Amortization based withdrawal

The time value of money formula, widely used in the field of finance, is used to calculate the future value of an asset when certain variables are known. There are several derivations of the formula (TVMF), but in most situations, the following five variables are used:


 * FV = future value
 * PV = present value
 * p = payment in each period
 * r = rate of return
 * n = number of periods

While primarily used to determine the future value of an asset, any of the above variables can be determined when the others are known. This can be useful for those who wish to make withdrawals from their portfolio to determine the needed size of the current withdrawal.

For instance, if an investor had $100,000 and wanted to amortize these funds over a period of ten years, then the annual withdrawal would be $10,000 ($100,000/10=$10,000). When a rate of return is introduced, then the time value of money formula must be used. In the above example, if the funds earned a 5% rate of return and the withdrawals were made at the beginning of each year, then the annual withdrawal would be $12,333.77.

The variable percentage withdrawal (VPW) is based on the TVMF. It uses historic returns of stocks and bonds as the estimated rate of return for various asset allocations in conjunction with the retiree's age to determine what percentage of the retiree's portfolio can be withdrawn in the current year. The number of periods remaining is set to 100 minus the retiree's age; hence, the VPW method depletes the retiree's portfolio precisely by age 100.

VPW is a very useful tool, especially for those who desire simplicity. However, there can be advantages to a more hands-on approach using the TVMF. Any of the variables in the formula can be changed by the user, which means that with the use of spreadsheets, irregular withdrawals (e.g. anticipated lump sum future expenses) and multiple income streams (e.g. Social Security benefits, pension payments, annuity payout) can be incorporated to determine the current year's withdrawal. Consequently, the time value of money formula is an extremely flexible tool.

Withdrawal smoothing
A potential strength of the TMVF approach for determining withdrawals is that adjustments can be made to the assumed rate of return, which can have the effect of smoothing the retiree's withdrawals compared to using the static return assumptions of the VPW approach. While there are many possible means of estimating future returns of various asset classes, perhaps the most widely used for stocks is the cyclically adjusted price to earnings ratio (CAPE), while the current yield to maturity is the most widely used for bonds. A weighted average of these estimates can be used to determine the expected return of a given portfolio.

For instance, on December 19th, 2019, the CAPE for U.S. stock was 30.73. Using 1/CAPE, a rough estimate of U.S. stocks' annualized return over the following decade is 3.25%, which is inflation-adjusted (i.e. real return). To determine the estimated return of bonds, the simplest approach is to use the current real yield of Treasury Inflation Protected Securities (TIPS). As of December 18th, 2019, the real yield of ten year TIPS was .16%. Using these two estimates, the forecasted rate of return for a 60/40 portfolio over the next decade would be 2.01%.

Now if stock prices suddenly fell by 20% but the earnings used to calculate the CAPE ratio did not, the portfolio balance would drop but the estimated rate of return would increase. The net result would be that the retiree's withdrawal would not change. Conversely, since the VPW method assumes a static rate of return, a change in the portfolio's balance will result in the same change in the retiree's withdrawal.