Tradin in the Rain: Attention Allocation and Investment Performance

Transcription

1 Tradin in the Rain: Attention Allocation and Investment Performance Dien Giau Bui * Department of Finance National Taiwan University Chih-Yung Lin ** College of Management Yuan Ze University Tse-Chun Lin *** Faculty of Business and Economics University of Hong Kong We would like to thank Antonio Gargano and Lin Peng for the helpful comments. Tse-Chun Lin gratefully acknowledges research support from the Faculty of Business and Economics, The University of Hong Kong. Chih-Yung Lin appreciates the financial support from Taiwan Ministry of Science and Technology. Any remaining errors are ours. * d @ntu.edu.tw ** Corresponding author. d @ntu.edu.tw *** tsechunlin@hku.hk

2 Tradin in the Rain: Attention Allocation and Investment Performance Abstract Using a comprehensive stock-day trading data at the brokerage branch level, we find that retail investors allocate more attention to the stock market on rainy days. This rainy day effect on investor attention is exhibited by (i) larger retail trading volume, (ii) more Google search volume on stock symbols, and (iii) lower stock return co-movement. The rainy day effect is not driven by mood-induced risk and skewness preferences as the results are significant irrespective of the levels of return volatility and skewness. Nor the rainy day effect is observed among institutional investors. More importantly, we find that trading profits are higher for retail trades made on rainy days. Overall, our evidence suggests that attention allocation not only affects return co-movement that has been shown in the literature but also has a positive impact on retail investment performances. JEL Classification: G11, G12, G14, G40 Keywords: Rainy days, attention allocation, investment performance, return co-movement, retail investors

3 1. Introduction A burgeoning theoretical literature has been applying investor attention allocation to explain puzzling patterns in financial markets that deviate from predictions of traditional models, including home bias (Van Nieuwerburgh and Veldkamp, 2009), under-diversification (Van Nieuwerburgh and Veldkamp, 2010), return co-movement (Peng and Xiong, 2006; Veldkamp, 2006; Veldkamp and Wolfers, 2007). These models, in general, imply that when marginal costs of allocating attention to the stock market are lower, investors would benefit from paying more attention to it. However, it is empirically challenging to test the causal effects of attention allocation on the investment performance for two reasons. First, attention allocation and investment performance are obviously endogenous. Hence, shocks to the marginal costs of paying attention to the stock market are needed for the identification. Second, investment performance data that links to the attention shocks has to be available, which is rarely the case in the U.S. and most markets. The innovation of our paper is to use rainy days as negative shocks to the opportunity cost of paying attention to the stock market and provide causal evidence that more investor attention on firm-level information improves investment performances of retail investors. The intuition is that the opportunity cost for paying attention to the stock market and spending time trading on days with good weather is higher for the retail investors (Schmittmann, Pirschel, Meyer, and Hackethal, 2015). It is arguably more enjoyable to get together outdoors with family and friends on good weather days, which represents a higher opportunity cost of paying attention to the stock market. This intuition is consistent with the argument in Hong and Yu (2009) who find lower stock 1

4 trading volume during the summer because market participants are on vacation. Hence, we argue that the attention allocation to the stock market would be higher for the attention-constrained retail investors on rainy days. Before we test whether investment performance improves on rainy days, we need to validate the prerequisite that retail investors indeed pay more attention to the stock market on these days. Using daily aggregate and comprehensive retail buy and sell volume data from 854 branches of 63 brokers from July 2012 to December 2016 in Taiwan, we provide three sets of evidence for the validation. 1 First, we find that retail investors trade (both buy and sell) more on rainy days. This result is consistent with Schmittmann, Pirschel, Meyer, and Hackethal (2015) who find that investors trade less in German stock market on good weather days based on one German discount brokerage. Second, Google search volume on each stock, a well-received retail attention measure, is also higher on rainy days. Third, we find that stock return co-movement and adjusted R 2 are lower on rainy days, indicating more firm-level information is incorporated into the prices. The lower return co-movement on rainy days provides direct evidence that more investor attention being allocated to the stocks as implied by the existing models (e.g., Peng and Xiong, 2006; Kacperczyk, Van Nieuwerburgh, and Veldkamp, 2014, 2016; Huang, Huang, and Lin, 2017). We then move on to our main test and examine whether retail investors, on average, make more profits on rainy days. As our data also contains the daily average purchase and sale price of each stock in each branch of brokerage firms by the retail investors, it allows us to calculate the average mark-to-market trading profits for retail investors at the city-day level. We find that retail investors have significantly positive 1 The local weather has a significant heterogeneity across cities in Taiwan. For example, the ratio of rainy days ranges from 13% to 35% in our sample. 2

5 trading profits for various holding periods from one day to five days. The results hold after controlling for several fixed effects including city, year, month-of-year, week, and day-of-week. Together with the previous tests on attention allocation, these results support our argument that retail investors pay more attention to the stock market on rainy days, leading to higher trading profits. One may concern that as the weather has been shown to affect investor mood and mood-induced risk-taking behavior, our results that retail investors perform better on rainy days might be driven by the mood or mood-induced risk-taking. 2 However, this line of literature usually suggests that when investors have better moods on sunny days, they take more risks. Hence, if the extra risks taken on sunny days are compensated, we should find higher trading profits on sunny days, not on rainy days. In addition, our analysis shows that the better trading performances of retail investors on rainy days exist for both high- and low-risk stocks, suggesting that our main finding is not driven by the mood-induced risk-taking behavior. Moreover, if the better mood on sunny days induces more loading on risks in the household portfolios, we should also find a higher trading volume on sunny days, not on rainy days. Besides, the weather-induced mood should be more likely to affect retail trading in the same direction, potentially causing a higher return co-movement, not a lower co-movement. Collectively, we find opposite patterns predicted by the mood explanation, suggesting that mood or mood-induced risk-taking is unlikely to drive our findings. The results of Google search volume are also in line with our attention allocation interpretation. Another concern is that some retail investors may consider trading as a form of a 2 See, for example, Saunders (1993), Hirshleifer and Shumway (2003), Kamstra, Kramer, and Levi (2003), Bassi, Colacito, and Fulghieri (2013). 3

6 fun and exciting gambling activity, and the weather would influence their tendencies to trade on lottery-like stocks (e.g., Barberis and Huang, 2008; Kumar, 2009; Grinblatt and Keloharju, 2009; Barber, Lee, Liu, and Odean, 2009; Gao and Lin, 2015). That is, if retail investors cannot have fun outdoors on rainy days, they might trade more lottery-like stocks as an alternative source of entertainment at home. To alleviate the concern, we re-examine the effect of rainy days on the retail trading profits from the subsamples of lottery-like and non-lottery-like stocks. Our analysis shows that the better trading performances of retail investors on rainy days exist for both lottery-like stocks and the other stocks, indicating that our main finding is not mainly driven by the lottery-like preference. We conduct several robustness checks to corroborate our main findings. First, we test whether the effect of rainy days also exists among institutional investors. 3 We do not find a significant increase in institutional trading more on rainy days. This is consistent with our attention argument as the literature mostly agrees that institutional investors are less subject to attention constraints, and it is the professional traders job to trade, irrespective of the weather. Second, we use the Google search item influenza in Mandarin as an alternative attention shock to retail investors and find consistent evidence for our attention argument. 4 Third, we find that market responses to earnings announcements on rainy days are quicker than those on the other days, providing additional support to the attention argument. Fourth, we also find that the rainy day effect exists in the time-series analysis by using the market level data. Fifth, the rainy effect on retail trading profits does not reverse, suggesting that attention allocation produces valuable information. Last, we find consistent results after 3 All the institutional investors trading is recorded in their headquarters, and almost all the headquarters of institutional investors in Taiwan are located in Taipei city. 4 Mandarin is the official language of Taiwan. 4

7 controlling for city-level variables such as city income and city population rather than adding city fixed effects. Our results are also robust to alternative definitions of rainy days. Our paper contributes to the literature in several ways. First, we add to the existing studies on the effect of attention allocation in financial markets (e.g., Sims, 2003, 2010; Hirshleifer, Lim, and Teoh, 2009; DellaVigna and Pollet, 2009; Kacperczyk, Van Nieuwerburgh, and Veldkamp, 2014, 2016). In particular, Gargano and Rossi (2017) use granular login information of 11,000 trading accounts and find that more attentive investors achieve higher returns. Our paper complements and differs from theirs as we use the exogenous attention shocks to provide a causal inference that paying more attention to the stock market improves the trading performance of retail investors. 5 Moreover, while the advantage of their data is the extreme granularity on account login activities, the advantage of ours is the full coverage of both retail and institutional trades in the Taiwan stock exchange. The full coverage of data combined with a retail-dominated market allows us to observe and validate the potential asset pricing impacts like the return co-movement and adjusted R 2 from the weather-induced attention allocation. This important validation test of rational attention allocation would not be feasible using data from a single brokerage firm. Second, our paper is also related to the literature regarding the weather effects on trading behaviors since we use rainy days as the shocks to the investors opportunity cost of paying attention to the stock market (e.g., Saunders, 1993; Hirshleifer and Shumway, 2003; Kamstra, Kramer, and Levi, 2003; and Goetzmann, Kim, Kumar, 5 In this regard, our results also relate to the retail attention literature (Da, Engelberg, and Gao, 2011; Sicherman, Loewenstein, Seppi, and Utkus, 2016; and Lu, Ray, and Teo, 2016). 5

