Fun with statistics

Mark Twain is often credited with the famous line, “There are three kinds of lies: lies, damned lies, and statistics.” It is a phrase describing the persuasive power of numbers, particularly the use of statistics to bolster weak arguments.

When I was growing up, I used to have fun playing around with statistics and how they were used. When I told my daughters about this, they looked at me and said, “Dad, you were a geek.” I protested and provided all kinds of facts and figures and macho tales to prove otherwise, to which they said, “You were still a geek.”

You can learn a lot from dead people. No, I don’t talk to them, but I do learn a lot from statistics about them. For example, an often-quoted statistic says that life expectancy in the U.S. has increased by thirty years since 1900. We hear that in 1900 people lived, on average, to the age of 48, while today, they live to the ripe old age of 78.

Think about that for a moment. That implies that back in 1900, there were no “old” people. That doesn’t make sense, so I did a little research. Sure enough, the average age of death for a man in 1900 was 48, and today it is just over 78—a 30-year difference. However, if you look at the death rate by age, the numbers look quite different.

Yes, the average age of death in 1900 was 48, BUT over 15 percent of the deaths occurred before the age of five. This enormous number of deaths before the age of five had the effect of dramatically lowering the average age of death in those days. For many of those who made it past five years old, they survived well into their 70s and 80s.

Interestingly, we commonly attribute the extension of life to advances in health science that allow us to live into old age. While some of that may be true, the far bigger reason was because advances in health science stopped many of us from dying as children.

This is another example of misleading averages. When you dig just a little deeper, it’s obvious that the average age of death in 1900 is a pretty useless number. The same thing happens in the world of investing. Since 1926, according to some analysts, the average return on large-cap stocks has been around 9 percent. That seems pretty good. I’d like a 9 percent return each year. Wouldn’t you?

But of course, the return is not 9 percent every year; it’s just the average. In fact, the returns are quite spread out. Technically speaking, the returns have a wide dispersion from the average of all the numbers. So if the average return is 9 percent, but there’s a wide dispersion from this number, then how do we know what to expect each year? Good question. I’m glad you asked.

Have you ever gone online and used one of those free financial planning programs to calculate what your investments might do in the future? Be careful. Most, if not all, financial software uses normal distributions and standard deviations to calculate expected returns for investments. Without getting too deep in the weeds, the software assumes that the returns are normally distributed (like a bell curve) with a set standard deviation (or how far each year strays from the expectation of the average). If the average return of large-cap stocks is 9 percent, but the standard deviation is 19 percent, that’s quite a different animal. (Keep in mind, this is all for illustration purposes only, and I’m not suggesting these may be the actual numbers.)

If you want to be 99 percent sure that your estimate of next year’s return is correct, you must be willing to accept a range of returns. In this case, that range is three standard deviations (three times 19) above and below the average of 9 percent. To be 99 percent sure—not 100 percent, mind you—that you have a reasonable estimate of next year’s return on large-cap stocks, you must be willing to accept a range of returns from 9 percent minus 57 percent (three standard deviations below) to 9 percent plus 57 percent (three standard deviations above). In other words, you could see a range of negative 48 percent to positive 66 percent, or a 114 percent spread around the expectation of 9 percent!

How do you feel now? What kind of financial planning is that?! Who in their right mind would be comfortable in something with the thought that it’s “okay” to have anywhere from a loss of almost 50 percent to a gain of more than 60 percent each year? That’s crazy! And yet that’s the exact way many financial planning software programs operate.

A common statement among market analysts is that “Over the long term, equities go up.” While that may be true over time, you need to keep that in context. What is your definition of long term? There can be a lot of swing in that number from year to year, and you need to understand your asset allocation strategy and when you plan to use the money.

There are better ways. Instead of simply plodding along, buying, and holding with the hope that it all works out in the end, be proactive! Take an active role in estimating the risk and reward potential of markets, industries, and individual securities. Look across the economic landscape at the different forces that are driving markets at the moment and ask yourself: “Does all this make sense?” If the answer is “no,” then unless you know what you’re doing, you could be set to experience the low end of the expectation range for equities! Not having fun with statistics now? Find someone who can help you sort it out. Thanks for reading.