Effect of mood on the stock market : the study of the effect of mood, influenced by the weather and/or day of the week, on the stock market in the Netherlands from 2005-2015

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EFFECT OF MOOD ON THE STOCK MARKET

The study of the effect of mood, influenced by the weather and/or day of the

week, on the stock market in the Netherlands from 2005-2015.

UNIVERSITY OF AMSTERDAM

BSc Economics & Business

Bachelor Specialisation Economics & Finance

Author:

N.M. Weijers

Student number:

10589872

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PREFACE

This thesis is written to complete my Bachelor Economics and Business at the University of Amsterdam. It is a mandatory part of the study. So I can conclude that my main motivation to write this thesis is to succeed my Bachelor and be able to start next year with my Masters. But my motivation for the topic of my thesis is different. Since I can remember I am interested in psychology. Before I started with Economics and Business I was for almost a year in doubt which study to choose. I did choose for Economics and Business with the following idea that ‘there is some psychology in economics and business, but we cannot say the same about some economics and business in psychology’. From the moment I did choose for Economics and Business I decided that at moments during my study I was able to choose some sort of direction or topic, I would choose to include aspects related to psychology. One of those moments is my thesis topic. That is why I did choose the broader topic Behavioural Finance and started searching for a more specific topic in this discipline. I am interested in this specific topic because it is related to the mind of people and the effect of their mind on the economy. I am relieved that I did choose a topic I am really interested in, because this made writing my thesis so much more easy and enjoyable. The process of the thesis went actually more or less fluently. Of course, there are always aspects that have to be changed or are forgotten and data which were unavailable, but next to that there were not major setbacks.

Nienke Weijers, Amsterdam, 16 January 2016, 19:07.

Statement of Originality

This document is written by Student Nienke Weijers who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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ABSTRACT

This paper examines the effect of the mood of traders, influenced by the weather and/or day of the week, on the stock volume in the Netherlands in the period 2005 - 2015. Historical data of the AEX are used, as well as data from the KNMI, with respect to the weather. The paper examines if a better or worse mood, influenced by sun, rain, or by the day of the week, results in different stock volumes. The results are that rain has a negative influence on our mood and lowers the stock market volume. Monday also had a negative effect on the trade volume and Friday a positive effect. The reason is that rain and Monday influence our mood in a negative way and that because of this people are negatively influenced in their decision making. A bad mood induces pessimism. In contrast, Friday has a positive effect on our mood because it is almost weekend. Therefore, on Fridays people are more optimistic and have more

confidence. This results in more trade. In this thesis it is shown that mood has influence on the stock market in the Netherlands.

Keywords: Behavioural finance, stock market anomalies, irrational behaviour, stock volume, mood. JEL Classification: G02

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LIST OF TABLES

Table 1 Results of weather variables from recent studies 5-6 Table 2 Results of day-of-the-week effects from recent studies 8-10

Table 3 Descriptive statistics table 14

Table 4 Skewness/Kurtosis tests for Normality 14-15

Table 5 Correlations 15-16

Table 6 Durbin-Watson statistics 19

Table 7 Breusch-Godfrey test 19

Table 8 Breusch-Pagan test 20

Table 9 Results Model 1 21

Table 12 Results Regression with Lagged Volume Return Variable 24-25 Table 13 Results Durbin-Watson and Breusch-Pagan test with Lagged 26 Volume Return Variable

Table 14 Results Regression with Variable Recession 28

Table 15 Output Regression Model 1 34

Table 16 Output F-test Model 1 34

Table 17 Output Durbin-Watson test Model 1 34

Table 24 Output Regression with Lagged Return Variable Model 1 36 Table 25 Durbin-Watson test with Lagged Return Variable Model 1 36 Table 26 Breusch-Pagan test with Lagged Return Variable Model 1 36 Table 27 Output Regression with Lagged Return Variable Model 2 37 Table 28 Durbin-Watson test with Lagged Return Variable Model 2 37 Table 29 Breusch-Pagan test with Lagged Return Variable Model 2 37 Table 30 Output Regression with Lagged Return Variable Model 3 38 Table 31 Durbin-Watson test with Lagged Return Variable Model 3 38 Table 32 Breusch-Pagan test with Lagged Return Variable Model 3 38 Table 33 Output F-Test Model 1 with Lagged Return Variable 38 Table 34 Output F-Test Model 2 with Lagged Return Variable 39

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Table 36 Output Regression Model 1 with Recession Variable 39 Table 37 Output Regression Model 2 with Recession Variable 40 Table 38 Output Regression Model 3 with Recession Variable 40

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CHAPTER 1 Introduction

Individuals are rational according to the traditional economic paradigm. This means that they make optimal decisions based on the information available to them (Daniel & Titman, 1999). But there is evidence of a growing number of ‘anomalies’ in the US stock markets. This casts doubt on the widely accepted efficient markets hypothesis (Agrawal & Tandon, 1994). The efficient market hypothesis predicts that asset prices fully reflect all available information. So that individuals who participate in financial markets are rational and therefore only use the relevant information for decision making (Daniel & Titman, 1999). The observed anomalies in financial markets are for example weather and calendar effects (Agrawal & Tandon, 1994). Behavioural finance offers an alternative paradigm to the efficient market theory, one in which individuals make systematic mistakes in the way they process information (Daniel & Titman, 1999).

A possible explanation is that the weather affects our mood. If for example sunlight affects our mood in a positive way, people tend to evaluate future prospects more optimistically. There exists a

possibility that people act different in the stock market when they are in a good mood than when they are in a bad mood (Hirshleifer & Shumway, 2003).

But not only the weather has an effect on the mood of people. Also the day of the week has influence. Numerous studies have documented that the average return in the USA is significantly negative on Mondays and is abnormally large on Fridays (Agrawal & Tandon, 1994).

Because there is evidence in other countries that participants in financial markets behave irrational, and yet no research has been done in the Netherlands, it is worthwhile to examine which effect mood has on the stock market in the Netherlands. Especially for this time period, before, during and after the crisis there is not much research. For this study we will take a look to the effect on the trading volume. The research of Statman, Thorley and Vorkink shows that trading volume is dependent on past returns over many months (Statman, Thorley, & Vorkink, 2006).

1.1 Hypothesis

To examine if mood has an influence on the stock market, we will investigate the weather and calendar effects separately, as well as combined. As variable for the stock market we will take the volume return of the AEX. The AEX is the most important stock index from the Netherlands. It represents the development of the 25 biggest stocks in the Netherlands. There is empirical evidence that trading volume can tell us something about future price movements (Llorente, Michaely, Saar, & Wang, 2002). Volume represents the number of transactions of a specific day.

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Dubois and Louvet believe in the explanation that a low trading volume suggests that investors are less active on that day (Dubois & Louvet, 1996). They refer to Louvet and Taramasco (1991) who show the correspondence between return and trading volume seasonality.

The first hypothesis is about the effect of the weather. We expect that the effect of sunny weather is positive, because this improves the mood of people. People are happier and will evaluate future prospects more optimistically (Hirshleifer & Shumway, 2003). The opposite will be true for rainy days.

𝐻0: 𝛽𝑠𝑢𝑛𝑛𝑦= 𝛽𝑟𝑎𝑖𝑛𝑦 𝐻1: 𝛽𝑠𝑢𝑛𝑛𝑦> 𝛽𝑟𝑎𝑖𝑛𝑦

The second hypothesis is about the effect of the day of the week. We expect that the mood of people will be worse on Monday because the workweek just begun. This will have a negative influence on the volume return. For Friday we expect the effect to be positive, because people are happier because it is almost weekend.

𝐻0: 𝛽𝐹𝑟𝑖𝑑𝑎𝑦= 𝛽𝑀𝑜𝑛𝑑𝑎𝑦 𝐻1: 𝛽𝐹𝑟𝑖𝑑𝑎𝑦> 𝛽𝑀𝑜𝑛𝑑𝑎𝑦

Besides these two separate hypotheses, we expect that the effect when it is sunny weather and a Friday will even be bigger than the effect of a sunny versus rainy day or Friday versus Monday. Because if it is sunny on a Friday, we are even happier, because it is weekend and the weather is sunny.

