Year 30 Balance

The balance at Year 30 is zero if you withdraw at the failure rate for that particular sequence. In all likelihood, the failure rate of an actual sequence is higher than the Year 30 Safe Withdrawal Rate.

The mathematics has the form:

(balance at Year 30)/(initial balance) = (total return of the actual sequence)*(1-withdrawal rate/failure rate of the actual sequence).

The sequence of returns affects the failure rate of the actual sequence. The total return depends upon annual returns, but not their sequence.

When you withdraw less than the amount that would have failed at Year 30, the excess grows as if it were never touched. If the return that would have failed equals 5% and you withdraw 4%, one-fifth of your funds are untouched. That is, (5%-4%)/5% is untouched. That is 20% of your original balance. It grows by the amount of the total return.

If the actual sequence grew by 6.5% per year (annualized), the total return at Year 30 would be (1.065)^30 = 6.61. If you left 20% of your original balance untouched, you would end up with 1.3 times your original balance. At today’s valuations, the total return would more likely be 5.65. But that still leaves you with your original balance and more at Year 30.

The same process works with dividend and income strategies. If you leave part of your income stream untouched, your untouched balance grows at the rate of the total return.

Summary

Your original balance has two parts: that which you consume at Year 30 through withdrawals and that which is untouched. The untouched portion grows by a factor equal to the total return.

Have fun.

John Walter Russell
July 29, 2008