(Bloomberg View) — 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.”
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.
I sat down last month with Sharpe to record a Masters in Business podcast. But his explanation of use of assets in retirement was so interesting it justified a broader discussion.
Many financial planners use a simple rule of thumb: withdraw 4% 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.