The effect of the weather on stock returns:
Empirical evidence from the Amsterdam stock exchange
Final version
By:
Marnix Dekker
S3850137
University of Groningen
Faculty of Economics and Business
MSc Finance
Supervisor:
Prof. dr. R.E. Wessels
Date: 04-06-2020
Abstract
1. Introduction
This paper examines the influence of the weather on stock returns. The papers by Saunders (1993) and Hirschleifer and Shumway (2003) are the first studies to test this relation empirically. Saunders (1993) finds that cloud cover negatively affects stock returns, and Hirschleifer and Shumway (2003) find that sunlight has a positive impact on stock returns. Both argue that this effect stems from the weather influencing mood, which in turn affects stock prices. Various studies have tried to replicate their results; not all of those studies find weather variables to affect stock returns. It is still not clear if and in what way the weather affects stock returns.
There are two proposed theories about in what way the weather could influence stock returns (also called transmission channels). First, the weather could have a direct effect on stock returns, as it is possible that the weather directly influences expected returns and risks of companies (the parameters of stock prices). Think of extreme weather (e.g., severe storms and heat waves) that inflict (economic) damage and could lower the level of economic activity (Heurta and Perez-Liston, 2011). The second transmission channel is that of an indirect relationship between the weather and stock returns. In the indirect transmission channel, the weather affects investors’ mood, which in turn influences financial decision making, and consequently affects stock markets. Mood could influence what kind of information is collected and in what way the information is interpreted. For example, Schwarz (1990) argues that a bad mood tends to stimulate people to engage in a more detailed analytical way. Furthermore, mood could cause people to estimate the probabilities of future events incorrectly and therefore, incorrectly estimate the expected returns and risks (Johnson and Tversky, 1983). Lastly, mood could affect investors’ risk perception (Isen and Patrick, 1983; Forgas, 1995). The empirical findings of Frühwirth and Sögner (2015) suggest that there is an indirect transmission channel between the weather and stock returns, as they find that the effects are mediated.
mood. Otherwise, investors could achieve excess returns based on weather forecasts and/or real-time weather measurements (information that is freely available for all investors). A significant indirect relationship between the weather and stock returns via mood indicates market inefficiency.
Many studies empirically examined the relationship between the weather and stock returns. Various weather variables are included in these studies. For example, Goetzmann and Zhu (2005) examined the effects of cloud cover, rain, and snow. Keef and Roush (2007) included cloud cover, temperature, and wind in their regressions. Sariannidis et al. (2016) tested the effects of humidity on stock returns.
Most of these studies perform their tests on data from countries in which it is quite unlikely that the same weather conditions apply to the entire country (e.g., the USA and Australia). Loughran and Schultz (2004) recommend future research to be performed on data from smaller countries in which the weather conditions likely apply to the entire country. This recommendation, in combination with the proximity trading bias, makes testing the indirect effects of the weather on stock returns a compelling case. The proximity trading bias suggests that local investors heavily invest and influence locally traded stocks; this effect is mainly observed at a national level (Solnik and Zuo, 2012; Huberman, 2001). In this study, the local investors are the investors influenced by the measured local weather conditions. Moreover, Coval and Moskowitz (1999) and Zhu (2002) argue that these biases more strongly influence small-cap stocks. That is why this study performs its statistical tests on a small-cap stock index from the Netherlands, namely the Amsterdam Small Cap Index (AScX). The research question of this paper is; does the weather in the Netherlands affect the daily returns of the Amsterdam Small Cap Index (AScX)?
This study examines the effects of several weather variables on the returns of the AScX. As this study lacks data about the mood of investors, this study cannot use proper empirical models to examine whether an observed relationship, between the weather and AScX returns, is mediated by investors’ mood or stems from direct effects. The weather variables examined in this study are the duration of sunshine, level of temperature, and level of relative humidity. These weather variables are selected based on the literature that suggests these variables influence people’s mood. For example, Howarth and Hoffman (1984) find that the duration of sunshine has a positive effect on mood, as sunshine positively influences optimism and negatively influences the level of anxiety.
2. Review of the literature
In this section, a review of the literature will be presented. First, the efficient market hypothesis and its assumptions will be addressed. After that, the possible transmission channels between the weather and stock returns will be discussed. Then the effects mood has on decision making will be discussed. After that, it is discussed how the weather could influence people’s mood. Subsequently, the results of previous studies examining the effects of the weather on stock returns will be presented and discussed. The last part presents the hypotheses of this paper.
2.1. Efficient market
Traditional economic models assume that the market is efficient, and investors behave rationally. For example, the CAPM sets up a relationship between expected returns and systematic risks. For each unit of additional risk, a rational investor wants to be compensated in terms of a higher expected excess return and vice versa (Sharpe, 1964). According to the CAPM, the only factors influencing asset prices are the market conditions (i.e., risk-free rate) and the two parameters of the model, namely expected return and risk. The same applies to the EMH by Fama (1970), which states: “A market in which prices always “fully reflect” available information is called “efficient”.” Prices that reflect all available information reflect the fundamental value of a company. The fundamental value of a stock is the present value of all expected future cash flows. The fundamental value is affected by expected returns and risk. In an efficient market, it should not be possible to achieve consistent excess returns above what would be expected, looking at the risk level.
This study can be seen as a test for market efficiency. Fama (1991) state that market efficiency cannot be directly tested, but must be tested jointly with some asset-pricing model. This way of testing leads to the joint-hypothesis problem. Evidence for anomalies can result from market inefficiency or an incomplete asset-pricing model.
1980). Numerous studies confirmed this effect using different samples (e.g., different periods, indexes, countries) (Wang, Li, and Erickson, 1997). The cause of this effect is also still not fully explained by economic theory. However, it is generally accepted that this anomaly exists. The final seasonal pattern discussed in this paper is the “Sell in May” effect, also called the Halloween effect. This effect suggests that returns in the winter (November until April) are significantly higher than returns in the summer (May until October) (Bouman and Jacobsen, 2002). They argue that investors in many countries are better off if they avoid putting money in the stock market in the summer and enter the market again in October. Bouman and Jacobsen (2002) do not find evidence for plausible explanations, like differences in risk between the two periods. The cause of the Halloween effect still is not explained and remains a puzzle (Jacobsen and Visaltanachoti, 2009). These seasonal patterns suggest that markets are not always efficient and that investors do not always make rational decisions.
2.2. Transmission channels
There are two proposed transmission channels for the weather to influence stock returns. First, the direct transmission channel is that the weather itself impacts expected returns and risks and thus the fundamental values of companies. Second, the indirect transmission channel, which is that the weather affects mood and mood in its turn influences (financial) decision making and consequently, stock returns.
