By William J. Bernstein

Most of you have seen the nifty retirement software available from the likes of Vanguard and T. Rowe Price which provides the mathematical muscle to help you plan your retirement. Input your retirement age, expected lifespan, required annual income, rate of inflation and investment return, and hey presto, you find out that to avoid a golden years diet of Alpo you need the GDP of the average Central American republic.

Problem is, it may quite possibly be worse than that. These calculators all make the same erroneous assumption — that your expected rate of return is the same each and every year. In other words, let’s assume that the real (inflation adjusted ) rate of return of the S&P 500 will be 7% in the future. You might conclude that you can withdraw an inflation adjusted $70,000 of your $1,000,000 Vanguard Index Trust 500 IRA each and every year indefinitely, and maintain yourself with the same real income in the long run. And you’d be wrong.

It turns out that if you have rotten returns in the first decade you will run out of money long before reversion to the mean saves your bacon in later years. To illustrate this phenomenon I went back to good old Uncle Fred’s infamous coin toss, with its return of either -10% or +30%. Let’s assume that these represent real returns. If over 30 years you toss 15 heads and 15 tails you earn a compounded rate of 8.17%. (If you don’t understand why you don’t earn the average return of 10% (the average of -10 and +30), then go back and read Chapter One of The Intelligent Asset Allocator.) If you start with a $1,000,000 portfolio and roll alternating heads and tails over the 30 year period, then you indeed can withdraw $81,700 (8.17% of the initial amount) over the next 30 years before all the money runs out. However, if you are unlucky enough to roll 15 straight tails before rolling 15 straight heads, you can withdraw only $18,600 per year. Reverse the process and roll the 15 heads followed by 15 tails, and you can withdraw $248,600 per year.

This phenomenon was first brought to the attention of the investing public by Philip L. Cooley, Carl M. Hubbard, and Daniel T. Walz from Trinity University. They looked at the “success rate” of various withdrawal strategies over numerous historical periods, and came to the conclusion that only a withdrawal rate of 4%-5% of the initial portfolio value (i.e., $40,000-$50,000 of a $1,000,000 portfolio) had a reasonable expectation of success. This article can be found in the February 1998 AAII Journal. You can also obtain a lucid explanation of their work as well as their “success tables” on Scott Burns’ excellent website.