𝐻0: 𝛽𝐹𝑟𝑖𝑑𝑎𝑦&𝑠𝑢𝑛𝑛𝑦= 𝛽𝑀𝑜𝑛𝑑𝑎𝑦&𝑟𝑎𝑖𝑛𝑦 𝐻1: 𝛽𝐹𝑟𝑖𝑑𝑎𝑦&𝑠𝑢𝑛𝑛𝑦> 𝛽𝑀𝑜𝑛𝑑𝑎𝑦&𝑟𝑎𝑖𝑛𝑦

1.2 Set up

The organization of this thesis is as follows. Chapter 2 discusses existing literature about the influence of mood on the stock market. In Chapter 3 we will describe the theoretical framework. Chapter 4 describes the data and used methodology. In Chapter 5 the empirical results will be discussed. Concluding remarks are contained in Chapter 6.

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CHAPTER 2 Literature review

One of the first studies about the effect of our mood on the stock market started in 1970. Multiple studies about this topic are done in recent years. All these studies differ from each other and have somewhat different results. We will start to discuss the studies into the weather effect and then into the day of the week effect. There has not been done any research into these two effects combined.

2.1 Weather effect

In recent years, there is a much research done into the effect of the weather upon the stock market. Almost all these studies have found significant effects for weather variables. These results are presented in the table at the end of this section.

One of the first studies is done by Saunders, who found that when the New York City cloud cover is negative, this significantly correlates with index returns (Saunders, 1993). One year later Trombley used the data from Saunders and examined them further using a different statistical methodology. The variation is in the choice which days of cloudiness to compare. Saunders compared hundred percent cloudy days with zero-twenty percent cloudy days. Comparison based on two points on each end of the range or on three points is more reasonable, according to Trombley. The results from his paper indicate that the relationship between security returns and Wall Street weather is neither as clear nor as strong as Saunders suggests. Trombley did not find a strong difference between returns on clear sunny days and on cloudy or rainy days. The returns on entirely cloudy days were not significantly different in comparison with returns on days with zero or ten percent cloud cover (Trombley, 1997).

A decade later Hirshleifer and Shumway published an article about how sunshine affects the stock returns in 26 countries. They found a highly positive and significant effect of sunshine on daily stock returns (Hirshleifer & Shumway, 2003). This result suggests that investors can benefit from becoming aware of their moods, in order to avoid mood-based errors in their judgment and trades (Hirshleifer & Shumway, 2003). According to Loughran and Schultz a limitation of the research of Saunders and Hirshleifer is that it measures the mood of individuals by local cloudiness in New York City, while in fact trade orders come from all over the world (Loughran & Schultz, 2004). That is why they take a different approach and examine the relationship of weather and stock returns taking the cloud cover in the city of a NASDAQ company’s listing as a proxy for the weather affecting investors submitting orders in the stock market (Loughran & Schultz, 2004). They find that in cities experiencing a lot of snow, trading volume falls by more than 17 percent on the day of the storm and the following day by almost 15 percent. In contrast, there is almost no relation found between local cloud cover and stock returns, even after adjusting for market returns (Loughran & Schultz, 2004).

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A year later Goetzmann and Zhu developed a potentially more powerful test of the hypothesis that weather influences stock trading activity (Goetzmann & Zhu, 2005). They find a negative and significant effect for total cloud cover on the stock returns. Thereafter they investigate whether individual investor behaviour is influenced by the seasonality in daytime or total cloud cover (Goetzmann & Zhu, 2005). For the variable net buy in shares (NBS) and buy-sell imbalance (BSI) they did not find any significant difference between sunny and cloudy days. Reasons for this

insignificance might be that individual trading data are noisy or that investors are not just influenced by the current weather, but also by the weather in the period preceding their investment choice. Next to that, they also did not find a significant effect on the trading volume (Goetzmann & Zhu, 2005). Keef and Roush explore the variation in the results of Hirshleifer and Shumway (2003), who did not explore them by themselves (Keef & Roush, 2007). Keef and Roush use two additional variables to explore the variations: latitude and per capita Gross Domestic Product. The motivation for this is that 26 stock exchanges are located in economies that span the whole globe. This meta-analysis leads to an important conclusion. The influence of cloud cover on stock returns is inversely varied with the latitude where the stock market is located. The closer to either pole, the greater the cloud cover effect (Keef & Roush, 2007). With this effect taken into account, the GDP does not have a significant effect.

A different approach is taken by Chang et al. They want to examine if it is possible that weather has different effects on trading variables in the opening trading interval and in the other trading intervals (Chang, Chen, Chou, & Lin, 2008). They find that greater cloud cover induces a significantly negative intraday return only in the first fifteen-minutes period of the trading day (Chang, Chen, Chou, & Lin, 2008). They further show that spreads and turnover ratios are not significantly related to cloud cover, but that it has a significantly positive effect on return volatility and a significantly negative effect on market depth. Their findings overall suggest that weather influences intraday trading behaviour because it affects investor mood (Chang, Chen, Chou, & Lin, 2008).

In the same year, Levy and Galili try to show that there exists a rather rich cross-sectional variation in individuals’ reactions to mood changes (Levy & Galili, 2008). They did not find a difference in the propensity of the average investor to buy or sell equities on cloudy or sunny days, consistent with Goetzmann and Zhu (Levy & Galili, 2008). There is also no difference between the buy-sell imbalances (BSI) affected by the cloud cover for men or woman or for different ages. But they find significant evidence in the propensity to buy or sell on cloudy days for the group with the lowest portfolio value (Levy & Galili, 2008).

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Table 1 - Results of weather variables from recent studies Author (publication year) Time period Geographical boundary Method Dependent variable Variables Coefficients Saunders (1993) 1927-1989

New York Regression Stock return Cloud cover 0.00042***

Trombley (1997)

1962-1989

New York Regression Stock return Cloud cover = 0% 0.00131 Cloud cover = 10-20% 0.00176 Cloud cover = 30-90% -0.00021 Hirshleifer and Shumway (2003) 1982-1997

Amsterdam Regression Stock return Cloud cover -0.011*

Logit Cloud cover -0.020*

Loughran and Schultz (2004)

1984-1997

United States Regression Volume Blizzard -0.17** Jewish Holiday -10,733** Logit Stock return Cloud cover -0.18**

Clear 0.26** Goetzmann and Ning (2005) 1991-1996

United States Regression Stock return Cloud coverage -0.00038**

NBS Cloud coverage -51.642 BSI Cloud coverage -0.000351 Trading value Cloud coverage -339.57 Keef and

Roush (2007)

1982-1997

Globe Regression Stock return Cloud coverage -0.011**

Stock return LAT -3.825E-04*

Stock return GDP -4.430E-07

Chang et al. (2008) 1994-2004 New York opening balance (9:30-9:45)

Regression Stock return Wind -0.0011

Snow 0.0798 Rain 0.1122** Temperature 0.0003 Monday effect 0.00116 Friday effect -0.0040 January effect -0.0896* December effect 0.1879*** Cloud cover -0.0379***

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Author (publication year) Time period Geographical boundary Method Dependent variable Variables Coefficients Levy and Galili (2008) 1998-2002

Israel Regression BSI Cloud cover 0.0043

Men 0.0104 Woman -0.0081 Age 20-30 0.0174 Age 31-45 0.0082 Age 46-65 0.0025 Age 66+ 0.0027 Portfolio value 0-100 0.0143* Portfolio value 100-500 -0.0005 Portfolio value 500+ 0.0024

* Significant at the 10-percent level ** Significant at the 5-percent level *** Significant at the 1-percent level **** Significant at the 0.1-percent level

2.2 Day-of-the-week effect

Cross (1973) is one of the first researchers who finds conscious evidence of price changes on Fridays and Mondays. The difference between the proportions of times in which there was an increase in the price change on Friday and on Monday is highly significant (Cross, 1973). In an earlier period Saunders found already evidence of a Monday effect, but his study did investigate in the first instance the weather effect (Saunders, 1993). All the results of the studies discussed in this section are

presented in the table at the end of this section.

