THE ACCUMULATION of empirical evidence inconsistent with the simple oneperiod capital asset pricing models of Sharpe (1964), Lintner (1965), and Black (1972) indicates that alternative models of capital market equilibrium deserve investigation. A minimum requirement for any alternative model should be that it explains the empirical anomalies which arise within the simple CAPM. One such anomaly is observed when portfolios are formed on the basis of firm size (see Banz [1978] and Reinganum [1980b, c]). Small firms systematically experienced average rates of return nearly 20% per year greater than those of large firms, even after accounting for differences in estimated betas. An adequately specified model of equilibrium should eliminate these persistent "abnormal" returns. The arbitrage pricing theory (APT) proposed by Ross (1976) is a plausible alternative to the simple one-factor CAPM. The appeal of the APT probably comes from its implication that compensation for bearing risk may be comprised of several risk premia, rather than just one risk premium as in the CAPM. Roll and Ross (1979) claim to find empirically at least three and probably four factors that are priced from 1962 to 1972. However, Roll and Ross do not offer an economic interpretation of these factors and admit that their test is a weak one. This research investigates empirically whether a parsimonious arbitrage pricing model can account for the differences in average returns between small firms and large firms which are traded on the New York and American Stock Exchanges. If a parsimonious APT can explain these differences, then one might feel more confident in using the APT as an empirical replacement for the CAPM, even though the economic nature of the risks is not fully understood. However, if a parsimonious APT fails to account for differences in average returns, then the model ought to be rejected. There can be no justification for embracing a complicated model if it does not convey any more information than does the simple model.