My goal is to develop a framework for evaluating a proposed strategy of this type, then use it to analyze some generic approaches based on industry practice.
To keep the analysis simple, I do not take into account other sources of income, liabilities, real property, insurance, taxes and other important aspects that may need to be considered in actual cases.
In most of the paper I follow the approach used in many papers in practitioner journals, assuming a fixed period of 30 years over which payments are made, without regard for mortality and the consequences for possible recipients of the fund (the initial investor or investors or beneficiaries). I will, however, argue that any of the strategies considered could be used as the basis for an annuity offered to a pool of investors with similar projected mortality probabilities, with such an annuity offered for a lower initial investment.
I use a relatively standard capital market model in which annual real returns on a diversified global portfolio of bonds and stocks are independent and identically distributed and follow a lognormal distribution for every horizon from one to multiple years. I employ an Arrow-Debreu state-price model and assume that only this global bond/stock portfolio is priced for any horizon. This determines a pricing kernel that can be used for valuation of any possible set of state-contingent cash flows. Moreover, for any given post-retirement financial strategy, the pricing kernel it can be utilized to infer functions for each multi-year horizon that would represent the marginal utility functions of any investor with time-separable utility for which the strategy is optimal.
Finally, I use this set of analytic tools to examine the properties of a few strategies based on industry practice, focusing on multi-year probability distributions of income, values of prospects for different horizons, and suitability for investors with different types of preferences.
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