The effect of weather on stock returns: A comparison between emerging and developed markets
Table of contents
2. Literature review
2.1. Weather, mood and decision making behavior
2.2. Weather and the stock market
2.3. Two decades of weather effect literature: a lack of consensus
3. Data description
3.1. Data collection
3.2. Data analysis
4. Methodology and results
4.2. Joint tests
4.2.1. Pooled least squares regression
4.2.2. Binary regression
5.2.1.Pooled least squares regression
Advocates of the efficient market hypothesis argue that security markets are rational and that prices on these markets reflect the underlying economic fundamentals (Fama, 1970). Nevertheless, numerous market anomalies came to light over the past decades. A prominent complementary paradigm is that investors’ trading behavior is shaped by psychological influences which are considered irrational. Shiller (2003) argues that this division of the financial literature - behavioral finance - is one of the most vital research areas.
One renowned and frequently researched anomaly over the last two decades, especially in the last years, is the weather effect. This can be defined as the effect that weather, measured using a variety of quantitative meteorological variables, has on the stock market returns. As argued by behavioral finance, economic agents have bounded rationality, allowing subjective factors to influence their decision making process. The weather effect is a pertaining component of this theory that can be placed within the psychology block of behavioral economics (Barberis and Thaler, 2003).
The extensive literature upon the weather effect has led to conflicting results. Starting with Saunders (1993), a considerable number of studies have found evidence supporting the impact that weather has on investors’ mood and consequently on stock market activity. Further investigation and a variety of methodological approaches have revealed a lack of results consistency. The weather effect has been discovered to exist in many countries – United States, Taiwan, Thailand, Finland, but critics followed as well. Most opponent papers are in favor of a weak form of efficient market and claim that the existence of the weather effect is merely a result of inaccurate data definition, discontinuous records and data mining.
Given these prior contradictory results, our research study investigates whether emerging stock markets are prone to deviate from fundamentals and to display a persistent weather influence relative to developed and more efficient markets. In this paper, our aim is to test whether stock prices are affected by weather in a significantly different manner depending on the level of market development. A significant difference would then explain why financial literature on the weather effect is devoid of consensus.
We expect that the weather effect is more important in emerging countries relative to developed ones based on two arguments. First, emerging markets are more likely to be inefficient compared to developed countries (Harvey, 1994); therefore, stock markets are more exposed to anomalies that can be explained throughout means of behavioral finance. Secondly, the proportion of local investors to foreign investors is higher in developing countries (Korajczyk, 1996), which could mean that these markets are more influenced by a set of common factors and local conditions that affect local investors – such as weather.
We demonstrate, however, that there is no difference in the weather effect between developed and emerging countries. Also, we find evidence of a cyclical pattern of the weather effect. For both types of countries the weather effect is small (if existing) and the significance of the influence of weather is declining over time. Within the cyclical pattern of the weather effect, we identify a breakpoint for developed countries around the year 2001, followed by a breakpoint for emerging countries around the year 2002. Furthermore, although there is no difference in the significance of the weather effect in emerging and developed countries, we show that emerging countries are relatively less efficient than developed countries.
The remainder of this paper is organized as follows. Section 2 provides a review of the literature on the weather effect, followed by a description of the data collection process and data analysis in Section 3. The methodology and the results for the different tests are presented in Section 4. We check for robustness to seasonal adjustment method in Section 5. Finally, we provide some potential explanations of our findings in Section 6 and present the conclusions of this study in Section 7.
2. Literature review
The literature investigating the relationship between the weather and the stock market prices considers two distinct sections. First, psychology literature supports and explains the connection between weather and mood and the further link between mood and behavior. Second, financial literature can be used to explore previous research on the relationship between weather and the behavior of investors on stock markets while connecting it to stock market quantitative variables.
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Figure 1: The relation between weather and the stock market (as used in financial literature)
Psychology literature - according to our knowledge – has not examined the direct link between weather and investors’ behavior on the stock market. Therefore, we make use of the reasoning applied in all the previous financial literature on the weather effect: weather affects the mood of investors, the mood of investors influence investors’ behavior and this reflects straightforward in stock market trading activity (figure 1).
2.1. Weather, mood and decision making behavior
Psychologists have studied the relationship between weather, mood and decision making behavior extensively. There are several links between weather (measured by different variables), mood (the relatively short state or quality of feeling at a particular time) and behavior.
