https://rady.ucsd.edu/faculty/directory/valkanov/pub/classes/mfe/docs/fama_french_jfe_1993.pdf

Common risk factors in the returns on stocks and bonds

Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market 3, size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the tests allow for variation in 3 that is unrelated to size, the relation between market /3 and average return is flat, even when 3 is the only explanatory variable. THE ASSET-PRICING MODEL OF Sharpe (1964), Lintner (1965), and Black (1972) has long shaped the way academics and practitioners think about average returns and risk. The central prediction of the model is that the market portfolio of invested wealth is mean-variance efficient in the sense of Markowitz (1959). The efficiency of the market portfolio implies that (a) expected returns on securities are a positive linear function of their market O3s (the slope in the regression of a security's return on the market's return), and (b) market O3s suffice to describe the cross-section of expected returns. There are several empirical contradictions of the Sharpe-Lintner-Black (SLB) model. The most prominent is the size effect of Banz (1981). He finds that market equity, ME (a stock's price times shares outstanding), adds to the explanation of the cross-section of average returns provided by market Os. Average returns on small (low ME) stocks are too high given their f estimates, and average returns on large stocks are too low. Another contradiction of the SLB model is the positive relation between leverage and average return documented by Bhandari (1988). It is plausible that leverage is associated with risk and expected return, but in the SLB model, leverage risk should be captured by market S. Bhandari finds, howev er, that leverage helps explain the cross-section of average stock returns in tests that include size (ME) as well as A. Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) find that average returns on U.S. stocks are positively related to the ratio of a firm's book value of common equity, BE, to its market value, ME. Chan, Hamao, and Lakonishok (1991) find that book-to-market equity, BE/ME, also has a strong role in explaining the cross-section of average returns on Japanese stocks.

http://www.business.unr.edu/faculty/liuc/files/badm742/fama_french_1992.pdf

The Cross‐Section of Expected Stock Returns

Previous work shows that average returns on common stocks are related to firm characteristics like size, earnings/price, cash flow/price, book-to-market equity, past sales growth, long-term past return, and short-term past return. Because these patterns in average returns apparently are not explained by the CAPM, they are called anomalies. We find that, except for the continuation of short-term returns, the anomalies largely disappear in a three-factor model. Our results are consistent with rational ICAPM or APT asset pricing, but we also consider irrational pricing and data problems as possible explanations. RESEARCHERS HAVE IDENTIFIED MANY patterns in average stock returns. For example, DeBondt and Thaler (1985) find a reversal in long-term returns; stocks with low long-term past returns tend to have higher future returns. In contrast, Jegadeesh and Titman (1993) find that short-term returns tend to continue; stocks with higher returns in the previous twelve months tend to have higher future returns. Others show that a firm's average stock return is related to its size (ME, stock price times number of shares), book-to-marketequity (BE/ME, the ratio of the book value of common equity to its market value), earnings/price (E/P), cash flow/price (C/P), and past sales growth. (Banz (1981), Basu (1983), Rosenberg, Reid, and Lanstein (1985), and Lakonishok, Shleifer and Vishny (1994).) Because these patterns in average stock returns are not explained by the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965), they are typically called anomalies. This paper argues that many of the CAPM average-return anomalies are related, and they are captured by the three-factor model in Fama and French (FF 1993). The model says that the expected return on a portfolio in excess of the risk-free rate [E(Ri) - Rf] is explained by the sensitivity of its return to three factors: (i) the excess return on a broad market portfolio (RM - Rf); (ii) the difference between the return on a portfolio of small stocks and the return on a portfolio of large stocks (SMB, small minus big); and (iii) the difference between the return on a portfolio of high-book-to-market stocks and the return on a portfolio of low-book-to-market stocks (HML, high minus low). Specifically, the expected excess return on portfolio i is,

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1540-6261.1996.tb05202.x

Multifactor Explanations of Asset Pricing Anomalies

This paper studies the cross-sectional properties of return forecasts derived from Fama-MacBeth regressions. These forecasts mimic how an investor could, in real time, combine many firm characteristics to obtain a composite estimate of a stockâs expected return. Empirically, the forecasts vary substantially across stocks and have strong predictive power for actual returns. For example, using ten-year rolling estimates of Fama- MacBeth slopes and a cross-sectional model with 15 firm characteristics (all based on low-frequency data), the expected-return estimates have a cross-sectional standard deviation of 0.87% monthly and a predictive slope for future monthly returns of 0.74, with a standard error of 0.07.

/pdf/the-cross-section-of-expected-stock-returns-3oji85htnb.pdf

The Cross-section of Expected Stock Returns

For many years, stock market analysts have argued that value strategies outperform the market. These value strategies call for buying stocks that have low prices relative to earnings, dividends, book assets, or other measures of fundamental value. While there is some agreement that value strategies produce higher returns, the interpretation of why they do so is more controversial. This paper provides evidence that value strategies yield higher returns because these strategies exploit the mistakes of the typical investor and not because these strategies are fundamentally riskier.

Contrarian Investment, Extrapolation, and Risk

Persuasive evidence of market inefficiency

The beta of a stock's investment return is the response coefficient to the \"market portfolio\" return. Another closely related definition of beta arises from a stock's statistical relationship to any \"systematic portfolio.\" We can decompose the stock return into two parts. One part is correlated with the systematic portfolio return, while the other, the residual, is uncorrelated with the systematic portfolio return.

Prediction of common stock betas

Is Beta Dead?” (Wallace [1980]) and other recent articles have asked whether broad consequences, disastrous to modern investment technology, would result from misspecification of the Capital Asset Pricing Model (CAPM), or worse yet, from falsehood of the model. The criticisms have cited imprecise specification of the market portfolio as a misapplication of the CAPM, and have emphasized the difference between the “efficient portfolio” and the market portfolio when the CAPM is false. The purpose of this article is to evaluate these criticisms.

The Capital Asset Pricing Model and the Market Model

C $? predictive model of common stock investment risk since December 1975. The model predicts systematic risks, common factor risks, and specific risks of individual common stocks.' The predictions are updated at the beginning of each month. The first step is to calculate descriptors of the variability of the stock price, stock trading activity, and the company's industry classification, variability of earnings, past success, size, maturity, growth, yield, and financial leverage. We then use risk prediction rules to convert these descriptors into the necessary risk predictions. We estimated the risk prediction rules over the time span from April 1966 through August 1974. The prediction rules have continued unchanged from December 1975 until the present, although we have made some improvements in the formulas for descriptors and the timeliness of the data. The model was superceded by a new risk model estimated in 1980 and released in 1982. The model reviewed here was then renamed the "El Model" to distinguish it from the revised E2 Model. Although the E l Model is now obsolete, we continue to use it, and it continues to perform well. This article will evaluate its predictive performance from the third quarter of 1974 until the present. Until December 1975, the model was being estimated and readied for commercial implementation. From December 1975 until June 1977, risk predictions were periodically updated but no ongoing evaluation occurred. Hence, we performed the evaluation of predictive performance through June 1977 retrospectively. From July 1977 until the present, we routinely evaluated predictive performance each month during

Barr Rosenberg

Papers

Persuasive evidence of market inefficiency

Prediction of common stock betas

The Capital Asset Pricing Model and the Market Model

Prediction of common stock investment risk