In response to a recent column of mine, a reader wrote, “Your article on annuities did not demonstrate that an annuity always improves a retirement plan.”

True, Warren Buffet’s retirement plan would not be improved by an annuity because he will not face the mortality and investment risks of a retiree with limited resources.

Retirees with limited resources face the risk that if they live too long, and/or their assets earn less than expected, they will run out of spendable funds. There is also the risk that if they die too soon, and/or their assets earn more than expected, they will leave financial assets to their estate that they would have preferred to spend on themselves.

Retirees exposed to these risks can reduce or eliminate them in only one way: by using some of their assets to buy an annuity, which pays them as long as they live.

This is a core feature of the Retirement Income Stabilizer (RIS) which I have been developing with Allan Redstone. With RIS, the retiree uses some of her assets to buy an annuity, payments from which are deferred for a period ranging from 5 to 25 years. The remaining assets are used as the primary source of spendable funds during the deferment period, with the amount drawn each year adjusted based on earnings during the year.

In this column, I will compare retirement plans with and without an annuity for a hypothetical retiree of 65 who has $1 million in her 401(k), half of it in common stock and half in intermediate-term government securities. She is deciding between the following options:

—A RIS-based withdrawal plan that includes a 10-year deferred annuity

—Following the 4 percent withdrawal rule, which is advocated by many advisers

With the RIS alternative, part of the $1 million purchases an annuity deferred 10 years. During the first 10 years the retiree draws on the assets remaining after the annuity purchase. At the end of the 10 years, those assets are gone and the annuity kicks in.

With the 4 percent rule alternative, the retiree makes monthly withdrawals equal to .04/12 of the initial balance, plus an annual inflation increase. I applied a 2 percent inflation adjustment to both schemes.

I am going to compare the monthly spendable funds that could be drawn by the retiree using these options, on two assumptions about future asset yields. One assumption is that yields are those expected, which I define as the median return during 1926-2012 among periods of the same length as the option. For the 4 percent rule, which must support the retiree until she dies, the period runs to age 104, or 39 years. The median return over 577 39-year periods was 9.4 percent. For the deferred annuity option, the relevant period is 10 years. The median return over 925 10-year periods was 8 percent.

Despite the higher expected rate over the longer period relevant to the 4 percent rule, spendable funds are consistently higher in the annuity case. The first month draws are $4,363 and $3,333, and the difference widens as the retiree ages.

The likely rejoinder of a 4 percent rule advocate is that the retiree in my example could break from the rule to increase withdrawals if necessary. At a return of 9.4 percent, the retiree’s assets using the rule increase over time, whereas in the annuity case the assets are gone after 10 years. The problem is that the 4 percent rule itself provides no guidance on how much extra can be safely drawn, and when. Further, the bias of advisers managing client assets is to avoid shrinking those assets.

In any case, projections based on expected returns have limited value. Retirees must be more concerned about a worse case, because if one happens they cannot begin their careers again. I define a worse case rate of return as the return earned during less than 2 percent of the relevant periods. When the rates of return for all 925 10-year periods during 1926-2012 are ranked, highest to lowest, the worst-case rate is 0.7 percent. The worst-case rate over 39-year periods is 2.6 percent

Despite the lower worst case rate during the shorter period, the annuity case works fine, generating larger spendable funds than the 4 percent rule except during ages 69-74. Furthermore, the worst case under the 4 percent rule runs out of money completely at age 92.

In sum, using part of the retiree’s nest egg to purchase a deferred annuity improved the retirement plan.

Jack Guttentag is professor emeritus of finance at the Wharton School of the University of Pennsylvania. Comments and questions can be left at mtgprofessor.com.

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