--- --- UNIVERSITY OF AMSTERDAM
WHAT IS THE EFFECT OF CLOUDINESS ON THE DAILY MARKET INDEX RETURNS IN
THE NETHERLANDS?
Author: Sophie van Oostenbrugge
Student number: 10380612
BSc Economics and Business Economics, Finance track
Thesis Supervisor: Dr. J. J. G. Lemmen
STATEMENT OF ORIGINALITY
I hereby certify, that to the best of my knowledge, the content of this thesis is my own work. No part of this thesis has been submitted for any degree, publication or other purposes. I declare that the intellectual content of this thesis is the product of my own work. All sources, techniques or other material from the work of other people have been acknowledged.
TABLE OF CONTENTS
List of Tables iv
Glossary v
Acknowledgments vi
Abstract vii
Chapter 1: Introduction 9
Chapter 2: Literature Review 11
2.1 Weather and Mood 11
2.2 Mood and Risk Aversion 12
2.3 Risk Aversion and the Daily Market Index Returns 12
2.4 Prior research 13
2.5 Control Variables 15
Chapter 3: Data 18
Chapter 4: Methodology 20
Chapter 5: Results 22
5.1 OLS with robust standard errors 22
5.2 OLS with robust standard errors, including a cross-‐product term 25
Chapter 6: Conclusions 28 References 30 Appendices 32
iv
LIST OF TABLES
Table 1. Summary findings of prior research 17 Table 2. Return data general description 18 Table 3. Results for autocorrelation and unit root test 22 Table 4. OLS with robust standard errors results 24 Table 5. OLS with robust standard errors result, including cross-‐product term 27
GLOSSARY
AEX: Amsterdam Exchange IndexHMACL-‐3: Howarth Multiple Adjective Check List NY: New York
NYC: New York City
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ACKNOWLEDGMENTS
I express special thanks to Dr. J. J. G. Lemmen, for the time and effort in checking my work and providing feedback. His guidance throughout this thesis writing helped me a lot. Also I would like to thank Dr. Ir. M. J. Boumans, because his class about economical writing inspired me to start writing this thesis.
ABSTRACT
What is the effect of cloudiness on the daily market index returns
in the Netherlands?
by Sophie van Oostenbrugge
This paper tests whether a relationship between cloudiness and the daily market index returns exists, while controlling for other weather variables and anomalies. Weather can influence people’s mood, making it worse when it’s cloudy outside. A bad mood will affect the decisions of investors, making them more pessimistic about the market prospects and more likely to sell stock, which results in a drop of stock prices. While some significant effects are found, there is little evidence of a systematic effect of cloudiness on the daily market index returns in the Netherlands. This means that you cannot predict the stock returns looking at the weather forecasts.
Keywords: Cloudiness, Risk aversion, Stock returns JEL Classification: G10, G14
Chapter 1
INTRODUCTION
It is 1970 when Fama introduces the Efficient Market Hypothesis (EMH hereafter), which claims that prices will reflect all of the available information when a market is efficient. Given that markets are driven by the rational behavior of investors, stock prices reflect relevant information and the prices will adjust whenever new important information is available (Fama, 1970). But Hirschleifer and Shumway (2001) contradict this by stating that investors do not behave in a rational way and that their decisions are influenced by different subjective factors e.g. mood and feelings.
The weather can influence people’s mood in a positive way when it is sunny outside, and it can create a negative perception of the world when it is cloudy or rainy (Howarth and Hofmann, 1984). Zadorozhna (2009) explains that this is mainly due to the fact that sunny weather makes colors seem more vibrant and this creates a positive feeling, while dark and grey colors do the opposite. Hence, weather can influence people’s mood and therefore the decision they make.
Research from Harding and He (2014) shows that a negative mood causes investors to be more risk averse and this will result in a fall in the stock prices. The connection between weather and stock prices is interesting because if stock prices are driven by investors’ actions based upon subjective factors instead of rational decision making, it suggests that mood can potentially influence the investor setting prices.
In 1993, Saunders concluded that cloudiness could indeed affect stock prices. He was able to show that a relation between cloudiness and the New York stock returns exists. And in support of this research, Hirschleifer and Shumway (2003) present further evidence for the relationship between weather and 26 international stock markets. However, Jacobsen and Marquering (2009) concluded that the relation between cloudiness and stock prices could just be data-‐ driven inference that depends on artificial correlation. And when Krämer and Ründe (1997) replicated Saunders’ research for Germany, they were unable to establish any type of relationship.
