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Abstract:
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.

stock returns, seasonality, behavioral finance, seasonal affective disorder, SAD, depression

Abstract:
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.

Stock returns, seasonality, behavioral finance, seasonal affective disorder, SAD, depression

Abstract:
A variety of test statistics have been employed in the finance and accounting literatures for the purpose of conducting hypothesis tests in event studies. This paper begins by formally deriving the result that these statistics do not follow their conventionally assumed asymptotic distribution even for large samples of firms. Test statistics exhibit a statistically significant bias to size in practice, a result that I document extensively. This bias arises partially due to commonly observed stock return traits which violate conditions underlying event study methods. In this paper, I develop two alternatives. The first involves a simple normalization of conventional test statistics and allows for the statistics to follow an asymptotic standard normal distribution. The second approach augments the simple normalization with bootstrap resampling. These alternatives demonstrate remarkable robustness to heteroskedasticity, autocorrelation, non-normality, and event-period model changes, even in small samples.

Abstract:
A variety of test statistics have been employed in the finance and accounting literatures for the purpose of conducting hypothesis tests in event studies. This paper begins by formally deriving the result that these statistics do not follow their conventionally assumed asymptotic distribution even for large samples of firms. Test statistics exhibit a statistically significant bias to size in practice, a result that I document extensively. This bias arises partially due to commonly observed stock return traits which violate conditions underlying event study methods. In this paper, I develop two alternatives. The first involves a simple normalization of conventional test statistics and allows for the statistics to follow an asymptotic standard normal distribution. The second approach augments the simple normalization with bootstrap resampling. These alternatives demonstrate remarkable robustness to heteroskedasticity, autocorrelation, non-normality, and event-period model changes, even in small samples, and they are useful for event studies with non-clustered events.

Abstract:
We explore the connection between equity returns and sleep disruptions following daylight-savings time changes. In international markets, the average Friday-to-Monday return on daylight-savings weekends is markedly lower than expected, with a magnitude 200 to 500 percent larger than the average negative return for other weekends of the year. This "daylight-savings anomaly" in financial markets is consistent with desynchronosis research which has identified the effects of changes in sleep patterns on judgment, anxiety, reaction time, problem solving and accidents. This paper suggests sleep effects of daylight-savings time changes may be impacting market participants internationally.

Abstract:
We explore the connection between equity returns and sleep disruptions following daylight-savings time changes. In international markets, the average Friday-to-Monday return on daylight-savings weekends is markedly lower than expected, with a magnitude 200 to 500 percent larger than the average negative return for other weekends of the year. This ``daylight-savings anomaly'' in financial markets is consistent with desynchronosis research which has identified the effects of changes in sleep patterns on judgment, anxiety, reaction time, problem solving and accidents. This paper suggests sleep effects of daylight-savings time changes may be impacting market participants internationally.

Abstract:
Previous papers on intraday and interday stock transactions have documented a variety of systematic patterns in spreads, volumes, returns, and returns volatility. Several theoretical models have also been proposed to explain the observed patterns, but none have fully explained the movement of returns during the course of the day. In this paper, I consider a mechanism by which intraday returns may vary in a systematic manner as a result of behavioral factors rooted in the psychology of depression. By surveying past studies in finance, I find evidence consistent with a close relationship between intradaily variation in human sentiment and patterns in intraday stock returns. In exploring this explanation, I find hourly returns do not follow the U-shaped pattern conventionally believed to hold for intraday returns. Instead, I find returns in the morning significantly exceed those in the afternoon across a variety of time periods and datasets, a novel discovery consistent with the behavioral explanation of returns.

Intraday stock returns, behavioral finance

Abstract:
Previous research has documented robust links between seasonal variation in length of day, seasonal depression (known as seasonal affective disorder, or SAD), risk aversion, and stock market returns. The influence of SAD on market returns, known as the SAD effect, is large. We study the SAD effect in the context of an equilibrium asset pricing model to determine whether the seasonality can be explained using a conditional version of the CAPM that allows the price of risk to vary over time. Using daily and monthly data for the US, Sweden, New Zealand, the UK, Japan, and Australia, we find that a conditional CAPM that allows the price of risk to vary in relation to seasonal variation in the length of day fully captures the SAD effect. This is consistent with the notion that the SAD effect arises due to the heightened risk aversion that comes with seasonal depression, reflected by a changing risk premium.

