The prosecutor's fallacy and commodity markets

There is an interesting fallacy associated with conditional probabilities which is also relevant for investors. It is called the Prosecutors Fallacy which is very simple problem but a trap that many of us fall into. The fallacy exists because the prosecutor argues that a small chance of innocence means there is a high likelihood of guilt.

The change that someone is innocent given some damning evidence is not the same as the chance of finding the damning evidence for someone who is innocent. If we find DNA that has a 1/500,000 chance of being present with the accused person, that is not same as saying that the accused had a 1/500,000 chance of being innocent.

We can apply this to the case of downturns in commodity markets and recessions. If we look at the number of recessions since 1970 based on annual data, there have been five. All  recession years have shown negative commodity returns. The probability of a negative returns for commodities conditional on a recession is 1. However, the probability of a recession given negative commodity returns is much less only 50%. These are not the same. Conditioning in one direction is not the same as conditioning in the other direction. This is a classic variation on the line of causality and the sample of data available.

Everyone knows that correlation does not mean causality but it still takes some time to digest what that means in any given situation. A high chance of two factors being linked is not the same as saying that one is the result of the other.