Winter Blues: A SAD Stock Market Cycle

1. Winter Blues: A SAD Stock Market Cycle By Mark J. Kamstra, Lisa A. Kramer and Maurice D. Levi The American Economic Review, Vol. 93, No. 1 (Mar., 2003), pp. 324-343 Lectured by Xi Zhang

2. What does this paper talk about? • We model differences in the seasonal variation of daylight across countries to capture the influence of daylight on human sentiment, risk tolerance, and hence stock returns.

3. Contents • I. SAD and the Stock Market • II. Market Returns Data • III. Measuring the Effect of SAD • IV. Influence of the SAD Effect • V. Robustness Checks (skipped) • VI. Market Segmentation and SAD Effects (skipped) • VII. Conclusion

4. I. SAD and the Stock Market • Depression has been linked with seasonal affective disorder (SAD), a condition that affects many people during the seasons of relatively fewer hours of daylight. • Seasonal depression is related to hours of day light, and hence the effects of SAD may be more pronounced in countries at more extreme latitudes where winter and fall days are relatively shorter—Michael A. Young (1997) • Research in psychology has documented a direct link between depression and heightened risk aversion—Marvin Zuckerman(1984) • The psychological studies strongly support the view that the depression associated with shorter days translates into a greater degree of risk aversion, leading to testable hypotheses in the context of stock market.

5. II. Market Returns Data

6. II. Market Returns Data

7. II. Market Returns Data

8. II. Market Returns Data • 《内经· 素问· 四气调神大论》曰：“冬三月，此谓闭藏，水冰地坼，无扰乎阳，早卧晚起，必待日光，使志者伏若匿，若有私意，若已有得，去寒就温，无泄皮肤，使气亟夺，此冬气之应，养藏之道也。逆之则伤肾，春为痿厥，奉生者少。”

9. III. Measuring the Effect of SAD Panels A through D in this figure plot the monthly means of daily percentage returns for each of the individual indices in the US.

10. III. Measuring the Effect of SAD Panels A through D in this figure plot the monthly means for Sweden, Britain, Germany and Canada.

11. III. Measuring the Effect of SAD Panels A through D in this figure plot the monthly means for New Zealand, Japan, Australia and South Africa. * The horizontal axis of the plot for each country starts with the month in which autumn equinox actually takes place in that country.

12. III. Measuring the Effect of SAD Figure 6 shows the cycles for the length of the night for several of the countries included in this study. For simplicity, the cycles reflect the length of night for the latitude at which a country’s stock exchange is located. For countries in the Northern Hemisphere, the longest night appears on winter solstice, December 21stand the shortest night appears on summer solstice, June 21st. For countries in the Southern Hemisphere, things are opposite.

13. III. Measuring the Effect of SAD—Supplements The angle illustrated by the green area is the λ in the model. As the rotational axis of the Earth is not perpendicular to its orbital plane, the Earth's equatorial plane is not coplanar with the ecliptic plane, but is inclined to it by an angle of about 23.4°, which is known as the obliquity of the ecliptic. Obliquity of the ecliptic is the main cause of the four seasons on the Earth Another cause is the distance between the Earth and the Sun changes from time to time as the orbit of the Earth is ellipse.

14. III. Measuring the Effect of SAD SAD is standardized measure of night hours in fall and winter. λ is the sun’s declination angle, and Julian is a variable that ranges from 1 to 365, representing the number of the day in the year. H is the number of hours of night. Dfall is the dummy variable that reflecting asymmetry around winter solstice.

15. IV. Influence of the SAD Effect We run a single regression for each country, allowing the impact of SAD to vary freely from country to country. Returns are regressed on up to two lagged returns (where necessary to control for residual autocorrelation). Besides the variables talked in last section, we have a dummy for Monday, a dummy for a tax-loss selling effect, cloud cover, precipitation and temperature.

16. IV. Influence of the SAD Effect The average annualized return due to SAD is positive in all countries, ranging from 5.7 to 17.5 percent. For the most part, countries at latitudes closer to the equator tend to have lower, less significant returns due to SAD. The average return due to the fall dummy is negative in all countries except for Australia. The positive return due to SAD combined with the negative return due to the fall dummy suggests that on balance the seasonally asymmetric effects of SAD are shifting returns from fall to winter.

17. IV. Influence of the SAD Effect In Panel A, we present parameter estimates with associated t-statistics in parentheses below. In Panel B, we present the R-square, for each regression as well as the p-value for a Chi-square test for autocorrelation up to ten lags.

18. IV. Influence of the SAD Effect

19. IV. Influence of the SAD Effect Tables 4A through 4C show that the SAD coefficient estimate is uniformly positive across all countries and is significant in all countries except Australia. The fall dummy coefficient estimate is negative in all countries except Australia and is significantly negative for all except Britain, Australia and South Africa. Null hypothesis of no residual autocorrelation is rejected only in the case of AMEX. The parameter estimates associated with cloud cover, precipitation and temperature are typically insignificant.

20. IV. Influence of the SAD Effect Strategy B All in Swedish index in fall and winter and all in Australian index in Southern Hemisphere’s fall and winter for 20 years 21.1% annualized return, 7.9% more than under the neutral strategy Strategy A—neutral • Equally invest in Swedish index and Australian index for 20 years • 13.2% annualized return

21. VII. Conclusion • The SAD effect in every northern country we consider is significant, and in general the effect is greater the higher the latitude. • Furthermore, evidence suggests the impact of SAD in the Southern Hemisphere is out of phase by six months relative to the north as expected. • We believe that we have identified another behavioral factor that should not be ignored in explaining stock returns.