Assessing goodness-of-fit of asset pricing models: the distribution of the maximal R²

The development of asset pricing models that rely on instrumental variables together with the increased availability of easily-accessible economic time-series have renewed interest in predicting security returns. Evaluating the significance of these new research findings, however, is no easy task. Because these asset pricing theory tests are not independent, classical methods of assessing goodness-of-fit are inappropriate. This study investigates the distribution of the maximal R² when k of m regressors are used to predict security returns. We provide a simple procedure that adjusts critical R² values to account for selecting variables by searching among potential regressors.