On Selection Biases in Book-to-Market Based Tests of Asset Pricing Models

Many studies have documented portfolio strategies that provide returns in excess of those expected, given the level of risk of the portfolio. Variables that seem to have predictive power for equity returns include the market capitalization of the firm’s equity and the ratio of the firm’s book equity to market equity (BE/ME). Firms with low market capitalization and high book-tomarket values seem to earn high returns. With respect to the book-to-market anomaly, it has been argued that the apparent superior performance is due to a subtle selection bias in a typical data source used to implement the tests of asset pricing models, the COMPUSTAT data. We use a sample of COMPUSTAT data that is free from this bias to investigate whether the previous evidence on the book-to-market anomaly is an artifact of this selection bias. The postulated selection bias does not seem to be important for samples restricted to NYSE/AMEX firms. There is some difference when NASDAQ firms are included in the standard COMPUSTAT sample. This may be due to a truly stronger BE/ME effect or to a more severe selection bias in that sample. Our data do not allow us to disentangle these two possible explanations. Standard asset pricing models imply that assets’ risk premia are determined by their sensitivity to innovations in investors’ marginal utility. In the Capital Asset Pricing Model (CAPM) of Sharpe (1964), Lintner (1965), Mossin (1966), Treynor (1961) and Black (1972), investors’ marginal utility is determined by the rate of return on the market portfolio (the portfolio of all assets, weighted by their relative market values). Thus, assets’ risk premia are determined by their sensitivity to unexpected movements in the market portfolio. For asset i, this sensitivity is measured by βi = cov(ri,rm)/var(rm), where ri is the return on asset i, rm is the return on the market portfolio, cov( , ) denotes covariance, and var( ) denotes variance. The predicted relation between expected returns and β is: E(ri) = γ0 + γ1 βi (1) where E( ) denotes the expectation, γ0 is the zero beta (or riskless) rate of return, and γ1 is the risk premium for market risk. The CAPM implies that there is a linear relation between expected returns and β and that, after controlling for β, no other variable should be able to explain differences in assets’ expected returns. That is, if we estimate a cross-sectional regression of asset returns on β and on a vector of other variables, say Z: ri = γ0 + γ1 βi + δZi + εi (2) then δ should be equal to zero. Over the past twenty years, the CAPM has been subjected to an enormous amount of empirical scrutiny. A number of studies have documented variables that seem to predict differences in asset returns in excess of those expected given the differences in asset betas. That is, δ is not zero in (2). For example, market capitalization [Banz (1981)], price to earnings (P/E) ratios [Basu (1983)], book equity to market equity (BE/ME) ratios [Stattman (1980)], dividend yield [Keim (1985)], and leverage [Bhandari (1988)] are among the variables that appear to be useful in constructing portfolios that earn high returns even after adjusting for risk. In addition, finding estimates of γ1 that are statistically significantly different from zero has proven difficult [Tiniç and West (1984)]. Fama and French (1992a) investigate the ability of a number of variables to explain crosssectional differences in returns earned by stocks. They conclude that the standard measure of non-diversifiable risk, β, has no explanatory power for returns once one controls for differences in size and book-to-market equity (BE/ME). Fama and French (1992a) argue, quite forcefully, that this accumulation of anomalous results calls into question the usefulness of the CAPM, as typically implemented. The arguments of Fama and French (1992a) have elicited much interest, both on the part of academics and of practitioners. We focus on an issue raised by Kothari, Shanken, and Sloan (1995). They argue that a portion of the apparent ability of BE/ME ratios to predict risk-adjusted returns is due to a selection bias induced by the manner in which data are included on the COMPUSTAT data files. These files include historical accounting data for a wide sample of firms. Many published studies use this source of accounting data when constructing many of the variables that seem to be able to explain cross-sectional differences in asset returns, such as BE/ME, P/E ratios, and leverage ratios. Kothari, Shanken, and Sloan (1995) argue that there are two related potential sources of bias. Regarding the first source of bias, they argue that when COMPUSTAT adds a firm to its data file, it often "back-fills" data. That is, if a firm is added in 1983, for example, COMPUSTAT might fill in data for the firm back to 1978. Consider the high BE/ME firms that