Does weather still affect the stock market? New insights into the effects of weather on returns, volatility and trading volume
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Muhlack, Nils; Soost, Christian; Henrich, Christian Johannes Article Does weather still affect the stock market? New insights into the effects of weather on returns, volatility and trading volume Schmalenbach Journal of Business Research (SBUR) Provided in Cooperation with: Schmalenbach-Gesellschaft für Betriebswirtschaft e.V. Suggested Citation: Muhlack, Nils; Soost, Christian; Henrich, Christian Johannes (2022) : Does weather still affect the stock market? New insights into the effects of weather on returns, volatility and trading volume, Schmalenbach Journal of Business Research (SBUR), ISSN 2366-6153, Springer, Heidelberg, Vol. 74, Iss. 1, pp. 1-35, https://doi.org/10.1007/s41471-021-00125-5 This Version is available at: https://hdl.handle.net/10419/286454 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/
ORIGINAL ARTICLE https://doi.org/10.1007/s41471-021-00125-5 Schmalenbach Journal of Business Research (2022) 74:1–35 Does Weather Still Affect The Stock Market? New Insights Into The Effects Of Weather On Returns, Volatility, And Trading Volume Nils Muhlack · Christian Soost · Christian Johannes Henrich Published online: 10 December 2021 © The Author(s) 2021 Abstract This paper examines the impact of weather phenomena on the German stock market, evaluating cloud cover, humidity, air pressure, precipitation, temperature, and wind speed as weather variables. We use stock market data (returns, trading volume, and volatility) from the DAX, MDAX, SDAX, and TecDAX for the period from 2003 to 2017 and show, with modern time-series (GARCH) models that air pressure is the only weather variable that exerts a potentially consistent effect on the stock market. Air pressure reduces the trading volume on the SDAX and TecDAX, and changes in air pressure lead to increases in returns on the DAX, MDAX and SDAX. The effects of the other weather variables show no clear pattern and are critically discussed. In addition, this article contains an overview of the historical research results on the effects of weather on stock markets. Keywords Weather effects · Air pressure · GARCH This paper was originally submitted and independently peer-reviewed at Schmalenbach Business Review, one of SBUR’s predecessor journals. It has been accepted by the same Editor-in-Chief for publication in the successor journal SBUR. Christian Soost () · Christian Johannes Henrich FOM University of Applied Sciences, Essen, Germany E-Mail: [email protected] Christian Johannes Henrich E-Mail: [email protected] Nils Muhlack Stockstadt a. Main, Germany E-Mail: [email protected] K
2 Schmalenbach Journal of Business Research (2022) 74:1–35 1 Introduction In the first empirical investigation of the impact of weather phenomena on the stock market, Saunders (1993) indicated of the limits of classical capital market theory, showing a significant negative effect of clouds on the returns of North American equity indices. Motivated by this empirical finding, numerous studies with different study designs and overall inconclusive results followed (e.g., Bassi et al. 2013; Chang et al. 2008; Dowling and Lucey 2008; Frühwirth and Sögner 2015; Hirshleifer and Shumway 2003; Kamstra et al. 2003; Krämer and Runde 1997; Symeonidis et al. 2010). These studies confirming the effects of weather contradict the predictions of classical capital market theory but are consistent with behavioral science findings that identify the influence of mood on decision-making processes. The theoretical basis for the existence of weather effects within stock markets is the assumption that there is an indirect functional chain of weather that influences investor mood, which in turn influences their decision-making processes (e.g., Bassi et al. 2013; Cao and Wei 2005; Frühwirth and Sögner 2015). If this indirect functional chain is operative to some extent and capital market anomalies in the form of weather effects actually exist, then these facts would lend support to theories of behavioral finance, an interdisciplinary field combining economics, psychology and sociology (Shiller 2003), while weakening the support for the efficient market hypothesis (Malkiel and Fama 1970). There have been many empirical investigations into the effects of the capital market weather anomaly on the New York Stock Exchange (NYSE) (e.g., Saunders 1993 and Trombley 1997), New Zealand Stock Exchange (Keef and Roush 2002), Madrid Stock Exchange (Pardo and Valor 2003), London Stock Exchange (Apergis et al. 2016), Australian stock market (Worthington 2009), Korean stock market (Yoon and Kang 2009), Taiwanese stock market (Chang et al. 2006), Chinese stock market (Lu and Chou 2012), and German stock market (Klein 2005). These studies differ with regard to the stock market examined and the possible indices, weather variables, time period and statistical method used in the analysis. For the German stock market, the weather capital market anomaly has not yet been exhaustively investigated. Overall, research gaps exist in terms of both content and methodology; the literature has not yet considered all important indices and all relevant weather variables simultaneously. Most studies, especially those on the German market, have analyzed only returns (Apergis et al. 2016; Cao and Wei 2005; Jacobsen and Marquering 2008; Klein 2005; Krämer and Runde 1997; Schneider 2014a). To our knowledge, no study has analyzed trading volumes, and only Dowling and Lucey 2008 investigated volatility. From a statistical point of view, the usage of ordinary least squares (OLS) regression models for time-series data is insufficient in most cases due to heteroskedasticity problems and poor robustness. The majority of existing studies use only OLS regressions (exceptions include, e.g., Dougal et al. 2012; Symeonidis et al. 2010; Yoon and Kang 2009), which may explain the different outcomes of studies on weather anomalies in capital markets. To address this shortcoming and provide more recent empirical evidence on weather anomalies in capital markets, we use generalized autoregressive conditional K
