6. DATA AND METHODOLOGY
6.3. Methodology
6.3.2. Measuring Seasonal Affective Disorder
SAD is linked to the daylight in the sense of length of day. Length of day is depended on season and latitude. According to prior studies (see Molin et al. 1996; Schwarz et al. 1983;
Young et al. 1997), SAD rises an individual’s risk aversion when the daylight is at its lowest, i.e. during the fall and winter.
Following Kamstra et al. (2003), SAD is measured based on the number hours between sunset and sunrise. As SAD is prevalent only during the fall and winter, the SAD variable has values different from zero only during the fall and winter. To obtain values for the SAD variable, standard approximations from spherical trigonometry are needed. This method is called the sine wave measure.
As Kamstra et al. (2003) demonstrate, the first step is to define juliant as number of the day in the year. This variable takes values ranging from 1 to 365 and to 366 in a leap year.
Meaning, the value for January 1st is 1, for January 2nd 2, and so on. Next, the sun’s declination angle λt is calculated:
(9)
λ
𝑡= 0,4102 ∗ sin[(
2𝜋360
)(𝑗𝑢𝑙𝑖𝑎𝑛
𝑡− 80,25)]
.After the declination angle of the sun has been calculated, the number of hours of night in the Northern Hemisphere is obtained by
(10)
𝐻
𝑡= 24 − 7,72 ∗ arccos [− tan (
2𝜋δ360
) tan (λ
𝑡)],
where arccos is the arc cosine and δ is the latitude, which is 60.19 in Helsinki. (Kamstra et al. 2003.)
After calculating Ht, I then deduct 12 from it to obtain the length of night that is relative to the annual average length of night. Furthermore, following Kamstra et al. (2003), the SAD variable is specified only for trading days in the fall and winter:
(11)
𝑆𝐴𝐷
𝑡= { 𝐻
𝑡− 12, 𝑓𝑜𝑟 𝑡𝑟𝑎𝑑𝑖𝑛𝑔 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑓𝑎𝑙𝑙 𝑎𝑛𝑑 𝑤𝑖𝑛𝑡𝑒𝑟
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 .
To examine the asymmetry explained with the Hypothesis 6, I follow Lin (2015) and generate two dummy variables, Fallt, which is equal to one if the profit warning is announced in the fall, and Wintert, which equals one if the profit warning is announced in the winter.
Figure 6 illustrates the daily SAD measure around the year. The day of the winter solstice has the highest SAD value, as it is the shortest day of the year. After that, daylight starts to increase, and SAD sufferers start to recover. This means a lower value for the SAD variable.
After September equinox, days start to shorten, and the SAD variable starts to have higher values. In other words, the SAD measure is negatively correlated with the amount of daylight.
Figure 6. Daily SAD measure around the year.
0 1 2 3 4 5 6 7
January January January January February February March March March March April April April May May May June June June July July July August August August September September September October October October November November November December December December
Finally, the regression equation is defined in the following way:
(12) 𝐶𝐴𝑅𝑖𝑡(−1, +1) = 𝛽
0 + 𝛽
1𝐹𝑎𝑙𝑙
𝑡 ∗ 𝑆𝐴𝐷
𝑡 + 𝛽
2𝑊𝑖𝑛𝑡𝑒𝑟
𝑡 ∗
𝑆𝐴𝐷
𝑡+ 𝛽
3𝑆𝑖𝑧𝑒
𝑖𝑡+ 𝛽
4𝑀𝐵
𝑖𝑡+ 𝛽
5𝐵𝑒𝑡𝑎
𝑖𝑡+ 𝛽
6𝑅𝑒𝑐
𝑖+ 𝛽
7𝐸𝑃
𝑖+ 𝛽
8𝑀𝑢𝑙𝑡𝑖𝑊
𝑖+ 𝜀 .
CARit(-1, +1) is the cumulative abnormal return over the three-day window centered on the profit warning date. When examining PEAD and the SAD effect, the dependent variable is changed to CARit(+2, +50). In addition, I also estimate the regression model with only SADt
and the controls, i.e. without the fall and winter dummy variables to examine the SAD effect as a whole. To control for cross-sectional differences, several control variables are added to the equation. These variables are known to influence investors’ response to earnings surprises. Specifically, it is important to control for size (see, Hong, Lim & Teoh 2000) and market to book ratio (see, Hirshleifer, Lim & Teoh 2009).
Sizeit is log of market capitalization of equity the day before the profit warning, MBit is market to book ratio the day before the profit warning, Betait is the beta from the market model, Reci is the consensus analyst recommendation on a scale from 1 to 5 (1 = strong buy and 5 = strong sell), EPi is the earnings-to-price multiple where the earnings is the consensus EPS estimate for the current financial year while price is the share price one day before the profit warning, and MultiWi is a dummy variable with a value of 1 if the company has three or more profit warnings with the same sign during the observation period. I include the final four variables to follow findings of Spohr (2014).
However, previous studies do not use that many independent variables when explaining abnormal returns of profit warnings. For example, Jackson et al. (2003a) use only the size variable and two different dummy variables that equal one when the company cites reduced revenue as the source of their profit warning and if the decline in earnings is expected to be major. Some studies, see for example Bartov, Radhakrishnan & Krinsky (2000), control for analyst coverage. However, as Hong et al. (2000) show, analyst coverage is strongly
correlated with firm size. Therefore, I control for size taking log of market capitalization of equity the day before the profit warning, as it is already highly correlated with analyst coverage. However, analyst recommendations may have a significant impact on the abnormal returns. Because of this, following Spohr (2014), I add analyst recommendations and EPS estimates as controlling variables. Furthermore, Chruch & Donker (2010) report that companies that announce profit warnings frequently have smaller responses to their warnings. For this reason, I also include the dummy variable MultiWi.
Firm size is generally thought to be important to control for, as Jackson et al. (2003) and Church et al. (2010) show, the response decreases with the size of the company. However, Jackson et al. (2007) find that firm size nor analyst coverage have any impact. Bulkey et al.
(2005) show that the market to book ratio does not have any significant impact on profit warnings, whereas Hirshleifer et al. (2009) show that it does affect investors’ response to earnings surprises. Because of this contradictory, I use several of these variables as control variables. Naturally, this also allows me to examine the contradictory of prior studies.
However, the main interest is in the SAD variable. In other words, I include various control variables and examine if SAD variable is still significant even when several company specifications are controlled for.