Stock market seasonality, conditional CAPM, time-varying risk aversion, behavioral finance, seasonal affective disorder

Abstract:
Previous research has documented robust links between seasonal variation in length of day, seasonal depression (known as seasonal affective disorder, or SAD), risk aversion, and stock market returns. The influence of SAD on market returns, known as the SAD effect, is large. We study the SAD effect in the context of an equilibrium asset pricing model to determine whether the seasonality can be explained using a conditional version of the CAPM that allows the price of risk to vary over time. Using daily and monthly data for the US, Sweden, New Zealand, the UK, Japan, and Australia, we find that a conditional CAPM that allows the price of risk to vary in relation to seasonal variation in the length of day fully captures the SAD effect. This is consistent with the notion that the SAD effect arises due to the heightened risk aversion that comes with seasonal depression, reflected by a changing risk premium.

stock market seasonality, Conditional CAPM, time-varying risk aversion, behavioral finance, Seasonal Affective Disorder

Abstract:
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 US 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 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 which 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 Simulated Method of Moments.

equity risk premium, simulated method of moments, SMM

Abstract:
Seasonal variation in bid-ask spreads, as well as variation conditional on inventory cost changes, adverse selection events, and competition among market makers, have been extensively documented in past studies. We contribute to the spreads literature by examining the extent to which spreads are influenced by a seasonal factor that has been shown to pervasively influence aspects of capital markets as varied as stock returns, bond returns, and mutual fund flows. Previous studies show these different facets of financial markets exhibit seasonal patterns related to seasonal depression (known as SAD, or seasonal affective disorder). The mechanism by which this medical condition influences financial markets is through the extensively documented connection between seasonality in the number of hours of daylight and depression, and through the experimentally validated link between depression and risk aversion. We explore the impact of seasonal depression on the inside spread of NASDAQ firms in the context of multiple heterogeneous market makers. We also consider more restrictive cases, including multiple homogeneous market makers, and a single market maker. We find theoretical and empirical results consistent with SAD having a narrowing influence on the inside spread during the fall and winter. The full extent of this narrowing amounts to 350 basis points for an equal-weighted index of NASDAQ firms and 20 basis points for a value-weighted index, which is substantial given average spreads are about 570 and 170 basis points respectively in the equal- and value-weighted indices. Consistent with prior research, we find that spreads are at their widest at year-end. However, without the narrowing influence of SAD, year-end spreads would be much wider still. Researchers wishing to model inside spreads, say to ascertain empirically the impact of adverse selection relative to inventory costs, monopoly power, or other considerations, need to be mindful of this strong seasonal, as does any market participant who has discretion in the timing of her trades.

Stock returns, time-varying risk aversion, seasonal affective disorder, depression, behavioral finance

Abstract:
The equity premium of interest in theoretical models is the extra return investors anticipate when purchasing risky stock instead of risk-free debt. Unfortunately, we do not observe this ex ante premium in the data; we only observe the returns that investors actually receive ex post, after they purchase the stock and hold it over some period of time during which random economic shocks affect prices. Over the past century U.S. stocks have returned roughly 6 percent more than risk-free debt, which is higher than warranted by standard economic theory; hence the "equity premium puzzle." In this paper we devise a method to simulate the distribution from which ex post equity premia are drawn, conditional on various assumptions about investors' ex ante equity premium. Comparing statistics that arise from our simulations with key financial characteristics of the U.S. economy, including dividend yields, Sharpe ratios, and interest rates, suggests a much narrower range of plausible equity premia than has been supported to date. Our results imply that the true ex ante equity premium likely lies very close to 4 percent.

equity risk premium, equity premium puzzle, Monte Carlo simulation

Abstract:
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, despite the unconditional positive comovement of equities and Treasuries. We show that the seasonal Treasury and equity return patterns we observe 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 opposing seasonal patterns in Treasury and equity returns are coincident with the incidence of seasonal depression observed clinically in North American populations, and depression has been shown to be associated with increased risk aversion. 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.

market seasonality, Treasury bond returns, stock returns, SAD

Abstract:
This comment discusses some errors in a recent paper by Jacobsen and Marquering [Jacobsen, B., Marquering, W., 2008. Is it the weather? Journal of Banking and Finance 32 (4), 526-540], in which the authors challenge our previous finding that stock market returns exhibit seasonal patterns consistent with the influence of seasonal affective disorder on investor risk aversion. We find that we cannot replicate the authors' findings, even after corresponding with them. Furthermore, we document several problems with their methodology, including misspecification of their economic model, misspecification of their econometric model, and use of inappropriate data. While we agree that seasonal affective disorder is not an explanation for all variation in equity markets, we do maintain that careful analysis leads to economically and statistically significant evidence of the effect we originally documented.

Seasonal affective disorder, SAD, Sell in May, Stock market cycles, Return seasonality