On the Interaction between Transfer Restrictions and Crediting Strategies in Guaranteed Funds

Guaranteed funds with crediting rates for fixed periods determined by a pension provider or insurance company are common features of accumulation annuity contracts. Policyholders can transfer money back and forth between these accounts and money market accounts that give them features similar to demand deposits, and yet they frequently credit a higher rate than the money market. Transfer restrictions are commonly employed to prevent arbitrage. In this article, we model the interaction between company and policyholder as a multiperiod game in which the company maximizes risk-neutral expected present value of profits and the policyholder maximizes his expected discounted utility. We find that the optimal strategy on the part of the company is to credit a rate higher than the money market rate in the first period to entice the policyholder to invest in the guaranteed fund. The company then credits the floor in the remaining periods as the policyholder transfers out the maximum amount. This does better for the policyholder in low interest rate environments and worse in high interest rate environments and acts as a type of “interest rate insurance” for the policyholder.