By Alex White, FIA C.Act, Global Head of Quantitative Modelling at Gallagher
On average, only about 5% of people get it right (though I suspect - and hope - my sample of Actuarial Post readers will show meaningful selection bias and outperform). It’s clear that you need to turn over the A. Many people assume you need to turn over the 7, but there’s no reason every 7 must have an A on the other side, so it doesn’t help. But the 8 might have an A on the other side, which would disprove the theory.
Now there are plenty of general takeaways for cognitive biases more broadly, especially confirmation bias- but it hints at a perspective that we’re not as a species instinctively wired to look for counterexamples. We’re better at asking “what does it mean if this is right?” than “what does it mean if this is wrong?” Popperian thinking often takes conscious effort and built in processes. But at first glance, this doesn’t translate directly to finance- after all, if we examine data to test whether P implies Q, we can simply look for every time P has happened and check that way.
The trouble is, the data is finite. The history is what happened, or if you prefer, what happened to happen. It wasn’t inevitable, or the only way things could have gone. And that means that the thought process of stress testing your beliefs and trying to prove them wrong is still valuable.
For example, take the hypothesis “if IG credit does poorly, equities will do poorly too”. It’s easy to think of broad market crashes, such as 2008, where this is true, and that makes it seem very plausible. But if we think “how might equities outperform credit in a downmarket”, we might come up with more varied economic scenarios, such as dispersion. That is, if lots of companies do very badly and some do very well, equities will benefit from the upside of the latter group, while credit won’t. And equities have outperformed credit in scenarios like this, such as in early 2022[1]. If AI companies do very well while traditional companies fail, we could see this effect more extremely.
As a softer point, I find this way of thinking also helps unearth more hidden assumptions. In the example above, the question is itself loaded, as it may not be like for like. An investor looking to earn around £5 in excess returns, at current spread levels, might need to invest around £800 in credit; or might expect the same returns from around £170 in equity with £630 in cash. On that basis, it’s very easy to see a small equity holding losing less than a large credit holding.
As an intriguing aside, people are much better at answering the problem when it’s framed differently. For example:
You see 4 people.
Each person has an age and a drink
You see a beer drinker, a soda drinker, a 35-year old, and a 10-year old,
Now the question becomes whom you should check to make sure no one under 18 is drinking beer. Almost everyone sees very quickly that you need to test the beer drinker (card A) and the 10-year old (card 8). Abstracted, the logic is identical, but we’re better at solving these problems when they’re framed in terms of adhering to social norms than when they’re framed in other terms. This is sometimes presented as evidence that we evolved our ability to do logic largely as a by product of increasingly complex social interactions, rather than any more straightforward path, such as the benefits of tool use. Whether that’s true or not though, our faculties certainly didn’t evolve for their ability to make strategic investment decisions, and we need all the mental tools we can get.
[1] S&P 500 vs ICE C0A0 index.
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