A first paper, "Option-Adjusted Equilibrium Valuation of Guaranteed Minimum Death Benefits in Variable Annuities" (with Steven E. Posner), models the fair economic value of the guaranteed minimum death benefit in a variable annuity. In this paper Professor Milevsky and Dr. Posner show that the high Mortality and Expense charges levied by life insurance companies bear no relation to the actual cost of providing the guaranteed minimum death benefit. They provide a closed-form solution demonstrating that the Mortality and Expense charges levied by the life insurance industry on variable annuities substantially exceed their fair economic value. Based on standard assumptions about such variables as interest rates and equity market volatility, the authors calculate Mortality and Expense fees equivalent to the fair economic value of the guaranteed minimum death benefit separately for the men and women. For a 50 year old female with a life expectancy of 35 years, they calculate the fair value of the Mortality and Expense charge to be 6.3 basis points. For a 50 year old male with a life expectancy of 30 years, they calculate the fair Mortality and Expense fee to be 8.3 basis points. The estimates of the fair equilibrium value of the guaranteed minimum death benefit generated in the paper are almost exactly equal to the fee charged by TIAA-CREF. Tellingly, the authors also calculate that when the Mortality and Expense fee is the industry standard 125 basis points, this fee is equivalent to one-quarter of the present value of the initial investment.
In a second paper "Asset Allocation, Retirement and Variable Annuities", Professor Milevsky modeled the optimal asset allocation in a variable life annuity. The modeling effort concentrated on the optimal percentage of exposure to equities in the variable annuity, pre and post-retirement. For ease of exposition, the author assumed the asset allocation choice is limited to equities or treasury bills.
In the model, the equity allocation is an increasing function of the equity risk premium, but a decreasing function of equity volatility and risk aversion. A 100 percent equity allocation is possible. Upon retirement, no bequest motive is assumed, and so all financial assets are optimally annuitized. The model in the paper focuses solely on variable annuities. The interesting, and surprising, result of the paper is that according to the model the equity allocation can be higher during the post-retirement phase. The exact allocation depends on the degree of risk aversion of the investor, the mortality rate, and the equity risk premium. Professor Milevsky finds that when risk aversion is sufficiently low, and the equity risk premium sufficiently high, exposure to equities may in fact increase during retirement. However, this result is dependent on the assumptions concerning the various parameters, especially the mortality assumptions in both the pre and post-retirement periods.