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Due to this contradicting evidence, this research will verify whether cloudiness has an effect on the daily market index returns in the Netherlands. To avoid that the conclusion is data-‐driven, the data will be corrected for different anomalies, heterogeneity, autocorrelation and heteroscedasticity.
This paper consists of six chapters. Chapter 2 reviews the academic literature to establish the effect the weather has on the daily market index returns. Chapter 3 introduces the data sets. This is followed by an explanation of the methodology in Chapter 4. The fifth chapter consists of a regression analysis and a discussion of the results. In this chapter the significance of the effect of cloudiness is also verified. Finally, the last chapter concludes this research, including limitations and suggestions for further evidence.
Chapter 2
LITERATURE REVIEW
2.1 Weather and Mood
In the academic literature there are numerous researches done to establish the effect of weather on people’s mood. Some of these researches found a significant relationship between different weather variables and how they influence people’s mood (Sanders & Brizzolara, 1982; Persinger, 1975).
Howarth and Hofmann (1984) were able to find a significant relationship between weather and mood by letting twenty-‐four male university students, aged 17 to 25, participate in their study. The students had to fill in an HMACL-‐3 for 11 consecutive days to assess their mood, while Howarth and Hofmann kept track of the different weather variables. Their conclusion after this research was that good weather, like high temperature and a lot of sunshine, brings out positive mood states while bad weather, for example cloudiness and rain, brings out more negative mood states (Howarth and Hofmann, 1984).
Bad weather can even make people more pessimistic (Eagles, 1994; Goetzmann et al., 2015). It can also cause a heavier degree of depression (Molin et al.,1996), or a seasonal affective disorder (SAD) which is a condition that affects people during seasons when there are relatively fewer hours of daylight (Kamstra et al., 2003).
When people rely on their mood as information when they make judgments about how happy and satisfied they are, they would make a more positive judgment when the weather is good instead of bad (Schwarz & Clore, 1983). The reason that good weather creates more positive judgments is because the perception of bright colors that occurs when there is a lot of sun evokes positive feelings, making people’s mood better. The opposite holds for bad weather, the darker colors evoke negative feelings and this gets people in a bad mood (Zadorozhna, 2009).
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Research from Wang et al. (2012) implies that there are statistical results that show that investors can benefit from considering the weather and the effect the weather has on their mood when making important decisions about buying or selling stocks. Dowling and Lucey (2005) conclude that mood influences decision-‐making in general, even when the mood has nothing to do with the decision that is being made.
2.2 Mood and Risk Aversion
There is different literature available about how mood can influence the level of risk aversion that individuals have. Harding and He (2014) employed a laboratory behavioral experiment to examine the relationships between investor mood and risk aversion. They found that negative and positive mood affects investors’ risk aversion in an opposite way. When there is a positive change in people’s mood they become less risk averse, while the opposite is true for a negative change in their mood. This means that subjective factors e.g. feelings and mood that are experienced at the time of decision making can change the decision in a way that is different from when rational investors would behave in the same situation (Loewenstein, 2000).
2.3 Risk Aversion and the Daily Market Index Returns
Mood has an effect on the level of risk aversion individuals have, and if a change in risk aversion has an effect on the stock returns, one could conclude that mood can influence stock returns through the channel of risk aversion.
According to Zadorozhna (2009) this is indeed the case. Because weather may have an impact on stock returns due to the fact that investors are more willing to buy stocks during sunny weather and they are more predisposed to sell stocks if there are bad weather conditions. He states that this is known as the deficient market hypothesis theory that predicts movements of the stock market based on psychological factors (Zadorozhna, 2009). Investors that are in a good mood are more confident and therefore invest in riskier projects, as they believe in a successful outcome (Arkes et al., 1988). Harding and He (2014) say that there’s a causal relationship between investors mood and stock returns. A negative mood causes investors to be more risk averse, and when investors are more risk averse the stock prices will fall (Harding & He, 2014).