8 and Wang, 2015). However, at odds with the mood or mood-induced risk-taking interpretation, our results are more in line with the rational inattention argument. In this sense, our paper relates to Schmittmann, Pirschel, Meyer, and Hackethal (2015) who find that investors in a German discount brokerage trade more on bad weather days as the opportunity cost of trading is lower. 6 Differing from theirs, our main focus and contribution are to document the weather influence on investor attention and the consequent trading profits. Finally, our paper belongs to a small group of studies using exogenous shocks to investor attention to study its causal effect on the financial market as well. For example, Huang, Huang, and Lin (2017) use large jackpot lotteries as exogenous shocks that attract investors attention away from the stock market and find evidence that stock returns co-move more with the market on these days. Peress and Schmidt (2018) use the sensational news as the shocks that attract noise traders attention from the stock market and find that trading activity, liquidity, and volatility drop on these days. Our paper differs from these studies as we focus on examining the causal effect of paying attention to the market and the investment performance among retail investors. 2. Data and descriptive statistics In this section, we describe the institutional details of our data, construct the variables of interest, and present descriptive statistics. 6 Consistent with attention argument, bad weather is also shown to increase indoor activities like internet traffic (Cardona, Stanojevic, and Cuevas, 2013), movies viewership (Gilchrist and Sands, 2016), and visits and pledges of crowdfunding activities on Kickstarter (Xu, 2017). 6

9 2.1 Sample We collect daily trading data of all listed firms in Taiwan Stock Exchange (TWSE) from Taiwan Economic Journal (TEJ). TEJ, a data vendor, provides comprehensive firm-day trading record at the brokerage branch level. In particular, for every branch of every brokerage firm in Taiwan, we could observe each stock s total number of shares bought and sold, total value of shares bought and sold, and average buy and sell prices within a trading day. As all headquarter branches of brokerage firms exclusively serve their institutional clients in Taiwan, we are able to separate retail traders and institutional traders based on the branch location. In total, our data contains daily trading data of 854 branches of 63 brokers for individual investors from July 2012 to December Since our weather data is at the city level (described in the next section), we need to construct city-day level portfolios to test the influence of weather on trading volume and investment performance in a two-step procedure. In the first step, we aggregate a firm s relevant variables (e.g., volume, value, and price) from branch-level to city-level. 7 Specifically, for each day t and each stock i, we sum trading volume and trading value that take place at branch b within the same city zip code z as follows: Volume B = Volume (1) izt,, ibt,, b= 1 Value B = Value (2) izt,, ibt,, b= 1 where B is the number of branches in a city z. 7 Because transactions of each stock take place at different branches, we aggregate these variables for branches located in the same city, allowing us to measure each stock s trading volume and performance of investors in a particular city. 7

10 We also calculate the turnover rate as the ratio of trading volume divided by the firm s outstanding shares (in percentage). In particular, for each firm i in city z on day t, the turnover is Turnoverizt,, = Volumeizt,, / Outstandingit,. For calculating the average buy and sell prices, on each day t, we take the trading-value-weighted average of price for each stock i that has shares traded at all branches b within the city zip code z as follows: B Price = w Price (3) izt,, ibt,, ibt,, b= 1 where wi,b,t is the trading value of stock i on day t at the branch b. Accordingly, for each stock i on day t, we have the average buy and sell prices for investors in every city. We follow Barber, Lee, Liu, and Odean (2009) to classify the trading of a stock i in each city into buy portfolio and sell portfolio and consider only the net trades of each day. For example, if a stock is bought 3,100 shares at an average buy price of 30 New Taiwan dollar (TWD) and is sold 3,000 shares at an average sell price of 29.5 TWD, then the buy portfolio is added 100 shares while the sell portfolio is added zero. In our example, this stock contributes 3,000 TWD (i.e., ) to the value of the buy portfolio, while it contributes zero to the sell portfolio on this day in the city. Next, we calculate returns of buy trades and sell trades for the stock i on day t in city z by comparing this stock s average buy and sell prices and its close price in the next one to five days: R buy, k day izt,, Price Price = 100 (4) close buy it, + k izt,, buy Priceizt,, 8

11 R sell, k day izt,, Price Price = 100 (5) sell close izt,, it, + k sell Priceizt,, Then, the trading profits of the buy portfolio and sell portfolio are calculated as the portfolio value at the close of trading on day t 1 multiplied by the daily excess return as follows: Profit = Portfoliovalue (R R ) (6) izt,, izt,, 1 izt,, mt, where R izt,, is the return of each portfolio defined as in Equations (4) and (5) and R mt, is the corresponding market index return. The trading profit, our main measure of investment performance, is the difference in profit between the buy portfolio and sell portfolio as that in Barber et al. (2009). In the second step, we aggregate the variables of interest from firm-level to city-level. For each city code z and each day t, we aggregate trading volume, trading value, turnover, and profit for all stocks (N) that are traded within the city code z as follows: Volume N = volume (7) zt, izt,, i= 1 Value N = Value (8) zt, izt,, i= 1 Turnover N = Turnover (9) zt, izt,, i= 1 Profit N = Profit (10) zt, izt,, i= 1 In the end, we have a sample of daily trading volume (shares, value, and turnover) and the trading profits of individual investors in 21 cities of Taiwan. We conduct most of our regression analyses at the city-day level. Finally, we also collect income and 9

12 population data from the Ministry of the Interior of Taiwan to control for the city-level characteristics, 2.2 Weather measures We collect the weather data from Central Weather Bureau of Taiwan, including daily rain volume (in millimeter) and sunshine hours for each city in Taiwan. We define a day as rainy day (RAIN) if the rain volume in one city is larger than three millimeters. In robustness checks, we use other thresholds such as zero millimeter or one millimeter (Alternative RAIN 1 and Alternative RAIN 2, respectively) and actual rain volume (Rain Volume) to define a rainy day in a city. Our results are qualitatively similar using these alternative definitions of rainy days. We also calculate the daily sunshine rate as the ratio of the number of sunshine hours divided by the number of daylight hours (in percentage) as an additional measure of rainy days and find similar results. 8 However, there are only 16 cities having the data of sunshine rate, while rain volume data is available for all 21 cities. Hence, we do not report these results, which are available upon requests. 2.3 Descriptive statistics Panel A of Table 1 presents the summary statistics of the main variables. The final sample includes 24,267 city-day observations of trading data. Among them, there are 22,897 observations with the corresponding weather data. Around 21 percent of the city-day observations are rainy days (RAIN). For the other two definitions, Alternative RAIN 1 and Alternative RAIN 2, there are 38.7 percent and 27.7 percent of 8 We rank the sunshine rate as an ordered variable, sunshine rank, from 0 (i.e., lowest) to 10 (i.e., highest). In particular, if the sunshine rate is zero, sunshine rank equals 0. If the sunshine rate is larger than zero and smaller than 10 percent, sunshine rank equals 1. Similarly, if the sunshine rate is larger than nine and smaller or equal to 100 percent, sunshine rank equals

13 rainy days, respectively. The average of Rain Volume is 5.13 millimeters. ALL RAIN is a dummy variable that equals one if all 21 cities are rainy, which is about four percent of the sample size. Appendix A lists the definitions of all the variables employed in this paper. The average daily buy and sell turnovers are percent and percent, respectively. The buy value and sell values are 236 million TWD and 228 million TWD per day. 10 The daily trading volumes are around 20 million shares for both buys and sells. 11 We also report the trading profits in the holding period of one, two, three, four, and five days (in billion TWD). [Insert Table 1] Panel B of Table 1 presents the weather data at the city level, with the top (bottom) of the panel representing the cities in the northern (southern) part of Taiwan. The results show that there is a sufficient amount of variation in weather conditions, with a high standard deviation in most rain variables. This variation of rainy day ratios among cities allows us to identify how weather conditions affect the investor attention and their trading behaviors Empirical results In this section, we first conduct three tests to validate more attention allocation to the stock market for retail investors on rainy days based on return co-movement, Google search volume index, and trading turnover. Second, we test our main 10 One U.S. dollar is around 30 TWD during our sample period. 11 These figures are consistent with the statistics in Appendix A of Gao and Lin (2015). 12 Pearson correlation coefficient matrix of the main variables are shown in Internet Appendix A. First, the results show that RAIN is significantly associated with higher trading turnover (value or volume) in both sides of trades and higher trading profits in the five different holding periods. Second, the correlation coefficients between RAIN and the other dependent variables are less than 0.033, indicating that multi-collinearity is not a concern. 11

14 hypothesis whether individual investors allocate more attention and have higher trading profits on rainy days than on non-rainy days. Finally, to alleviate the concern that our results are driven by mood or skewness preference, we examine whether our results exist on subsamples with high/low risk and skewness. 3.1 Rainy days and attention allocation The rational inattention and the co-movement of asset prices To test whether individual investors tend to allocate more attention on rainy days, we compare firms return co-movement with the market between rainy days and the other days. Following the study of Huang, Huang, and Lin (2017), we use two measures to capture the co-movement: Correlation Coefficient and Adjusted R 2. First, the Correlation Coefficient is the Pearson correlation coefficient between firm excess returns and market excess returns. Second, Adjusted R 2 is obtained from the market model between firm excess returns and market excess returns. We expect that individual investors allocate more attention to the stock market on rainy days, leading to lower Correlation Coefficient and Adjusted R 2 as more firm-level information is incorporated into stock prices. In particular, for each day, we calculate the ratio of rainy cities out of all 21 cities (i.e., rain ratio). Then, for each year, we split the sample into the top 20% highest rain ratio days and the other days. Next, for each firm, we calculate the time series Pearson correlation of stock excess returns and market excess returns on the top 20% highest rain ratio days and on the other days separately, and obtain the level difference in correlations (correlation on the highest rain ratio days minus the correlation on the other days) and its percentage change (the difference divided by the correlation on other days). 12

15 To calculate Adjusted R 2, we run the following regression for each firm i to obtain the Adjusted R 2 on the top rain ratio days and on the other days separately: Excess return = α + β Market excess return + ε (11) it, i i t it, where Excess return it, is the excess return of firm i and Market excess return is t market excess return on day t. The market excess return is the difference between the market return and the risk-free rate, which is the central bank one-month deposit rate from TEJ. For each firm, we get the difference in Adjusted R 2 (on the top highest rain ratio days and on the other days) and its percentage change (the difference divided by the Adjusted R 2 on other days). We report the means and medians of differences and percentage changes in Table 2. The paired t-test is used for testing the mean difference and Wilcoxon signed-rank test is employed for testing the median difference. The results show that the means and medians of the Correlation Coefficients and the Adjusted R 2 are lower on the top rainy days than those on the other days. Compared to the other days, the correlation coefficient s mean (median) drops about 13% (15%) on the top rainy days. Likewise, the mean (median) of Adjusted R 2 is also lower by about 33% (30%). All the differences and percentage changes are statistically and economically significant. These findings provide the first support to our conjecture that individual investors allocate more attention to the stock market on the rainy days than the other days. [Insert Table 2] Rainy days and Google search volume index Huang, Huang, and Lin (2017) show that large jackpot days are associated with lower Google search volume for abbreviations of firm names used by Yahoo! Finance 13

16 Taiwan as the lottery jackpots distract retail investors from their trading. With the same spirit, we predict that retail investors allocate more attention to financial markets on the rainy days, resulting in a higher Google search volume of firm names. To test this rainy days effect on attention, we define Top 20% Rain Ratio as a dummy variable that equals one if a day has the rain ratio is in the top 20% highest rain ratio (as defined in Section 3.1.1), and zero otherwise. Then, we run the firm-level regressions as below: SVI = β Top 20% Rain Ratio + u + y + m + d + ε (12) it, t i t t t it, Abnormal SVI = β Top 20% Rain Ratio + u + y + m + d + ε (13) it, t i t t t i, t where SVI is the adjusted daily Google search volume index (SVI) from Google Trends of the firm name abbreviations used by Yahoo! Finance Taiwan, and Abnormal SVI is the abnormal measure of SVI as in Huang, Huang, and Lin (2017). The adjusted daily SVI is calculated as follows: SVI = (Weekly SVI to which the day belongs) (Unadjusted daily SVI/Weekly average of unadjusted daily SVI). The abnormal SVI is calculated as the deviations of SVI from the median of SVI from the previous 25 th week to the 5 th week, scaled by that median. After excluding firm name abbreviations with generic meanings, there are 763 firms remaining in our sample. The sample period for SVI is from January 4, 2004, to June 30, In regressions, we control for the firm, year, month, and day-of-the-week fixed effects. Standard errors are clustered at the firm level. Superscripts *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively. Panel A of Table 3 presents regression results of SVI on a dummy of the top 20% highest rainy days. The results show that the estimated coefficients of Top 20% Rain Ratio are positive and statistically significant. These results are consistent with our 14

17 expectation that Google search volume increases on rainy days when retail investors pay more attention to the stock market. [Insert Table 3] Rainy days and trading turnover Furthermore, Schmittmann, Pirschel, Meyer, and Hackethal (2015) find that individual investors trade more on bad weather days, supporting that individual investors incur an opportunity cost for spending time trading on days with fine weather. Similarly, Huang, Huang, and Lin (2017) find that large jackpot days are associated with lower share turnover. Thus, on the rainy days, we anticipate that investors allocate more attention to financial markets, resulting in a higher trading turnover. To test this prediction, we perform the following regression: Turnover = β RAN I + c + y + m + w + d + ε (14) zt, zt, z t t t t zt where Turnover is trading turnover of individuals in the city z on day t for either zt, buy trades or sell trades; RAINz,t is the dummy variable that equals one if the rain volume in the city z on day t is larger than three millimeters and equals zero otherwise; cz, yt, mt, wt, and dt, are city, year, month, week, and day-of-week fixed effects, respectively; and ε is the error term. In all tables, t-values are calculated based on zt, the robust standard errors adjusted for heteroscedasticity and city-level clustering (Petersen, 2009). After controlled all fixed effects, the coefficient of RAIN measures how daily weather variation in the same city affects the trading turnover in that day. Panel B of Table 3 shows the regression results for both buy trades and sell trades as in Equation (14). In both models, we find a positive association between rainy days and trading turnover. The estimated coefficients of RAIN are significant for 15

18 both buy and sell trades. This finding appears to be consistent with Schmittmann, Pirschel, Meyer, and Hackethal (2015) that individual investors incur an opportunity cost for spending time trading on days with good weather and thus allocate more attention on rainy days. In sum, results in this section provide supportive evidence for the validation exercise that retail investors trade more on the rainy days as the opportunity cost of trading is lower on these days. This finding paves the way for our main test on the attention allocation and investment performance. 3.2 Retail trading profits on the rainy days In this section, we perform the following regression to test whether retail trading profits are higher on rainy days: Profit = β RAIN + c + y + m + w + d + ε (15) zt, zt, z t t t t zt, where Profit zt, is trading profits of individuals in the city z on day t; RAINz,t is the dummy variable that equals one if the rain volume in the city z on day t is larger than three millimeters and equals zero otherwise; cz, yt, mt, wt, and dt, are city, year, month, week, and day-of-week fixed effects, respectively; and ε is the error term. Besides, zt, we examine the trading performance of individual investors for different holding periods from one day to five days. Table 4 presents regression results for the effect of rainy days on the daily trading profits. In Models (1) to (5), the estimated coefficients of RAIN are positive and statistically significant. Individual investors earn higher trading profits on rainy days for various holding periods. In particular, on rainy days, individual investors in a city can earn around 131 to 296 million TWD (equivalently to around 1.9 to

19 million US dollars) trading profits, depending on the holding periods. In terms of economic magnitude, the 131 to 296 million TWD increases are approximately 81% to 122% compared with the average of the variables. Thus, the impacts of rainy days on trading profits are also economically meaningful. [Insert Table 4] 3.3 Mood-induced risk-taking or skewness preference One may concern that our findings could be driven by mood-induced risk-taking behavior or skewness preference. When the weather is good, retail investors have good moods and higher risk appetite such that they load on more risks by trading more risky stocks. Meanwhile, if retail investors cannot have fun outdoors on the rainy days, they might trade more lottery-like stocks as an alternative source of entertainment at home. To address these alternative explanations, we examine whether the rainy day effect exists on the subsamples based on the stock characteristics that are related to risk and lottery-like features. First, we use two measures to capture the risk of stocks: Beta and Idiosyncratic risk, which are calculated from a CAPM model. We use the estimation window of [-200;-30] and the event window is [-22;-1], respectively. In particular, for each day, we run the following CAPM model in the estimation window: Excess return = α + β Market excess return + ε (16) it, i i t it, where Excess return it, is the excess return of firm i on day t and Market excess return is market excess return on day t. Beta is the estimated t coefficient ˆi β in the above regression, while the Idiosyncratic risk is the standard deviation of residuals in the event window. Each day, we divide the ordered 17

20 distribution of stocks by the characteristic into three groups, representing the high 30%, middle 40%, and low 30% of the sample. We define the high and low risky stocks as those in the top and bottom group, respectively. We then repeat our analysis of the relation between rainy days and trading profits for these subsamples. Table 5 presents the results for the subsamples of high- and low-risk stocks, with Panels A to E for holding horizons from one day to five days, respectively. In all specifications from (1) to (20), the estimated coefficients of RAIN are positive and statistically significant, indicating that the rainy day effect exists in both high- and low-risk stocks, with the effect slightly stronger on high beta stocks and low idiosyncratic stocks. Overall, this finding suggests that our main results are not mainly driven by mood or mood-induced risk-taking behavior. [Insert Table 5] Second, following Gao and Lin (2015), we use three measures to capture the lottery-like feature of stocks: skewness, Pearson s median skewness coefficient, and up-to-down volatility (DUVOL). We only focus on the top 30% (lottery-like stocks) and bottom 30% (non-lottery-like stocks) of the sample like the analysis in Table 5. All definitions of them are in Appendix B. Table 6 shows that in all Models (1) to (30), the estimated coefficients of RAIN are positive and statistically significant. Moreover, we find that all the estimated coefficients of RAIN are very similar between non-lottery-like stocks and lottery-like stocks. Hence, our main findings are not driven by the skewness preference of individual investors either. [Insert Table 6] 18

21 4. Additional supporting evidence In this section, we provide further supportive evidence for our main hypothesis. We first investigate the relation between institutional investors trading and the weather in Taipei city in which all the institutional investors trading take place. Second, we use the Google search volume for influenza in Mandarin as an alternative measure for the attention shocks, with the assumption that influenza reduces investor attention. Third, we use market responses to earnings announcements on rainy days as an additional test for the attention effect. Fourth, we examine whether the rainy day effect exists in time-series analysis. Fifth, we test whether the rainy effect on investor performance reverses. Finally, we conduct several robustness checks by using various definitions of rainy days. 4.1 Institutional investor trading and Taipei weather Our focus is on individual investors as they tend to have limited attention capacity, thereby having a lower opportunity cost of trading on rainy days. In this subsection, we test whether the effect of rainy days also exists among institutional investors. Given that institutional investors are less subjected to attention constraints, and it is their job to trade in the trading room, this analysis serves as a placebo test. We anticipate that institutional trading would not be influenced by rainy day effect. We construct the institutional trading data from TEJ as well. As the institutional trades are exclusively handled by headquarter branches of brokers that are located in Taipei city, we can only perform a time-series regression with trading turnover and trading profits as dependent variables and the rainy day dummy of Taipei city as the main independent variable. Table 7 shows the results. Models (1) and (2) shows the results for trading 19

22 turnover, while Models (3) to (7) shows the results for trading profits. We find no significant differences in trading behaviors and trading profits of institutional investors on rainy days, confirming our prediction that professional traders opportunity cost to trade is unrelated to the weather. These results are at odds with Goetzmann, Kim, Kumar, and Wang (2015) who find that cloud cover can affect the perceptions of mispricing and trading decisions of institutional investors through weather-induced mood. This difference might be attributed to either the Taiwan market is retail-dominated one or there is no sufficient weather variation to identify the effect as all the institutional trading happens in one city for our study. [Insert Table 7] 4.2 Influenza as alternative shocks on retail attention This subsection provides additional evidence of the relation between investors inattention and trading performance by using an alternative attention shock of influenza. The assumption is that an outbreak of influenza would result in inattention of some retail investors to the stock market as they may have to spend time taking care of themselves or the family. Thus, the influenza is likely to be an exogenous shock that distracts investors from paying attention to their portfolios. To capture an outbreak of influenza, we adopt the daily Google s search volume (SVI) of the term influenza in Mandarin (i.e., 流感 ). In particular, we collect daily and weekly SVI of the term influenza from Google Trends. As Google does not provide SVI data at the city level in Taiwan, all the analyses in this section are at Taiwan market level. We first verify that SVI of influenza serves as an attention shock to the investors. Specifically, we test whether stock returns co-move more on days with high SVI of influenza, indicating less firm-specific information being incorporated into 20

23 stock prices. The prediction is that the correlation coefficient and adjusted R 2 would be larger on days with high Google search volume on influenza. For each year, we split the sample into the top 20% highest abnormal SVI (inattention shock portfolio) and the other days (normal portfolio). 15 For each firm, we separately calculate two measures for constructing the portfolios: (1) the Pearson correlation coefficient for each stock excess return and the market excess return; and (2) the adjusted R 2 from the market model of each stock. We obtain the mean (median) difference in these two measures between two portfolios and test the difference s significance using the paired t-test (Wilcoxon signed-rank test). Table 8 shows that on days with lower investor attention due to influenza, stock returns appear to co-move more than those on normal days. In particular, on high abnormal SVI days, the mean (median) of correlation coefficients is 17.82% (14.57%) higher than that on low abnormal SVI days. We observe the similar patterns for the Adjusted R 2. These results confirm that SVI of influenza is a plausible proxy for the investor inattention. [Insert Table 8] We then substitute the SVI of influenza for RAIN to test its effect on the daily turnover and trading profits. We aggregate the turnover and trading profit into the stock market level as the sum of corresponding city-level measures. In particular, we run the regression model as follows: Profit = α + β Abnormal SVI Influenza + ε (17) t t t Turnover = α + β Abnormal SVI Influenza + ε (18) t t t 15 We find similar results when we use different cut-offs to define the inattention shock portfolio such as 30%, 40%, and 50% highest abnormal SVI of influenza. In addition, we verify that the results are similar if we use the term flu in Mandarin (i.e., 感冒 ) to test. 21

24 where Abnormal SVI Influenza is the abnormal SVI of the term influenza in day t t and ε t is error term. In addition, we examine the trading performance of individual investors for different holding periods from one day to five days. Table 9 shows that the daily abnormal SVI of influenza is negatively associated with the trading turnovers and profits. The negative association remains for various of holding periods. This finding supports our argument that inattentive investors, distracted by influenza, tend to trade less and perform poorly. Together with the results in Table 4, these findings support our hypothesis that paying attention to the stock market causally improves the trading performance. [Insert Table 9] 4.3 Market responses to earnings announcements Our findings suggest that investors pay relatively more attention to firm-specific information and improves their investment performances on rainy days. In this subsection, we use the market response to earnings surprises as the alternative measure of investor attention to the stock market. This analysis can only be performed in a retail-dominated market like Taiwan as retail trading would be able to move the market. Following the literature (Chan, Jegadeesh, and Lakonishok 1996; Chordia and Shivakumar, 2006; Huang, Huang, and Lin, 2017), we measure earnings surprises by the standardized unexpected earnings (SUE). The SUE of firm i in quarter q is calculated as follows: SUE i, q EPS EPS iq, i, q 4 = (19) σ iq, where EPS iq, is the earnings per share at quarter q, EPSiq, 4 is the earnings per 22

