We propose a duration-based explanation for the premia on major equity factors, including value, profitability, investment, low-risk, and payout factors. These factors invest in firms that earn most of their cash flows in the near future and could therefore be driven by a premium on near-future cash flows. We test this hypothesis using a novel dataset of single-stock dividend futures, which are claims on dividends of individual firms. Consistent with our hypothesis, the expected CAPM alpha on individual cash flows decrease in maturity within a firm, and the alpha is not related to the above characteristics when controlling for maturity.

Heteroskedasticity and autocorrelation-robust (HAR) inference in time series regression typically involves kernel estimation of the long-run variance. Conventional wisdom holds that, for a given kernel, the choice of truncation parameter trades off a test’s null rejection rate and power, and that this tradeoff differs across kernels. We formalize this intuition: using higher-order expansions, we provide a unified size-power frontier for both kernel and weighted orthonormal series tests using nonstandard “fixed-b” critical values. We also provide a frontier for the subset of these tests for which the fixed-b distribution is t or F. These frontiers are respectively achieved by the QS kernel and equal-weighted periodogram. The frontiers have simple closed-form expressions, which upon evaluation show that the price paid for restricting attention to tests with t and F critical values is small. The frontiers are derived for the Gaussian multivariate location model, but simulations suggest the qualitative findings extend to stochastic regressors.

The classic papers by Newey and West (1987) and Andrews (1991) spurred a large body of work on how to improve heteroscedasticity- and autocorrelation-robust (HAR) inference in time-series regression. This literature finds that using a larger-than-usual truncation parameter to estimate the long-run variance, combined with Kiefer–Vogelsang (2002, 2005) fixed-b critical values, can substantially reduce size distortions, at only a modest cost in (size-adjusted) power. Empirical practice, however, has not kept up. This article therefore draws on the post-Newey–West/Andrews literature to make concrete recommendations for HAR inference. We derive truncation parameter rules that choose a point on the size-power tradeoff to minimize a loss function. If Newey–West tests are used, we recommend the truncation parameter rule S = 1.3T^1/2 and (nonstandard) fixed-b critical values. For tests of a single restriction, we find advantages to using the equal-weighted cosine (EWC) test, where the long run variance is estimated by projections onto Type-II cosines, using ν = 0.4T^2/3 cosine terms; for this test, fixed-b critical values are, conveniently, t_ν or F. We assess these rules using first an ARMA/GARCH Monte Carlo design, then a dynamic factor model design estimated using 207 quarterly U.S. macroeconomic time series.

In recalling a list of previously experienced items, participants are known to organize their responses on the basis of the items’ semantic and temporal similarities. Here, we examine how spatial information influences the organization of responses in free recall. In Experiment 1, participants studied and subsequently recalled lists of landmarks. In Experiment 2, participants played a game in which they delivered objects to landmarks in a virtual environment and later recalled the delivered objects. Participants in both experiments were simply asked to recall as many items as they could remember in any order. By analyzing the conditional probabilities of recall transitions, we demonstrate strong spatial and temporal organization of studied items in both experiments.

We study how overreaction and underreaction to signals depend on their informativeness. While a large literature has studied belief updating in response to highly informative signals, people in important real-world settings are often faced with a steady stream of weak signals. We use a tightly controlled experiment and new empirical evidence from betting and financial markets to demonstrate that updating behavior differs meaningfully by signal strength: across domains, our consistent and robust finding is overreaction to weak signals and underreaction to strong signals. Both sets of results align well with a simple theory of cognitive imprecision about signal informativeness. Our framework and findings can help harmonize apparently contradictory results from the experimental and empirical literatures.

We derive new bounds on the rational variation in asset prices over time. The resulting test requires no proxy for fundamental value, and it allows significantly more flexibility in preferences and discount rates than in standard volatility tests. We gain traction by focusing specifically on risk-neutral beliefs implied by option prices. While risk preferences distort prices away from subjective beliefs, one can nonetheless bound risk-neutral belief movement under a general assumption on the stochastic discount factor. Implementing our test empirically using index options, we find that there is so much movement in risk-neutral beliefs that the bounds are routinely violated.

We test whether the market has intertemporally consistent expectations about the log equity premium. We use option prices to estimate the expected future equity premium (the forward rate) and compare this to the equity premium estimated in the future (future spot rate). Forward rates are strong predictors of future spot rates, suggesting that the market qualitatively understands variation in the equity premium. The market does, however, make predictable and quantitatively significant forecast errors. To match the data, we propose a model in which an increase in the equity premium causes investors to overestimate the future equity premium.

I present evidence from index options that the price of risk over the value of the S&P 500 increases as the investment horizon becomes shorter. I show first how these risk prices may be estimated from the data, by translating the risk-neutral probabilities implied by options prices into physical probabilities that must provide unbiased forecasts of the terminal outcome. The risk price can be interpreted as the marginal investor’s effective risk aversion, and estimating this value over different option-expiration horizons for the S&P, I find that risk aversion is reliably higher for near-term outcomes than for longer-term outcomes: the market’s relative risk aversion over terminal index values decreases from around 15 at a one-week horizon to around 3 at a 12-week horizon. It is difficult to reconcile these findings with leading asset-pricing models, and I discuss necessary conditions for any such rational model to produce such a pattern. Models with dynamically inconsistent risk preferences, however, are capable of straightforwardly producing the findings presented here, and I discuss possible specifications of such models and their applicability to related results from previous literature.