Determining the Proper Interest Rate for Loss Reserve Discounting: An Economic Approach

By examining the underlying economic principles of insurance and finance, this paper shows how the proper interest rate for reserve discounting is a function of the degree of risk present in the outstanding reserve. When loss reserves are certain, the discounting interest rate is shown to be the market interest rate for a riskless security having a duration matching that of the loss payment. The unpaid loss is then allowed to be uncertain, and the risk adjustment to the discounting interest rate is derived. An analysis of empirical property-liability data over a 15-yr period is performed using a pricing model which incorporates the risk-adjusted interest rate. Results indicate that the risk adjustment for aggregate industry loss reserves is about three points of yield rate. The effect of income taxes on the discounting interest rate is then explored. The appropriate rate in this case is shown to be based upon the risk-adjusted rate in the absence of taxes, and is identical to the pre-tax value when the tax reserve evaluation uses the risk adjustment. Finally, several other applications of the risk-adjustment method are given, including asset valuation, reinsurance and pricing of products.