This paper develops and estimates a heteroskedastic variant of Campbell’s [Campbell, J., 1993. Intertemporal asset pricing without consumption data. American Economic Review 83, 487–512] ICAPM, in which risk factors include a stock market return and variables forecasting stock market returns or variance. Our main innovation is the use of a new set of predictive variables, which not only have superior forecasting abilities for stock returns and variance, but also are theoretically motivated. In contrast with the early authors, we find that Campbell’s ICAPM performs significantly better than the CAPM. That is, the additional factors account for a substantial portion of the two CAPM-related anomalies, namely, the value premium and the momentum profit.

Consistent with the post-1962 US evidence by Ang et al. [Ang, A., Hodrick, R., Xing Y., Zhang, X., 2006. The cross-section of volatility and expected returns. Journal of Finance 51, 259–299], we find that stocks with high idiosyncratic variance (IV) have low CAPM-adjusted expected returns in both pre-1962 US and modern G7 data. We also test in three ways the conjecture that IV is a proxy of systematic risk. First, the return difference between low and high IV stocks – that we dub as IVF – is a priced factor in the cross-section of stock returns. Second, loadings on lagged market variance and lagged average IV account for a significant portion of variation in average returns on portfolios sorted by IV. Third, the variance of IVF correlates closely with average IV, and the two variables have similar explanatory power for the time-series and cross-sectional stock returns.

Average idiosyncratic stock volatility forecasts the bilateral exchange rates of the US dollar against major foreign currencies in and out of sample. The US dollar tends to appreciate after an increase in US idiosyncratic volatility. Similarly, ceteris paribus, German and Japanese idiosyncratic volatilities positively and significantly correlate with future US dollar prices of the Deutsche mark and the Japanese yen, respectively. Our results suggest that exchange rates are predictable.

The aggregate default probability is significantly priced in equities because of its close relation with uncertainty. Ceteris paribus, the aggregate default probability positively predicts stock market returns, and loadings on its changes correlate negatively with the cross-section of expected stock returns. These findings are consistent with multifactor models in which aggregate uncertainty is a determinant of the conditional equity premium and innovations in aggregate uncertainty are a systematic risk factor. By contrast, credit spreads have negligible explanatory power for expected stock returns. Contrary to the conventional wisdom, credit spreads are poor proxies for aggregate credit risk.

Using options-implied variance, a forward-looking measure of conditional variance, we revisit the debate on the idiosyncratic risk-return relation. In both cross-sectional (for individual stocks) and time-series (for the market index) regressions, we find a negative relation between options-implied variance and future stock returns. Consistent with Miller’s (1977) divergence of opinion hypothesis, the negative relation gets stronger (1) for stocks with more stringent short-sale constraints or (2) when shorting stocks becomes more difficult. Moreover, the negative correlation of realized idiosyncratic variance or analyst forecast dispersion with future stock returns mainly reflects their close correlation with our conditional idiosyncratic variance measure.

We investigate the relative importance of various bankruptcy predictors commonly used in the existing literature by applying a variable selection technique, the least absolute shrinkage and selection operator (LASSO), to a comprehensive bankruptcy database. Over the 1980–2009 period, LASSO admits the majority of Campbell et al. (2008) predictive variables into the bankruptcy forecast model. Interestingly, by contrast with recent studies, some financial ratios constructed from only accounting data also contain significant incremental information about future default risk, and their importance relative to that of market-based variables in bankruptcy forecasts increases with prediction horizons. Moreover, LASSO-selected variables have superior out-of-sample predictive power and outperform (1) those advocated by Campbell et al. (2008) and (2) the distance to default from Merton’s (1974) structural model.