Support has been found for the influence of environmental factors and weather conditions on the mood of individuals (Watson, 2000). Kals (1982) concluded that one third of the people are weather sensitive and that mood and health vary with changes in the weather conditions. The influence of various types of weather has been found to be significantly related to individuals’ mood. Cunningham (1979) studied the relationship between weather (sunshine, temperature, humidity, wind and lunar phases), mood and behavior and found a significant result especially for sunshine and temperature. Howarth and Hoffman (1984) also noticed a positive effect of sunshine on mood when examining the effect of weather on mood variables. Their study concludes that sunshine leads to more optimism.
Further evidence has been found for the effect of humidity (e.g. Wyndham, 1969; Allen and Fischer, 1978; Howarth and Hoffman, 1984), wind (e.g. Denissen, Penke, Butalid and Van Aken, 2008), barometric pressure (Digon and Bock, 1966) and temperature (e.g. Bell and Baron, 1976; Howarth and Hoffman, 1984; Page, Hajat and Kovats, 2007) on mood. Anderson (2001) showed that low temperatures can lead to a more aggressive approach and high temperature to hostility or apathy. This in turn influences the risk taking behavior.
Loewenstein, Elke, Christopher and Welch (2001) argued that feelings and mood can affect behavior and decision making. When people are in a better mood they tend to have a more optimistic judgment about the future (Arkes, Herren and Isen, 1988; Bagozzi, Gopinath and Nyer, 1999). A good state of mind is related to overconfidence and less risk aversion. Therefore good mood can increase the likelihood of making riskier choices (e.g. Yuen and Lee, 2003; Kuhnen and Knutson, 2011), which can lead to poorer decision making (Au, Chan, Wang and Vertinsky, 2003). Johnson and Tversky (1983) observed that positive mood leads to optimistic choices whereas negative mood to pessimistic choices.
Another argument supporting our behavioral analysis is that the causes of the mood changes might have nothing to do with the choices being made (paramount when choosing a portfolio). In line with this argument, Schwarz and Clore (1983) concluded that mood influences decisions even when the cause of the mood deviation is not related to the decision that is to be made. This phenomenon is called ‘mood misattribution’ and it is an important component of behavioral finance. As a consequence, the mood variation (caused by different influences, for example the weather) has to be irrelevant for the efficient market hypothesis to hold because mood is not connected to the underlying fundamentals of assets.
In addition, Simon (1955) and Conlisk (1996) argue that investors face bounded rationality. They tend to choose satisfying decisions instead of optimal decisions. The feelings experienced when decisions are made by comparing the costs and benefits of different options deviate the decision in a different direction than is optimal (Loewenstein, 2000). Moreover, Forgas (1995) noticed that mood becomes more important for the risk assessment of the decision when the decision itself is more complex and uncertain.
Mehra and Sah (2002) directly related the effect of feelings and mood of investors on equity prices. As previously discussed, mood can affect the attitudes of people towards risk taking. The authors show that even small changes in mood can affect the prices of equities significantly if: the subjective parameters of investors (risk averseness, perceived discount rate) change over time by changes in the mood of the investors, a substantial part of the market participants experience the effects and the investors are not aware of the influence of mood on their decisions. Even if there is a mispricing (for example due to the changes in mood/weather effect), the mispricing can exist for a longer period (Barberis and Thaler, 2002). This also applies when the mispricing is caused by a small group of investors.
Schneider, Lesko and Garrett (1980) found that weather affects behavior, especially the interpersonal interactions. By analyzing the stock market, Shalen (1993) noticed that bad moods (caused for example by bad weather) lead to more disagreement among investors which causes higher volatility. Brown (1999) however argued that a good sentiment (good mood) leads to more trades and a higher volatility.
Psychology has shown that the weather (in different forms) can affect mood, which influences the behavior of investors. It is important to notice that the determinant factor is the occurrence of the weather itself and not the weather forecast (Hirshleifer and Shumway, 2003; Akhtari, 2011). Current weather affects mood and behavior, while mood and behavior are not affected by expectations about the weather (forecast).
2.2. Weather and the stock market
The literature connecting investor weather and stock market returns is differentiated based on the researched location. Saunders (1993) is the first one to investigate the United States market and find support for the influence of investors’ mood – which is affected by weather - on asset prices. The study showed that the weather in New York City had a significant correlation with the daily returns on the NYSE and AMEX index over 1962-1989 and the Dow Jones Industrial Average over the period 1927-1989. The amount of cloud cover (used as a proxy for the inverse of sunshine) was negatively related to the returns on the stock market. Also, the results are robust to the inclusion of other market anomalies. Further, the effect of extreme weather on market returns is even larger.
In addition to this study, Chang, Chen, Chou and Li (2008) also found that the stock market returns on the NYSE on cloudy days are lower than on sunny days. However, the influence of the cloud cover is only significant at the opening of the market (12-15 minutes). The findings also show that weather has a significant influence on the intraday trading patterns. The cloud coverage is positively related to the volatility in the market and negatively related to the market depth. Akhtari (2011) investigated the relationship between weather and stock market returns over time. She also found a positive correlation between sunshine and stock market returns for New York City over the period 1948-2010 after controlling for market anomalies and seasonal effects. The author concluded that this connection is slightly increasing over the past half century. Loughran and Schultz (2004) also found evidence of lower stock returns on the Nasdaq on cloudy days. The weather in the neighborhood of companies’ headquarters was, however, unrelated to the returns on the stocks of the companies.
However, the significance of the relationship is very much dependent on the period that is considered under the study. There are clear cyclical patterns visible in the weather effect. One possible explanation for the cyclical patterns is the emergence of non-rational investors in the stock market during certain periods in time - for instance for periods when investing in the stock market is popular. While less professional and, arguably, less rational investors enter the market, equity mispricing will occur more often (Akhtari, 2011).
In order to check if the weather effect is present globally, Hirshleifer and Shumway (2003) conducted a study investigating the influence of cloud cover in the morning (when the market opens) on 26 international stock markets for the period 1982-1997. The authors also found a significant negative relationship between cloud coverage and equity returns. Almost 70% of the countries showed a negative coefficient of cloud coverage on returns. When controlling for the cloudiness, snow and rain were not significantly related to market returns. Nonetheless, the authors conclude that it is very difficult to use trading strategies based on the weather effect. This requires frequent trading that can only be profitable when transactions costs are low and benefits are larger than these costs.
Cao and Wei (2005) investigated the link between temperature and the returns on nine stock indices around the world. The research observed a robust significant negative correlation between temperature and stock market returns for all globally dispersed countries. This relationship was stronger in winter than in summer. The impact of temperature on stock market returns was also more important than the influence of sunshine and the length of the night. Symeonidis, Daskalakis and Markellos (2011) focused on the influence of weather (cloudiness, temperature, precipitation and nighttime length) on the volatility of globally dispersed stock markets. In general, cloud coverage and the length of nighttime were significant and negatively related to stock market returns. However, the results proved to be depended on the location of focus.
The aforementioned studies have a found significant relationship between weather and stock market returns or market volatility. However, these studies were focused on the United States or multiple countries at once. Floros (2011) found a negative connection between temperature and stock market returns for Portugal. Sriboonchitta, Chitip, Sriwichailampham and Chaiboonsri (2011) came to the same conclusion for the stock market in Thailand. Keef and Roush (2002) found only a small significant relationship between stock market returns and temperature in New Zealand and no significant relationship between cloud coverage and returns. On the other hand, wind had a strong significant influence. Dowling and Lucey (2005) concluded that rain, lunar phases, daylight time and seasonal fluctuations are all significant and negatively related to equity returns on the Irish stock market. They did not find support for the impact of cloud cover and humidity. Kaustia and Rantapuska (2011) supports the influence of lunar phases (positive), daylight (negative), precipitation (negative) and sunlight (positive) on the return and volume of the Finnish stock market, while no support was discovered for the seasonal affective disorder (SAD) and temperature.
Chang, Nieh, Yang and Yang (2006) investigated the influence of temperature, humidity and cloud coverage on the stock market in Taiwan. The authors concluded that temperature and cloud coverage had the strongest negative effect on the stock returns. The findings in the paper of Shu (2008) partially support this result. This study found evidence for the argument that weather influences the mood of investors, which influences the behavior of investors and thus the stock prices. Better weather (here defined as low temperature, low humidity and high barometric pressure) leads to higher stock returns in Taiwan. Nonetheless, the relationship is stronger for individual investors than for institutional investors. Lee and Wang (2011) also found that cloud coverage had a strong negative significant impact on the Taiwanese stock market, especially in low cloud cover periods.
Kang, Jiang, Lee and Yoon (2010) found strong results for the weather effect in Shanghai. The stock market in Shanghai allows trading of two distinct categories of stocks: A-shares and B-shares. A-shares are for domestic investors only and B-shares can be traded by foreign investors. The underlying idea of this study is that domestic investors are more affected by the weather (measured as temperature, humidity and sunshine) than foreign investors. The results show that over the whole period the weather effect is only significant for the A-shares; however, when the B-share market was opened for domestic investors the weather effect became also significant for B-shares. The same pattern applies for the volatility of the stock market. Yoon and Kang (2009) found mixed results for the Korean stock market. The influence of temperature, cloud cover and humidity has weakened over time because of the increased efficiency. In addition, the effect of extreme weather has been found strongly significant. These results are only valid before the Asian crisis of 1997. Weather is insignificant thereafter with respect to stock market returns.
Moreover, there is no general consensus in prior research about the significance of the weather effect on the stock market. Trombley (1997) was amongst the first to confront the results of Saunders (1993) with new evidence. The paper shows that the relationship between the weather and the stock market in New York City is less clear and strong than presented by Saunders. The weather effect is not present for the period before 1962 and the effect is not systematic throughout the year. Therefore, the author deems Saunders’ conclusions as exaggerated. Krӓmer and Runde (1997) replicated the study of Saunders for the German market and found no significant systematic relationship between the weather and the stock market. According to the paper, the outcome of such a research depend strongly on the manner in which hypotheses are phrased, weather variables are defined and the type of test statistics to be used. The authors conclude that this type of research is more or less exposed to a form of data mining.
Furthermore, Gerlach (2007) argues that none of the weather effects (generated by e.g. rain, temperature) in the United States occur on trading days on which no macroeconomic announcements were made (more than 60% of the sample in the paper). The study provides support for the argument that macroeconomic announcements are the actual cause of stock price movements while the weather effect was coincidentally discovered to be significant on the days of macroeconomic events. These findings are in line with the efficient market hypothesis. Goetzmann and Zhu (2003) find no evidence for the influence of weather on the trading behavior for the individual trading accounts of investors (the data consists of over 80,000 investor accounts from the US). Pardo and Valor (2003) addressed the influence of sunshine and humidity on the returns of the stock market in Madrid. The paper used two different periods in time: a period with an open ‘outcry’ trading system and a period with the current computerized trading system. The authors found no support for the influence of sunshine and humidity on stock returns under both trading systems. Tufan and Hamarat (2004) discovered that cloudiness is not related with the stock market index of Istanbul. Instead, they found support for the weak form of efficiency.
Also, the returns on the Australian stock market are not significantly influenced by the weather (Worthington, 2006). No support has been found for the relationship between eleven weather variables and the stock market returns. The author noticed, however, that when the weather effect is not systematic at the market level individual investors might still be affected by weather. Levy and Galili (2008) concluded that cloudiness had no significant influence on the behavior of the average investor on the Israeli stock market. Nevertheless, the weather effect is significant for individual accounts of young men with low incomes. Yuksel and Yuksel (2009) studied the effect of temperature on daily stock market returns around the world. The authors concluded that the relationship is not spurious, but it is weaker as previously thought. Lu and Chou (2012) investigated the Shanghai stock exchange. The paper concluded that returns are unaffected by changes in the mood of investors caused by the weather (cloud coverage, temperature, humidity, precipitation and visibility). However, trading activities (market turnover, liquidity and volatility) are correlated with weather.
Kamstra, Kramer and Levy (2003) focused their research on the seasonal affective disorder (SAD). SAD is linked with the hours of daylight: the less hours of daylight, the higher the chance of depression. Psychology showed that this leads to more risk aversion. The authors found that SAD has a strong negative correlation with stock market returns for a global sample of nine countries. However, weather variables like cloud coverage, precipitation and temperature had no significant effect on the stock market. In a global research on the effect of weather on stock returns, Jacobsen and Marquering (2008) found little evidence to support the influence of temperature and SAD on the stock market. According to the authors, most studies use data-driven inference based on spurious correlations. As a consequence, they consider that it is premature to conclude that stock returns are influenced by changes in the mood of investors caused by the weather.
