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

Industry costs of equity

SEQUELS ARE RARELY AS good as the originals, so I approach this review of the market efficiency literature with trepidation. The task is thornier than it was 20 years ago, when work on efficiency was rather new. The literature is now so large that a full review is impossible, and is not attempted here. Instead, I discuss the work that I find most interesting, and I offer my views on what we have learned from the research on market efficiency.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1540-6261.1991.tb04636.x

Efficient Capital Markets: II

ARCH modeling in finance: A review of the theory and empirical evidence

This study investigates whether marketwide liquidity is a state variable important for asset pricing. We find that expected stock returns are related cross-sectionally to the sensitivities of returns to fluctuations in aggregate liquidity. Our monthly liquidity measure, an average of individual-stock measures estimated with daily data, relies on the principle that order flow induces greater return reversals when liquidity is lower. From 1966 through 1999, the average return on stocks with high sensitivities to liquidity exceeds that for stocks with low sensitivities by 7.5 percent annually, adjusted for exposures to the market return as well as size, value, and momentum factors. Furthermore, a liquidity risk factor accounts for half of the profits to a momentum strategy over the same 34-year period.

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Liquidity Risk and Expected Stock Returns

Sample evidence about the predictability of monthly stock returns is considered from the perspective of an investor allocating funds between stocks and cash. A regression of stock returns on a set of predictive variables might seem weak when described by usual statistical measures, but such measures can fail to convey the economic significance of the sample evidence when it is used by a risk-averse Bayesian investor to update prior beliefs about the regression relation and to compute an optimal asset allocation. Even when those prior beliefs are weighted substantially against predictability, the current values of the predictive variables can exert a strong influence on the portfolio decision.

On the Predictability of Stock Returns: An Asset-Allocation Perspective

The authors propose a likelihood-ratio test of the hypothesis that the minimum-variance frontier of a set of K assets coincides with the frontier of this set and another set of N assets. They study the relation between this hypothesis, exact arbitrage pricing, and mutual fund separation. The exact distribution of the test statistic is available. The authors test the hypothesis that the frontier spanned by three size-sorted stock portfolios is the same as the frontier spanned by thirty-three size-sorted stock portfolios. INVESTORS' CHOICES OF PORTFOLIOS of assets and the implications of these choices for assets' prices are major topics in financial economics. Students of the first topic-portfolio theory-often strive to derive separation results, i.e., seek conditions under which each investor allocates all of his or her savings among a small number of separating funds. These separating funds are the same across investors. The second topic entails a study of the aggregate behavior of security market participants. Students of the pricing issues derive equilibrium restrictions on security prices. We focus on the relations among mean-variance efficiency, mutual fund separation, and two prominent security-pricing models in finance: the CAPM and the APT. The investment universe under consideration includes K + N risky assets with returns that have a nonsingular covariance matrix. In addition, it may include a risk-free asset. We are particularly interested in forming K portfolios of the N + K original assets and then studying the relation between the minimum-variance frontier spanned by the K derived assets and the frontier of the original N + K

Mean-Variance Spanning

Sample evidence about the predictability of monthly stock returns is considered from the perspective of a risk-averse Bayesian investor who must allocate funds between stocks and cash. The investor uses the sample evidence to update prior beliefs about the parameters in a regression of stock returns on a set of predictive variables. The regression relation can seem weak when described by usual statistical measures, but the current values of the predictive variables can exert a substantial influence on the investor's portfolio decision, even when the investor's prior beliefs are weighted against predictability. INVESTORS IN THE STOCK market are interested in predicting future stock returns, and the academic literature offers numerous empirical investigations of stockreturn predictability. Many of these investigations report the results of estimating linear time-series regressions of stock returns on one or more predictive variables, and considerable effort has been devoted to assessing the strength and reliability of this regression evidence from a statistical perspective. Given that the regression coefficients are estimated with error, confronting the investor with what is commonly termed "estimation risk," to what extent might the regression evidence influence a rational, risk-averse investor's portfolio decision? Consider an investor who, on December 31, 1993, must allocate funds between the value-weighted portfolio of the New York Stock Exchange (NYSE) and one-month Treasury bills. The investor is given the results of estimating the following regression using monthly data from January 1927 through December 1993,

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The authors find that conditional means and variances of consumption growth vary through time, and this variation appears to be associated with the business cycle. A pricing model with fluctuating means and variances of consumption growth provides implications about conditional moments of returns for both short and long investment horizons, and these implications are explored empirically. The U-shaped pattern of first-order autocorrelations of returns, as well as business cycle patterns in the price of risk, appears to be consistent with the model, but the authors' exploration suggests that other implications about conditional return moments are at odds with the data. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

/pdf/expectations-and-volatility-of-consumption-and-asset-returns-qhztk9p5za.pdf

Expectations and Volatility of Consumption and Asset Returns

https://www.nber.org/system/files/working_papers/w3633/w3633.pdf

Shmuel Kandel

Papers

On the Predictability of Stock Returns: An Asset-Allocation Perspective

Mean-Variance Spanning

On the Predictability of Stock Returns: An Asset-Allocation Perspective

Expectations and Volatility of Consumption and Asset Returns

Asset Returns and Intertemporal Preferences