Lee et al. (2015) explain in more detail how a change in risk aversion can cause a change in the stock prices. They state that the level of risk aversion is affected by how pessimistic individuals are, and the level of risk aversion influences their perception when forming stock market returns expectations. In their research, they used data from the Dutch National Bank Household Survey from 2004 until 2006, and found that there is a negative and significant relationship between the level of risk aversion and the stock market expectations. This means that when you have a high level of risk aversion, you have a lower expectation of the stock market. Investors that are highly risk averse will demand a high equity premium, because their expectations of the stock market returns are negatively influenced by their risk aversion, and thus preventing them from participating in the stock market. This would imply that, given that the amount of stocks outstanding remains the same, the demand of stocks will be lower and therefore the prices will fall (Lee, B, Rosenthal, L, Veld, C, Merkoulova, Y. :2015).
Investors tend to be more optimistic when the level of cloudiness is low, and investors’ optimism increases the propensity of them to buy stocks (Goetzmann et al., 2015; Hirschleifer & Schumway, 2003). Investors’ stock market expectations are biased through different weather conditions, sunshine is positively correlated with stock returns (Hirschleifer & Schumway, 2003). But, according to Schneider (2014), short-‐term optimism cannot explain higher stock returns on more sunny days. Only long-‐term induced optimism is responsible for a change in returns (Schneider, 2014). This means that changes of risk aversion are a direct channel by which weather influences stock prices (Bassi et al., 2013).
2.4 Prior research
There are a few different weather variables that showed to have a significant effect on the stock returns. In order to look into the effect of cloudiness on the returns, it is important to take the other weather variables into account to get the most accurate result. Important weather variables are: sunshine (Hirschleifer & Shumway, 2001) and temperature (Cao and Wei, 2001). More variables and their significance are shown in table 1.
Saunders published his research in 1993. He paired data on cloud cover with data on stock prices on a daily basis. The cloud-‐cover measure was grouped into three categories (0-‐30% cloud cover, 40-‐70% and 80-‐100%). He performed a regression including different variables to
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control for anomalies. The factors Saunders included were: daily index capital gain or loss, month dummy, day dummy, cloud cover variable, a lagged return variable and an error term. He came to the conclusion that the weather in NYC has a long history of significant correlation with the stock index. More particularly, when it’s cloudy in New York, the New York Stock Exchange index returns tends to be negative. This effect appears to be robust with respect to different anomalies (Saunders, 1993).
After Saunders published his work, there were other researchers that tried to determine the effect of cloudiness on the stock returns. Frühwirth and Sögner (2015) examined the effect of cloudiness on New York stock returns, and they found that cloudiness has a significant effect on the S&P 500 returns. They were not able to establish any other significant relationships between weather variables and the stock returns (Frühwirth, M., Sögner, L., 2015). Cheng et al. (2008) also confirmed the significant influence of cloudiness on the market returns. They found that returns are generally lower on cloudier days, but this is only the case at the market open (Cheng et al., 2008).
Krämer and Ründe (1993) tried to replicate the findings in Saunders (1993) using German data, but they were not able to confirm any significant influence of cloudiness on the returns. In 2009 Jacobsen and Marquering looked into this contradiction and found that results that try to explain stock returns by looking at mood shifts that are caused by weather conditions, could just be data-‐driven inference based on spurious correlation. They also state that the conclusion that weather affects stock returns through mood changes of investors is premature (Jacobsen & Marquering, 2009).
Cao and Wei (2001) examined more than twenty markets in general, and eight international markets in dept. They found that there is a negative correlation between temperature and stock market returns. This correlation is statistically significant, even after controlling for the Monday effect, the tax-‐loss effect, cloudiness and SAD. They didn’t find a significant effect for cloudiness on the returns (Cao & Wei, 2001). Lu and Chou (2012) were also not able to find a significant effect for cloudiness.
Zadorozhna (2009) examined the effect of wind, cloudiness, pressure, precipitation, humidity, temperature and visibility on the stock returns across emerging markets of Central and Eastern Europe and Commonwealth of Independent States. He controlled for different anomalies, such as the seasons and the holiday effect. The results that he found are that the weather variable with the highest significant effect overall is temperature, and that cloudiness has a negative effect on
effects, there is not enough evidence to conclude that weather has an effect on the stock markets in Eastern Europe (Zadorozhna, 2009).
