By Ladd Kochman, DBA and David Bray, Ph.D. | Kennesaw State University
A key element in retirement planning is projecting the future value of a retiree’s investments. If we can assume an annual rate of return of 6%, a $500,000 portfolio today would seem to be worth $895,424 after 10 years—or $500,000(1.06)10. Yet, it is also possible that the same 6% average return could produce markedly different ending values. For example, if the portfolio returns 12% in each of nine years and loses 48% in one year, the average will again be 6% but the future value is only $721,0001. If the portfolio were to alternate returns of 18% and -6%, its average return is still 6% but its ending wealth would be $839,4972.
The explanation lies in the misuse of the arithmetic average. Its implicit assumption of simple interest acts to overstate values. The geometric average, on the other hand, assumes compound interest and leads to more reliable results. Since arithmetic and geometric averages are the same when returns are constant, our $895,424 ending value above is possible only if 6% were earned each year.
When returns are not the same, the geometric average will be lower. Where the future value is $721,000, the geometric average is 3.73%—or [(721,000/500,000)1/10 – 1]. For the $839,497 total, the geometric average is 5.32%—or [(839,497/500,000)1/10 – 1]. But many retirees would not distinguish between arithmetic and geometric averages and expect a 6% average return to improve their current portfolios by 79.1% over a 10-year span—or [(895,424/500,000) – 1]. An annual average of 3.73% generates a total return of only 44.2%—or [(721,000/500,000) – 1] while the 5.32% mean provides a 67.9% total return—or [(839,497/500,000)1/10 – 1].
The consequences of overstated ending wealth can be enormous. One example is a retiree’s required minimum distribution. According to RMD tables, a 70½-year-old with a wife not more than 10 years younger might expect a first-year distribution of $32,6803 from his retirement account based on the questionable $895,424, but instead receive only $26,3144. Retirement accounts that can be annuitized serve as another example. An annuity based on an ending wealth that is more expected than realized could simply result in running out of money. Retirees beware!
Reilly, F., and K. Brown. Investment Analysis and Portfolio Management. Cengage Publishing, 10th ed., 2012.
1. $500,000(1.12)(1.12)(1.12)(1.12)(0.52)(1.12)(1.12)(1.12)(1.12)(1.12) = $721,000
2. $500,000(1.18)(0.94)(1.18)(0.94)(1.18)(0.94)(1.18)(0.94)(1.18)(0.94) = $839,497
3. $895,424 / 27.4
4. $721,000 / 27.4
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