Return is the time‐series average of the monthly equal‐weighted portfolio returns (in percent). / E If current earnings proxy for expected future earnings, high‐risk stocks with high expected returns will have low prices relative to their earnings. Turning alphas into betas: Arbitrage and endogenous risk. / Thus, a simple size sort seems to support the SLB prediction of a positive relation between β and average return. Finally, Basu (1983) shows that earnings‐price ratios t BE BE The Fama-French’s Five-Factor Model Relation with Interest Rates and Macro Variables. 0.17 Modelling shares choice to enter in a portfolio using artificial neural networks (ANN). P Table IV shows average returns for July 1963 to December 1990 for portfolios formed on ranked values of book‐to‐market equity The average slopes for ln(ME) are close to the values in the univariate size regressions, and almost 4 standard errors from 0, but the average slopes for β are negative and less than 1 standard error from 0. The fit measure is the within-panel adjustedR2. Journal of Islamic Accounting and Business Research. / ME First, although ) = BE do not seem to be good proxies for β. Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) find that, as predicted by the SLB model, there is a positive simple relation between average stock returns and β during the pre‐1969 period. Stocks are assigned the post‐ranking (sum)β of the size portfolio they are in at the end of year E BE , the ratio of the book value of common equity to its market value. A P BE   / In FM regressions, the intercept is the return on a standard portfolio (the weights on stocks sum to 1) in which the weighted averages of the explanatory variables are 0 (Fama (1976), chapter 9). / ME portfolios in Table IV are formed in the same general way (one‐dimensional yearly sorts) as the size and β portfolios in Table II. The full text of this article hosted at iucr.org is unavailable due to technical difficulties. . BE One way to generate strong variation in β that is unrelated to size is to form portfolios on size and then on β. Negative BE (which results from persistently negative earnings) and high Finally, the tests mix firms with different fiscal yearends. We then estimate βs using the full sample (330 months) of post‐ranking returns on each of the 100 portfolios, with the CRSP value‐weighted portfolio of NYSE, AMEX, and (after 1972) NASDAQ stocks used as the proxy for the market. / ) This book‐to‐market relation is stronger than the size effect, which produces a t‐statistic of −2.58 in the regressions of returns on In(ME) alone. or earnings‐price ratio Since the FM intercept is constrained to be the same for all stocks, FM regressions always impose a linear factor structure on returns and expected returns that is consistent with the multifactor asset‐pricing models of Merton (1973) and Ross (1976). = For example, although the two extreme portfolios, 1A and 10B, have much different βs, they have nearly identical average returns (1.20% and 1.18% per month). / In the regressions of the size‐portfolio returns on β alone, the average premium for a unit of β is 1.45% per month. If so, it is not surprising that the variation in β within a size decile is unrelated to average return, or that size dominates β in bivariate tests. = Performance peer groups in CEO compensation contracts. Our bottom‐line results are: (a) β does not seem to help explain the cross‐section of average stock returns, and (b) the combination of size and book‐to‐market equity seems to absorb the roles of leverage and ), because preliminary tests indicated that logs are a good functional form for capturing leverage effects in average returns. from 4.72 to 0.87 The average return is the time‐series average of the monthly equal‐weighted portfolio returns, in percent. Cochrane (2009) argues that this is not a problem, because stock returns are likely to be uncorrelated over time. Ball (1978) argues that , firms. − ) name to become the American Accounting Association. Sorted on size alone, the post‐ranking βs range from 1.44 for the smallest ME portfolio to 0.92 for the largest. It would be interesting to test whether loadings on this or other economic factors, such as those of Chen, Roll, and Ross (1986), can explain the roles of size and book‐to‐market equity in our tests. are always positive and more than 4 standard errors from 0. observed in Table IV is also apparent when the BE The average residuals for regressions (1) and (2) (not shown) are quite similar to those for regressions (4) and (5) (shown). / Several techniques, for example firm dummy variables, one-way cluster-robust standard errors, Fama-MacBeth procedure, and Newey-West procedure, are documented as a solution in analyzing panel data. ME To avoid giving extreme observations heavy weight in the regressions, the smallest and largest 0.5% of the observations on. BE P E 1.27 There it lists the coefficients c1-ci for each portfolio, but the portfolios are not named similar to their original name, but as r1-r25. If this is a problem, post‐ranking βs for the size‐β portfolios should not be highly correlated across subperiods. Financial constraints and marketing investment: evidence from text analysis. / Both Pearson and nonparametric Spearman correlations are reported. Table AI shows average monthly returns and market βs for 12 portfolios of NYSE stocks formed on the basis of size (ME) at the end of each year from 1940 to 1989. E 1 10 1.17 ( BE / Finally, Roll (1983) and Keim (1983) show that the size effect is stronger in January. They can be regarded as different ways of extracting information from stock prices about the cross‐section of expected stock returns (Ball (1978); Keim (1988)). BE   E P We can also report that β shows no power to explain average returns (the average slopes are typically less than 1 standard error from 0) in FM regressions that use various combinations of β with size, book‐to‐market equity, leverage, and We examine the roles of size and β in the average returns on NYSE stocks for the half‐century 1941–1990, the longest available period that avoids the high volatility of returns in the Great Depression. t / is close to its value In the end, we have post‐ranking monthly returns for July 1963 to December 1990 on 100 portfolios formed on size and pre‐ranking βs. E firms are persistently strong performers, while the economic performance of high = ME Learn more. Adding both size and book‐to‐market equity to the International Review of Economics & Finance. 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