This paper proposes a measure of ex ante equity premium, IPOFDR, which is the average difference between the initial public offering (IPO) offer price and the 1st-trading-day close price. I test the idea in 3 ways. First, there is a positive relation between IPOFDR and future market returns. Second, changes in IPOFDR help explain the cross section of stock returns. Third, the predictive power of IPOFDR for stock returns reflects mainly its close relation with market variance and average idiosyncratic variance—arguably measures of systematic risk. These results cast doubt on the notion that the IPO 1st-day return is a measure of investor sentiment.

This paper presents a consumption-based model that explains the equity premium puzzle through two channels. First, because of borrowing constraints, the shareholder cannot completely diversify his income risk and requires a sizable risk premium on stocks. Second, because of limited stock market participation, the precautionary saving demand lowers the risk-free rate but not stock return and generates a substantial liquidity premium. This model also replicates many other salient features of the data, including the first two moments of the risk-free rate, excess stock volatility, stock return predictability, and the unstable relation between stock volatility and the dividend yield.

A spurious positive relation between exponential generalized autoregressive conditional heteroskedasticity (EGARCH) estimates of expected month t idiosyncratic volatility and month t stock returns arises when the month t return is included in estimation of model parameters. We illustrate via simulations that this look-ahead bias is problematic for empirically observed degrees of stock return skewness and typical monthly return time series lengths. Moreover, the empirical idiosyncratic risk-return relation becomes negligible when expected month t idiosyncratic volatility is estimated using returns only up to month t − 1.

We model conditional market beta and alpha as flexible functions of state variables identified via a formal variable-selection procedure. In the post-1963 sample, the beta of the value premium comoves strongly with unemployment, inflation, and the price–earnings ratio in a countercyclical manner. We also uncover a novel nonlinear dependence of alpha on business conditions: It falls sharply and even becomes negative during severe economic downturns but is positive and flat otherwise. The conditional capital asset pricing model (CAPM) performs better than the unconditional CAPM, but this does not fully explain the value premium. Our findings are consistent with a conditional CAPM with rare disasters.