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

Most individuals must decide how much, if any, of their wealth should be annuitized at about the time they retire. For many people a large portion of wealth is forcefully annuitized, for example pensions and government social security. In other cases and with remaining marketable wealth consumers have discretion in the matter. In its most general form, purchasing an immediate life annuity involves paying a non-refundable lump sum to an insurance company in exchange for a guaranteed constant life-long consumption stream that can not be outlived. The natural alternative to annuitization is individual strategic asset allocation amongst the various investment classes, such as equity, fixed income and real estate, together with a fixed periodic consumption from capital, dividends and interest. Unfortunately, this do it yourself strategy runs the financial risk of under-funding retirement in the event of long-run inferior investment returns in conjunction with unexpected human longevity. This paper develops a normative model that will provide a relevant framework for the choice between asset allocation and discretionary annuitization at retirement. The paradigm will be rich enough to accommodate the altruistic desire for bequest as well as the fundamental pre-occupation with consumption security. Our methodology deviates somewhat from the traditional financial economic approach to asset allocation and insurance, where the investor in question is assumed to maximize a well defined microeconomic utility function over all states of nature. Rather, we focus on the probability of consumption shortfall as the implicit risk measure and operational objective function. Our model allows individuals to input their own parameters for stochastic market performance and obtain the optimal age at which to annuitize, based on a probabilistic tolerance level. As a byproduct, using our own estimates, we are able to confirm the intuition shared by many in the financial planning community. Namely, given the empirical evidence on the cost structure of annuities, the adverse selection implicit in annuity mortality tables together with the long- run propensity for equities to outperform fixed income investments, otherwise known as time-diversification, it makes very little sense for consumers under the age of 80 to annuitize any additional marketable wealth. In essence, the rate of return from a life annuity can easily be "beaten" using alternative investment assets. The exception to this rule is the event in which (mean reverting) interest rates are extraordinarily high or when consumers have private (asymmetric) health information that would lead them to believe that they are much healthier than average, both of which rarely occur.