Despite the rich literature regarding this subject, as far as we are concerned no research has been conducted in order to investigate the different manner in which weather affects stock returns in developed and emerging countries. The starting point of our research question lies within previous studies examining market segmentation. A segmented market is equivalent with numerous local investors activating on the stock exchange while foreign participation in the local market is limited (Bekaert and Harvey, 1998). Previous studies have shown that market segmentation tends to be much larger for emerging countries than for developed markets (Korajczyk, 1996). Undoubtedly, local investors are more exposed to local conditions - and weather implicitly. Hence, following this flow of reasoning we would expect a stronger impact of weather variables on the returns on emerging stock markets relative to developed ones.
However, a smaller scale of this type of investigation has been performed in countries with dual classes of common equity. Kang et al. (2010) study the weather impact on restricted equity. They consider A-shares that can be held by domestic investors only and B-shares that are mainly in possession of foreign investors. Their results yield that the weather effect exists in A-shares only, thus supporting the idea that the weather effect manifests differently depending on market segmentation.
Also, most of the abovementioned studies support the idea that the relationship between weather and stock returns is more likely to be significant in emerging countries rather than in developed ones. Researchers found a significant and strong connection between the weather variables and returns in developing countries such as Thailand, Taiwan, China, Korea, whereas little or no evidence was discovered in New Zeeland, Germany, Spain and Australia. There are also mixed results for the United States, Ireland, Finland and Turkey that are counterintuitive with our expectations, further emphasizing the necessity of a research that studies distinctly emerging and developed countries.
2.3. Two decades of weather effect literature: a lack of consensus
The literature on the weather effect fails to converge towards a unique systematic and robust relationship between the weather and the stock market. Based on prior literature, it must be noticed that there are multiple potential causes for this lack of consensus.
Firstly, time might be a significant factor to be considered. Chang et al. (2008) showed that the impact of weather variable is only significant at the opening of the market. Akhtari (2011) discovered that the investigated relationship is not only dependent on the hour of the day, but also on the moment in time. Moreover, the weather effect has a cyclical pattern over the years. Trombley (1997) and Lee and Wang (2011) found that the effect is also varying throughout the year. Secondly, location is paramount. Keef and Roush (2002) argue that the effect of different weather variables depends on the specific location. This is supported by the paper of Symeonidis et al. (2011). Therefore, the different conclusions of similar researches might be explained by the wide variety of variables and locations. Nonetheless, Hirshleifer and Shumway (2003) found significant universal effects on average. Thirdly, the definitions and hypotheses used are crucial. The way in which the null hypothesis is formulated and the definitions are used have a large impact on the final conclusions (Krӓmer and Runde, 1997). Moreover, the type of investors considered is essential. Levy and Galili (2008) and Shu (2008) showed that the significance of the weather effect depends on the type of investors (average versus individuals). Finally, the procedure and test statistics might yield biased results (Krämer and Runde, 1997; Trombley, 1997).
Overall, the significance of the weather effect depends on time, location, definitions of weather, hypotheses formulation, investor type, the procedure and test statistic used in the research.
3. Data description
3.1. Data collection
In order to investigate the relationship between stock returns – the explained variable, and weather – the explanatory variables, two datasets are required. Daily data is used for 16 years over the period 1996-2011. This time span accounts for two issues we have encountered. First, all stock markets in both emerging and developed countries have been continuously trading within this period. Secondly, this time spans provides heterogeneity and eliminates a potential sample bias by inclusion of both expansion and crisis periods. Therefore, our data contains stock market crashes such as the Asian crisis, the Dotcom bubble and the Subprime crisis and Euro crisis.
For a balanced comparison, our analysis includes 10 developed and 10 emerging stock markets. In order to provide a consistent classification of the countries within a category, we use MSCI, FTSE and S&Ps criteria. This criterion includes quantitative benchmarks for stock market capitalization, market breadth and depth, but also qualitative factors such as restrictions to foreign investors, efficient market infrastucture etc. Our research encompasses the main stock market in the following developed countries: Australia, Canada, France, Germany, Japan, Netherlands, Norway, United Kingdom and the United States. The emerging stock markets considered are: Brazil, China, Czech Republic, India, Malaysia, Mexico, Poland, Russia, South Africa and Turkey.
