Vol 3, Issue 9. Quarter 2 – 2026.

I was recently reminded about a short lesson for children that I saw on PBS many years ago. As best I can recall, Lavar Burton rode a bicycle with the aid of the wind for 20 miles at a speed of 20 miles per hour. After a short rest, he turned around and rode against the wind over the same distance at a speed of 10 miles per hour back to the starting point. He then asked what the average speed was over the entire trip, and most people guessed 15 miles per hour because that is the average of 10 and 20. Of course, as a highly intelligent reader, you knew instantly that this answer was incorrect.   Right?

The issue is that it is natural to think in terms of miles per hour, because that is what you were presented with. The trick is that I did not say that you rode at 10 mph for 1 hour and at 20 mph for 1 hour. The unit of analysis needs to be hours, not miles. What happened is that you rode at 20 mph for 1 hour, and at 10 mph for 2 hours. Thus, you covered 40 miles in 1 + 2 =3 hours. Forty miles over 3 hours is 40/3 or 13 1/3 mph: considerably less than 15 mph. This is an interesting problem because many of you just read the explanation and will still argue that it had to be 15 mph because this is the average of 10 and 20.

This apparent conflict between what the math says and what our brains want to accept arises due to the framing of the problem.  If I had said that he rode at 10 mph for 2 hours and at 20 mph for 1 hour, you would immediately know that the average was not 15 because you saw 10 two times, and 20 only 1 time. Only speaking in terms of miles per hour frames the question in such a way that your brain focuses on the fact that you saw 10 one time, and 20 one time, thus, you get anchored on the value of 15, which is the average of the two.

Right about now you are likely to be thinking something like, “That’s cute Chester, but who gives a damn?” Well, you may not care about that particular problem instance, but you do care about the issue of framing, because the same mental process sets you up to do stupid things that involve money instead of distance.

Think about an asset with an expected return of 0% per period (oil or gold come to mind), but you do not know which one we are talking about. Since the Coefficient of Variation of Gold is much higher than it is for Oil consider 2 stylized settings.  Let’s assume that the return on Oil (Scenario A) has a standard deviation of 10% and the return on Gold (Scenario B) has a standard deviation of 20%. Do you care which one you actually have? Common sense might respond – no not really.

But consider this. Let’s begin with $100. In Scenario A let’s say it rises by 10% in period 1 and falls by 10% in period 2. Compare this to Scenario B in which it rises by 20% in Period 1 and falls by 20% in Period 2. Are these two settings equally attractive? You already know by the way that I set up this discussion that the answer is No! $100 times 1.1 times 0.9 moves from $100 to $110, and then back to $99. The 10% drop from $110 is more than the 10% gain from $100. Consider this the other way around. Start with $100, have a 10% drop, followed by a 10% gain. Here we move from $100 to $90, and then up to $99. It doesn’t matter if the gain follows the loss, or if the loss follows the gain, the variance makes you worse off in both cases.

Now, change the 10% figure to 20% and see what you get. In Scenario B you move from $100 to $120, and then down to $96, or you move from $100 down to $80 and then up to $96. In both sequences you are worse off. In addition, your loss has grown from $1 when we used the 10% figure to $4, when we use the 20% value. This is why you must demand a higher return from an investment with a higher variance even when the expected returns are the same. Variance costs money, even when everything else is held constant. When I frame the discussion in terms of percentages, rather than dollar values, you can easily fixate on the fact that +10% and -10% add up to 0, even though $100 +10% and then minus 10% is different because the 10% drop has to be calculated starting with a larger number.

This is why simply reading the marketing literature from your friendly neighborhood insurance salesman, financial planner, or good buddy explaining his new brilliant investing strategy will never be a sufficient way to evaluate an opportunity. Running the numbers yourself matters, because leaving the salesman with the ability to frame the problem creates opportunities to generate a story in your mind that works to their advantage, and no false claim has to be made to get this done.