The details of in what way the indirect transmission channel works is more elaborately discussed in part 2.3 and 2.4. In short, the (psychological) literature provide arguments for the existence of such a transmission channel. Hirschleifer and Shumway (2003) observe a significant relation between sunshine and stock returns, and they attribute this finding entirely to the indirect transmission channel. Hirschleifer and Shumway (2003) claim that the direct effect is non-existent, as daily weather measurements contain (almost) no valuable information (i.e., expected return and risk) for markets. Only the fundamental value of weather-related firms should be impacted by weather, like agricultural companies. However, these companies play a modest role in economies in the western world (Hirschleifer and Shumway, 2003). Furthermore, Hirschleifer and Shumway (2003) claim that daily weather measurements are not informative about harvests, as the weather variables are transitory, which means that today’s value is not informative about its value next week or next month. They conclude that there is no plausible economic theory for the daily weather conditions to influence stock returns directly.
damage done to the infrastructure and the agricultural sector, and the subsequent costs for the insurance sector (Heurta and Perez-Liston, 2011). Heatwaves lead to lower levels of productivity and may inflict some economic damage to infrastructure (Lehr et al., 2016). A period of extreme cold could hamper (public) transportation and therefore also decrease economic activity. Summarising, extreme weather hampers markets and commercial activities (Heurta and Perez-Liston, 2011). This indicates that the assumption made by Hirschleifer and Shumway (2003) is not correct. An observed relationship between the weather and stock returns cannot be entirely attributed to indirect effects.
The literature (e.g., Lehr et al., 2016) suggests that the weather only directly influences stock returns during extreme weather conditions. There is no economic explanation for the weather to influence stock returns directly during days with regular weather conditions. Therefore, this paper follows a modified version of the assumption made by Hirschleifer and Shumway (2003). The assumption in this paper is that daily weather contains no valuable information about the fundamental value of companies during days with regular weather. When a relationship between the weather and stock returns during regular weather conditions is observed, then this effect cannot be attributed to direct effects. It can be attributed to indirect effects, as it is in line with the (psychological) literature about the weather affecting mood, which in turn affects stock prices. In the case that the weather influences stock returns (during all trading days), and this effect is no longer observable during regular weather conditions. Then this paper is not able to explain from which transmission channel the observed effect stems.
Frühwirth and Sögner (2015) empirically tested through which transmission channel, weather influences stock returns. Their results suggest that the weather indirectly influences stock returns in the United States. Bassi et al. (2013) support this, as they find mood to play a significant role as a mediating variable.
When the weather systematically influences stock returns via mood in a predictable direction, there could be a bias in stock prices. Then arbitrage opportunities arise for investors abroad and investors that are not affected by the weather. These investors could follow a weather-based trading strategy, that profits from the trades that the weather influenced investors make. For example, investors on a rainy day could be more pessimistic about the future and interpret new information more negatively, resulting in (relatively) lower stock prices. If this occurs systematically, rational investors could profit from a weather-based trading strategy. In this case, that would mean buying stocks on rainy days.
between the weather and stock returns indicates market inefficiency. If the weather directly influences stock returns, it could be rationally explained by changes in expected returns and risks. Hence, a direct effect between the weather and stock returns is in line with the EMH.
2.3. Mood affects judgement and decision making
In the indirect transmission channel, the weather influences mood and mood in its turn influences (financial) decision making, consequently affecting stock returns. This part discusses how mood influences decision making and the valuation of stocks.
Mood affects the behaviour of people; for example, Isen (2000) shows that people in a good mood tend to perform better in creative problem-solving. Wright and Bower (1992) find that individuals in a good mood have more positive evaluations of many sorts (e.g., life satisfaction). Psychological research has also been performed on the relationship between mood and decision making. Etzioni (1988) argues that mood is an essential mechanism in economic decision making. Mood could affect decision making in a few different ways.
First, Schwarz (1990) argues that bad mood tends to stimulate people to engage in a more detailed analytical way. Conversely, a good mood is associated with less critical modes of information processing. A less critical mode of information processing implies that people (who are in a good mood) are more easily influenced by weakly argued information. Thus, mood changes the kind of information that is collected and in what way it is interpreted.
Second, mood may create cognitive biases in the estimation of the probabilities of future events (Johnson and Tversky, 1983). Loewenstein (2000) support this by claiming that mood affects the weighting of future long-term costs and benefits. Johnson and Tversky (1983) find that people who are in a good mood are more optimistic about the future and assign higher probabilities to positive events and vice versa.
Conversely, Drichoutis and Nayga (2013) claim that positive mood increases the level of risk aversion, thus supporting the MMH model. A good mood can theoretically either increase or decrease risk aversion of investors and subsequently influence their valuation of stocks. Important to note is that Guven and Hoxha (2015) observe that happy people in the Netherlands are more risk-averse and are less likely to own stocks or bonds.
To illustrate all these effects; a bad mood could lead to investors findings more negative information and lead them to scrutinise this information more thoroughly. Additionally, investors in a bad mood are prone to underestimate future returns and overestimate future risks. The risk perception of investors could also be affected, yet the precise effect is still unknown. Taking these effects into account, investors’ valuation of a company would be relatively low when the investor has a bad mood. Following the same line of reasoning, a good mood would lead to a relatively high valuation.
Forgas (1995) claims that the influence of mood on decision making is more substantial in situations with more uncertainty. Shu (2010) and Keef and Roush (2007) argue that small-cap stocks are more affected by this effect, as the level of uncertainty of small-cap stocks is relatively high.
With these findings in mind, it can be expected that investors’ valuations are influenced by the current mood of the investors. Mood could create a systematic bias in companies valuations. The direction of this bias is known beforehand (good mood higher stock price valuations, bad mood lower stock price valuations).
2.4. Weather affects mood
The previous part discussed the effects that mood has on decision making and company valuations. This part will discuss how people’s mood is affected by the weather. People feel different depending on the weather. For instance, people seem to have a higher level of life satisfaction on sunny days compared to rainy days (Lucey and Dowling, 2005). Numerous studies find that the weather influences the behaviour of people. For example, Allen and Fisher (1978) argue that weather influences the performance of people. Cunningham (1979) find that people tip more generously on days with good weather (sunshine).
Not only do studies find that weather influences behaviour, but studies also find that weather affects mood. Howarth and Hoffman (1984) examine the relationship between various weather variables and mood variables. They find that humidity, temperature, and the duration of sunshine have the most substantial effects on mood, especially humidity. The level of humidity negatively influences people’s concentration levels, suggesting that high humidity levels can be associated with a bad mood (Howarth and Hoffman, 1984).
of optimism. Moreover, Guven and Hoxha (2015) find that sunshine has a significant positive impact on the happiness of households in the Netherlands and Germany. Therefore, it can be expected that the duration of sunshine can be positively associated with a good mood.
Howarth and Hoffman (1984) find that higher levels of temperature can be associated with a lower level of anxiety, indicating that a higher temperature can be associated with a good mood. However, Keller et al. (2005) find that higher temperatures should be associated with a bad mood, as it can cause discomfort. Cao and Wei (2005) argue that lower temperatures can be associated with higher levels of aggression, and aggression could be related to a higher level of risk-taking. Denissen et al. (2008) find similar results and argue that higher temperatures are related to a bad mood. The literature is not in agreement about what the effect of the temperature will be on the mood of people. It will be interesting to see what the nature of such a relationship will be if a relationship is observed.
To summarise, the literature does find evidence for the weather to influence people’s state of mood. High levels of humidity can be associated with a bad mood, prolonged durations of sunshine can be associated with a good mood and the relationship between the temperature and mood is still debated.
2.5. Proximity-based trading
Even if the weather does influence mood and mood affects the valuations of stocks that local investors make. It is still not expected that the stock prices are affected by the weather variables. When these local investors trade based on their biased valuations, then arbitrage opportunities for rational investors or investors exposed to different weather conditions will arise. As a consequence, the biased trades should not alter the stock prices. So, in an efficient market, no indirect relationship between weather variables and stock returns will be observed.
However, Solnik and Zuo (2012) argue that stocks are disproportionally more traded by local investors compared to investors situated elsewhere. This proximity-trading bias suggests that local traders have a disproportionate amount of influence on the pricings of local stocks. Local traders could affect the local stock prices with their biased valuations with the influence they have. This phenomenon makes it possible to observe the weather to influence local stock returns indirectly.
can lead to people not investing in foreign stocks at all (Huberman, 2001). Loughran and Schultz (2004) find supporting empirical evidence. They observe that local investors significantly affect intraday trading patterns of local stocks. Coval and Moskowitz (1999) and Zhu (2002) find a more substantial presence of the proximity-trading bias in small-cap stocks compared to large-cap stocks.
Due to this proximity-trading bias, it may be possible to observe the weather variables to influence local stock returns indirectly.
2.6. Weather affects stock returns
This part discusses the results of preceding studies that examined whether the weather affects stock returns. Saunders (1993) was the first to test the relationship between weather and stock returns empirically. He tested three New York stock exchanges from 1927 till 1989 for this effect. The results of his study show that cloud cover negatively influences stock returns. The paper by Hirshleifer and Shumway (2003) researched the effects of sunshine in 26 countries on their respective stock exchanges. In their pooled results, they observe a positive relation between sunshine and stock returns.
Studies did not only look at the effect of sunshine (cloud cover) but used a multitude of weather variables. Like Keef and Roush (2007) who, besides cloud cover, also studied the effects of wind and temperature on stock returns in Australia. They only find a significant negative effect between temperature and stock returns. Sariannidis et al. (2016) looked to the effects of humidity, which they find to have a significant positive effect on the stock returns. Goetzmann and Zhu (2005) studied the effects of rain and snow in the USA.
Loughran and Schultz (2004) think the reason they and some other studies did not find significant results stems from the size of the countries from which they collected their data. The countries are often massive (e.g., the USA and Australia). Loughran and Schultz (2004) state that it is unlikely for these countries that the weather conditions in the stock exchange city apply to the entire country. This means that not even all national investors are influenced by the same weather conditions. They advise future research to study the effects in smaller countries, in which it is far more likely that the same weather conditions apply to the entire country, thus to all investors in that country.
As the literature shows the possible effects of the weather on stock returns is still very much debated. It is not yet known which weather variables do influence stock returns if any. More research is required to determine whether there truly is a relationship between the weather and stock returns.
2.7. Hypotheses
This study examines the influence of the weather on stock returns. Specifically, it studies whether there is a relationship between the weather in the Netherlands and the return of the Amsterdam Small Cap Index (AScX).
This study lacks data about the mood of investors. Therefore this study cannot use a proper empirical model to examine whether an observed relationship between the weather and stock returns, stems from direct effects or is mediated by mood. However, it will be tested if the relationship between the weather and stock returns is also observable during days with regular weather. When a significant relationship between the weather and stock returns is observed during regular weather, this suggests that the effect stems from the indirect transmission channel. When a relationship between the weather and stock returns is no longer observable in regular weather conditions, then this paper is not able to explain from which transmission channel this earlier observed effect stems.
When this study finds evidence for significant indirect effects, it indicates that such a weather-based trading strategy could achieve consistent excess returns above what the risk level would suggest. In an efficient market, it should not be possible to achieve consistent excess returns. Thus a significant indirect relationship between the weather variables and stock returns during regular weather indicates market inefficiency.
This research will be conducted on a stock market in the Netherlands, as previous studies (i.e., Loughran and Schultz, 2004) recommended conducting future research on data from smaller countries. The literature (e.g., Shu (2010)) also suggests testing the effects on the small-cap stock index, as it is expected that the effects of mood are more visible in the cap stock indices. Additionally, the proximity trading bias is more substantial for small-cap stocks (Coval and Moskowitz, 1999). In conclusion, the effects will be tested on the Amsterdam Small Cap Index (AScX).
The weather variables tested in this paper are the daily duration of sunshine, daily mean temperature, and daily mean relative humidity. The literature finds these weather variables to have the most substantial relationship with mood. If the weather is indirectly related to stock returns, then this relationship should be observed using these weather variables. When no significant indirect relationship is examined, then it is unlikely that other weather variables do have an indirect relationship with stock returns. The most often studied weather variable in previous papers is the duration of sunshine (or cloud cover) (e.g., Saunders, 1993; Hirshleifer and Shumway, 2003). It will be interesting to test whether the previously observed positive relationship between sunshine and stock returns is also present in the Netherlands. Literature suggests that temperature influences mood (Keller et al., 2005). However, the literature is not in agreement about whether temperature should be positively or negatively related to stock returns. When a significant relationship is observed, it will be interesting to see how this relationship works. Howarth and Hoffman (1984) argue that humidity has the most significant impact on mood. Additionally, Sariannidis et al. (2016) find a positive relationship between humidity and stock returns. It will be interesting to see whether this relationship can also be observed in the Netherlands.
This results in the following sub-question, namely:
Does the daily duration of sunshine in the Netherlands affect the daily returns of the Amsterdam Small Cap Index?
Does the daily temperature in the Netherlands affect the daily returns of the Amsterdam Small Cap Index?
3. Research method and data
3.1. Data
This part explains how the data for this study is collected. As stated before the stock index that will be examined in this study is the Amsterdam Small Cap Index (AScX). The AScX consists of 25 companies that operate predominantly locally. Data from the AScX gross return index (total return index) is collected. A gross return index “reinvests” cash distributions (i.e., dividends). Thereby, this index measures market performance as both capital gains and income from dividends. Using data from a gross return index excludes the impact of dividends on stock returns. The data is collected from 2 March 2005, the day the AScX opened, until 31 December 2019 (3,789 observations). Additionally, data of the MSCI World Index (gross return index) is collected for the same period. The MSCI World Index will be used as an explanatory variable, more on that later. Daily closing prices of both indexes are collected using Thomson Reuters Eikon. The daily return data is calculated by 𝑅𝑡= 100 × ln (𝑃𝑡/𝑃𝑡−1).
Data about the weather conditions in the Netherlands are collected from the KNMI (Koninklijk Nederlands Meteorologisch Instituut). The KNMI has numerous weather stations in the Netherlands, but only data from the weather station in “De Bilt” will be used. This weather station is centrally located within the Netherlands, which is why it is likely to represent the effect of the weather on all investors in the Netherlands. As stated before, data about the duration of sunshine, average temperature, and the average level of relative humidity are collected. The variable Sun is the duration of sunshine during a day measured in 0.1 hours. Temperature is the daily mean temperature measured in 0.1 degrees Celsius. Humidity is the daily mean level of relative atmospheric humidity, measured in percentages on a scale of 0-100%.
Not only the level of the weather variables can affect stock returns (and mood), but also the change in the weather can affect stock returns (Keef and Roush, 2007). New variables will be created to represent these changes in weather. The new weather variables (specified with the prefix ∆) are the daily values minus the average value of the five preceding trading days. So, these new weather variables will be the deviation of today’s weather level compared to the average weather level of the preceding week. This method also deseasonalises the weather variables. These new variables are more conservative measures of the possible effect that weather has on stock returns. Any contribution that the weather variables may have in explaining seasonal patterns in stock returns is excluded using this method (Hirshleifer and Shumway, 2003).
extreme weather. This paper follows those criteria. The KNMI defines a severe storm as a storm with an average hourly wind speed of at least 10 Beaufort (24.5 m/s). A cold wave is defined as five consecutive days with a maximum temperature below 0 degrees Celsius, of which at least three days have a recorded minimum temperature below -10 degrees Celsius. A heatwave is defined as at least five consecutive days with the maximum temperature above 25 degrees Celsius, of which three days have a maximum temperature above 30 degrees Celsius. In total, 69 observations meet the criteria of extreme weather (an overview of these observations can be found in Appendix C).
Descriptive statistics about the data are presented in Table 1. The correlation matrices can be found in Appendix A.
Descriptive Statistics
Variable Obs Mean Std.Dev. Min Max
ASCX 3789 .035 .985 -8.225 7.537 MSCI 3789 .026 .988 -7.317 9.097 Sun 3789 48.461 41.422 0 153 Temperature 3789 109.072 62.781 -85 297 Humidity 3789 80.574 9.758 34 100 ∆Sun 3784 .0303 29.6105 -105.6 132.6 ∆Temperature 3784 .0223 38.1225 -136.4 121.4 ∆Humidity 3784 -.0049 8.0275 -37.8 38.4
Table 1: Descriptive statistics of the dependent and independent variables. Sun is the daily sunshine duration (in 0.1 hours), Temperature is the daily mean temperature (in 0.1 degrees Celsius), and Humidity represents daily mean level of relative humidity (in percentages on a scale of 0%-100%). The weather variables with prefix ∆ represent the changes in those weather variables.
Control variables
estimated coefficients of the explanatory variables are thus biased (upwards/downwards) and inconsistent. The control variables used in this study are based on the control variables that previous papers, examining the effects of weather on stock returns, used. This part discusses what control variables are included in this study.
As mentioned above, the MSCI World Index will be used as a control variable. Tsutsui and Hirayama (2004) report that international stock indices are correlated with each other. Moreover, Dutt and Mihov (2013) find that country indices are becoming more and more correlated. The MSCI World Index is correlated with the returns of the AScX, yet unaffected by the weather in the Netherlands. In this study, the MSCI World Index controls for the influences of global events on the fundamental value of stocks on the AScX. This increases the level of efficiency of the regressions.
3.2. Methods
Previous studies have most often performed the Ordinary Least Squared (OLS) regression to examine the relationship between the weather variables and stock returns (e.g., Saunders, 1993; Hirshleifer and Shumway, 2003; Keef and Roush, 2007). So too will this study to get comparable results. The regressions in this study try to explain the returns of the AScX with the weather variables and the other explanatory variables. The first regression examines whether the observed daily levels of the weather variables are related to returns of the AScX. The observed levels are the duration of sunshine, average temperature, and level of relative humidity. This all results into the following regression;
𝑅𝑡𝐴𝑆𝑐𝑋 = 𝛼 + 𝛽1𝑆𝑢𝑛𝑠ℎ𝑖𝑛𝑒𝑡+ 𝛽2𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒𝑡+ 𝛽3𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑡+ 𝛽4𝑀𝑆𝐶𝐼𝑡+ 𝛽5𝑀𝑜𝑛𝑑𝑎𝑦𝑡+ 𝛽6𝐻𝑎𝑙𝑙𝑜𝑤𝑒𝑒𝑛𝑡+ 𝛽7𝐽𝑎𝑛𝑢𝑎𝑟𝑦𝑡.
(1)
Regression (1) uses the daily levels of weather variables to explain the returns of the AScX. As mentioned before it is also interesting to see the influences of the changes in the weather variables (i.e., deseasonalised weather variables). The deseasonalised weather variables (∆) will be included in the second regression. The second regression is as follows;
𝑅𝑡𝐴𝑆𝑐𝑋 = 𝛼 + 𝛽1∆𝑆𝑢𝑛𝑠ℎ𝑖𝑛𝑒𝑡+ 𝛽2∆𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒𝑡+ 𝛽3∆𝐻𝑢𝑚𝑖𝑑𝑖𝑡𝑦𝑡+ 𝛽4𝑀𝑆𝐶𝐼𝑡+ 𝛽5𝑀𝑜𝑛𝑑𝑎𝑦𝑡+ 𝛽6𝐻𝑎𝑙𝑙𝑜𝑤𝑒𝑒𝑛𝑡+ 𝛽7𝐽𝑎𝑛𝑢𝑎𝑟𝑦𝑡.
(2)
Gauss-Markov assumptions
To be able to perform proper OLS regressions, the Gauss-Markov assumptions should hold. These assumptions are;
1. Errors have zero mean;
2. Errors have constant variance (homoscedasticity); 3. Errors are uncorrelated between observations; 4. Errors and explanatory variables are uncorrelated; 5. Errors are normally distributed.