We choose the stock market index that is best available and has the largest number of stocks included – the appendix can be consulted on further information about stock market indices per country. Daily stock indices are retrieved from Datastream. The total return index is preferred to the price index given the fact that the former mentioned includes dividends and eliminates a potential bias and undervaluation of the equity index. However, due to data availability, we use the price index for four countries: China, India, Mexico and Turkey. Log returns are computed following the formula:
Log return = log (TRt/TRt-1 ) (1)
, where TR = total return index.
However, it is surprising that most authors investigating the weather effect do not use the total return index in their research. Akhtari (2010), Saunders (1993), Worthington, (2006) and others examine the price index instead of the total return, which could lead to a potentially biased dataset and erroneous results.
We consider six weather variables: cloud cover (SKC), temperature (TEMP), sea level pressure (SLP), visibility (VISIB), wind speed rate (WIND) and precipitation (PRECP). Previous studies (Lu and Chou, 2012; Shu, 2008; Worthington, 2006) provide a solid background for inclusion of the aforementioned variables, even though they have never been studied alltogether. Moreover, the SKC is amongst the most reserached variable, with most influence on stock returns. The meteorological data is retrieved from the National Climate Data Center (NCDC: http://www.ncdc.noaa.gov/oa/ncdc.html). NCDC provides reliable datasets of best quality. Data collection involves the following steps:
1. A weather station is chosen based on data availability and proximity to the location of the stock exchange (appendix, table 20).
2. SKC, SLP, TEMP and WIND are retrieved as hourly data, whereas VISIB and PRECP are only available as daily data. This approach ensures a better measurement due to the fact that stock exchanges have specific opening hours.
3. There is a relative small number of missing values – under 0.5% for developed countries and less than 1% for emerging countries. Instead of being removed, these have been replaced with the last recorded variable; given the high frequency of data and additional alteration that will be applied to the variables, further research will not be affected by means of accounting for missing values.
4. Hourly data is transformed into daily data by averaging the variables within the particular trading hours of each stock exchange. Also, we add an extra dimension for this. Motivated by the study of Chang et al. (2008) that observe that the weather effect is more significant at the opening hours of the stock exchange and by psychological research that claims that people decide whether they are optimistic when they wake up and are already influenced by weather in the morning (Watson, 2000), we take into consideration an extra hour (or half an hour) before the opening of the market.
By definition, SKC denotes the fraction of the total celestial dome covered by clouds or other obscuring phenomena. This is measured in oktas and ranges from 0 to 8, where 0 means no cloud cover and 8 is the maximum cloud cover. We expect an inverse relationship between SKC and stock returns since a higher degree of cloudiness induces less optimism, hence a worsening investor mood and lower returns. TEMP is equivalent to air temperature and is measured in ̊Celsius. Previous studies show that temperature has most influence on risk taking behavior if it records extreme values (Mehra and Sah, 2002). Therefore, we anticipate that excess temperature will have a negative influence on returns. SLP is the air pressure relative to mean sea level and is measured in hectopascals. High pressure is associated with good weather, hence the stock returns should increase. WIND represents the wind speed rate, the rate of horizontal travel of air past a fixed point measured in meters per second. Higher wind speeds would aggravate the individuals’ mood and stock returns should be lower. VISIB is the visibility for the day in miles and it should influence returns in the same manner as SKC. PRECP is the rain and/or melted snow during the day in inches and hundredths. Higher precipitation should induce lower stock returns.
Weather variables are highly seasonal. In summer, the temperature, precipitation and wind are on average higher than in winter. In order to avoid spurious regressions, all weather variables are deseasonalized. As a means of robustness check, we provide two different means of deseasonalizing. Section 4 presents the results by using a seasonal adjustment method identical to Hirshleifer and Schumway (2003). First, we compute the average of each week for each year in every location. Then, we determine the average for each week of the year using the 16 year sample (resulting 53 averages) and then subtracted this from the daily variable, giving the excess variable. In addition, by using excess variables we take into consideration the unexpected component of weather change.
Section 5 shows the results by accounting for some criticism brought to Hirshleifer and Schumway (2003) seasonal adjustment method. We follow a similar procedure, but we do not provide an average for the entire sample (resulting 53*16 averages). This means of seasonal adjustment mitigates the following potential problems: changing weather averages over time as a result of global warming and differences across countries located in different climate zones. Compared to the seasonal adjustment procedure used by Hirshleifer and Schumway (2003), we do not seek to find a average for each week of the year using the 16 year sample. Averaging all weeks over our time sample introduces a look-ahead bias into the analysis. As of the first week of January of 1996, no person could perfectly forecast January weather patterns for the future 16 years. Investors care about the weather at the precise actual moment in time, and not about future forecasts. However, a potential issue with deseasonalizing is that investors do not perceive weather based on a seasonal pattern. Individuals do no consider yearly trends and averages, but simply judge whether a particular day has good weather conditions – if it is sunny, rainy, windy, cold or not. This supports the second method of deseasonalizing.