A number of years after Cross’s findings, French examines the process generating stock returns by comparing the returns for different days of the week. For the returns on Monday there is a three-calendar-day investment present. This is from the close of trading Friday to the close of trading Monday (French, 1980). This is called the calendar time hypothesis, which implies that Mondays’ return represents a three-day return with an expected value equal to three times that for the other weekdays (Agrawal & Tandon, 1994). The mean return for Monday is significantly negative in each of the periods. To examine if these negative returns reflect some closed-market effect, French compares the returns for days following holidays with non-holiday returns (French, 1980). The result is an average higher return for Mondays, Wednesday, Thursdays, and Fridays followings holidays, while the average return for Tuesday is lower.

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This indicates that the negative returns for Monday are caused by some weekend effect, rather than by a general closed-market effect (French, 1980).

A year later, Gibbons and Hess find that Monday remains the most ‘unusual’ day of the week (Gibbons & Hess, 1981). To avoid the non-trading problem, autocorrelations because of non-trading of securities, as well as to determine the extent of the Monday phenomenon across securities, tests are also conducted with individual securities (Gibbons & Hess, 1981). The result is that for the overall period, all thirty securities of the Dow Jones have a negative mean on Monday.

Keim and Stambaugh undertake a further investigation of the weekend effect found by French. The Monday effect is similar as in earlier research and shows a significantly negative average Monday return. Besides that, they test the tendency for higher returns on the last trading day of the week, whether that last day is a Friday or a Saturday. The result indicates that Fridays’ return is significantly larger if Friday is the last trading day of the week. So, the last trading day of the week tends to have a higher average return (Keim & Stambaugh, 1984). The length of the weekend has no significant effect on the Monday.

In the same year, Rogalski published a study that differs from studies before by making a distinction between trading day and non-trading day returns. Rogalski decomposes the Friday close to Monday close return in two components: the Friday close to Monday open return (non-trading weekend effect) and the Monday open to Monday close return (Rogalski, 1984). Because of this distinction, the Monday effect becomes a non-trading weekend effect (Rogalski, 1984). Next to this, Rogalski shows that in January both the Monday effect and the non-trading weekend effect are different from the rest of the year. The Monday returns in January are on average higher for small firms (Rogalski, 1984).

However, Smirlock and Starks find contradicting evidence. For the pre-1974 period the entire weekend effect occurs during active trading on Monday, instead of the non-trading weekend effect (Smirlock & Starks, 1986). Next to that, a significant decline in Friday close to Monday open returns, the non-trading weekend effect, and a significant increase in returns during active trading on Monday are found. These results support the proposition of a shift in the weekend effect from a trading time to a non-trading time effect (Smirlock & Starks, 1986).

Additional information about the Monday effect is found by Jaffe, Westerfield and Ma. Returns on Monday are only negative when the market has declined in the previous week (Jaffe, Westerfield, & MA, 1989).

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A few years later, Chang, Pinegar and Ravicahndran try to examine the robustness of international day-of-the-week effects. They find different results for different countries. In the United States the day of the week effect becomes insignificant with either sample size or error term adjustments. In contrast, stocks in France, Italy, the Netherlands, Spain, Sweden, Switzerland, the United Kingdom, Canada and Hong Kong exhibit day-of-the-week effects that are robust to individual sample size or error term adjustments (Chang, Pinegar, & Ravichandran, 1993).

Because there is already enough evidence of the effects in the United States, Agrawal and Tandon examine seasonal patterns in the stock markets of eighteen countries, excluding the United States (Agrawal & Tandon, 1994). The seasonal patterns include for example the weekend and end-of-December effect. They show that most foreign markets experience day of the week effects in their respective stock markets, independent of the United States seasonal patterns (Agrawal & Tandon, 1994). Next to the negative Monday effect and the positive Friday effect, they find a strong negative Tuesday effect. For the Netherlands, they find a significant negative effect on Tuesday and a positive effect on Friday. A possible explanation for a Tuesday effect, instead of a Monday effect, is a time difference with the United States (Agrawal & Tandon, 1994). But the Netherlands do not have a time difference of more than twelve hours. Another explanation could be differences in settlement

procedures across countries. However, Agrawal and Tandon show that this should result in expected positive returns in the Netherlands on Tuesday, which is not the case. They find evidence for an explanation of an independent seasonal pattern in most countries. They find that the negative seasonal pattern on Mondays/Tuesdays tends to disappear in most of the countries in the eighties (Agrawal & Tandon, 1994). Next to that, they find evidence that the Monday returns are affected by the return in the previous week. However, this does not apply to the Tuesdays (Agrawal & Tandon, 1994).

Berument and Kiymaz are the first who examine if there is any day of the week variation in volatility (Berument & Kiymaz, 2001). They show that the highest and lowest volatility are observed on Friday and Wednesday. A possible explanation for the highest volatility on Friday is that it may be the result of news on Thursday and Friday (Berument & Kiymaz, 2001).

Table 2 - Results of day-of-the-week effects from recent studies

Author (publication year) Time period Geographical boundary Method Dependent variable Variables Coefficients French (1980) 1953-1970

New York Regression Stock return Monday effect -0.1681*** Friday effect 0.0873*** Gibbons and

Hess (1981)

1962-1978

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Author (publication year) Time period Geographical boundary Method Dependent variable Variables Coefficients Keim and Stambaugh (1984) 1928-1982

New York Regression Stock Return Monday effect -0.1859**** Return Friday Friday last day 0.234* Return Friday Saturday included 0.037 Rogalski

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1974-1984

New York Regression Stock return Monday close-to-close -0.1167** Monday (non-trading period) -0.1315** Monday (trading period) 0.0148** Smirlock and Starcks (1986) 1963-1968

United States Regression Stock return Monday effect -0.1692**

1968-1974 Monday effect -0.1933** Jaffe, Westerfield and Ma (1989) 1930-1962

United States Regression Stock return Monday (previous week negative) -0.39**** Monday (previous week positive) 0.06**** Chang, Pinegar and Ravichandran (1993) 1986-1992

Netherlands Regression Stock return Monday effect -0.0026*

Saunders (1993)

1927-1989

New York Regression Stock return January effect 0.00171**** Monday effect -0.0018**** Agrawal and

Tandon (1994) 1971-1987

Netherlands Regression Stock return Monday effect 0.006 Tuesday effect -0.072** Friday effect 0.146*** Berument and Kiymaz (2001) 1973-1997

United States Regression Volatility Monday effect -0.0046 Tuesday effect 0.0230*** Friday effect 0.0175** Goetzmann and Ning (2005) 1991-1996

United States Regression Stock return Monday effect 0.000777* January effect 0.000214

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Author (publication year) Time period Geographical boundary Method Dependent variable Variables Coefficients Chang et al. (2008) 1994-2004 New York opening balance(9:30-9:45)

Regression Stock return Monday effect 0.00116 Friday effect -0.0040 January effect -0.0896* December effect 0.1879*** * Significant at the 10-percent level

** Significant at the 5-percent level *** Significant at the 1-percent level **** Significant at the 0.1-percent level

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CHAPTER 3 THEORETICAL FRAMEWORK

3.1 Influence of mood

According to the traditional finance theory, the efficient markets hypothesis states that securities markets are rational (Chang, Chen, Chou, & Lin, 2008). Meaning that individuals make optimal decisions based on the information available to them (Daniel & Titman, 1999). But we started this thesis with the words that the anomalies on the stock market cast doubt on this efficient market hypothesis. In 1962 Osborne published an article which shows that the stock market, as a high-speed economic phenomenon, offers unique opportunities for the study of economic behaviour (Osborne, 1962). According to Chang et al., there is an interesting line of research that links psychological influences and financial markets (Chang, Chen, Chou, & Lin, 2008). The economic decisions of investors may be influenced by emotions, psychological quirks and moods (Rystrom & Benson, 1989). Empirical results suggest that investors’ mood is responsible for biases in their judgment and

behaviour (Kliger & Levy, 2003).

Studies suggest that when investors are in a good mood, which can be associated with the weather or day of the week, they tend to trade more, which in turn increases volatility (Symeonidis, Daskalakis, & Markellos, 2010). This effect can be explained mainly by investor overconfidence (Daniel & Titman, 1999). Individuals filter information and bias their behaviour in ways that allow them to maintain their confidence (Daniel & Titman, 1999). An overconfident trader trades too aggressively, and this

increases the trading volume (Gervais & Odean, 2001). There is psychological evidence that people tend to have a more optimistic evaluation of future prospects when they are in a better mood (Chang, Chen, Chou, & Lin, 2008). Individuals who are in good moods make more optimistic choices (Hirshleifer & Shumway, 2003).

In contrast, poorer social moods can be associated with more disagreement in valuation opinions among investors. This is inversely related with market volatility, so investors tend to trade less (Symeonidis, Daskalakis, & Markellos, 2010). Another explanation is the link between poor moods with an increase in the subjective probability of undesired outcomes. People who are in bad moods tend to fine negative material more available or salient (Hirshleifer & Shumway, 2003). So bad mood is associated with a pessimistic evaluation of future uncertainties (Kliger & Levy, 2003). Good mood seems to engender optimism and bad mood induces pessimism (Keef & Roush, 2007).

3.2 Effect of weather on the mood

The weather influences stock volume because it affects the mood of investors (Saunders, 1993). People usually feel better on a bright and sunny day than they do on a dull and cloudy day (Howarth & Hoffman, 1984).

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Several findings about seasonal effects suggest that exposure to sunlight immediately affects mood and cognition (Keller, et al., 2005). People often attribute their feelings to the wrong source, leading to incorrect judgements. This results that people feel happier on sunny days than on rainy days (Hirshleifer & Shumway, 2003).

3.3 Effect of the day-of-the-week on the mood

For many people, Monday is the start of five long days of work after two days of leisure, and many people begin their work with a certain amount of reluctance (Rystrom & Benson, 1989). By Friday, most of the people are looking forward to two leisure days with a positive attitude. So the moods of people can differ across the days of the week. There are a number of different studies to this hypothesis. Stone et al. find no significant results, but it was clear that Mondays differ from other days. On the weekends the mood was better than on the other days, with Mondays’ mood worse than on Friday (Stone, Hedges, Neale, & Satin, 1985). The subjects of this study believe that Monday is the worst day. Next to this study, Rystrom and Benson describe a research in their study from Christie and Venables, who show that the mood is lowest on Monday mornings and highest on Friday evenings (Rystrom & Benson, 1989).

But this is not the only possible explanation of the day-of-the-week effect. In many studies this effect is contributed to non-psychological influence. According to French the negative returns for Monday are caused by the weekend effect. Rogalski thinks that the Monday effect is influenced by a non-trading weekend effect. But Smirlock and Starks find a shift in the weekend effect from a non-trading time to a non-trading time effect. Jaffer, Westerfield and Ma find a totally different effect, namely that the returns from the previous week have influence on the Monday effect. Like many researchers write, ‘there is a need to refine existing theories and to explore alternative explanations, but we are sure that we cannot attribute these anomalies to noise, data snooping or selection biases’ (Agrawal & Tandon, 1994).

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CHAPTER 4 METHODOLOGY AND DATA

4.1 Data

The data used for the research are the data of the AEX and the weather data of the KNMI. The historical data of the AEX can be found at finance.yahoo.com. Data about the volume of the AEX are only available from 2005. To fulfil the data of the AEX, it was needed to calculate the volume return. This is done with the formula: ln (𝑉𝑜𝑙𝑢𝑚𝑒1

𝑉𝑜𝑙𝑢𝑚𝑒₀).

The KNMI has many different weather stations in the Netherlands. But only five of these weather stations are homogenized. The possibility that the time series of daily value may be inhomogeneous exists because of station moves and changes in observation. This means that these data cannot be used for trend analysis (Daily data from the weather in the Netherlands). The five homogenized stations are the Bilt, Beek, Vlissingen, The Kooy and Eelde. From these stations we take the average SQ and DR. SQ is the sunshine duration in 0.1 hour, DR is the precipitation duration in 0.1 hour. We take a rain variable instead of the cloud cover, because some studies find no significant effect for cloud cover. Besides that, there is not done much research to the effect of rain.

Next to these two variables, we also include other weather variables in the regression. Because the effect of rain and sun may be driven by other weather conditions (Chang, Chen, Chou, & Lin, 2008). By including them in the regression we control for these other variables. The other weather variables include wind speed (FG), temperature (TG), and cloud (NG). FG is the day wind chill at 0.1 m/s, TG is the average day temperature in 0.1 Celsius, and NG is the average coverage of the upper air into eighths. From all these variables the average from the five weather stations is taken. To make sure that the results are not driven by seasonal effects, we subtract from each weather variable its average value of each week (Chang, Chen, Chou, & Lin, 2008).

We also have to delete all the weekends in the data of the weather stations. Because of the fact that the stock market is closed in the weekends, we erase from the weather data all the weekends and other days that the stock market is closed.

For the data related to the days of the week we have to create dummy variables for Monday, Tuesday, Wednesday and Thursday. We do not include the weekend because of the closing of the stock market and Friday is excluded because of multicollinearity.

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The next step is to import all this data in Stata and run a regression. Below we can find a descriptive statistics table of the used data, table of the skewness/kurtosis tests for normality and a correlation table.

4.2 Descriptives of the data

Table 3 - Descriptive statistics table

Variable Observations Mean Standard Deviation Minimum Maximum

FG 2816 0.0032 12.4104 -44.6800 54.5600 TG 2816 0.0000 14.2343 -49.3200 58.3600 SQ 2816 0.0015 23.6875 -97.6000 74.1200 DR 2816 -0.0003 18.3470 -61.6400 126.6400 NG 2816 -0.0001 1.4149 -5.1200 4.8400 Return Volume 2816 0.0528 0.3952 -0.8980 5.4017 Monday 2816 0.1982 0.3987 0 1 Tuesday 2816 0.2013 0.4011 0 1 Wednesday 2816 0.2021 0.4016 0 1 Thursday 2816 0.2013 0.4011 0 1 Friday 2816 0.1971 0.3979 0 1 SQFriday 2816 -0.2094 11.0478 -89.1200 73.9200 DRMonday 2816 -0.0907 8.4539 -61.6400 102.6800

FG is the wind speed at 0.1 m/s, TG is the average day temperature in 0.1 Celsius, SQ is the sunshine duration in 0.1 hour, DR is the precipitation duration in 0.1 hour, NG is the average coverage of the upper air into eighths, SQFriday is the interaction variable of SQ and Friday and DRMonday is the interaction variable of DR and Monday.

The first column shows all the variables. In the second column we can find the number of observations of the variables, which are all the same. Then follows the mean and standard deviation of all the variables. In the last two columns the minimum and maximum value of all the variables is shown.

Table 4 – Skewness/Kurtosis tests for Normality

Joint Variable Observations Probability

(Skewness) Probability (Kurtosis) Adjusted Chi-square Probability > Chi-square FG 2816 0.0000*** 0.0000*** - 0.0000*** TG 2816 0.0000*** 0.0000*** 40.9000 0.0000*** SQ 2816 0.8680 0.9381 0.0300 0.9833 DR 2816 0.0000*** 0.0000*** - 0.0000*** NG 2816 0.0000*** 0.1287 47.4700 0.0000 Return Volume 2816 0.0000*** 0.0000*** - - Monday 2816 0.0000*** 0.0042*** - 0.0000*** Tuesday 2816 0.0000*** 0.0267** - 0.0000***

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Joint Variable Observations Probability

(Skewness) Probability (Kurtosis) Adjusted Chi-square Probability > Chi-square Wednesday 2816 0.0000*** 0.0384** - 0.0000*** Thursday 2816 0.0000*** 0.0267** - 0.0000*** Friday 2816 0.0000*** 0.0021*** - 0.0000*** SQFriday 2816 0.0104** 0.0000*** - 0.0000*** DRMonday 2816 0.0000*** 0.0000*** - -

FG is the wind speed at 0.1 m/s, TG is the average day temperature in 0.1 Celsius, SQ is the sunshine duration in 0.1 hour, DR is the precipitation duration in 0.1 hour, NG is the average coverage of the upper air intoeighths, SQFriday is the interaction variable of SQ and Friday and DRMonday is the interaction variable of DR and Monday.

Probability (skewness) and probability (kurtosis) shows the p-value according to the skewness and kurtosis that the sample is asymptotically approximately normal distributed. The adjusted chi-square is the statistic of the adjusted chi-square with the skewness and kurtosis both taken into account. The probability > chi-square is the p-value of this chi-square statistic. * Significant at the 10-percent level

** Significant at the 5-percent level *** Significant at the 1-percent level

The skewness/kurtosis test presents a test for normality based on skewness, kurtosis and these two combined. A probability below 0.05 for the skewness indicates that the variable is significantly different from the skewness of a normal distribution for a significance level of 5 percent. The same applies for a probability below 0.05 for the kurtosis. This indicates that all the variables, except from SQ, sunshine duration, and NG, cloud cover, have a skewness and/or kurtosis that is significantly different from the skewness and/or kurtosis of a normal distribution for a significance level of at least 5 percent.

A probability below 0.01 for the Chi-square, skewness and kurtosis both taken into account, means that we can reject the hypothesis that the variable is normally distributed for a significance level of 1 percent. This accounts for all the variables, except for SQ.

Therefore, almost all the variables of our sample are not asymptotically normal distributed.

Table 5 - Correlations FG TG SQ DR NG Return Volume Monday FG 1.0000 TG 0.1752 1.0000 SQ -0.1731 -0.0071 1.0000 DR 0.3147 0.0881 -0.4764 1.0000

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FG TG SQ DR NG Return Volume Monday NG 0.2030 0.0663 -0.8944 0.4399 1.0000 Return Volume 0.0087 -0.0588 -0.0083 -0.0299 -0.0036 1.0000 Monday -0.0162 -0.0130 0.0443 -0.0124 -0.0335 -0.2169 1.000 Tuesday -0.0214 -0.0602 -0.0129 -0.0005 0.0157 0.1954 -0.2496 Wednesday -0.0053 -0.0322 0.0031 -0.0231 -0.0026 0.0156 -0.2502 Thursday 0.0297 0.0535 -0.0122 0.0298 0.0095 0.0067 -0.2496 Friday 0.0132 0.0523 -0.0223 0.0062 0.0107 -0.0022 -0.2463 SQFriday -0.0745 -0.0164 0.4666 -0.2213 -0.4187 -0.0184 0.0094 DRMonday 0.1497 0.0356 -0.2181 0.4608 0.2171 -0.0361 -0.0216

Tuesday Wednesday Thursday Friday SQFriday DRMonday FG TG SQ DR NG Return Volume Monday Tuesday 1.0000 Wednesday -0.2527 1.000 Thursday -0.2521 -0.2527 1.000 Friday -0.2488 -0.2493 -0.2488 1.000 SQFriday 0.0095 0.0095 0.0095 -0.0383 1.000 DRMonday 0.0054 0.0054 0.0054 0.0053 -0.0002 1.000

FG is the wind speed at 0.1 m/s, TG is the average day temperature in 0.1 Celsius, SQ is the sunshine duration in 0.1 hour, DR is the precipitation duration in 0.1 hour, NG is the average coverage of the upper air into eighths, SQFriday is the interaction variable of SQ and Friday and DRMonday is the interaction variable of DR and Monday.

Above in the table of correlations we can find that all the weather variables (FG, TG, SQ, DR, and NG) are somewhat correlated with each other. This is the reason why we included them all in the regression, to control for them.

If we take for example the correlation between SQ and NG, we can see that this is large and negative. We can simply explain this because if the sun is shining (SQ) there are less clouds (NG), and the other way around.

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We can also simply explain the correlations between the days of the week, which have almost all the same value, 0.25. This is because the days of the week are dummy variables. To avoid

multicollinearity we exclude Friday in our regression.

Correlations are too high when they have a value of 0.7 or higher, which is not the case in this sample. Therefore, we do not have any problems with multicollinearity in the regression. No multicollinearity is one of the assumptions for an OLS regression. To run an OLS regression we have to make a few assumptions about our sample, as is described in the methodology.

4.3 Methodology

The first hypothesis is about the effect of the weather. I expect that the effect of sunny weather is positive, because this improves the mood of people. People are happier and will evaluate future prospects more optimistically (Hirshleifer & Shumway, 2003). The opposite will be true for rainy days.

𝐻0: 𝛽𝑠𝑢𝑛𝑛𝑦= 𝛽𝑟𝑎𝑖𝑛𝑦 𝐻1: 𝛽𝑠𝑢𝑛𝑛𝑦> 𝛽𝑟𝑎𝑖𝑛𝑦

We estimate the following equation by OLS for the first hypothesis: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐹𝐺𝑡+ 𝛽2𝑇𝐺𝑡+ 𝛽3𝑆𝑄𝑡+ 𝛽4𝐷𝑅𝑡+ 𝛽5𝑁𝐺𝑡+ 𝑒𝑡. Where 𝑉𝑅𝑡 is the volume return on day 𝑡, 𝐹𝐺𝑡 is the day wind chill at 0.1 m/s, 𝑇𝐺𝑡 is the average day temperature in 0.1 Celsius, 𝑆𝑄𝑡 is the sunshine duration in 0.1 hour, 𝐷𝑅𝑡 is the precipitation duration in 0.1 hour, 𝑁𝐺𝑡 is the average coverage of the upper air into eighths and 𝑒𝑡 is the error term. The coefficient 𝛽0 is the constant and the coefficients 𝛽1,𝛽2, … , 𝛽5 are the mean volume returns for the days. With an F-test we can estimate if the stock returns are higher on sunny days than on rainy days.

The second hypothesis is about the effect of the day of the week. I expect that the mood of people will be worse on Monday because the workweek just begun. This will have a negative influence on the volume return. For Friday I expect the effect to be positive, because people are happier that it is almost weekend.

𝐻0: 𝛽𝐹𝑟𝑖𝑑𝑎𝑦= 𝛽𝑀𝑜𝑛𝑑𝑎𝑦 𝐻1: 𝛽𝐹𝑟𝑖𝑑𝑎𝑦> 𝛽𝑀𝑜𝑛𝑑𝑎𝑦

For the second hypothesis about the days of the week, we need to test for differences in mean rates of volume return across the days of the week. We estimate the following equation by OLS: 𝑉𝑅𝑡= 𝛽0+ 𝛽1𝐷1𝑡+ 𝛽2𝐷2𝑡+ 𝛽3𝐷3𝑡+ 𝛽4𝐷4𝑡+ 𝑒𝑡.

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Where V𝑅𝑡 is the volume return on day 𝑡, 𝐷1𝑡, 𝐷2𝑡, … , 𝐷4𝑡 are binary dummy variables for the various days of the week, Monday, Tuesday,…, Thursday, and 𝑒𝑡 is the error term. The coefficient 𝛽0 is the constant, and in this case the Friday, and the coefficients 𝛽1, 𝛽2, … , 𝛽4 are the mean volume returns for the days. Friday is the referent dummy variable and is excluded because of multicollinearity. With an F-test we can estimate if the effect of Friday is bigger or positive in comparison with Monday.

For the third hypothesis, I expect that the effect when it is sunny weather and a Friday will even be bigger than the effect of a sunny versus rainy day or Friday versus Monday. Because if it is sunny on a Friday, we are even happier, because it is weekend and the weather is sunny.

𝐻0: 𝛽𝐹𝑟𝑖𝑑𝑎𝑦&𝑠𝑢𝑛𝑛𝑦= 𝛽𝑀𝑜𝑛𝑑𝑎𝑦&𝑟𝑎𝑖𝑛𝑦 𝐻1: 𝛽𝐹𝑟𝑖𝑑𝑎𝑦&𝑠𝑢𝑛𝑛𝑦> 𝛽𝑀𝑜𝑛𝑑𝑎𝑦&𝑟𝑎𝑖𝑛𝑦

For this third hypothesis about the combination of the two effects, we need interaction variables. We estimate the following equation by OLS: 𝑉𝑅𝑡= 𝛽₀+ 𝛽₁𝐹𝐺𝑡+ 𝛽₂𝑇𝐺𝑡+ 𝛽₃𝑆𝑄_𝑡+ 𝛽₄𝐷𝑅𝑡+ 𝛽₅𝑁𝐺𝑡+ 𝛽₆𝐷1𝑡+ 𝛽₇𝐷2𝑡+ 𝛽₈𝐷3𝑡+ 𝛽₉𝐷5𝑡+ 𝛽₁₀𝑆𝑄_𝑡𝐷5𝑡+ 𝛽₁₁𝐷𝑅𝑡𝐷1𝑡+ 𝑒𝑡. Where 𝑉𝑅𝑡 is the volume return on day 𝑡, 𝐹𝐺𝑡 is the day wind chill at 0.1 m/s, 𝑇𝐺𝑡 is the average day temperature in 0.1 Celsius, 𝑆𝑄𝑡 is the sunshine duration in 0.1 hour, 𝐷𝑅𝑡 is the precipitation duration in 0.1 hour, 𝑁𝐺𝑡 is the average coverage of the upper air into eighths, 𝐷1𝑡, 𝐷2𝑡, … , 𝐷5𝑡 are binary dummy variables for the various days of the week, Monday, Tuesday,…, Friday, 𝑆𝑄_𝑡𝐷5𝑡 the interaction variable is for sun and Friday, 𝐷𝑅𝑡𝐷1𝑡 the interaction variable is for rain and Monday and 𝑒𝑡 is the error term. The coefficient 𝛽0 is the constant and the coefficients 𝛽1, 𝛽2, … , 𝛽11 are the mean returns for the days. With an F-test we can estimate if the stock returns are higher on sunny Fridays than on rainy Mondays.

To run an OLS regression we have to make a few assumptions about our sample. We can check these assumptions by doing some statistic tests. We have to test for multicollinearity, normality, serial correlation and heteroscedasticity. As written above, almost all the variables of the sample are not asymptotically normal distributed. Next to that, there is no multicollinearity between the variables of our sample. The other two assumptions about serial correlation and heteroscedasticity will be discussed and tested in the next chapter.

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CHAPTER 5 RESULTS

5.1 Robustness Check

5.4.1. Serial correlation

We perform a Durbin-Watson test to detect the presence of a first-order serial correlation in the residuals from the regression analysis. A value of two means that there exists no autocorrelation in the sample. The Durbin-Watson statistics gives a higher value than two for all models. This indicates negative autocorrelation for all models.

Table 6 - Durbin-Watson statistics

Model Durbin-Watson statistic

Model 1 2.7112

Model 2 2.4714

Model 3 2.6968

The Durbin-Watson statistic indicates whether there is autocorrelation in the residuals. When this value is close to 2, there is no autocorrelation.

The value of this statistic lies between zero and four. When the value is two, there is no

autocorrelation in the residuals. A value lower than two, indicates positive autocorrelation and a value higher than two, indicates negative autocorrelation. Because the three values of the Durbin-Watson statistic are all above two, we will do an additional autocorrelation test. To test for higher-order serial correlation, we use the Breusch-Godfrey test. The results are presented in the table below.

Table 7 – Breusch-Godfrey test

Model Lags Chi-square df Probability > Chi-square

Model 1 1 361.002 1 0.0000*** 100 890.157 100 0.0000*** Model 2 1 157.430 1 0.0000*** 100 289.743 100 0.0000*** Model 3 1 347.432 1 0.0000*** 100 711.193 100 0.0000***

The Breusch-Godfrey method is used for testing higher-order serial correlation. The null hypothesis is no serial correlation. The column lags specify a list of numbers, indicating the lag orders to be tested. The default of this is order one. We also used lag(100) because we have daily data and a lot of observations. Chi-square gives the chi-square statistic and df is the number of degrees of freedom. The probability gives the p-value of this chi-square statistic.

* Significant at the 10-percent level ** Significant at the 5-percent level *** Significant at the 1-percent level

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The results in the table indicate that for all the Breusch-Godfrey tests the null hypothesis can be rejected because all the probabilities are significant for a significance level of 1 percent. This means that we have to reject the null hypothesis of no serial correlation.

Concluding, serial correlation is present in the regression. This means that there is a correlation of the same variable over various time intervals. This was to be expected because we use daily data over a time period of ten years. We can correct for this by using robust standard errors in our regression. 5.4.2. Heteroscedasticity

One of the OLS assumptions is homoscedasticity, which means that the variance of the error term is constant. We test this assumption for our models by using a Breusch-Pagan test for heteroscedasticity. The null hypothesis for this test is homoscedasticity. The results of this test for the 3 models are shown in the table below.

Table 8 - Breusch-Pagan test

Model Chi-square statistics Probability > chi-square

Model 1 11.09 0.0497**

Model 2 97.25 0.0000***

Model 3 119.90 0.0000***

The Breusch-Pagan test is to test homoscedasticity. The null hypothesis is homoscedasticity. The chi-square statistic is the test statistic. The probability gives the p-value of this test-statistic.

The results in the table show that for a 5 percent significance level all the models are heteroskedastic. If we use the 1 percent significance level, only model 2 and 3 are heteroskedastic. We can correct for this in the same way as for serial correlation, namely by using robust standard errors in our regression.

5.2 First Hypothesis

For the first hypothesis, we regress the variable volume return as dependent variable on all our weather variables, FG, TG, SQ, DR, and NG, using robust standard errors. The output table of this regression can be found at the end. The table below gives a short overview of the effects of the weather variables on the dependent variable. We estimate the following equation by OLS for the first hypothesis: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐹𝐺𝑡+ 𝛽2𝑇𝐺𝑡+ 𝛽3𝑆𝑄𝑡 + 𝛽4𝐷𝑅𝑡+ 𝛽5𝑁𝐺𝑡+ 𝑒𝑡.

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Table 9 - Results Model 1 Number of observations 2816 F (5, 2810) 2.65 Probability > F 0.0214** R-squared 0.0054 F-test SQ=DR 0.04

Variable Kind of weather Coefficient t-value P-value

FG Wind speed 0.0007 1.25 0.210

TG*** Temperature -0.0013 -2.69 0.007

SQ Sun -0.0007 -1.08 0.281

DR** Rain -0.0008 -2.10 0.036

NG Cloud cover -0.0059 -0.60 0.548

FG is the wind speed at 0.1 m/s, TG is the average day temperature in 0.1 Celsius, SQ is the sunshine duration in 0.1 hour, DR is the precipitation duration in 0.1 hour, NG is the average coverage of the upper air into eighths. The F (5, 2810) gives the value for the test that all coefficients are significantly different from zero. The probability > F is the p-value of this F-statistic. R-squared is the value for how much the model does explain the dependent variable. F-test SQ=DR is the value of the test statistic to test if SQ and DR are significantly different. T-value is the test statistic to test the significance of the variable. P-value is the p-value of this test statistic.

From the table we can find that all weather variables have negative effects on the volume return, except from the wind speed. So even the duration of sunshine has an insignificant, negative influence, which is contrary to the theory. We have to make a note here that this negative effect is smaller than the negative effects of the other variables and that it is insignificant, so we will ignore it for now. If we take a look at the effect of the rain, we observe that this is negative and significant. This corresponds with the theory and earlier studies. We can conclude that if it is raining, people will trade less. Also the temperature has a significant, negative effect on the volume of trades. The 𝑅2 of this regression is very low, almost close to zero. This means that the model does not explain the dependent variable that well. The F-value is 2.65, which means that we can reject the null hypothesis that all the coefficients are zero. The hypothesis is that the coefficient of the variable sun is bigger, or - according to the results of our regression - less negative, than the coefficient of the variable rain. We have tested if there is a difference between these coefficients. This test gives an F-value of 0.04, so we cannot reject the null hypothesis that the coefficient of the variable sun is significantly bigger than the coefficient of the variable rain.

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5.3 Second Hypothesis

For the second hypothesis we regress the dependent variable volume return on the dummy variables of the days of the week, Friday excluded, using robust standard errors. The output table of this regression can be found at the end. The table below gives a short overview of the effects of the day of the week variables on the volume return. We estimate the following equation by OLS for the second hypothesis: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐷1𝑡+ 𝛽2𝐷2𝑡+ 𝛽3𝐷3𝑡+ 𝛽4𝐷4𝑡+ 𝑒𝑡.

Table 10 – Results Model 2

Number of observations 2816

F (4, 2811) 39.95

Probability > F 0.0000***

R-squared 0.0685

F-test Monday=Friday 50.90***

Variable Coefficient t-value P-value

Monday*** -0.1707 -7.13 0.000

Tuesday*** 0.1555 6.39 0.000

Wednesday 0.0140 0.66 0.510

Thursday 0.0070 0.34 0.731

Friday*** 0.0511 3.26 0.001

The F (4, 2811) gives the value for the F-test that all coefficients are significantly different from zero. The probability > F is the p-value of this F-statistic. R-squared is the value for how much the model does explain the dependent variable. F-test Monday=Friday is the value of the test statistic to test if Monday and Friday are significantly different. T-value is the test statistic to test the significance of the variable. P-value is the p-value of this test statistic.

From the table we can find that only one day of the week variable has a negative effect. This is Monday with a significant effect. Also Tuesday and Friday have significant effects on the volume return, which are positive. Striking is that Tuesday has a positive, significant effect, because in other studies this is a negative, sometimes significant effect. For example, Agrawal & Tandon find a negative, significant Tuesday effect for the Netherlands in the time period 1971-1987. However, we have tested the time period (2005-2015). Maybe the financial market has changed. The Monday and Friday effect are the same as predicted. With a test we are able to find out if we can reject the null hypothesis. The F-value from this test is 50.90, so we can reject the null hypothesis. The coefficients of the variables Monday and Friday are significantly different. Next to that, we can conclude that Monday and Friday both have a significant, opposite effect on the volume return.

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The F-value of this model is 39.95, which means that all coefficients are significantly different from zero. The 𝑅2 is again really low.

5.4 Third Hypothesis

For the third hypothesis we first have to make two interaction variables, namely DRMonday and SQFriday. After that we regress the volume return on all the variables using robust standard errors. The output of this regression can be found at the end. The table below gives a short overview of the effects of the interaction variables on the dependent variable. We estimate the following equation by OLS for the third hypothesis: 𝑉𝑅𝑡= 𝛽₀+ 𝛽₁𝐹𝐺𝑡+ 𝛽₂𝑇𝐺𝑡+ 𝛽₃𝑆𝑄_𝑡+ 𝛽₄𝐷𝑅𝑡+ 𝛽₅𝑁𝐺𝑡+ 𝛽₆𝐷1𝑡+ 𝛽₇𝐷2𝑡+ 𝛽₈𝐷3𝑡+ 𝛽₉𝐷5𝑡+ 𝛽₁₀𝑆𝑄_𝑡𝐷5𝑡+ 𝛽₁₁𝐷𝑅𝑡𝐷1𝑡+ 𝑒𝑡

.

Table 11 – Results Model 3

Number of observations 2816 F (11, 2804) 30.26 Probability > F 0.0000*** R-squared 0.1262 F-test DRMonday=SQFriday 0.03

DRMonday -0.0010 -1.37 0.169

SQFriday -0.0009 -1.49 0.136

The F (11, 2804) gives the value for the F-test that all coefficients are significantly different from zero. The probability > F is the p-value of this F-statistic. R-squared is the value for how much the model does explain the dependent variable. F-test DRMonday=SQFriday is the value of the test statistic to test if DRMonday and SQFriday are significantly different. T-value is the test statistic to test the significance of the variable. P-value is the p-value of this test statistic.

From the table we can find that both interaction variables are not significant. Also the F-test does not give a significant result. The F-value of this test is 0.03, which indicates that we cannot reject the null hypothesis. So DRMonday and SQFriday are not significantly different from each other. The expected hypothesis does not yield at all. The effect of rain and Monday combined is worse than the two effects separately. The same counts for the effect of sun and Friday combined, but this effect is less negative than Monday and rain combined. The F-value of this model is 30.26, we can reject the null hypothesis that the coefficients of the variables are not significantly different from zero. The R2 is still low, but higher than in the other models.

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5.5 Additional Regressions

There are ways to improve our models, without using robust standard errors. In this section we will discuss the results of these improvements in our models.

5.5.1 Lagged return variable

We could add a lagged return variable as independent variable, 𝑅𝑡−1, to our regression because it corrects for first order auto-correlation. For our first hypothesis about the weather variables, the OLS equation used will then be: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐹𝐺𝑡+ 𝛽2𝑇𝐺𝑡+ 𝛽3𝑆𝑄𝑡+ 𝛽4𝐷𝑅𝑡+ 𝛽5𝑁𝐺𝑡+ 𝛽6𝑅𝑡−1+ 𝑒𝑡.

For the second hypothesis about the day-of-the-week, the OLS equation will be: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐷1𝑡+ 𝛽2𝐷2𝑡+ 𝛽3𝐷3𝑡+ 𝛽4𝐷4𝑡+ 𝛽5𝑅𝑡−1+ 𝑒𝑡.

For the third hypothesis about the two effects combined, the OLS equation will be: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐹𝐺𝑡+ 𝛽2𝑇𝐺𝑡+ 𝛽3𝑆𝑄𝑡+ 𝛽4𝐷𝑅𝑡+ 𝛽5𝑁𝐺𝑡+ 𝛽6𝐷1𝑡+ 𝛽7𝐷2𝑡+ 𝛽8𝐷3𝑡+ 𝛽9𝐷5𝑡+ 𝛽10𝑆𝑄𝑡𝐷5𝑡+ 𝛽11𝐷𝑅𝑡𝐷1𝑡+ 𝛽12𝑅𝑡−1+ 𝑒𝑡.

The table below presents the results for these regressions.

Table 12 - Results Regression with Lagged Volume Return Variable

Model 1 Number of observations 2815 F (5, 2810) 71.93 Probability > F 0.0000*** R-squared 0.1332 F-test SQ=DR 0.01

Variable Kind of weather Coefficient t-value P-value

FG Wind speed 0.0007 1.52 0.129 TG*** Temperature -0.0013 -3.46 0.001*** SQ Sun -0.0006 -1.07 0.285 DR* Rain -0.0006 -1.74 0.083* NG Cloud cover -0.0072 -0.81 0.419 Rt-1 -0.3583 -20.35 0.000

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Model 2 Number of observations 2815 F (5, 2810) 79.36 Probability > F 0.0000*** R-squared 0.1238 F-test Monday=Friday 61.61***

Monday*** -0.1743 -7.85 0.000 Tuesday*** 0.1131 5.06 0.000 Wednesday** 0.0487 2.19 0.029 Thursday 0.0080 0.36 0.716 Friday*** 0.0660 4.19 0.000 Rt-1*** -0.2433 -13.31 0.000 Model 3 Number of observations 2815 F (5, 2810) 73.25 Probability > F 0.0000*** R-squared 0.2388 F-test DRMonday=SQFriday 0.00

DRMonday -0.0009 -1.25 0.212

SQFriday -0.0009 -1.59 0.111

Rt-1*** -0.3567 -20.35 0.000

FG is the wind speed at 0.1 m/s, TG is the average day temperature in 0.1 Celsius, SQ is the sunshine duration in 0.1 hour, DR is the precipitation duration in 0.1 hour, NG is the average coverage of the upper air into eighths, SQFriday is the interaction variable of SQ and Friday, DRMonday is the interaction variable of DR and Monday and Rt-1 is the lagged volume return variable.

