An Exploratory Investigation of the Firm Size Effect

Topics: Inflation, Interest, Capital asset pricing model Pages: 36 (10249 words) Published: March 16, 2011

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...

References: Banz, Rolf, 1981, The relationship between return and market value of common stocks. Journal of Financial Economics 9, 3-18. Black, Fischer, 1972, Capital market equilibrium with restricted borrowing, Journal of Business 45, 444-454. Black, F.. M. Jensen and M. Scholes, 1972, The capital asset pricing model: Some empirical tests, in: Michael Jensen, ed., Studies in the theory of capital market (Praeger, New York). Breeden, Douglas, 1979, An intertemporal asset pricing model with stochastic consumption and investment opportunities, Journal of Financial Economics 7, 265-296. Brown, P., A. Kleidon and T. Marsh, 1983, New evidence on the nature of size related anomalies in stock prices, Journal of Financial Economics 12, 33-56. Chen, N., 1981, Arbitrage asset pricing: Theory and evidence, Unpublished doctoral dissertation (University of California, Los Angeles, CA). Chen, N., 1983, Some empirical tests of the theory of arbitrage pricing, Journal of Finance 38, 1393-1414. Chen, N. and J. Ingersoll, 1983, Exact pricing in linear factor models with finitely many assets: A note, Journal of Finance 38, 985-988. Chen. N., R. Roll and S. Ross, 1983, Economic forces and the stock market, CRSP working paper no. 119 (University of Chicago, Chicago, IL). Connor, G., 1984, A unified beta pricing theory, Journal of Economic Theory, forthcoming. Cox. J., J. Ingersoll and S. Ross, 1976, Intertemporal asset pricing theory, Econometrica, forthcoming. Fama, E., 1970, Multiperiod consumption-investment decisions, American Economic Review 60, 163-174. Fama, E., 1976, Foundations of finance (Basic Books, New York). Fama, E., 1981, Stock returns, real activity, inflation and money, American Economic Review 71, 545-565. Fama, E. and M. Gibbons, 1982, Inflation, real returns and capital investment, Journal of Monetary Economics 8.297-324. Fama, E. and M. Gibbons, 1984, A comparison of inflation forecasts, Journal of Monetary Economics 13, 327-348.
Chun er al.. Mul~r-Juctorpncrng
models und the size effect
Fama, E. and J. MacBeth, 1973, Risk, return and equilibrium: Empirical tests, Journal of Political Economy 81, 607-636. Friedman, M. and A. Schwartz, 1963, A monetary history of the United States. 1867-1960 (Princeton University Press, Princeton, NJ). Gibbons, M., 1980, Estimating the parameters of the capital asset pricing model: A minimum expected loss approach, Unpublished manuscript (Graduate School of Business, Stanford University, Stanford, CA). Gibbons, M., 1982, Multivariate tests of financial models: A new approach, Journal of Financial Economics 10, 3-27. Huberman, G., 1982, Arbitrage pricing theory: A simple approach, Journal of Economic Theory 28, 183-191. Hsieh, D., 1983, A heteroscedasticity-consistent covariance matrix estimator for time series regressions, Journal of Econometrics 22. 281-290. Ibbotson, R., 1979, The corporate bond market: Structure and returns, Unpublished manuscript (University of Chicago, Chicago, IL). Ibbotson, R. and Sinquefield, 1982, Stocks, bonds, bills and inflation: The past and the future (The Financial Analysts Research Foundation, Charlottesville, VA). Ingersoll, J., 1984, Some results in the theory of arbitrage pricing, Journal of Finance 39, 1021-1039. Keim, D., 1983, Size related anomalies and stock return seasonality: Empirical evidence, Journal of Financial Economics 12, 13-32. Long, J., 1974, Stock prices, inflation and the term structure of interest rates, Journal of Financial Economics 1, 131-170. Lucas, R., 1978, Asset prices in an exchange economy, Econometrica 46, 1429-1445. Merton, R., 1973, An intertemporal capital asset pricing model, Econometrica 41, 867-887. Reinganum, M., 1981, Misspecification of capital asset pricing: Empirical anomalies based on earnings’ yields and market values, Journal of Financial Economics 9, 19-46. Ross, S.. 1976, The arbitrage theory of capital asset pricing, Journal of Economic Theory 13, 341-360. Schultz, Paul, 1983, Transaction costs and the small fum effect: A comment, Journal of Financial Economics 12, 81-88. Shanken, Jay, 1982, An asymptotic analysis of the traditional risk-return model, Unpublished manuscript (University of California, Berkeley, CA). Shanken, Jay, 1985, Multivariate tests of the zero-beta CAPM, Journal of Financial Economics 14, this issue. Stoll, Hans and Robert Whaley, 1983, Transaction costs and the small firm effect, Journal of Financial Economics 12, 57-79. Van Home, J., 1978, Financial market rates and flows (Prentice-Hall, Englewood Cliffs, NJ).
Continue Reading

Please join StudyMode to read the full document

You May Also Find These Documents Helpful

  • Small Firm Effect Essay
  • Essay on The Effects of Sox on Audit Firms
  • Essay on Optimal Size of a Firm
  • Investigation of the effect of particle size distribution on the flow properties of bulk solids Essay
  • Effect of Reducing Class Size Essay
  • The Effects of Dna on Criminal Investigation Essay
  • Exploratory Essay
  • Investigation Of The Effects Of Acid Rain Essay

Become a StudyMode Member

Sign Up - It's Free