2.5 Control Variables
There are a number of variables that are included in prior research to control for different anomalies. The variables that are shown to have a significant effect on returns, and therefore are important to include, are: a lagged return variable (Saunders, 1993; Cao & Wei, 2005; Kamstra et al., 2003), NBER recession dummy (Jacobsen & Marquering, 2009), seasonal dummy (Jacobsen & Marquering, 2009; Kamstra et al., 2003; Zadorozhna, 2009), temperature variable (Jacobsen & Marquering, 2009; Cao & Wei, 2005; Kamstra et al., 2003; Zadorozhna, 2009), SAD dummy variable (Jacobsen & Marquering, 2009; Cao & Wei, 2005; Dowling & Lucey, 2005; Kamstra et al., 2003), holiday effect dummy (Jacobsen & Marquering, 2009; Zadorozhna, 2009), Monday variable (Cao & Wei, 2005; Kamstra et al., 2003), tax-‐loss selling effect dummy (Cao & Wei, 2005; Kamstra et al., 2003) and a rain variable (Hirschleifer & Shumway, 2003; Dowling & Lucey, 2005; Kamstra et al., 2003; Zadorozhna, 2009).
A lagged return variable, 𝑅!!!, is important to include in the regression because it corrects for
first order auto-‐correlation in returns. Prior research showed that weather variables like temperature and rain have a significant effect on the returns and therefore they’re important to consider.
The NBER dummy is a recession dummy. It gets the value of 1 when there is a period of recession according to the NBER. The holiday effect is a dummy variable that gets the value of 1 in the December and January months. These months are included because the activity of the investors increases due to the holiday rush. A Monday dummy is included because the stock market has a tendency to drop on Mondays, because of the bad news that might have been released over the weekend or due to the fact that the investors are in a gloomy mood because the workweek started again. The seasonal dummy is included because the markets tend to have strong returns during the summer months, while September is traditionally a down month
The dummy variable that controls for the tax-‐loss selling effect has a value of 1 for the first 10
days of the taxation year and 0 otherwise. The taxation year starts January 1st in the Northern
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for trading days in the fall and winterotherwise
returns just before year-‐ends tend to be negative. This is the case because investors sell securities in which they have losses just before year-‐ends to lower their taxes on net capital gains, resulting in lower returns in December. The prices rebound in January, making the returns in January positive (Sikes, 2014).
Kamstra et al. (2003) were the first to show the significance of the SAD effect on the stock returns. SAD measures fluctuations in hours of sunlight per day for the period between the
Autumn Equinox (September 21st) and the Spring Equinox (March 20th). The SAD variable can be
calculated following the formula constructed by Kamstra et al. (2003):
𝑆𝐴𝐷! = 𝐻0 !− 12
The formula for Ht equals:
𝐻!= 24 − 7.72 × − 𝑡𝑎𝑛
2𝜋𝛿
360 𝑡𝑎𝑛 𝜆
where δ represents the latitude north of the location from the equator (Amsterdam is 52.37° north), and λ is the angle between the sun’s rays and earth’s surface and calculated as follows:
𝜆 = 0.4102 × sin 2𝜋
365 𝑗𝑢𝑙𝑖𝑎𝑛 − 80.25
Julian stands for the number of the day in the year, where January 1st would get a value of 1 and January 2nd a value of 2 and so on.
Author Time period Geographical boundary1
Method Variables Coefficients Kamstra,
Kramer and Levi (2003)
1928-‐2000 New York Regression Monday effect -‐0.209*** Tax-‐loss selling effect 0.065 SAD measure 0.038*** Fall -‐0.058** Cloudiness 0.115 Precipitation -‐0.002 Temperature 0.003** Jacobsen & Marquering (2009)
1970-‐2004 Netherlands Regression Temperature -‐0.12*** Halloween 1.53***
SAD 0.18
Cao & Wei
(2005) 1962-‐2001 US Regression Monday effect Tax-‐loss selling effect -‐0.3054*** 0.1798*** Temperature -‐0.0031** Cloudiness -‐0.0035 SAD -‐0.0144** Hirschleifer & Shumway (2003)
1982-‐1997 Amsterdam Regression Cloudiness -‐0.005 Raininess -‐0.064 Snowiness -‐0.075 Krämer &
Ründe (1997)
1960-‐1990 Germany Regression Cloudiness Not significant Saunders
(1993)
1927-‐1989 New York Regression January effect -‐0.0009**** Monday effect -‐0.0017**** Cloudiness 0.00049** Chang et al.
