July 6, 2010
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There is a wonderful folk theorem in the world of investment advice that says an annual withdrawal amount of roughly 4% of the initial balance of a retirement account can last an investor almost indefinitely. One source of this idea is Jonathan Guyton, who says:
"Typically, the safe initial withdrawal rate for pretax portfolios is around 4% when all the equities are U.S. large-cap stocks; when smaller-cap stocks are introduced, usually the safe initial withdrawal rate increases modestly to about 4.5%."
Guyton’s finding and other research on this topic rely on many assumptions, some of which may not hold in today’s environment.
Instead, I provide a new, transparent analysis of the safe withdrawal rate (SWR), one that enables investors to explicitly update their SWR based on new beliefs about their future returns and inflation. Historical data are not required.
Overview of current SWR work
Once the initial balance of a pre-tax retirement account is established, its hypothetical investor can set an annual spending goal for a time horizon of his choosing. The investor withdraws an amount of money equal to the initial balance times his initial withdrawal rate, an amount that hopefully suffices for the investor's purposes. The problem he and his advisor face is to find the maximum withdrawal rate (called SWR) possible when the time horizon is unforeseeable or indefinite, as most retirements are.
Under this traditional approach, both returns and inflation determine how account balances evolve. My approach, however, is independent of historical returns and inflation. Rather, we determine the SWR based on various future states of the world as defined by the investor’s subjective probability distributions of returns and inflation.
Previous research has used historical market data, assumptions about portfolio allocations (e.g., 60% stock, 40% bonds) intended to achieve sufficient returns, and a variety of simulations and back tests to calculate the account’s yearly balances for a given withdrawal rate. Then the largest withdrawal rate for a sufficiently long time horizon is chosen as the SWR, given the chosen portfolio allocations.
Put briefly, most current research analyzes SWR for back-tested, hypothetical portfolios. Essentially, researchers calculate the SWR for an investor by requiring him to assume their future balances will evolve according to historical return rates and inflation. (See, for example, Cooley, Korn, and Considine. A summary review can be read on Bogleheads.)
A clear problem with these SWR approaches is the possibility that the near future will present substantially larger return volatility. Global deleveraging, residual fear from recent market panics, massive government spending and the possibility of unanticipated inflation all make added volatility highly likely.
How many investors or advisors would want to use historical portfolio performance data to design long-term portfolios under these conditions? I think not many, but that is just what current approaches to the SWR problem do.
How can we account for other beliefs?
I offer a new approach: Let the investor incorporate his beliefs, however they are formed, about the evolution of his own future returns, and let him define the inflation levels he expects. The investor can explicitly capture those beliefs about the future (which beliefs always drive his decisions anyway) to produce a personalized result for the SWR. This approach requires a model, since it doesn’t use back-testing. My model is built around a “closed form” formula for SWR as the basis to incorporate investor beliefs.
Account withdrawal mechanics
First, let’s be clear about the investment account’s cash flows. The initial withdrawal amount is adjusted annually based on the rate of inflation; it would be constant if inflation were zero. Also, at the end of each period, the remaining balance grows based on the returns earned on its investments.
Figure 1 below shows how the account balance changes over time under two scenarios: a return of 4.75%, inflation of 2%, and a withdrawal rate of 3.5% in one case; and a return of 5.5%, inflation of 2%, and a withdrawal rate of 5% in the other.
Figure 1: Example of Normalized Balances 
The inflation rate is the same for both curves, but account balances diminish more rapidly with the higher return rate. Because the withdrawal rate is greater for the high-return case, the account is drawn down faster than it grows, compared to the low-return situation with a smaller withdrawal rate.
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