Knowledge of the one‐month interest rate is useful in forecasting the sign as well as the variance of the excess return on stocks. The services of a portfolio manager who makes use of the forecasting model to shift funds between bills and stocks would be worth an annual management fee of 2% of the value of the assets managed. During 1954:4 to 1986:12, the variance of monthly returns on the managed portfolio was about 60% of the variance of the returns on the value weighted index, whereas the average return was two basis points higher.

We present evidence consistent with operational constraints leading firms to use high discount rates that average twice the firms’ cost of financial capital. Based on a survey of Chief Financial Officers matched to archival data, we find that firms with abundant access to capital but limited qualified management or manpower appear to forgo profitable projects in preparation for more profitable future investment opportunities. Consistent with this explanation, firms that use high discount rates have strong balance sheets, low leverage, and large cash holdings. In addition, firms appear to increase discount rates to account for idiosyncratic risk.

We present a latent variable model of dividends that predicts, out‐of‐sample, 39.5% to 41.3% of the variation in annual dividend growth rates between 1975 and 2016. Further, when learning about dividend dynamics is incorporated into a long‐run risks model, the model predicts, out‐of‐sample, 25.3% to 27.1% of the variation in annual stock index returns over the same time horizon, with learning contributing approximately half of the predictability in returns. These findings support the view that investors' aversion to long‐run risks and their learning about these risks are important in determining stock index prices and expected returns.

The stochastic discount factor (SDF) method provides a unified general framework for econometric analysis of asset‐pricing models. There have been concerns that, compared to the classical beta method, the generality of the SDF method comes at the cost of efficiency in parameter estimation and power in specification tests. We establish the correct framework for comparing the two methods and show that the SDF method is as efficient as the beta method for estimating risk premiums. Also, the specification test based on the SDF method is as powerful as the one based on the beta method.

Without the assumption of conditional homoskedasticity, a general asymptotic distribution theory for the two‐stage cross‐sectional regression method shows that the standard errors produced by the Fama–MacBeth procedure do not necessarily overstate the precision of the risk premium estimates. When factors are misspecified, estimators for risk premiums can be biased, and the t ‐value of a premium may converge to infinity in probability even when the true premium is zero. However, when a beta‐pricing model is misspecified, the t ‐values for firm characteristics generally converge to infinity in probability, which supports the use of firm characteristics in cross‐sectional regressions for detecting model misspecification.

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.

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.

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.