Decomposing excess returns in stochastic linear models

We present a theorem helpful in estimating the mean and variance of a linear function with arbitrary multivariate randomness in its coefficients and variables. We derive a generalized decomposition result from two random linear functions in which the result can be applied to most models using event study analysis. Taking the 1989 minimum wage hike as an example, we found that the apparent lack of an effect is a consequence of two off-setting forces: 1) a negative effect arising from firm-specific traits and 2) a positive effect arising from market performance. In sum, we bring to the analysis a method that helps provide additional insights and can be applied to much of the work using event study.