REVISION: Time Variation of the Equity Term Structure
I document that the term structure of holding-period equity returns is counter-cyclical: it is downward sloping in good times, but upward sloping in bad times. The counter-cyclical variation is consistent with theories of long-run risk and habit, but these theories cannot explain the average downward slope. At the same time, the cyclical variation is inconsistent with recent models constructed to match the average downward slope. More generally, any one-factor model will fail to explain both the average downward slope and the counter-cyclical variation. I therefore introduce a new model with two priced risk factors to solve the puzzle.
New: Duration-Driven Returns
We propose a duration-based explanation for the return to major equity risk factors, including value, profitability, investment, low risk, and payout factors. Both in the US and globally, firms with high expected returns predicted by these factors also have a short cash-flow duration, meaning that these firms are expected to earn most of their cash flows in the near future. The returns to the factors can thus be explained by a simple model where near-future cash flows have high risk- adjusted returns, which is consistent with the evidence on the equity term structure. We find evidence for such a model using a novel dataset of single-stock dividend futures that allow us to study fixed-maturity equity claims for a cross-section of firms.
REVISION: Higher-Moment Risk
We estimate and analyze the ex ante higher order moments of stock market returns. We document that even and odd higher-order moments are strongly negatively correlated, creating periods where the return distribution is riskier because it is more left-skewed and fat tailed. Such higher-moment risk is negatively correlated with variance and past returns, meaning that it peaks during calm periods. The variation in higher-moment risk is large and causes the probability of a two-sigma loss on the market portfolio to vary from 3.3% to 11% percent over the sample, peaking in calm periods such as just before the onset of the financial crisis. In addition, we argue that an increase in higher- moment risk works as an "uncertainty shock" that deters firms from investing. Consistent with this argument, more higher-moment risk predicts lower future industrial production.
REVISION: Conditional Risk
We show theoretically that the required compensation for time-varying betas in the CAPM can be estimated by a precisely defined conditional-risk factor, which can be used in factor regressions. Both in the U.S. and global sample covering 23 countries, all major equity risk factors load on our conditional-risk factor, meaning that their market betas vary over time and that this variation explains part of their average returns. Studying the economic drivers of these results, we find evidence that this conditional risk arises from variation in discount rate betas (not cash flow betas) due to the endogenous effects of arbitrage trading.
REVISION: Betting Against Correlation: Testing Theories of the Low-Risk Effect
We test whether the low-risk effect is driven by (a) leverage constraints and thus risk should be measured using beta vs. (b) behavioral effects and thus risk should be measured by idiosyncratic risk. Beta depends on volatility and correlation, where only volatility is related to idiosyncratic risk. We introduce a new betting against correlation (BAC) factor that is particularly suited to differentiate between leverage constraints vs. lottery explanations. BAC produces strong performance in the US and internationally, supporting leverage constraint theories. Similarly, we construct the new factor SMAX to isolate lottery demand, which also produces positive returns. Consistent with both leverage and lottery theories contributing to the low-risk effect, we find that BAC is related to margin debt while idiosyncratic risk factors are related to sentiment.