(2008) 1994-‐2004 New York Regression Cloud cover Wind speed -‐0.0316*** 0.0007 Snowiness 0.1351 Raininess 0.0720 Temperature Monday effect Friday effect January effect 0.0023 -‐0.0149 0.0105 -‐0.0572 December effect 0.1032** Dowling & Lucey (2005)
1988-‐2000 Ireland Regression Cloud cover -‐0.000112 Raininess -‐0.000797** Humidity 0.002381
Geomagnetic storms -‐0.000077
Lunar phases 0.000030
SAD -‐0.000048
Daylight savings time
changes -‐0.004294* Halloween -‐0.001667 Holiday effect -‐0.000103 Monday effect -‐0.000714
Notes:
* Significant at the 10-percent level, one-sided. ** Significant at the 5-percent level, one-sided. *** Significant at the 1-percent level, one-sided. **** Significant at the 0.1-percent level, one-sided.
1 Some researches had a wider range of geographical boundaries, but only the ones with the most added values to this research are shown here. For
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Chapter 3DATA
The present research considers the AEX index to represent the daily market index returns in the Netherlands from October 1992 until June 2015. The reason why this time frame is chosen is because the KNMI keeps record of the weather data since 1992, and therefore we cannot perform a regression of the stock returns and the weather variables before this time period.
The AEX is a stock market index that is composed of a maximum of 25 of the most actively traded securities on the exchange. The level of the AEX price index is considered, this reflects only the change in the level of stock prices and it does not include any return from reinvested dividends. This data is available from the Yahoo! Finance database.
The weather data is available at the KNMI historical archive that contains data for different weather variables, such as cloudiness and temperature. There are 37 weather stations in the Netherlands, but not all of them were active during the chosen timeframe. The weather stations that are used to get the most accurate average are stationed across the Netherlands. The following stations were used: Eelde, Twenthe, Berkhout, De Bilt, Rotterdam, Gilze-‐Rijen, Eindhoven, Voorschoten, IJmuiden and Schiphol. The reason that it is important to consider multiple weather stations that are positioned across the Netherlands is because investors from all over the country can buy and sell stocks that affect the AEX and therefore looking at the average weather in the Netherlands will give a more accurate result.
Table 2. Return data general description
Variable Obs St dev Min Max Skewness Kurtosis AEX
returns 5772 0.013761 -‐0.0954148 0.1006526 0.3242854 9.461612
Note: a more detailed description can be found in Appendix A
Returns are calculated as follows: 𝑅! = !"#$% !"#$%!!!"# !"#$%!
!!! − 1
Table 2 shows that the statistic on skewness is higher than zero, and this means that there are frequent small negative outcomes and large outliers are not very likely. The distribution is right
values to the right.
When the data follows a normal distribution, the value for kurtosis is 3. The value that is found in this dataset is higher than 3, which indicates a leptokurtic distribution. This distribution is more peaked than a normal distribution, with values that are concentrated around the mean and it has thicker tails. This means that there is a high probability for extreme values in this dataset. Data on stock returns exhibit non-‐normality.
Weather data includes the following variables: temperature, cloud cover, precipitation and SAD. Cloud cover ranges from 0 to 8, 0 is clear skies and 8 is when the whole sky is covered with clouds. Precipitation shows the amount of rain that has fallen that day in mm. When the amount of rain that has fallen is between 0 – 0.5 mm, the KNMI recognizes this with a value of -‐0.1. SAD is measured 0 when it is summer or spring, and a small negative value when it’s fall or winter. Descriptive statistics of weather variables can be found in Appendix B.
Other variables to control for anomalies are: lagged return to correct for first order auto-‐ correlation in returns, NBER recession dummy, seasonal dummy, holiday effect dummy, Monday and Friday dummy and a tax-‐loss selling effect dummy.
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Chapter 4METHODOLOGY
In statistics, ordinary least squares (OLS hereafter) is a method of linear regression. It estimates variables while minimizing the sum of squared residuals. OLS can be used to test the relationship between stock returns and weather variables. This method makes the assumption that the variance of the error term is constant. It assumes homoscedasticity. But stock market data exhibit heteroscedasticity (result of heteroscedasticity test can be found in Appendix C), which means that the OLS estimates are no longer BLUE. That means that, among all the unbiased estimators, OLS does not provide the estimate with the smallest variance. Significance tests can be either too high or too low.
To avoid this problem, the OLS with robust standard errors is used. This method has the advantage that it does not assume homoscedasticity. There will be no difference in the estimated coefficients provided by a simple OLS regression, but the standard errors and the significance tests will change.