Moreover, our aim is to identify the exclusive influence of weather on stock returns. Therefore, in order to cater for the unspecified explanatory variables and macroeconomic events that impact stock exchanges globally we provide a differentiated treatment for outliers. We define outliers according to Hampel (2011) as the values that exceed the following interval:
[ median – 5.2*median absolute deviation ; median + 5.2*median absolute deviation ] (2)
,where mean absolute deviation=median( |variable-median(variable)| ).
Identified outliers are bounded to the minimum, respectively the maximum value of this interval. By applying this procedure we avoid misidentification of a significant weather influence on stock returns when in fact stock price movements are caused by macroeconomic events such as the crisis destabilizations or expansions excessive returns. Censoring the returns in this manner also balances the data to account for the criticism that Gerlach (2007) formulated against the weather effect. On the other hand, weather variables will not be censored since our purpose is to quantify the impact of extreme weather as well since severe weather conditions have been linked by previous literature with investors’ mood and behavior (Bell, 1976).
3.2. Data analysis
The following section provides a statistical analysis of the data that will be further used in our empirical approach. Table 1 presents the descriptive analysis of the daily stock returns over the period 1996-2011. It reports raw log returns, whereas we proceed in following sections using censored data. However, censoring is only applied to excessive returns which account for approximately 3% of the total observations. The table shows that the average daily returns are very similar between countries, with the exception of Turkey. As expected, emerging countries have higher returns and standard deviations than developed countries. Thus, developing countries are riskier and more volatile. This can also be observed by analyzing the minimum, maximum, skewness and kurtosis. Volatility and extreme values are determined chiefly by the expansion and crisis periods that we have included in our sample.
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Table 1: An overview of the descriptive statistics of daily raw returns of each index for each country. The log returns is calculated Rt = Log (TRt/TRt-1), where TR is the total return index. The mean, median, standard deviation, kurtosis, skewness, minimum and maximum are reported for the log returns. The analyzed period is 1996-2011.
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Table 2 shows the daily mean of the all weather variables. This table reports the raw meteorological data statistics before adjusting for seasonality. Excess variables are closer to an average of 0. Unlike the return variables, there are large differences in the world regarding all weather variables – mainly due to location and climate. The precipitation is higher in developed countries because of the location of these countries – on average they are situated in the Northern hemisphere, whereas emerging countries are spread in both hemispheres. This also applies to temperature - that is on average higher for emerging countries. Further, the median, standard deviation, kurtosis, skewness, minimum and maximum are also reported for each weather variable (consult appendix, table 21 until 26).
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Table 2: An overview of the mean of all the daily raw weather variables over the period 1996-2011, precipitation (PRECP), sky cloud clover (SKC), sea level pressure (SLP), temperature in Celsius (TEMP), visibility (VISIB) and wind speed rate (WIND). PRECP is the rain and/or melted snow during the day in inches and hundredths. It has a 0 or at least 0. SKC is ranging from 0 to 8. SKC is measured in oktas. SKC denotes the fraction of the total celestial dome covered by clouds or other obscuring phenomena. SLP is the air pressure relative to mean sea level. This is measured in hectopascals. TEMP is measured in ̊Celsius for the air temperature. VISIB is the visibility for the day in miles. WIND is the wind speed rate, the rate of horizontal travel of air past a fixed point.
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4. Methodology and results
The purpose of our empirical investigation is to study the difference in the weather effect between developed and emerging countries. We approach this question by analyzing individual regressions for each city to examine if weather has a significant influence on the selected stock markets, then we proceed to pooled regressions to account for individual heterogeneity and make a clear separation between developed and emerging countries. Further, a logit model is employed to investigate the influence of weather on the probability of recording a positive, respectively a negative return and to determine the marginal effects of weather variables on stock market returns.
