On the interpretation and estimation of the market model R-square

The R-square of the market model is largely employed in finance and accounting studies as a measure of stock price informational efficiency. Individual firms R-squares are usually aggregated at the country-level by using the individual firm total risk over the country total risk as weighting factor. This paper shows how to interpret the country-level R-square as a Chisini mean of the firm-specific R-squares and under what conditions it may be related to the R-square of a Seemingly Unrelated Regression (SUR) model. In particular we show that for the latter a necessary constrain is that returns must be centered on zero, which appears to be in this context not only a common practice but also a methodological assumption.