The size effect reversal in the USA

Abstract

The paper examines the size effect reversal in the USA over the period 1970–1999, using data for the ten size deciles in the CRSP tapes during this 40-year period. Betas for small-firm portfolios increase as the return interval analysed increases, and are lower than large-firm portfolios for daily data but higher for monthly and quarterly data. Differences between small- and large-firm portfolio returns are associated with higher betas as return intervals increase, with lower betas for daily data, and higher for quarterly data. Before 1981 when the small-firm effect was published, smaller firms’ relative risk coefficients were biased downwards compared to aggregated coefficients, while larger firms’ were biased upwards, as expected. But after 1981, a partial reversal occurred with larger firms’ relative risk coefficients also biased downwards and by more than the smaller firms. In the post-period, relative risk measures generated higher abnormal returns for large firms than for small firms, effectively a large-firm effect, because large firms’ risks were more understated, possibly due to their relatively less frequent trading. However, these abnormal returns were reduced for large (and small) firms when using more appropriate aggregated risk coefficients.

Notes

¹This approach replicates the same regressions used by Stoll and Whaley (1983), except that the sample is increased to include an additional 264 monthly returns from the CRSP tapes.

²The model is selected using Akaike and Schawartz information criterion. An arbitrary one-period lagged and leading variable model is initially selected, and then models with different specifications are constructed. The model with the smallest information criterion is selected.

³Breeden (1979) first developed the consumption based CAPM (CCAPM).