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# Sequences

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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.)

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?

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This subject will be continued in the October issue of Life Insurance Selling, in my The Investment Edge column, a venue where there is more space to spread things out and get into the nitty gritty. Of course, since I didn’t pay enough attention in school math classes, I may make a mess of things; in which case, readers will have a source of low-cost entertainment.

In the meantime ask yourself a few questions —

• Why can’t mutual fund companies, following a disastrous year like 2008, wait until there are five years beyond the crisis year? In other words, why does the advertising switch to subjects other than returns following troubling times?
• Why do fund companies (and rating companies) bother with showing averages for 3-, 5- and 10-year periods, when the averages may be accurate but not true? (Well, an average is an average, but you may see, in the case of Bob and Larry, that an average rate of 4 percent yearly in two different situations produces widely varying dollar results, and, sorry to say, that’s SoR.)

For about 2.9 years after 2008, a.k.a. The Great Credit Debacle, most of the mutual fund ads seemed to brag about the number of Morningstar stars for a given fund or the fund’s customer service rating. Now, after the poor 2008 returns don’t bring down the averages so much (all investments pretty much have different year-by-year returns; B. Madoff had one of the few seemingly consistent year-after-year results, maybe not exact, but close enough to exact to tip the scam to Harry Markopolis), the ads are back to the numbers-and-averages game.

Have a sensational and wonderful week, as we exit the summer season and move into fall — the temperature may not change much, but our calendar seasonality seems to be based on school schedules more than the weather.

For more from Richard Hoe, see: