Lisa A. Kramer

Winter Blues: A SAD Stock Market Cycle

This paper investigates the role of seasonal affective disorder (SAD) in the seasonal time-variation of stock market returns. SAD is an extensively documented medical condition whereby the shortness of the days in fall and winter leads to depression for many people. Experimental research in psychology and economics indicates that depression, in turn, causes heightened risk aversion. Building on these links between the length of day, depression, and risk aversion, we provide international evidence that stock market returns vary seasonally with the length of the day, a result we call the SAD effect. Using data from numerous stock exchanges and controlling for well-known market seasonals as well as other environmental factors, stock returns are shown to be significantly related to the amount of daylight through the fall and winter. Patterns at different latitudes and in both hemispheres provide compelling evidence of a link between seasonal depression and seasonal variation in stock returns: Higher latitude markets show more pronounced SAD effects and results in the Southern Hemisphere are six months out of phase, as are the seasons. Overall, the economic magnitude of the SAD effect is large.

This is Your Portfolio on Winter: Seasonal Affective Disorder and Risk Aversion in Financial Decision Making

This study found that people who suffer from seasonal affective disorder (SAD) displayed financial risk aversion that varied across the seasons as a function of seasonally changing affect. The SAD-sufferers had significantly stronger preferences for safe choices during the winter than non-SAD-sufferers, and they did not differ from non-SAD-sufferers during the summer. The effect of SAD on risk aversion in the winter was mediated by depression.

Seasonally Varying Preferences: Theoretical Foundations for an Empirical Regularity

We investigate an asset pricing model with preferences cycling between high risk aversion and low EIS in fall/winter and the reverse in spring/summer. Calibrating to consumption data and allowing plausible preference parameter values, we produce returns that match observed equity and Treasury returns across the seasons: risky returns are higher and risk-free returns are lower or stable in fall/winter, and they reverse in spring/summer. Further, risky returns vary more than risk-free returns. A novel finding is that both EIS and risk aversion must vary seasonally to match observed returns. Further, the degree of necessary seasonal change in EIS is small.

Opposing Seasonalities in Treasury Versus Equity Returns

We demonstrate a novel and striking annual cycle in the US Treasury market, with a variation of over 80 basis points from peak to trough in monthly returns. The Treasury return seasonal pattern is opposite to that evident in equity returns, and the opposing patterns are not due to unconditional negative correlation between Treasury and stock returns. We show that the seasonal Treasury and equity return patterns are unlikely to arise from macroeconomic seasonalities, seasonal variation in risk, cross-hedging between equity and Treasury markets, investor sentiment, seasonalities in the Treasury market auction schedule, seasonalities in the Treasury debt supply, seasonalities in the FOMC cycle, or peculiarities of the sample period considered. The seasonal cycles become more pronounced during periods of high market volatility, consistent with the notion that the seasonal cycles are a result of time-varying risk aversion among market participants. The seasonal patterns in equity and Treasury returns are coincident with the incidence of seasonal depression observed clinically in North American populations, and depression has been shown to be associated with reduced risk tolerance. The White (2000) reality test confirms that the correlation between returns and the clinical incidence of seasonal depression cannot be easily dismissed as the simple result of data snooping. Our findings are all the more remarkable given that it is expert traders who dominate the Treasury market.

Estimating the Equity Premium

Existing empirical research investigating the size of the equity premium has largely consisted of a series of innovations around a common theme: producing a better estimate of the equity premium by using better data or a better estimation technique. The equity premium estimate that emerges from most of this work matches one moment of the data alone: the mean difference between an estimate of the return to holding equity and a risk-free rate. We instead match multiple moments of U.S. market data, exploiting the joint distribution of the dividend yield, return volatility, and realized excess returns, and find that the equity premium lies within 50 basis points of 3.5%, a range much narrower than was achieved in previous studies. Additionally, statistical tests based on the joint distribution of these moments reveal that only those models of the conditional equity premium that embed time variation, breaks, and/or trends are supported by the data. In order to develop the joint distribution of the dividend yield, return volatility, and excess returns, we need a model of price and return fundamentals. We document that even recently developed analytically tractable models that permit autocorrelated dividend growth rates and discount rates impose restrictions that are rejected by the data. We therefore turn to a wider range of models, requiring numerical solution methods and parameter estimation by the simulated method of moments.

Effects of daylight-saving time changes on stock market volatility: a comment.

In a recent article in this journal, Berument, Dogan, and Onar (2010) challenged the existence of the previously documented daylight-saving effect. Kamstra, Kramer, and Levis original finding (2000) was that average stock market returns on Mondays following time changes are economically and statistically significantly lower than typical Monday returns. Kamstra, et al. hypothesized that the effect may arise due to heightened anxiety or risk aversion on the part of market participants after they experience a 1-hr. disruption in their sleep habits, in accordance with prior findings in the psychology literature linking sleep desynchronosis with anxiety. Berument, et al. replicated the original findings using ordinary least squares estimation, but when they modeled the mean of returns using a method prone to producing biased estimates, they obtained puzzling results. The analysis here, based on standard, unbiased modeling techniques, shows that the daylight-saving effect remains intact in the U.S.

Effects of Daylight-Saving Time Changes on Stock Market Returns and Stock Market Volatility: Rebuttal

In a 2011 reply to our 2010 comment in this journal, Berument and Dogen maintained their challenge to the existence of the negative daylight-saving effect in stock returns reported by Kamstra, Kramer, and Levi in 2000. Unfortunately, in their reply, Berument and Dogen ignored all of the points raised in the comment, failing even to cite the Kamstra, et al. comment. Berument and Dogen continued to use inappropriate estimation techniques, over-parameterized models, and low-power tests and perhaps most surprisingly even failed to replicate results they themselves reported in their previous paper, written by Berument, Dogen, and Onar in 2010. The findings reported by Berument and Dogen, as well as by Berument, Dogen, and Onar, are neither well-supported nor well-reasoned. We maintain our original objections to their analysis, highlight new serious empirical and theoretical problems, and emphasize that there remains statistically significant evidence of an economically large negative daylight-saving effect in U.S. stock returns. The issues raised in this rebuttal extend beyond the daylight-saving effect itself, touching on methodological points that arise more generally when deciding how to model financial returns data.