Invert, Always Invert!*

The more that I learn about investing, the more I learn that investing is simply rediscovering commonsense lessons about everything in life through statistics. Here’s one a great lesson in how to think about a problem (any problem) by turning it on its head. (Optional investing lesson at the end.)

During World War II, the Allied Air Command was understandably concerned about bomber losses during raids over Germany. Enemy anti-aircraft batteries were shooting down the lumbering bombers – mostly B-17s – at an alarming rate.

The British and Americans considered adding armor to the aircraft, but the added weight would slow the planes down even more, so the Allies wanted to be sure that the metal would be used most effectively.

After examining the returning planes, the British initially proposed to add armor to the areas that had taken the most hits. However, to be sure of their decision, the Allies brought in the mathematician Abraham Wald, who had fled Austria for the United States in 1938 to escape the Nazis.

Wald began by examining the planes overall design and where the returning planes had taken flack. Like the British, he noticed that while the returning planes had shots in numerous locations, there was a pattern to the location of those hits, i.e. there were areas that were commonly hit and areas relatively unscathed. However, Wald then turned the problem on its head, by thinking about the planes that DIDN’T return. Where had they likely been hit and what would it take to bring a plane down?

Wald realized that the planes that returned were taking hits in exactly the areas that could handle the incoming flack, while the planes that went down likely were taking hits in the most vulnerable parts of the planes – exactly the spots undamaged in the returning planes. The last thing that the Allies needed to do was reinforce the areas damaged in the returning planes. They needed to reinforce the areas that weren’t hit (around the main cockpit and the fuel tanks). Those were spots that brought down planes.

Like Sherlock Holmes in The Dog That Didn’t Bark, Wald understood that the most important evidence was the missing data, not the available data.

Optional Investing Lesson

So, how does this lesson help us in investing? Well, first, it tells us that instead of spending all of our time examining successful investors, we might learn valuable lessons by examining investors that failed. Can we discover the mistakes that caused them to fail and avoid those missteps?

Turns out, yes, we can. If you look at unsuccessful investors, they tend to have one or more of these attributes:

  1. Performance chasing
  2. High Costs
  3. Lack of diversification
  4. Short time horizons
  5. Inappropriate risk levels
  6. Home country bias in stocks
  7. Tax inefficiency

Becoming another Buffet may not be possible (he’s a genius with a unique skill set), but avoiding becoming a failed investor looks pretty simple and very much achievable.

Another lesson that we learn by turning problems on their head involves Value investing – buying only cheap stocks. It turns out that a good part of the premium that you get from buying cheap stocks doesn’t come from owning the cheap stocks themselves but from avoiding expensive stocks. Expensive stocks tend to dramatically under perform the market, so having a strategy that eschews those stocks improves your returns – even if you didn’t then buy cheap stocks. In truth, a Value strategy really should be called the Buy Cheap, Avoid Expensive strategy.

So, the next time that you’re looking at a problem remember to invert, always invert.

*The phrase Invert, always invert (“man muss immer umkehren”) was coined by the German 19th century mathematician Carl Jacobi who believed that the solution for many difficult problems could be found if the problems were expressed in the inverse – by working backward.


About Mark Helm, CFP, EA

Mark Helm is a Certified Financial Planner and Enrolled Agent. He is the founder of Helm Financial Advisors, LLC, a fee-only financial planning firm dedicated to helping people reach their life goals.
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1 Response to Invert, Always Invert!*

  1. Bear says:

    Interesting story. Of course the box formations that they used were supposed to help protect them from the fighters (which didn’t pan out) also made them great flak targets that the Germans could concentrate their fire on. One other thing was that flack is an area weapon as opposed to a bullet. You can’t aim it at a particular point on the plane so I would expect an equal likelihood that all parts of the plane (accounting for it’s shape, forward motion, and where the flack shells would explode) would be hit. I would think that would make the statistical analysis a bit easier.

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