The first four assumptions should be satisfied to get Best Linear Unbiased Estimators (BLUE). To be able to conduct proper hypotheses testing, the fifth assumption should also be satisfied. Tests have to be performed to check whether these assumptions hold. In case these assumptions are violated, remedial actions have to be taken such that the assumptions are no longer violated. The following parts will discuss what statistical tests will be performed to check whether the assumptions hold and what remedial actions have to be taken in the case the assumptions are violated.
Errors have zero mean
The first assumption requires that the average value of the errors is zero. If the average value of the errors is not zero, there is a bias in the model, as the model makes predictions that are systematically too high or too low. A constant in the model will force the average value of the errors to be zero. Adding a constant to the model will thus absorb this bias. The regressions in this paper include a constant term. Hence assumption 1 is satisfied.
Heteroskedasticity
Autocorrelation
The next assumption states that there should be no pattern in the errors (no autocorrelation). Presence of autocorrelation could mean that the standard errors are inappropriate. The estimated coefficients are still unbiased but are now inefficient. The Breusch-Godfrey test will be performed to check for the presence of autocorrelation. In the case of autocorrelation, heteroskedasticity and autocorrelation consistent standards errors will be used. This means the standards errors will be corrected with the Newey-West procedure, which allows making correct inferences about the result (Newey and West, 1987). This type of standard error requires an optimal lag order for which the autocorrelation is accounted. This paper uses the procedure proposed by Newey and West (1994) to determine the optimal number of lags.
Endogeneity
This assumption states that the error term should be uncorrelated with the explanatory variables. Endogeneity is that the error term is correlated with the explanatory variable(s). Endogeneity can occur when an explanatory variable outside of the regression is correlated with an explanatory variable that is included in the regression. When endogeneity is present, the regression will incorrectly attribute some part of the variance of the error term to the explanatory variables that are included in the regression. These explanatory variables will then explain too much (or too little) in the model compared to reality. Hence, endogeneity is that the estimated coefficients of the explanatory variables are biased and inconsistent.
There are a few sources of endogeneity. The previously discussed omitted-variable bias is a form of endogeneity. Furthermore, endogeneity can arise due to measurement errors. This occurs when explanatory variables cannot be appropriately measured. The variables in this study are easy and to measure objectively. Furthermore, the data used in this study is collected from institutions which verify their data. Measurement errors are highly unlikely to cause endogeneity problems in this study. Another form of endogeneity stems from reverse causality. It can be reasonably expected that this is also unlikely to cause endogeneity problems in this study, as stock returns cannot possibly influence the weather.
Normality
This assumption states that the error term should be normally distributed. This assumption does not need to be satisfied to obtain BLUE estimators. However, this assumption needs to be satisfied to allow for proper statistical hypothesis testing. Frequently, financial return data is non-normally distributed, errors exhibit excess peakedness at the mean and fat tails.
normal distribution, as the sample size increases. This paper uses a considerable amount of observations (3,789 observations). According to the central limit theory, this sample size makes the violation of normality inconsequential. No further actions are required.
Multicollinearity
An underlying assumption of the OLS method is that the explanatory variables are not correlated with one another. Multicollinearity is that explanatory variables are highly correlated with one another, in a way that both variables cannot independently predict the value of the dependent variable. Multicollinearity results in high standard errors of the correlated variables, diminishing the significance of their estimated coefficients.
A priori it can be reasonably argued that weather variables are correlated with each other. It makes sense that on days with much sunshine, the temperature will be (relatively) higher. Relative humidity can also be negatively related to temperature, as the air can hold more water vapour when temperatures are higher. Holding the amount of water vapour equal, the level of relative humidity will decrease (increase) with higher (lower) temperatures. Correlation matrices are presented in Appendix A. The matrices report high levels of correlation between the weather variables. The largest reported correlation between the weather variables is -0.7140 (between the duration of sunshine and level of relative humidity).
To test whether there are multicollinearity problems in the data, the Variance Inflation Factors (VIF) will be calculated. In order to determine whether the explanatory variables are too highly correlated, we need the tolerance factor. The tolerance factor is 1/VIF. For variables with a tolerance factor below 0.2, multicollinearity is assumed to be problematic in which case remedial action is needed, for example, not including all the weather variables in the same regression.
Stationarity
As the data concerns time series data, it is necessary to check whether the data is stationary or not. The use of non-stationary data can lead to spurious regressions. A spurious regression is a regression with an explanatory variable that coincidentally aligns with the dependent variable, when, in fact, there is no relationship between the variables. Such a regression will produce good statistical measures (e.g., high 𝑅2), when in reality the regression has no valuable meaning.
Autoregressive conditional heteroscedastic (ARCH) effects
Above, it is mentioned that the variance of the error can change over time. In a financial time series, this is likely the case, as financial time series often feature volatility clustering. Volatility clustering is that large changes in stock prices follow large changes and small changes in stock prices follow small changes. Think of the difference in volatility during a crisis (high turbulence) and periods of relative tranquillity. When the variance of the error changes over time, there is an ARCH effect in the data. These ARCH effects can be modelled.
This study will test for the presence of ARCH effects in its data. The presence of ARCH effects will be tested for up to 21 lags (average number of trading days in a month). When ARCH effects are observed, it will implicate that the standard errors of the OLS regressions could be incorrect, making inferences possibly misleading. Therefore, an ARCH model should be implemented to obtain correct standard errors. The Generalised ARCH (GARCH) model by Bollerslev (1986), is a parsimonious model as it only contains three parameters. Nevertheless, it models the ARCH effects for all past lags. Ideal for when a standard ARCH model needs to contain a large number of parameters to model all the ARCH effects, as that increases the chance of violating the non-negativity constraint.
Besides volatility clustering, financial time series could also have a different response of volatility to positive and negative shocks in stock prices. Meaning that a negative (positive) shock is likely to cause volatility to rise by more than a positive (negative) shock of the same magnitude. The GJR-GARCH model includes an asymmetry term (Glosten et al., 1993). That is why Sariannidis et al. (2016) use the GJR-GARCH (1,1) model when studying the effects of humidity on stock returns.
When ARCH effects are observed in the data, then this study will use the GJR-GARCH (1,1) model as a robustness test for regressions (1) and (2). The conditional variance of this model is given by:
𝜎𝑡2 = 𝛼0+ 𝛼1𝑢𝑡−12 + 𝛽𝜎𝑡−12 + 𝛾𝑢𝑡−12 𝐼𝑡−1, (3)
4. Results
In this section, the results of this study are presented and discussed. The first part presents the outcomes of the statistical tests that examine whether the Gauss-Markov assumptions are violated or not. Then the results of the OLS regressions will be presented. The final part presents the outcomes of the robustness test.
