Optimal Asset Allocation towards the End of the Life Cycle: To Annuitize or Not to Annuitize?

Abstract

INTRODUCTION ...It is a well known fact that annuity contracts, other than in the form of group insurance through pension systems, are extremely rare. Why this should be so is a subject of considerable current interest. It is still ill-understood. Adverse selection, causing an unfavorable payout, and the fact that some utility may be derived from bequest are, presumably, an important part of the answer.... Franco Modigliani, December 9, 1985 Nobel Prize acceptance speech in Stockholm, Sweden.(1) Most individuals must decide how much, if any, of their wealth should be annuitized near the time they retire. For many individuals a large portion of wealth is forcefully annuitized; for example, pensions and government social security. In other cases they have discretion in the matter. In its most general form, purchasing a life annuity involves paying a non-refundable lump sum to an insurance company in exchange for a guaranteed constant life-long consumption stream that cannot be outlived. The natural alternative to annuitization is investment amongst the various asset classes, such as equity, fixed income and real estate, together with a fixed periodic withdrawal equivalent to the consumption stream generated by the annuity. This do-it-yourself strategy incurs the financial risk of under-funding retirement in the event of long-run inferior investment returns in conjunction with unexpected human longevity. As Modigliani (1986), Friedman and Warshawsky (1990), Miter (1994), Poterba and Wise (1996) and many others have pointed out, very few people consciously choose to annuitize their marketable (liquid or discretionary) wealth, as evidenced by the comprehensive Health and Retirement Survey (HRS), conducted in the United States.(2) Only 1.57 percent of the HRS respondents reported annuity income. Likewise, only 8.0 percent of HRS respondents with a defined contribution pension plan selected an annuity payout. This phenomenon is especially puzzling within the paradigm of the Ando and Modigliani (1963) Life Cycle Hypothesis (LCH), under which individuals seek to their lifetime consumption by annuitizing wealth. What better way is there to smooth and consumption for the rest of one's natural life? The most common answer is to simply abandon the strict form of the life-cycle hypothesis and declare that individuals have strong bequest motives, as Bernheim (1991), Hurt (1989) and many others have suggested. Another approach, which we prefer, is to argue that even when individuals have negligible bequest motives, annuities are simply too expensive, as was hypothesized by Warshawsky (1988) and Friedman and Warshawsky (1990). This means that the implied rates of return from life annuities are much lower as a result of transaction costs, or loads, than those available from other investment assets, considering the life-long consumption guarantee which they provide. The contribution of this paper is to give prescriptive advice in the face of these costs. We suggest that most individuals should defer annuitization, via the do-it-yourself scheme, until is no longer possible to beat the mortality adjusted rate of return from the life annuity. We call this approach the do-it-yourself-and-then-switch strategy. Our methodology deviates from the traditional financial economic utility maximizing approach to asset allocation by focusing on the probability of consumption shortfall, as the measure of risk. The classic utility-based approach would involve solving the following dynamic stochastic optimization problem: [Mathematical Expression Omitted], (1) where U([C.sub.t]) denotes the instantaneous utility of consumption; [Rho] is the personal discount rate for consumption; B([W.sub.T]) denotes the utility of bequest; [Gamma] is the discount rate for bequest; T is the stochastic time of death; [a.sub.t] is the amount of annuities; [C.sub.t] is the rate of consumption; [W. …