest Sensitive Cash Flows

In order to apply asset-liabilitymanagement techniques to property-liability insurers, the sensitivity of liabilities to interest rate changes, or duration, must be calculated. The current approach is to use the Macaulay or modified duration calculations, both of which presume that the cash flows are invariant with respect to interest rate changes. Based on the structure of liabilities for property-liability insurers, changes in interest rates-given that interest rates are correlated with inflation-should affect future cash flows on existing liabilities. This paper analyzes the effect that interest rate changes can have on these cash flows, shows how to calculate the resulting effective duration of these liabilities, and demonstrates the impact of failing to use the correct duration measure on asset-liability management for property-liability insurers.