Understanding the behavior and hedging of segregated funds offering the reset feature

North American Actuarial Journal, Apr 2002 by Windcliff, Heath, Roux, Martin Le, Forsyth, Peter, Vetzal, Kenneth

5.2.3 Antiselective Lapsation

Because of investors' ability to lapse antiselectively, institutions that have removed the reset feature from their product offerings may not have reduced their risk exposure as much as one might initially believe. Consider a case where there are no reset provisions or mortality benefits, so we have just a 10-year European put option. Assume for simplicity that the correct proportional fee is being charged for this contract and that there are no back-end fees, so investors can lapse without penalty. In the absence of explicit reset options, investors have the ability to create resets synthetically by lapsing and then re-entering the contract.

Why then does it appear that the explicit reset option creates so much additional value? The reason is that we haven't adequately valued the ability of investors to perform resets synthetically. When investors are not charged a single up-front fee, they have a valuable type of default option: They can avoid continuing to pay for a deep out-of-the-money put and acquire a new at-the-money guarantee with no additional expense. If we simply think of these contracts as 10-year puts and ignore this default option, we significantly undervalue them.

Our model, which incorporates resets, is effectively including this option, and this is why it appears to generate much higher values.9 Of course, in practice, various factors do constrain investors' ability to follow this synthetic reset strategy. Back-end fees are levied in the first few years. There may be tax consequences associated with withdrawing funds from an account. Moreover, to the extent that the proportional fees being charged are too low, investors have an incentive to remain in their existing contracts. However, our main point is that removing explicit reset provisions may not be a panacea if investors can effectively reset on their own.

6. CONTRACT MODIFICATIONS

To this point, we have shown that it can be very expensive to hedge contracts that include the reset feature. This section explores possible approaches to reducing the cost of providing these guarantees. Specifically, we explore some ways of modifying these contracts so that they remain attractive to the investor, yet are less expensive to hedge in the market.

In our research, we have investigated many possible modifications of these contracts and found that limiting contract features that depend on the optimality of investors' actions does not reduce the value of these contracts as much as might be expected.

6.1 Effect of Number of Reset Opportunities

One example of a contract modification that depends on the optimality displayed by investors is altering the number of reset opportunities per annum. Clearly, the value of the contract must decrease as the number of reset opportunities decreases. In Figure 9 we show the cost of providing a segregated fund guarantee with one to four reset opportunities per annum, for both 25% and 100% levels of investor optimality.

If we look at the lower collection of curves, corresponding to a 25% optimal investor profile, the cost does decrease as expected, but the curves are virtually indistinguishable. Furthermore, in the accompanying table, we see that the required proportional fee is virtually unaffected and is approximately 80 bp for either one, two, or four resets allowed per annum. Why is the effect of this contract modification so small? The reason is that we are already assuming a high degree of investor nonoptimality. In effect, we are limiting a feature we assume the investors are not using efficiently anyway.