You run a monthly cross sectional regression of stock returns on a standardised value score over 240 months. The mean slope is 0.25% per month with a 1.2% standard deviation across months. What is the t statistic, and what does the slope itself represent?

You run a monthly cross sectional regression of stock returns on a standardised value score over 240 months. The mean slope is 0.25% per month with a 1.2% standard deviation across months. What is the t statistic, and what does the slope itself represent?

Approach: Treat the series of monthly slopes as one time series and test its mean. Then read the slope as the return of a portfolio with unit exposure to the score.

3.23. The Fama-MacBeth t statistic is the mean slope over the standard error of the slope series, so the standard error is 1.2%/sqrt(240) = 0.0775% and t = 0.25/0.0775 = 3.23. Each monthly slope is the return of a portfolio with one cross sectional standard deviation of exposure to the score and zero net exposure, so 0.25% a month is 3% a year at a volatility of 1.2%*sqrt(12) = 4.16%, an information ratio of 0.72. The procedure avoids estimating a residual covariance matrix by collapsing each cross section into one number, at the cost of assuming those numbers are serially independent, so autocorrelated slopes inflate the t statistic and need a Newey-West correction.

Follow-up: How does the interpretation change if the score is a raw ratio rather than a cross sectional z score?

Key concepts: cross sectional regression, fama-macbeth, t statistic, information ratio.