An Exploratory Investigation of the Firm Size Effect

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of Financial


14 (1985) 451-471.




Nai-fu CHEN

and David A. HSIEH

University of Chicago, Chicago, IL 60637, USA Received August 1983, final version received April 1985 We investigate the firm size effect for the period 1958 to 1977 in the framework of a multi-factor pricing model, The risk-adjusted difference in returns between the top five percent and the bottom five percent of the NYSE firms is about one to two percent a year, a drop from about twelve percent per year before risk adjustment. The variable most responsible for the adjustment is the sensitivity of asset returns to the changing risk premium, measured by the return difference between low-grade bonds and long-term government bonds.

1. Introduction
The ‘firm size’ effect was documented by Banz (1981) and Reinganum (1981). In their studies, small firms had higher average returns than large firms even after adjusting for risk via the Capital Asset Pricing Model (CAPM). Therefore, their results can be considered a rejection of the joint hypotheses that the CAPM is correct and that the market is efficient. In a recent empirical study of the Arbitrage Pricing Model (APT),’ Chen (1981, 1983) found that the firm size effect is essentially captured by the factor loadings of the APT. In his study portfolios of different size firms did not have significantly different average returns after adjusting for factor risks. Chen’s results are consistent with the hypotheses that risk is the explanation for the firm size effect and that the market is efficient. *We thank Eugene Fama, Merton Miller, and Myron Scholes for their many comments and suggestions, Roger Ibbotson for providing us with some of the necessary data, and the Center for Research in Security Prices for financial support. We also benefited from discussions with John Abowd, Rolf Banz, Doug Breeden, Stephen Brown, George Constantinides, Wayne Ferson, Mike Gibbons (the referee), Bob Hamada, Richard Leftwich, Richard Roll, Stephen Ross, Bill Schwert, Victor Zamowitz, and workshop participants at Chicago, Dartmouth, Northwestern, Stanford, UCLA, and Yale. ‘See Ross (1976). Huberman (1982), and Connor Ingersoll (1984) and Chen and Ingersoll (1983). (1984) for the formal development; see also


1985, Elsevier Science Publishers

B.V. (North-Holland)


K. C. Chan et al., Multi-factor pricing

models and the sire effect

To further interpret the size effect, we use identifiable economic variables directly in a pricing equation. While this reasoning was originally motivated by the APT, it is also compatible with intertemporal pricing models such as those of Merton (1973) Long (1974), Cox, Ingersoll and Ross (1976) Lucas (1978), and Breeden (1979). Therefore, rather than focusing on the distinctions among the models, we shall simply call the pricing equation that we investigate a multi-factor pricing equation. The paper is organized as follows. In section 2, we describe the variables to be included in the pricing equation. Section 3 contains the cross-sectional results of the model and its ability to explain average returns of portfolios ranked according to firm size. Section 4 presents results containing the proxy variable ‘In MI/’ - the natural logarithm of the market value of a firm’s equity. We re-examine the ‘January seasonal’ in section 5 and summarize our findings in section 6. 2. The stock market and the macroeconomy We believe that stock returns react to changes in the economic environment. This relation can indicate not only the type of risks that we face when investing in stocks but also the type of changes in the economic environment that we can hedge against using current investment opportunities. An effort to link the stock market to the macroeconomy is described in an empirical study by Chen, Roll and...
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