4.1. Gauss-Markov assumptions
In the methodology section, the assumptions of Gauss-Markov for OLS regressions were explained. It is mentioned what statistical tests will be performed to check whether the assumptions hold and what to do in case the assumptions are violated. In this part, the outcomes of these statistical tests will be presented. Furthermore, it will be mentioned what remedial actions are taken in this study to get BLUE estimators in the OLS regressions.
First, the White’s general test for heteroskedasticity is performed to check for the presence of heteroskedasticity. Highly significant evidence is found for the presence of heteroskedasticity in the variance of the regressions (all at a 1% significance level (Appendix B)). Second, a statistical test for the presence of autocorrelation is performed. To be specific, the Breusch-Godfrey test is performed. All regressions have a presence of autocorrelation as all tests are significant at a 1% level (Appendix B). Hence the null hypothesis (no serial correlation) can be rejected. Both the presence of heteroskedasticity and autocorrelation make the standard errors inappropriate for making inferences. To be able to make correct inferences about the results of the regressions, heteroskedasticity and autocorrelation consistent standards errors will be used. In this study, the Newey and West standard errors will be used. Newey and West standard errors handle all the autocorrelation up to and including a specified number of lags. As mentioned in the methodology, this paper uses the procedure proposed by Newey and West (1994) to determine the optimal number of lags. That procedure suggests the use of 45 lags.
Using the Newey and West standard errors to account for the presence of heteroskedasticity and autocorrelation, means that the assumptions of Gauss-Markov are satisfied and that the estimated estimators will be BLUE.
Multicollinearity
The results of this test are shown in Appendix B. Regression (1) with the weather variables as levels, has the lowest tolerance factors. The weather variables and the Halloween variable all have a relatively low tolerance factor. The temperature variable has the lowest tolerance factor, namely 0.3786. Following the rules of thumb that tolerance factors lower than 0.2 are problematic, we can assume that multicollinearity is no problem in any of the regressions.
Stationarity
The data is tested for stationarity using the Augmented Dickey-Fuller test. The outcomes are presented in Appendix B. The outcomes are highly significant at a 1% level, leading to a rejection of the null hypothesis that the series contains a unit root. The Augmented Dickey-Fuller test indicates that the data are stationary. No further action is needed.
Autoregressive conditional heteroscedastic (ARCH) effects
This study tested its data on the presence of ARCH effects in its residuals. The outcomes are presented in Appendix B. The error term of all four regressions have a presence of ARCH effects at least up till 21 lags (maximum number of lags tested). As mentioned in the methodology section, this study will use the GJR-GARCH model to model these ARCH effects in its time-series data. The GJR-Models will be performed as a robustness test for all four regressions. As there are ARCH effects in the data, the GJR-GARCH model is a better fit to model the relationship between the weather and stock returns. Therefore, the outcomes of GJR-GARCH should be used to make correct inferences about the relationship between the weather and AScX returns.
4.2. Regression analysis
This part presents and discusses the outcomes of the regressions. First, the outcomes of the regression using the levels of the weather variables to explain AScX returns are presented. After that, the results of the regression using the changes in the weather variables to explain AScX returns are presented. Then the previous tests are performed yet again, this time using only the observations with regular weather conditions. The last part provides the outcomes of a robustness test, namely the GJR-GARCH model.
The weather variables as levels
Monday effect is statistically significant at a 5% level. However, it has a positive estimated coefficient while literature (e.g., French, 1980) argues that returns on a Monday are lower compared to the other trading days. The coefficient of the MSCI and Halloween variables do match to the expectations, and both are highly statistically significant at a 1% level. When the returns of the MSCI World Index change by 1%, the expected returns of the AScX change by 0.6499%. Furthermore, daily AScX returns in the winter period (November-April) are 0.0768% higher compared to the daily returns in the summer period. The estimated coefficient of the Halloween variable is in line with Bouman and Jacobsen (2002), as they too observe that daily returns in the months November until April are significantly higher.
VARIABLES Control Variables Regression (1a)
Sun 0.0007* (0.0004) Temperature -0.0005* (0.0003) Humidity 0.0004 (0.0017) MSCI 0.6499*** 0.6498*** (0.0286) (0.0288) Monday 0.0741** 0.0719** (0.0289) (0.0290) Halloween 0.0768*** 0.0489 (0.0268) (0.0328) January 0.0103 0.0068 (0.0503) (0.0498) Constant -0.0343** -0.0311 (0.0169) (0.1683) Observations 3,789 3,789
Table 2: OLS regressions estimated on AScX returns. In column 2, the results of the
regression using only the control variables as explanatory variables are presented. In column 3, the results of regression (1a) (the regression with the weather variables as levels) are presented. Newey and West standard errors are used with a lag of 45. Standard errors in
parentheses.
*** p<0.01, ** p<0.05, * p<0.1
returns. The variable Sun, representing the duration of daily sunshine in 0.1 hours, is weakly statistically significant at a 10% level. This variable has a weak economic interpretation as an increase in the duration of sunshine with 1 hour would explain only a 0.0072% increase in the return of the AScX. Even between the day with the most prolonged recorded duration of sunshine and the days with no sunshine at all, the expected return changes with only 0.1095% (15.3 hours of sunshine x 0.0072%). This result is in line with the findings of Saunders (1993) and Hirshleifer and Shumway (2003).
The temperature variable representing the level of temperature in 0.1 degrees Celsius, is also weakly statistically significant at a 10% level. The estimated coefficient of the temperature variable is -0.0005%, indicating that daily AScX returns are higher on colder days. This result is in line with the findings of Cao and Wei (2005) and Keef and Roush (2007). The difference in the expected AScX returns between the coldest and hottest recorded days is 0.185% ((29.7 + 8.5) x 0.0048%). The negative coefficient can theoretically be explained by heatwaves having a direct negative effect on the fundamental value of companies, or by the literature supporting the indirect effects channel. Cao and Wei (2005) argue that this negative effect stems from that lower temperatures cause higher levels of risk-taking.
The humidity variable represents the daily mean relative atmospheric humidity, measured in percentages on a scale of 0%-100%. This study does not find statistically significant results for the level of humidity to be related to AScX returns. This contradicts with the literature that supports the indirect effects channel, as Howarth and Hoffman (1984) find that humidity has the most significant effect on mood. Furthermore, this result is not in line with the findings of Sariannidis et al. (2016). They find a statistically significant relationship between humidity and stock returns. However, this result is similar to the findings of Pardo and Valor (2003). They too did not find humidity to influence stock returns.
Changes in the weather
In this part, the weather variables are the daily deviations from the average value of the preceding week. These weather variables are the deseasonalised weather variables. These variables are not correlated with the observed Halloween calendar effect (see Appendix A). Any contribution that the weather variables may have in explaining this seasonal pattern is excluded in this regression. These weather variables are used in regression (2a) to explain the AScX returns. The results of this regression are presented in Table 3.