Seasonal dummies, like winter, spring, autumn and summer, are added into the regression to control for seasonality (Jacobsen & Marquering, 2008; Zadorozhna, 2009). And following Saunders (1993) and Jacobsen and Marquering (2008), January and December dummies are included into the regression to control for the ‘holidays effect’ when the investors’ activity increases, and therefore the stock market shows upward movements in stock prices.
Welfare et al. 2012 researched the effect of a recession on people’s mood. Their overall conclusion was that a recession has a negative effect on people’s mood, while Christmas and Halloween have a positive effect on people’s mood. A more detailed conclusion that they make is that a few days before the government announces a cut, due to the recession, and numerous days after this announcement, people’s mood is worse (Welfare et al., 2012). This means that people’s mood is worse in times of a regression. According to the literature review, also cloudiness has a negative effect on people’s mood. It could be the case that these two variables amplify each other. To test whether this is the true, a second regression analysis is performed
NBER.
All weather variables represent exogenous influence on the stock returns, which means that the model avoids endogeneity problems because the daily market index returns cannot influence the weather variables. Omitted variable bias is not an issue, because it is assumed that weather variables are not correlated with other possible factors that affect stock returns.
If the regression analysis shows that there is a relationship between cloudiness and the daily index market returns in the Netherlands, it means that investors are influenced by cloudiness. Their mood depends on the weather, and this can change the decisions that they make. Asset-‐ pricing models should account for this impact. It is expected that cloudiness affects the market index returns in a negative way. This is also the case in studies conducted by Saunders (1993), Hirschleifer and Shumway (2003) and Zadorozhna (2009).
Finally, a low R-‐squared value is expected, as variation in cloudiness cannot count for all of the variation in stock returns.
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Chapter 5RESULTS
Following Zadorozhna (2009), first a Portmanteau and a Durbin-‐Watson test will be performed
to detect the presence of autocorrelation in the residuals.2 After this, an augmented Dickey-‐
Fuller test and a Phillips-‐Perron test are performed to see whether a unit root is present in the time series sample.
Table 3. Results for autocorrelation and unit root test
Portmanteau p-‐value Durbin-‐Watson d-‐statistic Augmented Dickey-‐Fuller test Phillips-‐ Perron AEX returns 0.000 1.500** -‐24.709*** -‐60.581***
Notes: * significant at 10%; ** significant at 5%; ***significant at 1%.
The conclusion that can be made when considering the Portmanteau and the Durbin-‐Watson values is that the null hypothesis, that the residuals from an ordinary least-‐squares regression are not autocorrelated, can be rejected. This means there is autocorrelation in the residuals. Therefore it is important to include a lagged variable in the regression to correct for the autocorrelation (Kamstra et al., 2003; Jacobsen & Marquering, 2008).
The values from the Phillips-‐Perron and the augmented Dickey-‐Fuller tests show that the hypothesis that there is unit root can be rejected. Therefore no correction needs to be made.
5.1 OLS with robust standard errors
Because of the heteroscedastic data set, the standard regression method that is used is the OLS with robust standard errors. The first regression includes all variables (4.1).
𝑟! = 𝛼!+ 𝛼!𝑟!!!+ 𝛼!𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!+ 𝛼!𝑇𝑒𝑚𝑝!+ 𝛼!𝑅𝑎𝑖𝑛!+ 𝛼!𝑆𝑢𝑛ℎ𝑜𝑢𝑟𝑠!+ 𝛼!𝑆𝐴𝐷!
+𝛼!𝐷!!"#$+ 𝛼!𝐷!!"#+ 𝛼!"𝐷!!"#+ 𝛼!!𝐷!!"#+ 𝛼!"𝐷!!"#$%&+ 𝛼!"𝐷!!"#+ 𝛼!"𝐷!!"#+ 𝜀!
(4.1)
where 𝑟! is the daily market index returns and 𝑟!!! is the lagged returns variable to correct for
the first-‐order auto-‐correlation in returns. 𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!, 𝑇𝑒𝑚𝑝! and 𝑆𝑢𝑛ℎ𝑜𝑢𝑟𝑠! represent the
daily levels of the weather variables and 𝑆𝐴𝐷! stands for the seasonal affective disorder. 𝐷!!"#$ and 𝐷!!"# are dummy variables for recession or taxation periods, 𝐷!!"# and 𝐷!!"# are dummy variables for specific days of the week. 𝐷!!"#$%& stands for the seasonal dummy3. The dummy variables for January and December are 𝐷!!"# and 𝐷!!"#.