Schmalenbach Journal of Business Research (2022) 74:1–35 3 heteroskedastic (GARCH) time–series models and show, with data on German stock market indices (DAX, MDAX, SDAX, and TecDAX) covering August 2003 to July 2017, that weather has an impact on volatility and trading volume. The remainder of this paper is organized as follows. In the first section, we discuss the indirect functional chain linking weather, mood and decision-making. Then, we provide a literature review of the empirical results on a possible weather anomaly in capital markets. Thereafter, we briefly discuss the use of GARCH models for our analysis and present our results. Finally, we discuss the results and provide conclusions. 2 Theoretical Background and Hypotheses The theoretical reasoning behind studies on the effect of weather on stock markets is the assumption of an indirect functional chain whereby weather influences investors’ mood, which in turn influences their decision-making processes (e.g., Bassi et al. 2013; Cao and Wei 2005; Frühwirth and Sögner 2015). Mood is an affective state that can be influenced by external factors such as an individual’s overall (biological) condition and health status. Weather can have an impact on these external factors and, thus, on mood. A study by Fletcher (1988) found that people reported increased joint pain, headaches, irritability, and nervousness in relation to exposure to Chinook winds in Canada. In addition, Guedj and Weinberger (1990) showed that weather can impact physical health, finding that changes in weather related to air pressure, temperature, and precipitation increased the pain sensitivity of rheumatism patients. Moreover, Jamison et al. (1995) obtained similar results. Other studies have focused on the effects of weather on mental health. Rosenthal et al. (1984) discovered, for example, a type of annually recurring depression in autumn or winter known as seasonal affective disorder (SAD). The symptoms of this disease change depending on the climate and latitude. Howarth and Hoffman (1984) identified a negative effect of humidity on concentration and a positive effect on tiredness, as well as a positive correlation between temperature and skepticism and a positive effect of sunshine on optimism. Recent studies by Denissen et al. (2008) and Kööts et al. (2011) have shown similar results and identified a negative impact of sunshine on tiredness. Schwarz and Clore (1983) observed that study participants generally thought more positively about their life on sunny days. The authors concluded that people use their current mood, here influenced by the weather, as a source of information for decision-making. Allen and Fischer (1978) observed that humidity influences mental efficiency, while Delyukov and Didyk (1999) showed that memory performance was impaired by aperiodic variations in air pressure. A meta-analysis of performance as a function of temperature was carried out by Pilcher et al. (2002) and found that both cold and hot temperatures generally have a negative influence on cognitive efficiency. Keller et al. (2005) obtained similar results and showed that high temperatures and high air pressure have a positive impact on memory performance and mental receptiveness. Thus, a variety of external factors related to weather have an impact on mood and ultimately influence decision-making. The most commonly used models for explaining the influence of positive or negative affective states (which can be significantly influenced by weather) on (risk) K
4 Schmalenbach Journal of Business Research (2022) 74:1–35 Table 1 Weather, the AIM, and the MMH Mood Maintenance Affect Infusion Hypothesis (MMH) Model (AIM) Positive affective state Risk-averse Risk-seeking (good weather) Negative affective state Risk-seeking Risk-averse (bad weather) behavior are Forgas’ affect infusion model (AIM) (Forgas 1994,1995) and Isen and Patrick’s mood maintenance hypothesis (MMH) (Isen and Patrick 1983). However, these explanatory approaches differ in terms of their mechanisms of action and are therefore briefly presented below while also providing the basis for hypothesis development. The MMH describes that individuals who are in a positive affective state try to maintain it (Isen and Simmonds 1978). Then, it follows that individuals in a negative affective state try to leave it (mood repair) to get back to a positive affective state (Cialdini et al. 1973). If this hypothesis is translated to risky situations, such as investment decisions in stock markets, then a positive affective state leads to riskaverse behavior and a negative affective state to risk-seeking behavior (Isen 2008). The AIM argues diametrically and can be described via affect priming and affect as information (Forgas 1995). Affect priming leads to a selective perception of information needed for decision-making; thus, the decision is indirectly influenced by the current affective state. Affect as information describes the adoption of the affective state as an evaluation criterion for decision-making. The affective state then possibly leads to a decision that corresponds to the affective state (Forgas 1994), which, for decisions under risk, results in risk-seeking behavior for positive affective states and risk-averse behavior for negative affective states. The following table shows the relationships