Consider some of the most challenging problems in finance: the equity-premium puzzle; binomial-option pricing models; do zero interest rates spur inflation or damp it; are stocks cheap or overpriced?
Challenging as those may appear, none compare to what Nobel laureate William Sharpe, 82, calls “decumulation,” or the use of savings in retirement. It is, he says, “the nastiest, hardest problem in finance.”
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Just consider that this is coming from the man who figured out how to price portfolios via the capital-asset-pricing model, and how to measure risk via the “reward to variability ratio,” or what has come to be known as the Sharpe ratio.
Many financial planners use a simple rule of thumb: withdraw 4 percent a year from your savings until you either die or run out of money. This one-size-fits-all solution is suboptimal for a reality where the potential outcomes are almost infinite, or as Sharpe describes it, a “multiperiod problem with actuarial issues, in a multidimensional scenario matrix.”
What makes this such a challenging problem? Consider a couple planning for when they stop working. Sharpe starts his analysis with two protagonists trying to figure out how much money to withdraw from their portfolios annually in retirement. To reach the optimal answer requires considering six interrelated sets of variables. None are especially complex, but combining all of them is another matter.
The first unknown confronting retirement planners is built out of standard actuarial tables. The multiplicity of possible mortality outcomes for any given year is simple – who survives and who doesn’t. But the possible combinations during roughly 30 years for two people is surprisingly large.
The second dimension comes from the 100,000-plus possible market outcomes for a global bond and stock portfolio each year. Apply all of those possible outcomes back to the mortality scenarios above and you begin to get a sense of the enormous range of potential outcomes.
Third, create a matrix for thousands of potential inflation results – this determines the purchasing power of a retiree’s income. It’s not overstating it to call this a proxy for financial flexibility, security and even quality of life for a couple living off of their investments.
The next matrix is tied to inflation, and it is the 100,000-plus possible market returns that Treasury Inflation Protected Securities, or Tips, will pay – a combination of the twice-annual interest payments, plus the adjusted principal at maturity.
A fifth matrix is all the incomes the couple will receive, including Social Security, insurance and any employment. Then take into account whatever they withdraw from their portfolio.
The final variable may be the most subjective and difficult to assess: the utility of income in each subsequent year.
Each of these six factors has an enormous range of potential outcomes; each single factor outcome must be considered in light of every other matrix outcome. The results are a vast range of choices. Selecting the proper one is as challenging as it is important.
Sharpe has created what he calls the retirement-income scenario matrix project. He has published all of his materials, programs, findings and the underlying data at his Stanford University website, and made them available free of charge. He hopes that a graduate-level course in financial engineering will build upon his work.
Comprehending the range of possible future scenarios from any retirement income strategy is difficult; choosing the proper strategy seems to be an almost impossible task. Sharpe said he hopes “this material will help will make it easier for financial advisers to help investors make better choices among the many possible alternative approaches for the provision of future income.”
The need is great, and the stakes are high.