Market states and the risk-based explanation of the size premium

•Distress risk story of size effect implies small firms earn premium in up markets.•We find the relationship between size and returns holds only in down markets.•Results are robust to proxies of up-down markets and beta estimates.•Results suggest if payment to size is based on risk then other reasons are needed.•Instead, the size effect may be due to idiosyncratic risk or behavioral factors.

The distress risk explanation of the size effect implies that payment for distress risk ought to occur in up market periods, not in down market periods where distress risk ought to depress the price of securities with such risk. We find that, given the influence of the market beta, the relationship between size and returns is significant only in down markets. Further, we find a size effect in January regardless of the market state. In months other than January, a small-firm effect exists in down markets, but a large-firm effect exists in up markets. Out results are robust to different definitions of up and down markets using credit spreads and various estimations of beta. These results suggest that if payment to size is based on systematic risk then some other explanation should be developed. Alternatively, the explanation of the size effect may depend on payment to idiosyncratic risk or it might be associated with behavioral factors. In all cases, current methods of risk adjusting in academic studies are questioned.