Two professors and a financial adviser have created a methodology they claim can identify the “perfect withdrawal amount.” This is the amount a retiree can withdraw each year and pass away with either zero dollars or with a specified proportion of the portfolio to be bequeathed. The authors of the paper introducing this methodology say it is designed to ensure the retiree takes the maximum withdrawal each year without outliving his or her savings or having excess savings at the end of his or her life. Though a practical application is still under development, the methodology offers an alternative way of determining withdrawal rates.

The formula behind the methodology is withdrawals (w) equaling the rate of return over the retirement period (R_n) times the starting balance (K_s) minus the ending balance (K_e) multiplied by a sequencing effect (S_n). In mathematical terms, it is:

w = (R_nK_s – K_e)S_n

The ending balance can either be an amount to be bequeathed, or zero if no bequeathed amount is desired.

A starting withdrawal amount is calculated at the beginning of retirement. Then the withdrawal amount is recalculated each year thereafter. The authors say the annual recalculation is necessary to capture all new information. This makes the methodology adaptive to portfolio and market changes.

Annually recalculating the withdrawal amount will lead to varying withdrawal amounts. This is a logical outcome if the mathematical goal is to end the forecast period with a set amount of savings, such as $0 on the last day of life, exclusive of any amount to be bequeathed.

For those who prefer stability in the annual withdrawal amounts, the authors suggest basing the withdrawal rate on a band of confidence intervals and then only adjusting the withdrawal rate when it falls out of that range—for example, say a retiree chooses a withdrawal amount based on a 70% chance of portfolio success (a low probability of having to reduce the withdrawal rate in the future). The withdrawal amount stays unchanged as long as each subsequent recalculation shows that the withdrawal amount remains within a range of acceptable confidence intervals (e.g., between a 50% and 90% chance of portfolio success).

Source: “The Perfect Withdrawal Amount: A Methodology for Creating Retirement Account Distribution Strategies,” E. Dante Suarez, Antonio Suarez and Daniel T. Walz, SSRN, November 11, 2014.

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