A Sustainable Spending Rate without Simulation

Financial commentators have called for more research on sustainable spending rates for individuals and endowments holding diversified portfolios. We present a forward-looking framework for analyzing spending rates and introduce a simple measure, stochastic present value, that parsimoniously meshes investment risk and return, mortality estimates, and spending rates without resorting to opaque Monte Carlo simulations. Applying it with reasonable estimates of future returns, we find payout ratios should be lower than those many advisors recommend. The proposed method helps analysts advise their clients how much they can consume from their savings, whether they can retire early, and how to allocate their assets. As the Baby Boomers approach their retirement years, the finance profession is developing a pressing need for more research on sustainable spending rates from suitable investment portfolios. This article meets the demand by developing a forward-looking framework for modeling sustainable spending rates as a function of biological age and portfolio composition. The framework is also applicable to endowments and foundations that hold diversified investment portfolios.We introduce the concept of a stochastic present value (SPV) of a retirement plan that parsimoniously meshes portfolio investment parameters, mortality estimates, and inflation-adjusted spending rates. We avoid resorting to opaque and hard-to-replicate Monte Carlo simulations or backward-looking historical analyses for computing probabilities of “retirement ruin”—that is, the probability that a retirement plan is unsustainable. At best, these analytics can be used to calibrate and test the accuracy of more complicated simulations.The article's key analytic contribution is to recognize that the SPV is well approximated by a reciprocal gamma distribution. Therefore, the probability of sustainability—or 1 minus the probability of retirement ruin—can be computed by evaluating the cumulative distribution function of this distribution at the current value of the retirement nest egg.In fact, the resulting formula is easily coded in Microsoft Excel. Using it, we show that a 65-year-old retiree faces a 10 percent chance of running out of money during the stochastic length of the retirement if he or she consumes more than $4 per $100 principal of an all-equity portfolio with an expected real return of 7 percent and volatility of 20 percent (which leads to a geometric mean return of 5 percent). A diversified portfolio of stocks and bonds can support retirement spending of $5 per $100 at age 65 with the same 10 percent probability of ruin.The payout ratios implied by these examples are well below the optimistic spending rates recommended by many investment advisors, who erroneously believe that a portfolio earning a real return of 7 percent on average can support a spending rate of 7 percent on average. Moreover, if one's view on real equity returns and risk premiums is that they will be much lower than 7 percent arithmetically or 5 percent geometrically, then spending rates must be suitably reduced.These results should also shed light on the relative merits of longevity insurance and payout annuities for individuals, which can be shown—within this framework—to increase the sustainability of a portfolio by creating an income stream that cannot be outlived.In summary, the ideas we develop should help financial analysts advise their clients about (1) how much they can consume from their savings, (2) whether they can afford to retire early, and (3) the ruin implications of various investment strategies. On a broader scale, we hope this research motivates practitioners in the financial services industry to change their mind-set from a wealth accumulation framework to an income and disbursement mode.