The Danger of Relying on Averages

My mom was a complete failure as a Tiger Mom, by Amy Chua standards.

She never made me take piano lessons. She never knew from one day to the next whether I did my homework or not. And she waited until the day I received my high school diploma, when I was up to my ears in flower leis, to ask why I didn’t graduate with honors.

Jeez, I thought, I got into Princeton for Pete’s sake. What are you hassling me for?

So when I met Kaiser Fung at a Princeton alumni event — he with the degrees from Princeton, Harvard and Cambridge — I was willing to bet his mother was a much better Asian parent than mine.

In addition to being well brought up, Kaiser is a whiz at statistics. His book Numbers Rule Your World (soundbite: it’s the Freakonomics of statistics) was so interesting and fun to read that I sent my clients a copy as a New Year’s present.

I liked him even more when he wrote “Don’t be average!” in my book.

That, after all, is my battle cry.

We had something else in common, despite one of us being woefully undereducated relative to the other — we both despise that single-point estimate otherwise known as an average.

“Averages are like sleeping pills, they put you in a state of stupor, and if you overdose, they may kill you, says Kaiser.”

In investing there are a couple of ways we get averages wrong, both of which have to do with a failure to “unpack” the numbers. The first has to do with the components of average returns; the second relates to extrapolating trends from averages and compounding them into idiocy.

Average returns need to be unpacked

Consider the compound average growth rate of a business or a portfolio. Kaiser said he’s been struck by the number of business people who have trouble wrapping their heads around the dangers inherent in keying into an average return that does not take variability into account.

As he points out, “While the compound annual growth rate provides a useful basic summary of the past, it conveys a false sense of stability when used to estimate the future.”

For example, let’s say three investment managers have a compound annual growth rate (CAGR) of 10%. One may have suspiciously little variability (think Bernie Madoff). Another may have huge swings deep into negative territory and high into positive. And a third may have moderate variability (i.e., some, but not the kind that keeps you up at night).

So I ask you, if you were Goldilocks, which 10% return do you want?

Too little, too much, or just the right amount of variability?

Whichever one you pick, it should be clear that while they each have a CAGR of 10%, these investment managers are not the same! Each 10% was generated with humongous differences in portfolio holdings, tactics and skills.

Without unpacking the average, you can’t know which bowl of porridge to choose.

Kaiser goes on to explain that part of the seduction of relying on an average is our urge to ignore variability: “Such variability leads to uncertainty, which creates anxiety.”

Paradoxically, variability-inspired anxiety (even if the average return justifies the variability) will cause a money manager to be fired. If you constantly flip-flop from the top to the bottom of the performance tables — even if you compound fabulously over time — you’re toast.

If there’s a reason so many index-huggers passing for active managers continue to survive despite mediocre returns, this is it.

And while variability is something investors pay more attention to these days than they used to, even those single-point measures of volatility leave something to be desired. No one number can tell you what you need to know.

Aside from variability, averages have other traps embedded in them. Consider, for example, the modeling of financial statements and the howlers caused by the gross abuse of an average.

Kaiser has a brilliant example of this on his blog Junk Charts, regarding a calculation justifying the valuation of Facebook. The investment case for Facebook was based on extrapolating the trend of two average growth rates while paying no heed to the components that made up those growth rates. Looking at the components of the averages would have told you the calculation was illogical and the result impossible.

You can’t straight-line an average growth rate into the future without unpacking all the bits that are needed to make it happen.

If you could, you might assume that when my son was fourteen and grew ten inches in a year, he would be 8’ 2” by the time he graduated High School.

As a statistician, Kaiser confirms my belief that charts, data and in this case averages, are merely numbers attempting to describe the world.

Numbers are not a substitute for reality.

Illustration credit: Brooke, L. Leslie (Leonard Leslie) (1862–1940)