The F (5, 2810) gives the value for the F-test that all coefficients are significantly different from zero. The probability > F is the p-value of this F-statistic. R-squared is the value for how much the model does explain the dependent variable. T-value is the test statistic to test the significance of the variable. P-value is the p-value of this test statistic.

From the table above we can conclude that for all the models the R-square and F-statistic are much higher with the lagged return variable included. This means that those models are better in explaining our dependent variable than the models without the lagged return variable.

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For the first model, almost all the t-statistics and p-values have the same meaning as before. Only the weather variable for rain is less significant, but still negatively significant for a significance level of ten percent. If we test our hypothesis that the variable sun is less negative than the variable rain, we get an F-value of 0.01. Therefore, we still cannot reject the null hypothesis that the coefficient of the variable sun is significantly bigger than the coefficient of the variable rain.

For our second model, next to the significant effects of Monday, Tuesday and Friday, also Wednesday has now a positive significant effect on the volume return. When we test our second hypothesis if Monday and Friday are significantly different, we get an F-value of 61.61. This means that we again can reject our null hypothesis. The coefficients of Monday and Friday are still significantly different.

The interaction variables of our third model are still not significant. When we use an F-test to test if the variables SQFriday and DRMonday are significantly different from each other, we get an F-value of 0.00. This indicates that the variables are still not significantly different from each other. Notable is that the coefficients from the variables are even the same now.

Table 13 - Results Durbin-Watson and Breusch-Pagan Test with Lagged Volume Return Variable

Model Durbin-Watson statistic Breusch-Pagan statistic Probability > Breusch-Pagan statistic

Model 1 2.1621 5.83 0.3230

Model 2 2.0492 29.31 0.0000***

Model 3 2.1423 143.65 0.0000***

The Durbin-Watson statistic indicates whether there is autocorrelation in the residuals. When this value is close to 2, there is not autocorrelation. The Breusch-Pagan test is to test homoscedasticity. The null hypothesis is homoscedasticity. The chi-square statistic is the test statistic. The probability gives the p-value of this test-statistic.

The table above shows for all our models that the Durbin-Watson statistic is much closer to two than before. From this finding we can conclude that there is almost no serial correlation in the models anymore. Next to that, we cannot reject the null hypothesis of homoscedasticity anymore for model 1. This means that the variance of the errors of model 1 is constant.

5.5.2 Key determinants volume return

When we run the regression of a model over-and-over again with removing the less significant variables every time, we will end with the key determinants of the volume return.

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For our first regression with the OLS equation: 𝑅𝑡 = 𝛽0+ 𝛽1𝐹𝐺𝑡+ 𝛽2𝑇𝐺𝑡+ 𝛽3𝑆𝑄𝑡+ 𝛽4𝐷𝑅𝑡+ 𝛽5𝑁𝐺𝑡+ 𝑒𝑡, the key determinant of the volume return is the variable TG. This is the average

temperature on a day. Which is easy to explain, because this is, as can be seen in the tables 9 and 12, the most significant variable.

For our second regression with the OLS equation: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐷1𝑡+ 𝛽2𝐷2𝑡+ 𝛽3𝐷3𝑡+ 𝛽4𝐷4𝑡+ 𝑒𝑡, the key determinants of the volume return are the variables Monday, Tuesday and Friday. All these variables are significant for a significance level of 1 percent. This again is consistent with our results of the regressions, as included in tables 10 and 12.

For our third regression with OLS equation: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐹𝐺𝑡+ 𝛽2𝑇𝐺𝑡+ 𝛽3𝑆𝑄𝑡+ 𝛽4𝐷𝑅𝑡+ 𝛽5𝑁𝐺𝑡+ 𝛽6𝐷1𝑡+ 𝛽7𝐷2𝑡+ 𝛽8𝐷3𝑡+ 𝛽9𝐷5𝑡+ 𝛽10𝑆𝑄𝑡𝐷5𝑡+ 𝛽11𝐷𝑅𝑡𝐷1𝑡+ 𝑒𝑡, the key determinants of the volume return are the variables Monday and Tuesday. Both variables are significant for a

significance level of 1 percent. This is also consistent with the results of the regression done on this model. The variables SQFriday and DRMonday are not significant, as can be found in tables 11 and 12. And the variable rain is a little bit less significant than the variables Monday and Tuesday, which can be found in table 12.

5.5.3 Recession dummy variable

The time period from 2005 until 2015 is known as a period where a big economic recession occurred. To control for this recession, we will add a recession dummy variable to our regression. This dummy variable is one when there was a negative average stock return in that quarter of the year and zero when there was not. The regression equations when we add the recession dummy variable will look as follows:

Model 1: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐹𝐺𝑡+ 𝛽2𝑇𝐺𝑡+ 𝛽3𝑆𝑄𝑡+ 𝛽4𝐷𝑅𝑡+ 𝛽5𝑁𝐺𝑡+ 𝛽6𝑅𝑡−1+ 𝛽7𝑅𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 + 𝑒𝑡. Model 2: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐷1𝑡+ 𝛽2𝐷2𝑡+ 𝛽3𝐷3𝑡+ 𝛽4𝐷4𝑡+ 𝛽5𝑅𝑡−1+ 𝛽6𝑅𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 + 𝑒𝑡.

Model 3: 𝑉𝑅𝑡 = 𝛽0+ 𝛽1𝐹𝐺𝑡+ 𝛽2𝑇𝐺𝑡+ 𝛽3𝑆𝑄𝑡+ 𝛽4𝐷𝑅𝑡+ 𝛽5𝑁𝐺𝑡+ 𝛽6𝐷1𝑡+ 𝛽7𝐷2𝑡+ 𝛽8𝐷3𝑡+ 𝛽9𝐷5𝑡+ 𝛽10𝑆𝑄𝑡𝐷5𝑡+ 𝛽11𝐷𝑅𝑡𝐷1𝑡+ 𝛽12𝑅𝑡−1+ 𝛽13𝑅𝑒𝑐𝑒𝑠𝑠𝑖𝑜𝑛 + 𝑒𝑡.

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Table 14 - Results Regression with Variable Recession

Model Variable Coefficient P-value

Model 1 FG 0.0007 0.129 TG -0.0114 0.001*** SQ -0.0006 0.285 DR -0.0006 0.082* NG -0.0072 0.419 Recession 0.0039 0.747 Model 2 Monday -0.1743 0.000*** Tuesday 0.1130 0.000*** Wednesday 0.0487 0.029** Thursday 0.0080 0.716 Friday 0.0665 0.000*** Recession -0.0016 0.918 Model 3 SQFriday -0.0009 0.108 DRMonday -0.0009 0.213 Recession 0.0057 0.619

FG is the wind speed at 0.1 m/s, TG is the average day temperature in 0.1 Celsius, SQ is the sunshine duration in 0.1 hour, DR is the precipitation duration in 0.1 hour, NG is the average coverage of the upper air into eighths, SQFriday is the interaction variable of SQ and Friday, DRMonday is the interaction variable of DR and Monday and Recession is the dummy variable for recession. The probability gives the p-value of the test-statistic about the significance of the variable.

As can be seen in the table above, there are no improvements of the models with the recession variable included. In none of the models this recession variable is significant and nothing has changed in the significance of the other variables.

Effect of mood on the stock market : the study of the effect of mood, influenced by the weather and/or day of the week, on the stock market in the Netherlands from 2005-2015