Lies, Damned Lies
and Statistics
and Statistics
Well, let’s just say that statistics of any kind can never be more than a half-truth. After all, their very purpose is to distill the complicated into easily understood and communicated information. The whole truth is often a meaningless and unwieldy array of dates and numbers. So, whether we like it or not, the use of statistics is necessary. Unfortunately, few people understand them well enough to judge whether the statistical information they are being given serves to expose the truth or to twist it. This is no less the case for investment statistics.
Averages are a simple kind of statistic, and average returns are commonly used in the investment world. Let me illustrate with an example how even these can be misunderstood. [This is a purely hypothetical example and does not reflect any particular investment.]
Suppose you were to invest a sum of money and make a 100% return the first year. On this same investment, you then suffer a 50% loss the second year. What is your average annual percentage return for the two years?
Would your first step be to subtract from the 100% first-year percentage gain the 50% second-year percentage loss? The result of that calculation would be 50%. Would you then calculate the average return for the two years by dividing this 50% by two? The result of that calculation would be 25%.
In summary, based on this calculation method, your average annual percentage return for the two-year period would be 25%. Important question: Does this statistic reflect reality?
Well, let’s do an acid test. Let’s assume our original investment was $1. One dollar increased by 100% in the first year, as per our above example, grows to $2. Now we calculate the 50% loss that we assumed for the second year. Reducing $2 by 50%, that is, by half, leaves $1 remaining. Result: we begin with a dollar investment and after two years we have exactly the same amount. Our true return for the two year period is nothing. Nada. Zilch. Snake. Zero. NOT 25%!
The little exercise above may seem obvious to some readers and opaque gobbledygook to others. Either way, that’s okay, as long as you see the main point: that even a statistic as simple as an average can be grossly misleading. [For readers who do understand fundamental statistics, the principle illustrated here is clearly that percentages with different bases should never be averaged. But, of course, they sometimes are.]
A closing comment about statistics. The average annual temperature in Shreveport-Bossier, is approximately 65 degrees Fahrenheit. That information tells you nothing about the fry-an-egg-on-the-sidewalk afternoons of July and August, and nothing about the occasional January or February ice storm. Applying this principle to the investment realm, ask yourself the following questions. How important, really, are fifty and hundred year averages when your personal financial time horizon is much shorter? And even more to the point, how useful is any average during unusual times? Wouldn’t a more useful statistic be one that tells you what the extremes have been, good and bad, and how often either extreme has occurred, and about any pattern in those variations? While you are not likely to find these more sophisticated statistics in the general press, they are available from a qualified, conscientious professional, and so are clarifying explanations.
Of course, dear reader, no amount of historical fact or analysis or interpretation will ever tell you the future with certainty. The good news, however, is that you don’t have to know the future to prepare for it.
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