Bayes for days
What to do with signal.
Investors are constantly barraged with new information concerning their investments—and when it surfaces, they must weigh its significance and update their thinking and investment decisions accordingly. But this is more easily said than done.
Fortunately, there is a useful tool to help us in this regard: Bayes’ Theorem. Developed in the 18th century, Bayes provides a rational way to update probabilities based on new evidence. On the surface it can seem daunting, but this needn’t be the case. When you deconstruct the equation, it is basically asking three key questions:
1. What is the base rate (the prior probability of the event happening)? P(H)
2. How rare is the new evidence? 1/P(E)
3. How relevant is the evidence? P(E|H)
So the formula is:
As an example, let’s say you notice the U.S. yield curve has inverted and you’re curious about what this means for the probability of a U.S. recession. Using Bayes, you’d first calculate the base rate, or the prior probability of a recession in the U.S. Based on data from 1962 to present (our sample period for this example), you’d find that there have been seven recessions. This makes our base rate P(H) 13% (seven instances/55 years).
Then you’d ask how rare is this new information? You’d find that inversions are rare; they’ve only happened 22% of the time in our sample period. Therefore, the P(E) would be 22%.
Finally, to determine the relevance of this new evidence, you’d look at the relationship between the recessions and inverted yield curves. Specifically, you’d identify the number of recessions since 1962 (seven cases) where the yield curve was inverted. In this case, you’d find that the yield curve was inverted in every case. This gives us a P(E|H) of 100%.
Therefore, our equation to solve for the probability of a U.S. recession given yield curve inversion is:
13 x 1/22 x 100% = 59%
Approximately 59%, a meaningful number and one that’s significantly higher than our base rate of 13%—indicating that yield curve inversions are important signals to pay attention to.
We have found Bayes to be a useful mental model for investing. Not only does it provide a theoretically sound process for evaluating the relevancy of new information, it helps to effectively differentiate between signal vs. noise—an essential tool in our world of rampant storytelling.