The weather variables that are statistically significant, according to the first regression, are 𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠! and 𝑇𝑒𝑚𝑝!. Other significant variables are 𝑆𝐴𝐷! , 𝐷!!"#$ and 𝐷!!"#. The coefficient of 𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠! is 0.0003812, which means that it is slightly positive. And this is not what was expected according to the literature review. The same counts for 𝐷!!"#$. The signs of the other coefficients are as expected. The results are shown in table 4.
After the first regression, a VIF test is performed to check for multicollinearity. The results can be found in Appendix D. Variables that can be problematic have a value of 4 or higher. These variables will be dropped. According to the VIF test, the value for sun hours is larger than 4, which indicates that the number of sun hours is multicollineair. This makes sense, because the number of sun hours is included in the calculation of the 𝑆𝐴𝐷! variable. After the number of sun hours variable is removed from the regression, no multicollinearity exists.
The second regression includes all variables, except for sun hours (4.2).
𝑟! = 𝛼!+ 𝛼!𝑟!!!+ 𝛼!𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!+ 𝛼!𝑇𝑒𝑚𝑝!+ 𝛼!𝑅𝑎𝑖𝑛!+ 𝛼!𝑆𝐴𝐷!+ 𝛼!𝑁𝐵𝐸𝑅!
+ 𝛼!𝐷!!"#+ 𝛼!𝐷!!"#+ 𝛼!"𝐷!!"#+ 𝛼!!𝐷!!"#$%&+ 𝛼!"𝐷!!"#+ 𝛼!"𝐷!!"#+ 𝜀!
(4.2)
When 𝑆𝑢𝑛ℎ𝑜𝑢𝑟𝑠! is dropped as a variable, the coefficients of the remaining variables are slightly
changed, but the same variables remain significant. The signs also stay the same.
The third regression consists of the variables that were statistically significant in the second regression. The reason that this regression is being performed, is to see what the effect is of removing all non-‐significant variables. (4.3).
𝑟! = 𝛼!+ 𝛼!𝑟!!!+ 𝛼!𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!+ 𝛼!𝑇𝑒𝑚𝑝!+ 𝛼!𝑆𝐴𝐷!+ 𝛼!𝑁𝐵𝐸𝑅!+ 𝛼!𝐷!!"#+ 𝜀! (4.3)
3 When performing the regression there is a dummy variable for every season, except for fall. Fall is omitted because
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the conclusion that the variables that show significant effect on the daily market index returns are 𝑇𝑒𝑚𝑝!, 𝑁𝐵𝐸𝑅! and 𝐷!!"#. The coefficient of 𝑇𝑒𝑚𝑝
! is 0.000061. This means that temperature
has a positive effect on the returns of the AEX. This is in line with the expectations, because good weather will lead to a better mood and less risk aversion what will result in higher returns. The
coefficient of 𝑁𝐵𝐸𝑅! is 0.0020169, meaning that during periods of regression the index returns
are higher. This is not what was expected according to the literature. The coefficient for 𝐷!!"# is -‐0.0017521 what implies that the month December has lower returns on average.
5.2 OLS with robust standard errors, including a cross-‐product term
The same regression procedure is followed; the standard method that is used is the OLS with robust standard errors. The first regression consists of all the variables, including the cross-‐ product term 𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!𝐷!!"#$ (5.1): 𝑟! = 𝛼!+ 𝛼!𝑟!!!+ 𝛼!𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!+ 𝛼!𝑇𝑒𝑚𝑝!+ 𝛼!𝑅𝑎𝑖𝑛!+ 𝛼!𝑆𝑢𝑛ℎ𝑜𝑢𝑟𝑠!+ 𝛼!𝑆𝐴𝐷! +𝛼!𝐷!!"#$+ 𝛼!𝐷!!"#+ 𝛼!"𝐷!!"#+ 𝛼!!𝐷!!"#+ 𝛼!"𝐷!!"#$%&+ 𝛼!"𝐷!!"# + 𝛼!"𝐷!!!"+ 𝛼!"𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!𝐷!!"#$+ 𝜀! (5.1)
The results are shown in table 5. The only weather variables that has a statistically significant effect is 𝑇𝑒𝑚𝑝!. It has a positive sign, meaning that a higher temperature leads to a higher
returns. Other significant variables are 𝑆𝐴𝐷! and 𝐷!!"#. 𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠
! is not significant, the same
counts for 𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!𝐷!!"#$. But because a cross-‐product term is included, multicollinearity is
expected and therefore correction is needed. This is examined by performing a VIF test4.
