Sign and size the bias from omitting market beta
Asked at DE Shaw
The true return model is , where is your signal and is the market return (variables centered, exogenous). You regress on alone. Suppose the market loading is , and the auxiliary regression of on has slope .
What does your estimated slope on converge to, and is it biased up or down?
Show a hint
Substitute the true model into the short-regression slope and use .
Your answer
This one is open-ended. Work it through, then check your reasoning against the full solution.