# The Cross‐Section of Expected Stock Returns

TL;DR: In this paper, Bhandari et al. found that the relationship between market/3 and average return is flat, even when 3 is the only explanatory variable, and when the tests allow for variation in 3 that is unrelated to size.

Abstract: 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.

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TL;DR: In this article, the authors identify five common risk factors in the returns on stocks and bonds, including three stock-market factors: an overall market factor and factors related to firm size and book-to-market equity.

Abstract: This paper identities five common risk factors in the returns on stocks and bonds. There are three stock-market factors: an overall market factor and factors related to firm size and book-to-market equity. There are two bond-market factors. related to maturity and default risks. Stock returns have shared variation due to the stock-market factors, and they are linked to bond returns through shared variation in the bond-market factors. Except for low-grade corporates. the bond-market factors capture the common variation in bond returns. Most important. the five factors seem to explain average returns on stocks and bonds.

24,874 citations

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TL;DR: In this article, the authors show that strategies that buy stocks that have performed well in the past and sell stocks that had performed poorly in past years generate significant positive returns over 3- to 12-month holding periods.

Abstract: This paper documents that strategies which buy stocks that have performed well in the past and sell stocks that have performed poorly in the past generate significant positive returns over 3- to 12-month holding periods. We find that the profitability of these strategies are not due to their systematic risk or to delayed stock price reactions to common factors. However, part of the abnormal returns generated in the first year after portfolio formation dissipates in the following two years. A similar pattern of returns around the earnings announcements of past winners and losers is also documented

10,806 citations

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TL;DR: In this article, the authors show 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).

Abstract: 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,

6,737 citations

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TL;DR: In this paper, the authors show that standard errors of more than 3.0% per year are typical for both the CAPM and the three-factor model of Fama and French (1993), and these large standard errors are the result of uncertainty about true factor risk premiums and imprecise estimates of the loadings of industries on the risk factors.

Abstract: Estimates of the cost of equity for industries are imprecise. Standard errors of more than 3.0% per year are typical for both the CAPM and the three-factor model of Fama and French (1993). These large standard errors are the result of(i) uncertainty about true factor risk premiums and (ii) imp ecise estimates of the loadings of industries on the risk factors. Estimates of the cost of equity for firms and projects are surely even less precise.

6,064 citations

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TL;DR: In this paper, the authors investigate the determinants of capital structure choice by analyzing the financing decisions of public firms in the major industrialized countries and find that factors identified by previous studies as important in determining the cross-section of the capital structure in the U.S. affect firm leverage in other countries as well.

Abstract: We investigate the determinants of capital structure choice by analyzing the financing decisions of public firms in the major industrialized countries. At an aggregate level, firm leverage is fairly similar across the G-7 countries. We find that factors identified by previous studies as important in determining the cross- section of capital structure in the U.S. affect firm leverage in other countries as well. However, a deeper examination of the U.S. and foreign evidence suggests that the theoretical underpinnings of the observed correlations are still largely unresolved.

5,935 citations

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TL;DR: In this paper, the authors present a body of positive microeconomic theory dealing with conditions of risk, which can be used to predict the behavior of capital marcets under certain conditions.

Abstract: One of the problems which has plagued thouse attempting to predict the behavior of capital marcets is the absence of a body of positive of microeconomic theory dealing with conditions of risk/ Althuogh many usefull insights can be obtaine from the traditional model of investment under conditions of certainty, the pervasive influense of risk in finansial transactions has forced those working in this area to adobt models of price behavior which are little more than assertions. A typical classroom explanation of the determinationof capital asset prices, for example, usually begins with a carefull and relatively rigorous description of the process through which individuals preferences and phisical relationship to determine an equilibrium pure interest rate. This is generally followed by the assertion that somehow a market risk-premium is also determined, with the prices of asset adjusting accordingly to account for differences of their risk.

17,922 citations

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TL;DR: In this article, the relationship between average return and risk for New York Stock Exchange common stocks was tested using a two-parameter portfolio model and models of market equilibrium derived from the two parameter portfolio model.

