Size Premium, Distress Risk and Distress Anomaly

As documented in Fama and French (1992), small firms’ expected equity returns are usually larger than big firms.’ Notably, Fama and French (1995) attributed this return pattern, dubbed as size premium, to a notion that small firms are assigned a higher risk premium because they face greater risk of distress. However, “distress anomaly” papers including Campbell, Hilscher, and Szilagyi (2008) empirically have shown that firms with greater distress risk tend to generate lower expected returns thus imply that small firms are assigned a lower risk premium (empirically confirmed by Fama and French (2015)). In this paper, I attempt to reconcile these two seemingly contradicting set of results. I assume that firm’s true distress risk exposure is determined by Z-score (Altman (1968)) and firm size. To the extent that distress risk is sensitive to firm size, the model captures size premium. Moreover, I assume that the firm size’s sensitivity to distress risk changes over Z-score. This leads to a hump-shaped return profile over Z-score and, more interestingly, implies hump-shaped size premium over Z-score. Moreover, consistent with the model’s implication, I empirically find that unconditional size premium increases by more than three times after I exclude low-Z firms. Lastly, I extend the model to show that size premium depends on government debt. I empirically find that government’s debt and size premium are negatively correlated.