involving weather as an affective state. Forgas (1995) concluded that the impact of mood on decision-making processes is stronger for uncertain, riskier, and more abstract situations which applies to financial decisions (Frühwirth and Sögner 2015). Consequently, mood can influence investors’ decision-making processes in a way that may impact the capital market. It is therefore reasonable to assume that weather might influence the capital market. This relationship is also known as a capital market anomaly, which cannot be explained by classical capital market theory and thus provides a justification for the interdisciplinary behavioral finance approach, which combines economics, psychology, and sociology (e.g., Shiller 2003). While there are many capital market anomalies (e.g., Dimson 1988), the following paragraphs discuss only the weather anomaly in relation to returns, volatility, and trading volume. 2.1 Return Saunders’ first study on weather phenomena in capital markets (Saunders 1993) marked the beginning of a research trend that continues to this day. The empiri- K
Schmalenbach Journal of Business Research (2022) 74:1–35 5 Table 2 Weather effects on returns Author(s) Cloud cover Sunshine Temperature Precipitation Wind Air pressure Humidity Visual range Snow Saunders (1993)▼ Krämer and Runde (1997) Keef and Roush (2002) ▼▼ Hirshleifer and Shumway (2003) ▼ Kamstra et al. (2003)* ▼▲▼ Krivelyova and Robotti (2003) Pardo and Valor (2003) Loughran and Schultz (2004) ▼ Tufan and Hamarat (2004) Cao and Wei (2005) ▼▼ Dowling and Lucey (2005) ▼▲ Goetzmann and Zhu (2005) ▼ Klein (2005)▼▲ Chang et al. (2006)* ▼▼ K
6 Schmalenbach Journal of Business Research (2022) 74:1–35 Table 2 (Continued) Author(s) Cloud cover Sunshine Temperature Precipitation Wind Air pressure Humidity Visual range Snow Keef and Roush (2007) ▼ Chang et al. (2008) ▼ Dowling and Lucey (2008)* ▼ Jacobsen and Marquering (2008) ▼ Worthington (2009) Yoon and Kang (2009)* ▼▼ ▼ Zadorozhna (2009)* Kang et al. (2010)* ▼ Akhtari (2011)▼ Floros (2011)* ▼ Lu and Chou (2012) ▼ Schneider (2014a) ▲▼ Frühwirth and Sögner (2015) ▲ Goetzmann et al. (2015) ▼ Apergis et al. (2016) ▼▼▼▼ ▼ K
Schmalenbach Journal of Business Research (2022) 74:1–35 7 Table 2 (Continued) Author(s) Cloud cover Sunshine Temperature Precipitation Wind Air pressure Humidity Visual range Snow Sariannidis et al. (2016)* ▲▲ Pizzutilo and Roncone (2017) Positive effect (%) 020578171400 Negative effect (%) 52 20 53 20 17 0 22 0 17 Noeffect(%)4860427375836410083 no significant effect, ▼significant negative effect, ▲significant positive effect, sources marked with * use GARCH K
8 Schmalenbach Journal of Business Research (2022) 74:1–35 cal results of the abovementioned studies, which consider returns as a dependent variable, are shown in the Table 2. The table lists an effect only if a consistent direction of the effect has been identified in at least one model within a study. If different statistical methods have been applied, then the table reports the results of the regression analysis. Cloudiness is by far the most frequently studied variable, followed by temperature and precipitation. For cloudiness and temperature, more than half of the studies found their negative impacts on returns. In contrast, the remaining studies could not detect any effect for the two variables on returns. For other weather variables, the majority of the studies showed no significant correlation. Air pressure has been one of the least studied weather variables, although it is the only weather phenomenon to which people are exposed inside buildings (Schneider 2014a). The dominant statistical method used in these related studies is OLS regression, the majority of which have attempted to take into account the special nature of finance data by applying White or Newey-West standard errors to correct for bias in the results arising from heteroskedasticity problems. Only Chang et al. (2006); DowlingandLucey(2008); Floros (2011); Kamstra et al. (2003); Kang et al. (2010); Sariannidis et al. (2016); Yoon and Kang (2009), and Zadorozhna (2009)used modern financial market econometrics in the form of GARCH models. Therefore, the possibility cannot be excluded that the effects identified in these studies that use traditional models are based on an insufficient data representation. As previously described, weather impacts people’s mood. The AIM and MMH provide different theoretical explanations for the impact of weather on the stock market. Empirical evidence can be found for both approaches, although the majority of the results favor the AIM. Good weather conditions positively influence mood, which in turn leads to a positive impact on stock returns (AIM). The predictions arising from this line of reasoning are in contrast to the findings of studies that reported a correlation between bad weather1and high returns (MMH). But differences can also be identified for the different weather variables. For example, most studies revealed a negative influence of temperature on returns, which might be explained by an increased willingness to take risks under certain weather conditions. According to this line of argument, cold temperatures lead to aggressive behavior, a greater willingness to take risks and, ultimately, increased returns. More pronounced risktaking behavior in bad weather is in line with the results of Raghunathan et al. (2006), who observed riskier behavior among subjects who reported experiencing sadness (Raghunathan and Pham 1999). However, the different empirical results, the majority of which are in favor of the AIM over the MMH, do not allow for a clear theoretical positioning. According to the AIM and MMH, two competing hypotheses can be concluded. Hypothesis 1a: Good (bad) weather conditions lead to higher (lower) returns on the German stock market (AIM). 1The climate in Germany belongs to the cool temperate climate zone, so bad weather represents an increase in cloud cover, fewer hours of sunshine, higher relative humidity, lower barometric pressure, more precipitation, lower temperature and higher wind speed. K
Schmalenbach Journal of Business Research (2022) 74:1–35 15 Table 7 Descriptives of stock market data I Variable Mean Sd Jarque Bera RETDAX 0.00035 0.01341 5,545.1*** RETMDAX 0.00053 0.01352 4,328.1*** RETSDAX 0.00044 0.01062 6,711.4.3*** RETTECDAX 0.00045 0.01493 4,116.9*** TURDAX 118,852.28 50,727.35 11,910.85*** TURMDAX 18,064.70 8,656.94 113,001.90*** TURSDAX 1,976.94 2,290.92 17,232.79*** TURTECDAX 140.63 87.30 3,348.98*** Signif. codes: p<0.05; p<0.01; p<0.001 Table 8 Descriptives of stock market data II Variable Ljung-Box Ljung-Box Ljung-Box ADF KPSS Q(5) Q(10) Q(20) RETDAX 15.60** 20.70* 40.57** 15.31*** 0.05 RETMDAX 33.64*** 40.84*** 51.09*** 15.59*** 0.09 RETSDAX 78.16*** 82.42*** 109.92*** 13.11*** 0.14 RETTECDAX 41.23*** 43.77*** 56.55*** 14.76*** 0.09 TURDAX 4,926.21*** 7,907.77*** 12,455.62*** 6.90*** 3.5417*** TURMDAX 5,974.95*** 10,245.81*** 16,829.46*** 6.33*** 3.91*** TURSDAX 11,081.81*** 20,219.52*** 37,327.57*** 5.53*** 17.82*** TURTECDAX 5,223.63*** 9,352.30*** 16,129.67*** 4.74*** 7.26*** TUR*DAX 648.13*** 698.88*** 793.26*** 22.09*** 0.003 TUR*MDAX 475.84*** 525.60*** 624.58*** 21.22*** 0.005 TUR*SDAX 454.04*** 465.00*** 485.16*** 20.91*** 0.02 TUR*TECDAX 429.33*** 282.03*** 310.92*** 17.69*** 0.04 Signif. codes: p<0.05; p<0.01; p<0.001 3.3 Model Stock market returns have specific characteristics that cannot be adequately represented by classical time-series models or simple OLS regressions. These characteristics include leptokurtic distributions, higher-order autocorrelations and volatility clusters. The autoregressive conditional heteroskedasticity (ARCH) models introduced by Engle (1982) can handle time series with these specific characteristics and assume that conditional variance is a function of the available information from previous periods. In this way, the error term varies over time. To model financial time series, ARCH models have been replaced by GARCH models, which allow for a more parsimonious specification. Classic ARCH or GARCH models assume a symmetrical effect of positive and negative errors on volatility. According to this assumption, both good and bad news should have symmetrical effects on the variation in the data. However, this assumption often does not stand up to empirical scrutiny for certain capital market data. In the case of stock returns, for example, it has been observed that volatility reacts more sensitively to falling prices or bad K
16 Schmalenbach Journal of Business Research (2022) 74:1–35 news than to rising prices or good news, respectively. This asymmetrical reaction of volatility is called the leverage effect (Black 1976) and is considered in the exponential GARCH (E-GARCH) model proposed by Nelson (1991) and the threshold GARCH (T-GARCH or GJR-GARCH) model proposed by Glosten et al. (1993). Indeed, our dataset displayed the abovementioned characteristics. The LB test revealed strong autocorrelation in the returns and trading volume series, and the data showed volatility clustering. As a result, and following other studies (e.g., Chang et al. 2006;Floros2011;Kangetal.2010, and Yoon and Kang 2009), we applied GARCH models to capture this volatility clustering and to consider heteroskedasticity in the estimation (Bollerslev 1986). To investigate the relationship between stock returns and abnormal weather conditions, we chose a linear autoregressive (AR(2)) model with the GJR-GARCH(1,1) process from Glosten et al. (1993). In all models, following good empirical research practices, we applied Bollerslev-Wooldridge error terms from the maximum likelihood estimation, which were robust to conditional nonnormality (Zivot 2009). RETi;t Dmui;0Cw1RETi;t1Cw2RETi;t2Cw3WIND*tCw4PREC*tC w5SKC*tCw6PRES*tCw7TEMP*tCw8HUMI*tCw9DJIAt1Cw10MONC w11DEC Cw12Halloween Cw13JAN Cw14TURN Cw15TUR* Ci;t; (1) 2 tD˛0C q X iD1 .˛iCdt1/2 t1C p X jD1 ˇj2 tj:(2) Eq. (1) includes autoregressive processes to correct for the autocorrelation of returns. In addition, the weather and control variables are included as explanatory variables. The error term tis a zero-mean white noise process and is normally distributed. Eq. (2) gives the specification of the conditional variance of 2 tat time t,where˛represents the lagged squared residuals and can be interpreted as the news coefficient, with higher values implying that more recent news has a greater impact. ˇis the conditional variance of previous periods, showing the impact of past variance, and ˛Cˇmeasures the persistence of volatility (Bollerslev 1986). The GJR specification allows for an asymmetric impact of bad and good news on conditional variance. The leverage effect is considered via the dummy variable d, where dtD1ift<0anddtD0 otherwise. In this way, good and bad news can have different impacts on conditional volatility. Good news (t0) has an impact of ˛i, while bad news (t<0) has an impact of ˛C.Ifis significant and positive leverage exists, then bad news increases volatility. For D0, the model is reduced to a symmetric GARCH model. The nonnegativity constraint is satisfied if ˛0>0, ˛iC>0, ˇj>0. K
Schmalenbach Journal of Business Research (2022) 74:1–35 17 A similar model with a GJR-GARCH(1,1) process is adopted to assess the relationship between stock returns and daily changes in weather. RETi;t Dmui;0Cw1RETi;t1Cw2RETi;t2Cw3WINDtCw4PRECtC w5SKCtCw6PREStCw7TEMPtCw8HUMItCw9DJIAt1C w10MON Cw11DEC Cw12Halloween Cw13JAN Cw14TURN Cw15TUR* Ci;t: (3) To analyze the relationship between stock volatility and weather factors, we selected the linear autoregressive (AR) model with the E-GARCH(1,1) process from Nelson (1991) because it avoided nonnegativity constraints for the parameters in the variance equation, which now include weather and control variables. The logarithmic function of the conditional variance (Eq. 5) ensures that the variance is positive. E-GARCH models, like for GJR-GARCH processes, can capture asymmetry in the volatility. RETi;t DmuiCiRETi;t Ci;t:(4) ln.2 i;t/D˛0C˛iCg.zt1/Cˇiln2 i;t1C l X kD1 mikMik;t;(5) with g.zt1/D‚ˇˇˇˇ t1 t1ˇˇˇˇEˇˇˇˇ t1 t1ˇˇˇˇCt1 tj :(6) Eq. (5) assumes that returns follow an AR(1) process with drift, analogous to the series in Symeonidis et al. (2010). Mrepresents the weather and control variables. In equation (6), shows the sign and leverage effect, ‚indicates the size effect, and ˇdisplays the persistence. The impact of weather on trading volume was tested with several models. Based on (unreported) tests (namely, LBQ statistics and an Engle’s ARCH test), a linear AR(5) model with the GJR-GARCH(1,1) process was identified as the most appropriate model. The weather and control variables were regressed against the first difference of the logarithmized trading volume (TUR*). The variance equation conformed to the return models. TUR*i;t Dmui;0C 5 X lD1 zilTUR*il;t Ch1WIND*tCh2PREC*tCh3SKC*tC h4PRES*tCh5TEMP*tCh6HUMI*tCh7RETi;t1Ch8DJIAt1Ch9MONC h10DEC Ch11Halloween Ch12JAN Ch13TURN Ci;t: (7) 3.4 Regression Diagnostics and Robustness For maximum-likelihood-based procedures, the quality of the model fit was determined by means of the Akaike and Bayesian information criteria (AIC and BIC, K
18 Schmalenbach Journal of Business Research (2022) 74:1–35 Table 9 Regression diagnostics: ARCH-LM test ARCH-LM test ARCH Lag[3] ARCH Lag[5] ARCH Lag[7] RETDAX 0.50000 1.44000 2.31500 RETMDAX 0.60880 2.91540 3.47590 RETSDAX 0.00649 0.02014 0.30375 RETTecDAX 0.43950 1.65740 2.21660 RETDAX 0.29890 1.11630 1.47910 RETMDAX 0.81600 3.38600 4.04400 RETSDAX 0.50000 1.44000 2.31500 RETTecDAX 0.51400 1.66000 2.31800 VOLDAX 0.38770 0.67800 0.78430 VOLMDAX 0.55720 1.87930 2.60890 VOLSDAX 0.04046 2.63291 3.29208 VOLTecDAX 0.38360 5.361107.16380 TUR*DAX 0.63850 0.82830 0.91440 TUR*MDAX 0.87660 0.92040 1.68400 TUR*SDAX 0.10730 0.89200 2.30540 TUR*TecDAX 1.94900 3.91600 8.88100 Note: RET: regression with changes in weather Signif. codes: p<0.1; p<0.05; p<0.01; p<0.001 respectively), which are mainly used for model selection and the detection of overfitting and thus are not relevant for our purposes. To test for the existence of residual heteroskedasticity, we used the Lagrange multiplier (LM) test proposed by Engle (1982). Nonsignificant test results indicated homoscedastic residuals. Table 9shows the ARCH-LM test results for different lag parameters. With the exception of lag 7 for turnover by volume on the TecDAX, all test results were nonsignificant. Accordingly, we could assume homoscedastic residuals. The autocorrelation of the residuals was tested by means of the LB test with different lags and with standardized and squared standardized residuals (Table 10). The LB test on standardized residuals evaluated the dependence of the first moments with a time lag. The LB test on the squares of standardized residuals, similar to the ARCH-LM test, evaluated the dependence of the second moments with a time lag. The clearly significant results for the turnover-by-volume model for the DAX, MDAX, SDAX, and TecDAX reflected an autocorrelation problem that was already present upon model selection (see Sect. 3.3) and could not be completely resolved by our AR(5) model. However, all further changes to the model specification (e.g., a higher number of lags and the multiple differentiation of trading volume) did not lead to an improvement but, in fact, worsened the diagnostic values. Therefore, we retained the GJR-GARCH(1,1) AR(5) model. The LB test on the squares of standardized residuals and the ARCH-LM test showed no problems. In summary, the regression diagnostics showed the good usability of the models, even if there were autocorrelation problems for the turnover-by-volume model. K
Schmalenbach Journal of Business Research (2022) 74:1–35 19 Table 10 Regression diagnostics: LB test LB test .t=t/LB test .t=t/2 Lag[1] Lag[5] Lag[9] Lag[1] Lag[5] Lag[9] RETDAX 0.03151 0.43471 1.87715 0.02683 3.22962 4.20941 RETMDAX 0.14820 0.71850 2.09850 0.26220 1.51610 3.09490 RETSDAX 0.18570 0.96970 1.72670 0.00019 0.98106 1.60406 RETTecDAX 0.01437 0.36005 0.82740 0.05361 1.22115 2.47688 RETDAX 0.03402 0.37079 1.63298 0.04475 3.27127 4.28241 RETMDAX 0.15550 0.62770 2.06780 0.25240 1.64940 3.49520 RETSDAX 0.22090 1.00760 1.77860 0.00007 1.02777 1.75085 RETTecDAX 0.01309 0.39370 0.85401 0.06416 1.17048 2.45924 VOLDAX 0.08579 0.80823 3.28666 1.32800 1.90400 2.53100 VOLMDAX 3.555007.13200 12.76700 0.77310 1.77530 3.22150 VOLSDAX 1.89400 1.98900 2.80600 1.13100 2.74400 4.49000 VOLTecDAX 4.999005.03300 6.050002.60000 4.61800 9.81900 TUR*DAX 1.51000 20.42000 28.85000 0.84570 1.69770 2.01980 TUR*MDAX 0.34480 55.04910 75.04070 2.53000 4.71500 5.71800 TUR*SDAX 0.74870 44.48750 57.31300 3.747004.19000 5.66500 TUR*TecDAX 0.61260 39.72400 51.84830 0.10860 2.17470 7.19200 We tested the robustness of the results in two ways. First, we removed all outliers from the data and then recalculated the GARCH models. The results remained constant, even with the outliers excluded. Another robustness test was carried out to vary the distribution assumption of the GARCH specification. For this, the models were computed with the generalized error distribution (GED) and Student’s t distribution, instead of the normal distribution we used for our calculations. Except for the results for trade volume, the effects changed only slightly, even after varying the distribution assumptions. One reason for the lack of robustness in trade volume could be the heteroscedasticity problem discussed earlier. Therefore, we saw no evidence of a lack of robustness in the results. We can provide the comprehensive robustness results upon request. 3.5 Results The results are presented in detail in Tables 16–19 in the appendix and in concise form in Tables 11–14 in this section. For the interpretation of the results, we used only the abridged tables. In contrast to the findings of traditional studies, here, we could not observe a sunshine or cloud cover effect. One reason for this might be that almost all former studies identifying a sunshine or cloud cover effect adopted classic OLS or time-series models, which cannot accurately represent stock market data, as they are characterized by autocorrelation and volatility clustering. As a consequence, it cannot be ruled out that the significant results detected in the prior literature might be spurious. Only Yoon and Kang (2009) used a model that was appropriate for capital market data, namely, a GJR model, to identify a significant impact of cloud cover on K
20 Schmalenbach Journal of Business Research (2022) 74:1–35 Table 11 Regression results overview: Returns Weather variables DAX MDAX SDAX TecDAX WIND* PREC* SKC* PRES* ▲ TEMP* HUMI* DJIAt1▲▲▲▲ MON ▼ DEC Halloween JAN ▲▲▲ TURN ▲▲▲ TUR* ▼▼▼ ▼significant negative effect, ▲significant positive effect Table 12 Regression results overview: Changes in weather and returns Weather variables DAX MDAX SDAX TecDAX WIND PREC SKC PRES ▲▲ ▲ TEMP ▲▲ HUMI DJIAt1▲▲ ▲ ▲ MON ▲ DEC Halloween ▼ JAN ▲▲▲ TURN ▲▲ TUR* ▼▼ ▼significant negative effect, ▲significant positive effect stock returns in Korea in the period prior to the Asian financial crisis (1990–1997); however, this impact disappeared in the post-crisis period (1998–2006). In total, 8 significant effects could be found that could be assigned to the theoretical construct of the AIM and 3 significant effects in connection with the MMH. These findings can be taken as a weak indication that good weather leads to riskseeking behavior and that bad weather to risk-averse behavior in the stock market. A more detailed discussion is provided in Sect. 4. K
Schmalenbach Journal of Business Research (2022) 74:1–35 21 Table 13 Regression results overview: Volatility Weather variables DAX MDAX SDAX TecDAX WIND* ▼ PREC* SKC* ▲ PRES* TEMP* HUMI* ▼ MON ▲▲▲ DEC Halloween ▼▼ JAN ▼ TURN TUR* ▲▲▲▲ ▼significant negative effect, ▲significant positive effect Table 14 Regression results overview: Trading volume Weather variables DAX MDAX SDAX TecDAX WIND* PREC* SKC* PRES* ▼▼ TEMP* HUMI* RETit1▼ DJIAt1 MON ▼▼ ▼ DEC ▲▼▼ Halloween ▲▲ JAN ▲▲ ▲ TURN ▲▲ ▼significant negative effect, ▲significant positive effect 3.6 Returns The results mainly showed no weather effects in any of the German stock markets when the dependent variable was returns. There was only a statistically significant effect of air pressure on SDAX returns. Thus, good weather conditions may have a positive effect on returns (AIM), but the predominantly missing effects point to a rejection of H1a and H1b. In addition, we modeled the effect of daily changes in weather on returns and found more significant effects. If air pressure increases, then the returns of the DAX, MDAX and SDAX increase (AIM). Only for the TecDax does no significant cor- K
22 Schmalenbach Journal of Business Research (2022) 74:1–35 relation with air pressure appear. In addition, our results show positive effects of a temperature improvement on the DAX and MDAX (AIM). In contrast to the literature (see Table 2), which found mainly negative effects on returns from temperature increases, an increase in temperature in the German market leads to a positive effect on returns, which can be attributed to the temperate climate in Germany, in that a rising temperature represents a positive change in weather, whereas in Asian markets, for example, a rise in temperature tends to denote a worsening of the weather. Given these effects of the changes in weather in terms of air pressure and temperature, this indicates the confirmation of H1c. However, since the effects are not consistently observable across the large and small indices and since other weather influences are absent, we also cannot confirm H1c. 3.7 Volatility Among the weather variables, we observed three statistically significant effects (see Table 13). Wind speed reduced the volatility of the SDAX (AIM), and relative humidity reduced the volatility of the TecDAX (AIM). Thus, bad weather conditions may have had a negative effect on volatility, which is indicative of risk-averse behavior and thus attributable to the AIM. In contrast, cloud cover had a positive impact on TecDAX volatility, which is attributable to the MMH. Since there were no weather effects for the DAX and MDAX and only 3 contradictory effects for the SDAX and TecDAX, we could not confirm H2a or H2b. 3.8 Trading volume The regression results show significant negative effects of air pressure on trading volume for the SDAX and TecDAX. A rise in air pressure could be associated with good weather, which leads to decreased trading (MMH). These effects are in line with H3b, which posited that good weather conditions lead to a lower trading volume. However, since we did not observe effects from any of the other variables, the existing effects could be shown for only the SDAX and TecDAX, and there were still some autocorrelation problems for the analysis of trading volume (see Sect. 3.4), we were not able to confirm H3b. 3.9 GARCH vs. OLS The majority of past empirical weather anomaly studies used OLS regression. However, this was not adequate in most cases due to heteroskedasticity issues, even when controlling for heteroskedasticity using White or Newey-West standard errors. Our literature review showed that for returns, for example, not even one-third of the studies used modern financial econometrics for empirical analysis (see also Sect. 2). How serious an influence the choice of method has on the results can be shown by a comparative analysis. A calculation of our models with OLS using White estimators led to completely different results compared to those identified using the GARCH model. The following Table shows an overview of the GARCH and OLS K
Schmalenbach Journal of Business Research (2022) 74:1–35 23 Table 15 Regression results overview: GARCH vs. OLS Weather variables DAX MDAX SDAX TecDAX Return PRES* ▲ PRES ▲▲▲ TEMP ▲▲ SKC 4 Trading Vo l um e PRES* ▼▼ WIND* 4 SKC* 5 PRES* 555 TEMP* 555 HUMI* 5 ▼significant negative effect GARCH, ▲significant positive effect GARCH, 5significant negative effect OLS, 4significant positive effect OLS results. If there is interest in the detailed regression tables, they can be provided upon request. Table 15 shows that only one significant effect is detectable with OLS regression for the impact of weather on returns. For changes in weather, the results showed a positive influence of sky cover on the DAX. The GARCH model, conversely, identified one positive effect of air pressure on returns in the SDAX and five positive effects of changes in air pressure and temperature on the DAX, MDAX and SDAX. The analysis of trading volume also showed that OLS regression provided a completely different picture of these relationships. Although the GARCH model showed only two negative effects of air pressure on trading volume for the SDAX and TecDAX, OLS regression showed one positive effect of wind on trading volume and eight negative effects of sky cover, air pressure, temperature and humidity for the DAX, MDAX and SDAX. These different results make it clear that the choice of method has a significant impact on the results or that the violation of application requirements of econometric models for the detection of financial market anomalies can lead to incorrect conclusions. At the same time, it is of great importance to consider which control variables are used. In particular, month effects (e.g., Halloween effect and Monday, January, and December dummies) should be controlled; otherwise, they could be incorrectly assigned to weather. 4 Conclusions This study attempts to answer the question of whether there are indeed effects of weather on stock markets. The application of modern time-series regressions to data from the most important German stock indices shows a mixed picture, and thus, this question cannot be answered conclusively. As we mentioned in the results section, we do not regard isolated significant effects of weather variables as an indication of a significant capital market anomaly. This applies, in particular, to the effects of K
24 Schmalenbach Journal of Business Research (2022) 74:1–35 weather on volatility (the negative effect of wind on the SDAX, the positive effect of clouds on the TecDAX, and the negative effect of humidity on the TecDAX). However, the effect of air pressure shows more consistent results for the various key figures and capital markets. We find a positive effect of air pressure on the returns of the SDAX but not on those of the TecDAX. At the same time, trading volume decreases on the SDAX and TecDAX as air pressure increases. These results show, on the one hand, that air pressure is an important weather variable to be considered and, on the other hand, that the effects of investor mood may be particularly relevant for small-capitalization indices (Baker and Wurgler 2006; Klein 2005; Lee et al. 2002; Schneider 2014a; Statman et al. 2006). Therefore, it may be reasonable to have a higher proportion of domestic investors in small caps compared to blue chips. However, the analysis of the changes in air pressure and temperature also shows effects on the returns of larger indices such as the DAX and MDAX. This finding contradicts the assumption that only the proportion of domestic investors makes the effects of weather detectable. Rather, the strength of the weather influence also seems to play a role. One explanation for the effects on the DAX and MDAX could accordingly be that changes in weather have a stronger influence on people’s health and behavior than does the weather itself, and thus, the proportion of domestic investors as an explanation for the effects of weather on the stock market moves into the background. However, the divergence between the results in the literature and those of this study may also be due to methodological reasons. For example, it is noticeable that some authors use fewer control variables and OLS regression, and thus, their results are only comparable to a limited extent. The comparison of the GARCH model and OLS regression (see Table 15 and Sect. 3.9), for example, shows no OLS effects for air pressure and temperature and thus shows absolutely opposite results based on the method used. This finding shows that a comparison of the studies is questionable when using different financial market econometrics. Nevertheless, no uniform picture of this situation emerges. Changes in air pressure have a positive effect on the returns of the DAX, MDAX and SDAX, but not on those of the TecDAX. At the same time, it is difficult to explain why changes in temperature have a positive effect on the DAX and MDAX, but not on the SDAX and TecDAX. Accordingly, our results show no empirical evidence that small caps are more vulnerable to the effects of weather than are blue chips due to more local investors. We therefore conclude that changes in weather lead to the most empirically meaningful results in this study. However, the results are not completely conclusive and further research is needed in this area with a focus on changes in weather. In addition, there should be more focus on the composition of the indices and the type of investors to better explain the effects of weather. When the results are viewed against the background of the AIM or the MMH, a clear positioning for the AIM emerges. A total of eleven statistically significant effects can be demonstrated, eight of which can be attributed to the AIM. If we exclude the results for trading volumes, then since the heteroscedasticity problem could not be completely solved for these models, only one effect for volatility (see Table 18) can be assigned to the MMH and all others to the AIM. Our results should therefore be taken as further empirical evidence for the effects of the AIM. K
Schmalenbach Journal of Business Research (2022) 74:1–35 31 Table 19 Regression results: Trading volume Dependent variable: Trading volume (1) DAX (2) MDAX (3) SDAX (4) TecDAX mu 0.00056 0.01503 0.00314 0.01509 (0.00368) (0.00148) (0.00215) (0.00584) AR(1) 0.50976 0.49175 0.48986 0.43599 (0.03141) (0.02186) (0.02168) (0.02454) AR(2) 0.36948 0.39787 0.33565 0.35732 (0.03803) (0.02174) (0.02040) (0.02599) AR(3) 0.24913 0.30784 0.25519 0.27982 (0.03579) (0.02229) (0.02040) (0.02198) AR(4) 0.16559 0.19782 0.16929 0.17665 (0.03310) (0.01975) (0.02060) (0.02130) AR(5) 0.064980.09145 0.08252 0.11651 (0.03456) (0.01757) (0.01724) (0.01994) WIND* 0.00024 0.00049 0.00018 0.00173 (0.00114) (0.00071) (0.00095) (0.00280) PREC* 0.00015 0.00021 0.00003 0.00145 (0.00053) (0.00036) (0.00060) (0.00128) SKC* 0.00125 0.00067 0.00062 0.00174 (0.00163) (0.00084) (0.00103) (0.00280) PRES* 0.00004 0.00001 0.000310.00115 (0.00018) (0.00013) (0.00016) (0.00051) TEMP* 0.00010 0.00018 0.00033 0.000040 (0.00042) (0.00023) (0.00036) (0.00090) HUMI* 0.00020 0.00017 0.00012 0.00007 (0.00027) (0.00014) (0.00018) (0.00047) RETit10.10550 0.273660.24372 0.03802 (0.20635) (0.11008) (0.16476) (0.32362) DJIAt10.39163 0.22907 0.08651 0.16994 (0.25766) (0.16479) (0.20008) (0.43807) MON 0.08152 0.08125 0.00827 0.16362 (0.00784) (0.00582) (0.00763) (0.01902) DEC 0.01974 0.00844 0.006120.00409 (0.00696) (0.00308) (0.00309) (0.00872) Halloween 0.01296 0.00052 0.00138 0.01169 (0.00292) (0.00117) (0.00169) (0.00475) JAN 0.02009 0.00965 0.00350 0.04237 (0.00588) (0.00276) (0.00369) (0.01392) TURN 0.00703 0.00955 0.00068 0.02423 (0.00505) (0.00283) (0.00416) (0.01084) ˛00.00223 0.002560.00020 0.01111 (0.00079) (0.00106) (0.00006) (0.00331) K
32 Schmalenbach Journal of Business Research (2022) 74:1–35 Table 19 (Continued) Dependent variable: Trading volume (1) DAX (2) MDAX (3) SDAX (4) TecDAX ˛10.10456 0.080360.03042 0.04723 (0.08518) (0.03197) (0.00801) (0.02186) ˇ10.73153 0.69093 0.96280 0.80632 (0.08889) (0.09688) (0.00069) (0.04620) 00.08853 0.02972 0.00334 0.06008 (0.09467) (0.03968) (0.01744) (0.03502) AIC 1.38460 1.62480 0.98812 0.43754 BIC 1.34470 1.58480 0.94816 0.49692 Note: p<0.1; p<0.05; p<0.01; p<0.001 References Agrawal, A., and K. Tandon. 1994. Anomalies or illusions? Evidence from stock markets in eighteen countries. Journal of International Money and Finance 13(1):83–106. Akhtari, M. 2011. Reassessment of the weather effect: stock prices and wall street weather. Undergraduate Economic Review 7(1):19. Allen, M.A., and G.J. Fischer. 1978. Ambient temperature effects on paired associate learning. Ergonomics 21(2):95–101. Apergis, N., A. Gabrielsen, and L.A. Smales. 2016. (Unusual) weather and stock returns – I am not in the mood for mood: further evidence from international markets. Financial Markets and Portfolio Management 30(1):63–94. Baker, M., and J. Wurgler. 2006. Investor sentiment and the cross-section of stock returns. The Journal of Finance 61(4):1645–1680. Bassi, A., R. Colacito, and P. Fulghieri. 2013. O sole mio: an experimental analysis of weather and risk attitudes in financial decisions. The Review of Financial Studies 26(7):1824–1852. Bernardo, A.E., and O. Ledoit. 2000. Gain, loss, and asset pricing. Journal of Political Economy 108(1):144–172. Black, F. 1976. Studies of stock price volatility changes. Proceedings of the 1976 meeting of the business and economic statistics section., 177–181. Washington DC: American Statistical Association. Bollerslev, T. 1986. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31(3):307–327. Bouman, S., and B. Jacobsen. 2002. The halloween indicator, “sell in may and go away”: another puzzle. American Economic Review 92(5):1618–1635. Brown, G.W. 1999. Volatility, sentiment, and noise traders. Financial Analysts Journal 55(2):82–90. Cao, M., and J. Wei. 2005. Stock market returns: a note on temperature anomaly. Journal of Banking & Finance 29(6):1559–1573. Chang, S.C., S.S. Chen, R.K. Chou, and Y.H. Lin. 2008. Weather and intraday patterns in stock returns and trading activity. Journal of Banking & Finance 32(9):1754–1766. Chang, T., C.C. Nieh, M.J. Yang, and T.Y. Yang. 2006. Are stock market returns related to the weather effects? Empirical evidence from Taiwan. Physica A: Statistical Mechanics and its Applications 364:343–354. Cialdini, R.B., B.L. Darby, and J.E. Vincent. 1973. Transgression and altruism: a case for hedonism. Journal of Experimental Social Psychology 9(6):502–516. Connolly, M. 2008. Here comes the rain again: weather and the intertemporal substitution of leisure. Journal of Labor Economics 26(1):73–100. Delyukov, A., and L. Didyk. 1999. The effects of extra-low-frequency atmospheric pressure oscillations on human mental activity. International Journal of Biometeorology 43(1):31–37. Denissen, J.J., L. Butalid, L. Penke, and M.A. van Aken. 2008. The effects of weather on daily mood: a multilevel approach. Emotion 8(5):662–667. K
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