Variables that correlate with other predictor variables are removed.
The second OLS regression is performed with the variables that do not exhibit multicollinearity (5.2): 𝑟! = 𝛼!+ 𝛼!𝑟!!!+ 𝛼!𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!+ 𝛼!𝑇𝑒𝑚𝑝!+ 𝛼!𝑅𝑎𝑖𝑛!+ 𝛼!𝑆𝐴𝐷! +𝛼!𝐷!!"#+ 𝛼 !𝐷!!"#+ 𝛼!𝐷!!"#+ 𝛼!"𝐷!!"##$%+ 𝛼!!𝐷!!"# + 𝛼!"𝐷!!!!+ 𝛼 !"𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!𝐷!!"#$+ 𝜀!
(5.2)
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Variables that needed to be removed due to multicollinearity are: 𝑆𝑢𝑛ℎ𝑜𝑢𝑟𝑠!, 𝐷!!"#$, 𝐷!!"##,𝐷!!"#$%& and 𝐷!!"#$%&. It is expected that 𝑆𝑢𝑛ℎ𝑜𝑢𝑟𝑠
! needs to be removed, because that was also the case in regression (4.2). The cross-‐product term is highly correlated with the NBER dummy variable, and therefore this dummy variable needs to be removed from the regression.
When performing the third OLS regression, the non-‐significance variables – except cloudiness -‐ and the variables that correlate with each other are removed (5.3):
𝑟! = 𝛼!+ 𝛼!𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!+ 𝛼!𝑇𝑒𝑚𝑝!+ 𝛼!𝐷!!"#+ 𝛼!𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠!𝐷!!"#$+ 𝜀!
(5.3) The results can be found in table 4. According to this final regression, 𝐶𝑙𝑜𝑢𝑑𝑖𝑛𝑒𝑠𝑠! is the only variable that is not significant. 𝑇𝑒𝑚𝑝! has a positive effect on the returns. The coefficient of the December month dummy is negative, and the coefficient of the cross-‐product term is 0.0004769. This means that the results are not in line with Welfare et al. (2012), because according to them and according to the literatue review about the effect of cloudiness, a negative sign was expected.
The signs of some of the variables are not what would be expected according to the academic literature. A thing to note is that the R-‐squared value in the regression is not very high. This means that the model that is used is not very good at explaining the variation in the stock returns. When more variables would have been added, and R-‐squared would be higher, the signs might be different. This analysis tries to reveal whether investors behave in accord with the EMH where they weight costs and benefits and make rational decisions, or that they are influences by the weather through the channels of mood and risk aversion.
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Chapter 6CONCLUSIONS
This paper tests the relationship between the daily market index returns in the Netherlands and cloudiness while controlling for other weather variables and other common anomalies. Weather is considered to be a proxy for the mood that affects decisions of investors. It is hypothesized that people’s mood tends to be better if the weather is warm and sunny, and due to the positive change of mood the investors might be more optimistic about the market prospects. When people’s mood is negatively influenced by bad weather, they become more pessimistic about the weather prospects. This means that investors would be more willing to buy stocks when the weather is good and they will be more likely to sell them when the weather is bad.
To test this relationship, an OLS regression with standard robust errors is performed to test the significance of all of the weather variables and different anomalies. After this regression, a VIF test is performed to check for multicollinearity. The second regression excludes variables that correlate with other predictor variables according to the VIF test. The last regression includes all variables that were statistically significant in the second regression to see whether this influences the conclusion. The second regression analysis is performed following the same steps, only now a cross-‐product term is added to check whether cloudiness and the recession period amplify each other’s negative effect.
Results from the first OLS regressions show that the variables that have a significant effect on the daily market index returns are temperature, NBER and December. The second OLS regressions show that temperature, December and the cross-‐product are significant. Cloudiness showed a significant effect in the first regression of the first analysis, but because it is no longer significant in the second and third regression there is little evidence to conclude that cloudiness has a systematic effect on the daily market index returns.
When future research is done to the effect of cloudiness on the daily market index returns, it is important to include more independent variables that have a statistically large effect on the returns. The R-‐squared during this regression analysis was very low, and when this value is higher you can conclude with more certainty whether variables have a statistical effect on the dependent variable or not. A second remark is that there are some weather variables that were not included, for example humidity or snow. These variables can also affect people’s mood, risk