Abstract: This paper tests the relationship between average return and risk for New York Stock Exchange common stocks. The theoretical basis of the tests is the "two-parameter" portfolio model and models of market equilibrium derived from the two-parameter portfolio model. We cannot reject the hypothesis of these models that the pricing of common stocks reflects the attempts of risk-averse investors to hold portfolios that are "efficient" in terms of expected value and dispersion of return. Moreover, the observed "fair game" properties of the coefficients and residuals of the risk-return regressions are consistent with an "efficient capital market"--that is, a market where prices of securities

14,171 citations

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TL;DR: In this article, the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish is discussed.

Abstract: Publisher Summary This chapter discusses the problem of selecting optimal security portfolios by risk-averse investors who have the alternative of investing in risk-free securities with a positive return or borrowing at the same rate of interest and who can sell short if they wish. It presents alternative and more transparent proofs under these more general market conditions for Tobin's important separation theorem that “ … the proportionate composition of the non-cash assets is independent of their aggregate share of the investment balance … and for risk avertere in purely competitive markets when utility functions are quadratic or rates of return are multivariate normal. The chapter focuses on the set of risk assets held in risk averters' portfolios. It discusses various significant equilibrium properties within the risk asset portfolio. The chapter considers a few implications of the results for the normative aspects of the capital budgeting decisions of a company whose stock is traded in the market. It explores the complications introduced by institutional limits on amounts that either individuals or corporations may borrow at given rates, by rising costs of borrowed funds, and certain other real world complications.

9,970 citations

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TL;DR: In this article, a study of market efficiency investigates whether people tend to "overreact" to unexpected and dramatic news events and whether such behavior affects stock prices, based on CRSP monthly return data, is consistent with the overreaction hypothesis.

Abstract: Research in experimental psychology suggests that, in violation of Bayes' rule, most people tend to "overreact" to unexpected and dramatic news events. This study of market efficiency investigates whether such behavior affects stock prices. The empirical evidence, based on CRSP monthly return data, is consistent with the overreaction hypothesis. Substantial weak form market inefficiencies are discovered. The results also shed new light on the January returns earned by prior "winners" and "losers." Portfolios of losers experience exceptionally large January returns as late as five years after portfolio formation. As ECONOMISTS INTERESTED IN both market behavior and the psychology of individual decision making, we have been struck by the similarity of two sets of empirical findings. Both classes of behavior can be characterized as displaying overreaction. This study was undertaken to investigate the possibility that these phenomena are related by more than just appearance. We begin by describing briefly the individual and market behavior that piqued our interest. The term overreaction carries with it an implicit comparison to some degree of reaction that is considered to be appropriate. What is an appropriate reaction? One class,,of tasks which have a well-established norm are probability revision problems for which Bayes' rule prescribes the correct reaction to new information. It has now been well-established that Bayes' rule is not an apt characterization of how individuals actually respond to new data (Kahneman et al. [14]). In revising their beliefs, individuals tend to overweight recent information and underweight prior (or base rate) data. People seem to make predictions according to a simple matching rule: "The predicted value is selected so that the standing of the case in the distribution of outcomes matches its standing in the distribution of impressions" (Kahneman and Tversky [14, p. 416]). This rule-of-thumb, an instance of what Kahneman and Tversky call the representativeness heuristic, violates the basic statistical principal that the extremeness of predictions must be moderated by considerations of predictability. Grether [12] has replicated this finding under incentive compatible conditions. There is also considerable evidence that the actual expectations of professional security analysts and economic forecasters display the same overreaction bias (for a review, see De Bondt [7]). One of the earliest observations about overreaction in markets was made by J. M. Keynes:"... day-to-day fluctuations in the profits of existing investments,

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TL;DR: Ebsco as mentioned in this paper examines the arbitrage model of capital asset pricing as an alternative to the mean variance pricing model introduced by Sharpe, Lintner and Treynor.

Abstract: Examines the arbitrage model of capital asset pricing as an alternative to the mean variance capital asset pricing model introduced by Sharpe, Lintner and Treynor. Overview of the arbitrage theory; Role of the arbitrage model in explaining phenomena observed in capital markets for risky assets; Influence of the presence of noise on the pricing relation. (Из Ebsco)

6,763 citations