The Extrapolation Issue

Traditional Safe Withdrawal Rate studies select the lowest surviving rate among 30-Year historical sequences. They identify this as being a SAFE withdrawal rate. It is close to 4% of the original balance (plus adjustments to match inflation).

This approach uses the range of actual outcomes to describe a statistical characteristic. It is not too bad an approximation so long as you are talking about the inner portion of the data. This corresponds roughly to the range P/E10=10 to 20.

The proper way to treat the Historical Surviving Withdrawal Rates, if not using valuations, is to approximate them with a normal (Gaussian, bell shaped) probability distribution of percentage gains and losses (i.e., a lognormal distribution). This works well so long as you limit yourself to the inner portion of the probabilities. It works poorly in the tails.

NOTE: Professor Peter Ponzo (Gummy) has shown that the surviving withdrawal rate distribution is lognormal if portfolio gains and losses are lognormal. In addition, he has developed closed form solutions under reasonable simplifying assumptions. This was a significant advance to the theory.

Peter Ponzo’s (Gummy Stuff) Web Site

Using linear regression based on the percentage earnings yield (100E10/P) extends the range of applicability to the range of completed historical sequences, P/E10=5 to 27. All of the data are used in the statistical estimates.

Extrapolation becomes less reliable as one goes further from the historical data.

Theory helps. The combination of Gummy’s Safe Withdrawal Rate formula and the Gordon Model (a version of the Dividend Discount Model) justifies using a linear approximation of withdrawal rates versus the percentage earnings yield (100E10/P). To do this, I use smoothed earnings as a surrogate for dividend yield.

The percentage earning yield historically (among completed 30-year sequences) was from 3.7% to 20%. Extending P/E10 to 44 is the same as reducing the percentage earnings yield to 2.3%. The extrapolation is less severe using the percentage earnings yield than with P/E10.

I define the SAFE withdrawal rate as the lower confidence limit of rates likely to survive. Look at the Year 30 SWR (Retirement Risk Evaluator) calculator. Even though Year 2000 had a SAFE withdrawal rate of 2%, there is still about a 20% chance that a 4% withdrawal rate will make it to Year 2030. It would not be SAFE, but it might survive.

Have fun.

John Walter Russell
October 21, 2008