Customer Bob Smith finishes 10 years of investing with you, and he has averaged exactly 4 percent (nothing, not even a fractionalized fraction, after the decimal) yearly. At the end of the 10 years, he has $1,480,244 in his brokerage account. There are no withdrawals.
His brother, Larry, also a customer, finishes the same 10 years of investing with you, and he also has averaged exactly 4 percent (nothing after the decimal, not even the tiniest of fractions) yearly. At the end of 10 years, he has $1,208,232 in his brokerage account. Larry also had no withdrawals.
Clearly, Larry has $272,012 less than his brother, Bob. How is this possible?
The math is correct for both. What is different is the sequence of returns, or what Moshe Milevsky refers to as SoR. (Milevsky points out that the CFA Institute and other investment associations, when there are withdrawals, favor a dollar-weighted IRR calculation instead of averages. In these examples, though, there are no withdrawals — any negative numbers are investment results for a given year. Even if there were withdrawals, it is doubtful — given the extra complexity in calculation — that the database services, like Morningstar, Thomson Reuters, etc.; fund companies; and advisors would change.)
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The percentage gains in Bob’s situation are 10 equal 4 percent returns. In other words, Bob makes no less and no more than 4 percent each and every year, or 4 percent, 4 percent, 4 percent, 4 percent, 4 percent, 4 percent, 4 percent, 4 percent, 4 percent, and — you guessed it! — 4 percent for the 10th year, too.
Larry’s gains and losses are variable. The years go like this: -35 percent, -12 percent, 10 percent, 8 percent, -20 percent, 12 percent, 36 percent, 22 percent, 15 percent and 4 percent.
You may plug either Bob’s or Larry’s numbers into either Lotus 1-2-3 or Excel or in your trusted RPN financial calculator, and you’ll discover that the average is exactly 4 percent for each brother. So, 4 percent as an average does not always create the same ending result, does it?