Collider bias: why momentum and value fight inside your screen

Question

In the full universe of stocks, a name's momentum score and its value score are essentially uncorrelated. But among the stocks that pass your screen, which admits a stock if it has high momentum OR cheap valuation, the two scores show a clear negative correlation. A teammate wants to build a model that uses this negative relationship.

Explain why selecting on the screen manufactures a negative correlation between two independent variables, and why building on it is a mistake.

Accepted Answer

This is collider bias (Berkson's paradox): conditioning on a common effect of two variables induces an association between them, even when they are independent to begin with. The mechanism. The screen's pass/fail flag is a common effect of momentum and value: a stock gets in if momentum is high OR value is high. Look only at the stocks that passed and ask about one with weak momentum. To have made it in, it must have had strong value, otherwise it would have been rejected. Symmetrically, a passer with weak value must have strong momentum. Among passers, weakness in one signal implies strength…

Collider bias: why momentum and value fight inside your screen

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