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The Deception of Numbers

Finance

Issue: October 2009

By: Jerry Mosher, CFP

One of the human responses I’ve observed over the years is a tendency to want to calculate an investment rate of return after the market has declined. This urge is much greater after a decline than it is after the market has risen. After any decline, trailing numbers will naturally be lower and, if the decline was significant, the results will usually be dismal. This dismal result can be anticipated so perhaps the tendency to want to measure after the decline is some kind of masochistic gene coming to the surface.

If a portfolio had risen 80% and was then subject to a 50% decline, common sense might have us conclude the investor would still be ahead by 30%. However, if you do the math, you’ll find the investor has actually had a 10% loss on their original investment. Try the calculation yourself starting with a $100,000 original investment.

There are other calculation flaws that can also surface. If you add up the money you have put into an account and subtract it from the ending value, as a form of comparison with other alternatives, you end up ignoring the timing impact of when the money was actually invested. The effective return could have been exactly the same during the period you’re measuring, but additions may have come just before a decline, which skews your results. Or, if one account had all the money at the beginning and another had the money invested over many different incremental periods, your total dollar results could be dramatically different, even though the investment returns were exactly the same during the investment period.

If the amounts of money that had been invested were substantially different, then the methodology of adding up invested dollars and ending values doesn’t provide any useful comparative information. Likewise, if the time periods of investment are not the same for the two different accounts, then the dollars in and ending method of calculating your performance isn’t a viable comparison. To quote an old phrase, “You’re comparing apples to oranges.”

The method of calculation that has been adopted in financial circles—one that eliminates the flaws of different starting periods, varying amounts of initial capital and the effect of future additions but is much more difficult to calculate—is to adjust the value of the account along the way as you continue to calculate the performance number that is occurring. When you add together the performance numbers, and establish what occurred for each year or accounting period as a percentage i.e. +15%, -10%, etc., you now have a valid method for comparing returns to an alternative investment for a period of time. You, of course, have to compare the percentage return for the same year or time period!

Although the percentage return number may not seem as real to us as using the total dollars invested method, it is the only effective way to compare returns on different accounts or investment alternatives.

Another irony that surfaces in a down market is the fact that an account that has done very well prior to a decline will have a larger amount of total dollar reduction than an account that had performed poorly prior to the decline. If two different people started with $1,000,000 and in one case their initial investment increased to $2,000,000 while in the other case the account only grew to $1,200,000, a 30% decline would cause the first account to lose $600,000 and the second would only have a $360,000 decline. You have more remaining dollars left in the first account, which would be my preference, but the focus on the amount of decline suggests the first account had the poorer performance. When you are making a comparison based only on total decline dollars, which ignores prior performance, you may be easily misled and come to a wrong conclusion.

This doesn’t mean you shouldn’t pay attention but it does mean there are some inherent flaws in certain methods of calculation, and they could be the basis for an inaccurate assessment.

Jerry Mosher, CFP® is a 30 year veteran of the financial planning industry and is president of Mosher & Ellis Financial Planning in Lafayette, California. He has been selected three times as one of the 150 best financial advisers for doctors by Medical Economics. Jerry may be reached at (925) 284-9470. Securities offered through AMERICAN INVESTORS COMPANY Member NASD/SIPC.

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