The Lie of Averages

The Lie of Averages

by Corey Hoffstein, Newfound Research


  • Averages are often used to summarize data: but sometimes fitting for the average means fitting nothing at all.
  • Expected returns are a meaningful input to portfolio construction, but are unlikely to be the returns actually realized. Reality rarely looks average.
  • The world is dynamic and forecasts can change. Not only should we expect that things will not be average, but we should expect that our definition of average will also change.
  • We believe that maintaining a degree of flexibility within a portfolio – both with long-term strategic outlooks and short-term tactical tilts – can help investors adapt to the path they are on.

How would you design a cockpit?

Ever thought about it?  We haven’t.  (Or, at least, until this commentary did not give it much thought.)

But the U.S. Airforce faced this this very problem back in the 1920s.  How high should the windshield be?  How far should the pedals be from the stick?

Their solution was to measure 100 of their pilots along a number of physical dimensions (e.g. length of their arms, size of their torso, et cetera).  Using these figures, they calculated the average for each dimension and used it to guide their design.

By the 1950s, planes had become faster and more mechanically complex.  And pilots were losing control of their planes left-and-right.

Military engineers wondered if perhaps the pilots of the 1950s were simply no longer represented by the average from the 1920s.  So, they redid the calculations: this time with 4000 pilots and along 140 different physical dimensions.

One scientist – Lt. Gilbert S. Daniels – was skeptical.  Perhaps the problem was not with the averages themselves, but with the use of averaging.  After all, how many pilots were actually average shaped?

With all the data collected, Daniels took 10 of the primary dimensions and asked a simple question: how many pilots fell within the middle 30% of the range for each of these dimensions?  As an example, if the average height of a pilot was 5’9”, how many pilots fell between 5’7” and 5’11”?

How many pilots did Daniels find that fell between this range on all 10 primary dimensions?  Zero.

Perhaps that was just too strict a test?  What if we chose just 3 of the dimensions?  How many pilots fell within the middle 30% of the range for at least 3 dimensions?  Just 3.5%.

The cockpits had been designed for an average pilot who simply did not exist.  Fitting the average meant fitting no one.[1]

Relying on Expectations

In the last year or so, we’ve spent numerous pages of our commentaries exploring the published expected returns of firms like J.P. Morgan, BlackRock, and Research Affiliates.

We think it is worth pointing out that with these outlooks, expected is just another way of saying average.  What they are really saying is, “of the infinite potential futures that could unfold, we believe the average result is X.”

Of course, we do not experience infinite potential futures.  We realize just a single one of those future paths.  With expected returns for dozens of asset classes, we have to ask: what are the odds that future actually looks average?

To answer this question, we will take a similar approach as Lt. Daniels.  First, we use J.P. Morgan’s capital market assumptions to simulate 10,000 possible future 10-year return scenarios.

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