Since Saunders (1993), the most frequently used method to investigate the weather effect on stock returns is the ordinary least squares (OLS) regression model. Akhtari (2011), Hirshleifer and Shumway (2003), Dowling and Lucey (2005) and other studies examine the existence of the weather effect based on OLS regression. Other methods that have been used cater for the ARCH effects and include different GARCH models: GJR-GARCH (Kang et al., 2010), AR-GARCH (Sriboonchitta et al., 2011), ARMA-GARCH Worthington (2006) etc. Our study requires a focus on stock returns and not on volatility, hence the OLS procedure is most suitable. Even though we identify the presence of heteroskedasticity, this is corrected by using heteroskedasticity consistent standard errors so our inference still holds.
In addition to the six weather variables, our regression includes a one-day lagged stock return. This dynamic structure allows us to conclude upon the efficiency of the stock market and to account for the autocorrelation of the error terms. Prior literature provides further motivation for including an autoregressive structure of stock returns. Saunders (1993) uses the lagged return Ri,t-1 to account for the non-synchronous trading effects. Cao and Wei (2003) also incorporate the Ri,t-1 to correct the first order autocorrelations. Akhtari (2010) uses Ri,t-1 to control price movement persistence.
Moreover, in order to reduce the sources of omitted variables and to account for a pure effect of weather we include two dummy variables, one for the January effect and one for the Monday effect. Lakonishok and Smidt (1988), Jaffe and Westerfield (1985), Haugen and Philippe (1996) investigated various calendar effects and found significant results for month-of-the-year effect and day-of-the-week effect. Also, authors that studied the weather effect use dummies for calendar effects to control the results of the weather impact. Saunders (1993) uses dummy variables for the January effect and the Monday effect. Goetzmann and Zhu (2003) and Akhatari (2011) control these effects as well. Further, Cao and Wei (2005), Dowling and Lucey and Tufan and Hamarat (2004) control for the Monday effect. Other authors cater for these effects in a different manner. For instance, Cao and Wei (2005) and Kamstra et al. (2003) used the tax loss selling as a dummy.
4.1. City-by-city tests
So as to avoid spurious regressions, both stock returns and weather data is checked for stationarity. This ensures that our series have a constant mean, variance and autocovariance regardless of the moment of maesurement. We implement both the Augmented Dickey-Fuller and Phillips-Perron procedure that test under the null hypothesis if the series has a unit root, with the difference that Phillips-Perron test is robust to heteroskedasticity and error term autocorrelation. The statistics reject the null hypothesis for every series for a confidence level of over 99%, concluding that the data is stationary.
Before presenting the final results of the OLS regressions, we proceed with employing specific tests in order to examine if our regressions are consistent with the classical linear model assumptions. All tests are performed and inference is built by setting a 1% significance level and results are reported in table 3. First, homoskedasticity is analyzed by using the Breusch-Godfrey-Pagan test with the null hypothesis of constant variance of error tems. For each of the 20 regressions this hypothesis is rejected for a confidence level of 99% (the F-statistics of the test is shown in the table 3), which implies that the resulting coefficients are inefficient. Error terms autocorrelation is further investigated with the aid of Breusch-Godfrey test with the null hypothesis of independent errors. The number of lagged residuals that are included in the residual test equation are selected based on the minimum Akaike Information Criterion. Most residual series are correlated with a one-day lagged value, while the maximum number of lags is 5 – a conservative number given the frequency of the data. The results of the test show that most countries comply with error term independence assumption, even though results vary from state to state.
Depending on the results of the aforementioned tests, we use heteroskedasticity and autocorrelation consistent standard errors in order to draw correct inference on the significance of the variables. If these tested assumptions of the linear model are violated, coefficients remain unbiased and consistent while losing efficiency. This is corrected by using either White standard errors in the presence of heteroskedasticity and Newey and West (1987) variance-covariance estimators in the presence of both heteroskedasticity and autocorrelation. Therefore, the estimated values of the coefficients are on average equal to their true values and significance is examined on an efficient basis.
Moreover, normality is examined by the use of the Jarque-Bera test with the null hypothesis of normal error distribution. The Jarque-Bera statistic is reported in table 3. Given a 1% significance level, none of the residual series comply with this assumption since most of them are leptokurtic even though they are symmetrical. These results are consistent with the fat tails of the series and the fact that the sample includes a profusion of both positive and negative events that induce extreme values. However, violation of this assumption is virtually inconsequential for our analysis considering the large sample we selected.