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Most empirical studies of the static CAPM assume that betas remain constant over time and that the return on the value-weighted portfolio of all stocks is a proxy for the return on aggregate wealth. The general consensus is that the static CAPM is unable to explain satisfactorily the cross-section of average returns on stocks. We assume that the CAPM holds in a conditional sense, i.e., betas and the market risk premium vary over time. We include the return on human capital when measuring the return on aggregate wealth. Our specification performs well in explaining the cross-section of average returns.A SUBSTANTIAL PART OF the research effort in finance is directed toward improving our understanding of how investors value risky cash flows. It is generally agreed that investors demand a higher expected return for investment in riskier projects, or securities. However, we still do not fully understand how investors assess the risk of the cash flow on a project and how they determine what risk premium to demand. Several capital asset-pricing models have been suggested in the literature that describe how investors assess risk and value risky cash flows. Among them, the Sharpe-Lintner-Black Capital Asset Pricing Model (CAPM)1 is the one that financial managers use most often for assessing the risk of the cash flow from a project and for arriving at the appropriate * Jagannathan is from thebaugh, as well as with participants at numerous finance workshops in the United States, Canada, and East Asia. Special thanks go to the anonymous referee and the managing editor of the journal for valuable comments. We are grateful to Eugene Fama for providing us with the Fama-French factors and Raymond A. Dragan for editorial assistance. All errors in this paper are the authors' responsibility. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System. Ravi Jagannathan gratefully acknowledges financial support from the National Science Foundation (grant SBR-9409824). Zhenyu Wang gratefully acknowledges financial support from the Alfred P. Sloan Foundation (doctoral dissertation fellowship, grant DD-518). An earlier version of the paper appeared under the title, "The CAPM Is Alive and Well." The compressed archive of the data and the FORTRAN programs used for this paper can be obtained via anonymous FTP at ftp.socsci.umn.edu. The path is outgoing/wang/capm.tar.Z. 1 See Sharpe (1964), Lintner (1965), and Black (1972). 3 4The Journal of Finance discount rate to use in valuing the project. According to the CAPM, (a) the risk of a project is measured by the beta of the cash flow with respect to the return on the market portfolio of all assets in the economy, and (b) the relation between required expected return and beta is linear. Over the past two decades a number of studies have empirically examined the performance of the static version of the CAPM in explaining the crosssection of realized average returns. The results reported in these studies ...

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH‐M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH‐M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility. There is general agreement that investors, within a given time period, require a larger expected return from a security that is riskier. However, there is no such agreement about the relation between risk and return across time. Whether or not investors require a larger risk premium on average for investing in a security during times when the security is more risky remains an open question. At first blush, it may appear that rational risk-averse Most of the support for a zero or positive relation has come from studies that use the standard GARCH-M model of stochastic volatility.2 Other studies, using alternative techniques, have documented a negative relation between expected return and conditional variance. In order to resolve this conflict we examine the possibility that the standard GARCH-M model may not be rich enough to capture the time series properties of the monthly excess return on stocks. We consider a more general specification of the GARCH-M model. In particular, (1) we incorporate dummy variables in the GARCH-M model to capture seasonal effects using the procedure first suggested by Glosten, Jagannathan, and Runkle ( THE TRADEOFF BETWEEN RISK and return has long been an important topic in II. Estimating the Model A. Econometric IssuesThe parameter p in the model given by (2) cannot be estimated without specifying how variances change over time, since Var(xt + 1? Ft) is not directly observed by the econometrician. To appreciate the difficulties involved, project both sides of (2) on Gt, the econometrician's information set, which is a strict subset of the agents' information set Ft. The term on the left in equation (4) Since the estimated slope coefficient cl is a consistent estimate of /3 bl, and d1 provides a consistent estimate of b1, the ratio of any two corresponding elements of cl and d1 provides a consistent estimate of /8. If zt-, is not a scalar, then we may impose the constraint that the slope coefficients in (5) and the slope coefficients in (6) differ only by the scale factor, /3. Such a restriction also provides a natural test for the validity of the model specification. We call this approach Campbell's Instrumental Variable Model. Another approach, the GARCH-M model, assumes that Var(vtllGt_-) is identically zero, and that zt-1 consists of innovations and variances that, while unobservable, can be...

for helpful comments. We thank the editor, Richard Green, and two anonymous referees, for a number of suggestions that have helped us sharpen the focus of the article. We are responsible for any errors or omissions. The views expressed herein are those of the authors and not necessarily those of the National Bureau of Economic Research.