VARIABLES Regression (2a)
∆Sun 0.0006* (0.0004) ∆Temperature 0.0001 (0.0004) ∆Humidity 0.0003 (0.0016) MSCI 0.6505*** (0.0287) Monday 0.0726** (0.0290) Halloween 0.0770*** (0.0268) January 0.0090 (0.0502) Constant -0.0337** (0.0169) Observations 3,784
Table 3: Outcomes of OLS regression (2a) estimated on AScX returns. The explanatory
weather variables are the changes in the weather variables. Newey and West standard errors are used with a lag of 45. Standard errors in parentheses.
*** p<0.01, ** p<0.05, * p<0.1
0.0871% change in the expected AScX return. Therefore this variable has weak economic significance. Again, the results of this estimated coefficient are in line with the findings of Saunders (1993) and Hirshleifer and Shumway (2003).
The deseasonalised temperature variable (∆Temperature) is not statistically significant in explaining AScX returns. This is not in line with the findings of Keef and Roush (2007), as they find that the deseasonalised temperature has a more substantial adverse effect on stock returns than the level of temperature. Furthermore, the estimated coefficient is no longer negative, and this is not expected following the results from Keef and Roush (2007) and the theoretical explanation of Cao and Wei (2005). Cao and Wei (2005) argue that a decrease in temperature increases risk-taking behaviour.
The variable ∆Humidity is also not statistically significant, just as the level of humidity was not significant in regression (1a). This study does not find evidence for the relative humidity to be related to AScX returns. This indicates that relative humidity has no direct effect on the fundamental value of companies and that relative humidity has no indirect effect on stock returns via mood. Again, this is not what is expected according to Howarth and Hoffman (1984) who find that humidity has the most significant effect on mood. Nor are these results in line with the findings of Sariannidis et al. (2016), as they find evidence of humidity affecting stock returns.
The estimates for the control variables (MSCI, Monday, and January) are again quite similar to their previous estimates. The estimated coefficient of the Halloween variable changed compared to its value in regression (1a). In regression (2a), the estimated coefficient is again highly statistically significant at a 1% level. The estimated coefficient (0.077) is also comparable to the estimated coefficient in the regression using only the control variables as explanatory variables (0.0768). In regression (1a) the weather variables possibly tried to explain part of this Halloween calendar effect, in regression (2a) this is no longer the case. Suggesting that the estimators in this regression truly measure the effects daily weather has on daily stock returns and not a seasonal pattern.
Regular weather conditions
In this part, the preceding regressions are performed for a second time. This time days with extreme weather conditions are excluded from the regression. The weather variables in these regressions should no longer directly influence stock returns. In the case that these regressions find statistical significant weather variables, it indicates that the weather indirectly affects stock returns even during regular weather conditions. These new regressions have a suffix “b”. The results of these regressions are presented in Table 4.
significant (p=0.10). There is no appealing economic explanation for the duration of sunshine to affect AScX returns during regular weather conditions. However, it is in line with the literature that suggests that the weather affects investors’ mood, which in turn affects decision making and stock prices. As such, it supports the findings and claims of Saunders (1993) and Hirshleifer and Shumway (2003), even though they did not exclude the effects of extreme weather like this study does.
VARIABLES Regression (1b) Regression (2b)
Sun 0.0007* (0.0004) Temperature -0.0004 (0.0003) Humidity 0.0007 (0.0018) ∆Sun 0.0006 (0.0004) ∆Temperature 0.0001 (0.0004) ∆Humidity 0.0007 (0.0017) MSCI 0.6493*** 0.6499*** (0.0289) (0.0287) Monday 0.0805*** 0.0812*** (0.0296) (0.0296) Halloween 0.0508 0.0762*** (0.0331) (0.0271) January 0.0068 0.0095 (0.0506) (0.0508) Constant -0.0620 -0.0356** (0.1712) (0.0173) Observations 3,720 3,715
Table 4: Outcomes of OLS regressions (1b) and (2b) estimated on AScX returns while
excluding observations with extreme weather conditions. Regression (1b) uses the levels of the weather variables as explanatory variables. Regression (2b) uses the changes in weather
variables as explanatory variables. Newey and West standard errors are used with a lag of 45. Standard errors in parentheses.
The effects of temperature during regular weather conditions is not statistically significant. This paper is unable to conclude whether the previously found effect stems from direct and/or indirect effects. Humidity is still not statistically significant. This is in line with expectations, as relative humidity is also not statistically significant in the regressions that use all the observations.
The estimated coefficients of the control variables are in line with the outcomes of the regressions using all the observations. This applies to both regression (1) and regression (2). Nothing surprising is to note here.
In regression (2b), none of the weather variables is statistically significant in explaining AScX returns. So, during regular weather conditions, the deseasonalised weather variables do not predict returns of the AScX. Only when combined with the effects at times of extreme weather, does the deseasonalised sun variable affects the weather. This paper cannot empirically examine whether this earlier observed effect of sunshine is a direct effect or is mediated by mood. The changes in the temperature and humidity are again not significantly related, this is expected.
Robustness test - ARCH effects
As a robustness test, the GJR-GARCH (1,1) model will be used. The preceding regressions will be performed again in combination with the GJR-GARCH model that models the volatility. The outcomes of regressions (1a) and (2a), in combination with the GJR-GARCH model, are presented in Table 4. All the parameters of the GJR-GARCH model are highly significant. The ARCH parameter has a coefficient of 0.1578 and 0.1581 for respectively regression (1a) and regression (2a). The GARCH parameters have a coefficient of 0.8464 and 0.8463, respectively. Moreover, the asymmetry term is highly significant with coefficients of -0.1066 and -0.1072, respectively. The negative values indicate that the volatility rises more after a positive shock than a negative shock of the same magnitude.
The outcomes of the control variables in these regressions are quite similar to their equivalents in the preceding OLS regressions. More importantly, in this model, none of the weather variables is significant in explaining AScX returns in either of the regressions. This contradicts with all the literature that find weather variables to be related to stock returns, like Hirshleifer and Shumway (2003) and Sariannidis, et al. (2016). This finding is in line with, for example, Pardo and Valor (2003) and Loughran and Schultz (2004) who did not find any significant evidence for weather variables to predict stock returns.
VARIABLES Regression (1a) Regression (2a) ASCX Sun 0.0005 (0.0003) Temperature -0.0004 (0.0003) Humidity 0.0011 (0.0014) ∆Sun 0.0005 (0.0003) ∆Temperature -0.0000 (0.0003) ∆Humidity 0.0013 (0.0015) MSCI 0.5971*** 0.5978*** (0.0112) (0.0112) Monday 0.0573** 0.0579** (0.0239) (0.0240) Halloween 0.0586* 0.0844*** (0.0304) (0.0212) January -0.0007 0.0039 (0.0392) (0.0377) Constant -0.0873 -0.0221 (0.1373) (0.0153) Volatility model ARCH 0.1578*** 0.1581*** (0.0137) (0.0139) Asymmetry term -0.1066*** -0.1072*** (0.0126) (0.0128) GARCH 0.8464*** 0.8463*** (0.0130) (0.0131) Constant 0.0246*** 0.0247*** (0.0029) (0.0029) Observations 3,789 3,784
Table 4: Outcomes GJR-GARCH(1,1) model for regressions (1a) and (2a) estimated on AScX
returns. Regression (1a) uses the levels of the weather variables as explanatory variables. Regression (2a) uses the changes in weather variables as explanatory variables. Standard
5. Discussion
When performing OLS regressions, some of the weather variables are weakly significantly related to the returns of the AScX. The duration of sunshine, the level of temperature, and the change in the duration of sunshine are all weakly related to AScX returns. The duration of sunshine and the change in the duration of sunshine are positively related to AScX returns. This finding is in line with the findings of previous studies, such as Saunders (1993) and Hirschleifer and Shumway (2003). The level of temperature is negatively related to AScX returns, and this is in line with the findings of Keef and Roush (2007). This study is not entirely in line with the findings of Keef and Roush (2007), as they observe that the change in the level of temperature is more significantly related than the level of temperature. Conversely, this study does not find any significant correlation between the change in the level of temperature and stock returns.
These significant results could stem from the direct and/or indirect (via mood) transmission channel between the weather and stock returns. As this study does not have data about investors’ mood, it is not possible to empirically study whether the observed effect is direct or is mediated by mood. Saunders (1993), Hirschleifer and Shumway (2003), and Keef and Roush (2007) who obtained similar results claimed that the daily weather is not informative about possible direct effects on stock returns. So they attributed their results entirely to the indirect effects channel, without using an empirical model to confirm their assumption. However, this seems like a weak assumption, as it is possible for extreme weather to directly affect the fundamental value of companies (Heurta and Perez-Liston, 2011).
This study does not immediately allocate the observed effects to the indirect effects channel. This study examines whether the previously observed effects are still observable when excluding observations with extreme weather conditions from the regressions. This should exclude the impact of the direct effects that the weather has on stock returns, as there is no economic explanation for the weather to influence stock returns during regular weather conditions directly. Hence, a significant result implies that the relationship between the weather and AScX returns stems from the indirect effects channel. Such a significant result is in line with psychological literature that suggests that the weather affects mood, which in turn affects decision making and stock prices. If the weather variables are no longer significant, this paper is unable to attribute the earlier observed result to the direct and/or indirect transmission channel.
This study is unable to allocate the earlier observed effects to either one of the transmission channels.
Remarkably, the level of sunshine duration is still weakly statistically correlated with AScX returns (while only using observations with regular weather). As stated above, economic theory cannot easily explain why the duration of sunshine during regular weather conditions should be related to AScX returns. However, the finding is in line with the psychological literature suggesting that the duration of sunshine affects mood, which in turn affects stock prices. This indirect effect creates the possibility of a weather-based trading strategy able to achieve consistent excess returns above what would be expected, looking at the risk level. The strategy would entail buying stocks of the AScX when the daily duration of sunshine is short, preferably no sunshine at all and sell those stocks on a day with a prolonged duration of sunshine. However, the size of the excess returns is rather small, as a one hour increase in the duration of sunshine explains only an increase of 0.0072% in the AScX return. At tops, the duration of sunshine explains only 0.1095% of the AScX return (the difference between no sunshine and most prolonged duration of sunshine recorded). This trading strategy requires frequent trading. Frequently trading the AScX will be costly, think of the trading costs such as commissions1 and the bid-ask spread. Those costs will quickly evaporate the potential excess returns. Taking these trading costs into account, traders will not be able to obtain these excess returns. Hence, this very small bias does not indicate market inefficiency.
Moreover, the presence of ARCH effects in the data suggests that the standard errors of the OLS regressions could be incorrect. This paper uses the GJR-GARCH (1,1) model to model the volatility of the AScX and to obtain standard errors that take these ARCH effects into account. When performing the regressions once more using this model, none of the weather variables is significantly related to AScX returns. As this non-linear model is a better fit to model the relationship between the weather and AScX returns, this model should be leading in making inferences about the relationship.
The outcomes of the GJR-GARCH model suggest that there is no relationship at all between the weather in the Netherlands and AScX returns. This contradicts with both the literature claiming the weather directly affects stock returns and the (psychological) literature claiming the weather indirectly affects stock returns via mood. As the weather does not appear to influence AScX returns indirectly, there is no weather-induced bias in the stock prices of which can be profited. Hence, the weather does not appear to be an anomaly of the EMH.
1
6. Conclusion
This study examined the effects the weather has on stock returns in the Netherlands. The weather variables examined in this study are the daily duration of sunshine, daily mean temperature, and daily mean level of relative humidity.
When performing OLS regressions, this study finds weak statistical evidence for the duration of sunshine and the change in the duration of sunshine to be positively related to the returns of the AScX. The level of temperature is negatively related to AScX returns, while the change in temperature is not statistically significant in predicting returns of the AScX. The level of humidity and the change in the level of humidity are both insignificant, indicating that humidity plays no role in explaining AScX returns. As some weather variables appear to be related to AScX returns, the findings of this model suggest that the weather in the Netherlands is related to the returns of the AScX.
The duration of sunshine is still weakly related to AScX returns when using only observations with regular weather conditions. This finding cannot be easily explained by economic theory. It can, however, be explained by (psychological) literature that suggests an indirect relationship via mood. Such a significant indirect relationship implies that there is a market inefficiency, as there is a predictable bias in stock prices. However, the obtainable excess returns are small, and trading costs outweigh these excess returns. Hence, this finding does not indicate market inefficiency.
More importantly, the presence of ARCH effects implies that the GJR-GARCH model is a better fit to model this relationship than the OLS regression. When using the GJR-GARCH model, it can be concluded that during the time frame of this study, none of the examined weather variables is related to AScX returns. This contradicts with all the literature that claim that there is a (direct/indirect) relationship between the weather and stock returns. The weather does not indirectly affect AScX returns. Therefore the weather does not create profitable weather-based trading strategies that use publicly available information (weather forecasts and/or real-time weather measurements). Hence, the weather does not appear to be an anomaly of the efficient market hypothesis.
able to empirically assess in what way a possible relationship between the weather and stock returns works.
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