As my masthead states, I aspire to make my perspectives data-driven. Too much analysis (in the investment world and beyond) is driven by ideology. I reject that idea and maintain that every idea and every claim — even ideas and claims I would normally be prone to accept on account of my pre-existing values, beliefs and expectations — should be judged first and foremost by the data and evidence that support (or fails to support) them.
We are all prone to innumeracy, which is “the mathematical counterpart of illiteracy,” according to computer scientist Douglas Hofstadter. It describes “a person’s inability to make sense of the numbers that run their lives.” Although Hofstadter coined the term, mathematician John Allen Paulos popularized the concept with his book, Innumeracy: Mathematical Illiteracy and Its Consequences. While illiteracy strikes mostly the uneducated, we are all prone to innumeracy.
For example, most people would consider it an unlikely coincidence if any two people would share the same birthday in a room with 23 people in it. People would generally look at it like this: since one would need 366 people (in a non-leap year) in a room to be certain of finding two people with the same birthday, then it seems to make sense that there is only a 6.28% chance of that happening with only 23 people in a room (23 divided by 366). However, 99% probability is actually reached with just 57 people in a room and 50% probability exists with only 23 people (more on the “birthday problem” here).
In the investment world, we intuitively tend to think that if we start with $1,000 and suffer a 50 percent loss on Day 1 but make 50% back on Day 2 (day-to-day volatility being exceptionally high, donchaknow), we’re back to even. However, were that to happen, our $1,000 would be reduced to a mere $750 (more on the “arithmetic of loss” here). Similarly, a sum of money growing at 8 percent simple interest for ten years is the same as 6 percent (6.054 percent to be exact) compounded over that same period. Most of us have trouble thinking in those terms.
These examples are pretty (pardon the pun) simple. When things get more complicated we can really go off the rails, especially when the answer seems straightforward. To illustrate, if you have two children and one of them is a boy born on a Tuesday, what is the probability you have two boys? If you do not answer 13/27 or 0.481 — as opposed to the intuitive 1/2 — you’re wrong (to find out why go here).
The consequences for us as investment professionals should be obvious. As a starting point, we need to be careful to understand the math ourselves. We also need to use math appropriately and well. For example, virtually every investment presentation is replete with charts and numbers. But do these charts really show what they are offered to show (see below)?
Chart sources: Rolling Stone; U.S. Department of Energy (do a bit of research on Boobquake and watch this for other examples of correlation not implying causation and check out this thoughtful post from Interloper about the misuse of charts and more).
Similarly, we need to be careful to check the work (as best we can) of those upon whom we rely — whether economists or other investment professionals. Finally, we have to communicate investment realities, largely predicated upon math, to our clients carefully, appropriately and meaningfully, even though they may well be severely challenged by innumeracy. Doing so is much easier said than done.