If asset returns have systematic skewness, expected returns should include rewards for accepting this risk. We formalize this intuition with an asset pricing model that incorporates conditional skewness. Our results show that conditional skewness helps explain the cross-sectional variation of expected returns across assets and is significant even when factors based on size and book-to-market are included. Systematic skewness is economically important and commands a risk premium, on average, of 3.60 percent per year. Our results suggest that the momentum effect is related to systematic skewness. The low expected return momentum portfolios have higher skewness than high expected return portfolios. THE SINGLE FACTOR CAPITAL ASSET PRICING MODEL ~CAPM! of Sharpe ~1964! and Lintner ~1965! has come under recent scrutiny. Tests indicate that the crossasset variation in expected returns cannot be explained by the market beta alone. For example, a growing number of studies show that “fundamental” variables such as size, book-to-market value, and price to earnings ratios

This paper explores the ability of conditional versions of the CAPM and the consumption CAPM—jointly the (C)CAPM—to explain the cross section of average stock returns. Central to our approach is the use of the log consumption–wealth ratio as a conditioning variable. We demonstrate that such conditional models perform far better than unconditional specifications and about as well as the Fama-French three-factor model on portfolios sorted by size and book-to-market characteristics. The conditional consumption CAPM can account for the difference in returns between low-book-to-market and high-bookto-market portfolios and exhibits little evidence of residual size or book-to-market effects. We are grateful to Eugene Fama and Kenneth French for graciously providing the

The value premium in U.S. stock returns is robust. The positive relation between average return and book-to-market equity is as strong for 1929 to 1963 as for the subsequent period studied in previous papers. A three-factor risk model explains the value premium better than the hypothesis that the book-tomarket characteristic is compensated irrespective of risk loadings. Firms with high ratios of book value to the market value of common equity have higher average returns than firms with low book-to-market ratios (Rosenberg, Reid, and Lanstein (1985)). Because the capital asset pricing model (CAPM) of Sharpe (1964) and Lintner (1965) does not explain this pattern in average returns, it is typically called an anomaly. There are four common explanations for the book-to-market (BE/ME) anomaly. One says that the positive relation between BE/ME and average return (the so-called value premium) is a chance result unlikely to be observed out of sample (Black (1993), MacKinlay (1995)). Out-of-s...

This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work and on the trade-off between risk and return. Modern research seeks to understand the behavior of the stochastic discount factor ~SDF! that prices all assets in the economy. The behavior of the term structure of real interest rates restricts the conditional mean of the SDF, whereas patterns of risk premia restrict its conditional volatility and factor structure. Stylized facts about interest rates, aggregate stock prices, and cross-sectional patterns in stock returns have stimulated new research on optimal portfolio choice, intertemporal equilibrium models, and behavioral finance. This paper surveys the field of asset pricing. The emphasis is on the interplay between theory and empirical work. Theorists develop models with testable predictions; empirical researchers document “puzzles”—stylized facts that fail to fit established theories—and this stimulates the development of new theories. Such a process is part of the normal development of any science. Asset pricing, like the rest of economics, faces the special challenge that data are generated naturally rather than experimentally, and so researchers cannot control the quantity of data or the random shocks that affect the data. A particularly interesting characteristic of the asset pricing field is that these random shocks are also the subject matter of the theory. As Campbell, Lo, and MacKinlay ~1997, Chap. 1, p. 3! put it: What distinguishes financial economics is the central role that uncertainty plays in both financial theory and its empirical implementation. The starting point for every financial model is the uncertainty facing investors, and the substance of every financial model involves the impact of uncertainty on the behavior of investors and, ultimately, on mar-* Department of Economics, Harvard University, Cambridge, Massachusetts

In this paper we investigate the properties of the standard two-pass methodology of testing beta pricing models with misspecified factors. In a setting where a factor is useless, defined as being independent of all the asse t returns, we provide theoretical results and simulation evidence that the second-pass cross-sectional regression tends to find the beta risk of the useless factor priced more often than it should. More surprisingly, this misspecification bias exacerbates when the number of time series observations increases. Possible ways of detecting useless factors are also examined. When testing asset pricing models relating risk premiums on assets to their betas, the primary question of interest is whether the beta risk of a particular factor is priced (i.e., whether the estimated risk premium associated with a given factor is significantly di#erent from zero). Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) develop a two-pass methodology in which the beta of each asset with respect to a factor is estimated in a first-pass time series regression, and estimated betas are then used in second-pass cross-sectional regressions (CSRs) to estimate the risk premium of the factor. This two-pass methodology is very intuitive and has been widely used in the literature. The properties of the test statistics and goodness-of-fit measures under the two-pass methodology are usually developed under the assumptions that the asset pricing model is correctly specified and that the factors are correctly identified. Shanken (1992) provides an excellent discussion of this two-pass methodology, especially the large sample properties of the two-pass CSR for the correctly specified model under the assumption that returns are conditionally homoskedastic. Jagannathan and Wa...

This paper investigates the efficiency of household investment decisions in a unique dataset containing the disaggregated wealth and income of the entire population of Sweden. The analysis focuses on two main sources of inefficiency in the financial portfolio: underdiversification of risky assets (“down”) and nonparticipation in risky asset markets (“out”). We find that while a few households are very poorly diversified, the cost of diversification mistakes is quite modest for most of the population. For instance, a majority of participating Swedish households are sufficiently diversified internationally to outperform the Sharpe ratio of their domestic stock market. We document that households with greater financial sophistication tend to invest more efficiently but also more aggressively, so the welfare cost of portfolio inefficiency tends to be greater for these households. The welfare cost of nonparticipation is smaller by almost one half when we take account of the fact that nonparticipants would be unlikely to invest efficientlyiftheyparticipatedinrisky asset markets.

An integrated econometric view of maximum likelihood methods and more traditional two-pass approaches to estimating beta-pricing models is presented. Several aspects of the well-known “errors-in-variables problem ” are considered, and an earlier conjecture concerning the merits of simultaneous estimation of beta and price of risk parameters is evaluated. The traditional inference procedure is found, under standard assumptions, to overstate the precision of price of risk estimates and an asymptotically valid correction is derived. Modifications to accommodate serial correlation in market-wide factors are also discussed Sharpe (1964) and Lintner (1965) demonstrate that, in equilibrium, a financial asset’s expected return must be positively linearly related to its “beta, ” a measure of systematic risk or co-movement with the market portfolio return: 1 This article is an extension of the second chapter of my doctoral dissertation at Carnegie Mellon University. Recent versions were presented in seminars

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.

In this paper, we point out that the widely used stochastic discount factor (SDF) methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology.

We test the mean-variance efficiency of a given portfolio using a Bayesian framework. Our test is more direct than Shanken's (1987b), because we impose a prior on all the parameters of the multivariate regression model. The approach is also easily adapted to other problems. We use Monte Carlo numerical integration to accurately evaluate 9O-dimensional integrals. Posteriorodds ratios are calculated for 12 industry portfolios from 1926-1987. The sensitivity of the inferences to the prior is investigated by using three different distributions. The probability that the given portfolio is mean-variance efficient is small for a range of plausible priors.