25 share at the same quarter in the previous year, and σ iq, is the standard deviation of EPS EPS in the previous eight consecutive quarters. iq, iq, 4 Abnormal returns are calculated from a market model, which is estimated from 300 trading days to 46 trading days before the announcement date. Abnormal returns are AR ˆ, = Excess return, β Market Excess return, where Excess return it, is firm i's it it i t excess return and Market Excess return is the market excess return. Cumulative t abnormal returns (CAR) are the sum of abnormal returns over the event windows: (0,0), (0,1), (2,5), and (6,60). In particular, we run the regression model as follows: CAR = α + β SUE + β SUE ALL RAIN + β ALL RAIN + γz + u + y + m + d + ε (20) it, 1 it, 2 it, t 3 t it, i t t t it, where ALL RAIN is a dummy variable that equals one if RAIN in all cities equals one in a day, and equals zero if otherwise; SUE is standardized unexpected earnings. Following Huang, Huang, and Lin (2017), we control for a set of control variables (Z), firm, year, month, and day-of-week fixed effects. Control variables include market capitalization on announcement day, the number of announcements on announcement day, the past 22 days average retail trading ratios before announcement day, the past 22 days average returns before announcement day, past 22 days idiosyncratic volatility before announcement day, and share turnover on announcement day. Table 10 presents the results. We find that the estimated coefficients of SUE ALL RAIN are significantly positive for announcement-day abnormal returns and CAR(0,1) ( β2 are and 0.065, respectively). In contrast, the interaction term is not significantly related to CAR(2,5) or CAR(6,60). This result implies that market reactions to earnings surprises are significantly quicker on rainy days, supports our argument that retail investors pay more attention to firm-specific information on rainy days. [Insert Table 10] 23

26 4.4 The rainy day effect: Time-series analysis In this subsection, we further discuss whether the rainy day effect exists in the time-series analysis by using the stock market level data. Like the previous section, we construct the dummy variable, ALL RAIN, that equals one if RAIN in all cities equals one in a day, and equals zero if otherwise. We use this variable to replace the RAIN as in Equations (14) and (15). The dependent variables are buy and sell turnover rates and the trading profits of individual investors in Taiwan. Table 11 shows a significant coefficient of ALL RAIN in Models (1) and (2), supporting that individual investors on average trade more on rainy days. Moreover, we find a significant coefficient of ALL RAIN in Models (3) (7), suggesting that individual investors on average have better investment performances on rainy days, compared with the other days. Hence, both city-day level analysis and time-series analysis support the idea that retail investors pay more attention to the stock market and perform better. [Insert Table 11] 4.5 Is there any reversal in trading profits? In this subsection, we examine whether the better performance on the trades made on rainy days reverses. If that is the case, the attention paid to the stock market does not produce valuable information but only temporary trading pressure. Table 12 presents regression results for the effect of rainy days on the daily trading profit in longer holding periods. The dependent variables are the trading profit of investors in a city z for the holding periods of (5,10), (5,15), (5,20), (5,25), and (5,30). First, we find significantly positive coefficients of RAIN in Models (1) and (2), 24

27 confirming that our rainy day effect lasts up to fifteen days. Second, the coefficients of RAIN in Models (3) (5) still remain insignificantly positive, suggesting that the attention effect on investor performance is not driven by temporary price pressure but most likely information. [Insert Table 12] 4.6 Robustness checks Controlling for city-level factors The rainy day effect in the previous findings could stem from time-varying demographic factors at the city level. We thus control for income per capita and population (both in natural logarithm) in the regressions, instead of adding city fixed effect. These city characteristics are available until 2015, so our regressions sample sizes reduce to 17,865 observations. Internet Appendix B shows the regression results. Similar to Table 7, Models (1) and (2) present the results for trading turnover, while Models (3) to (7) present the results for trading profits. RAIN remains positively related to both buy and sell turnovers, after controlling for income and population. City income and population are also positively associated with turnovers. RAIN is also positively related to trading profits in Models (3) to (7), in line with our argument Alternative measures of rainy days In this subsection, we first use alternative thresholds to define rainy days. Alternative RAIN 1 and Alternative RAIN2 are dummy variables that equal one if the rain volume in a city z is larger than zero and one millimeter in a day, respectively. Moreover, we also adopt actual rain volume (Rain Volume) as an alternative measure 25

28 of rainy days. We replace RAIN in Equations (14) and (15) with three alternative measures and repeat our analyses. Internet Appendix C shows that our findings are robust to the definitions of rainy days. We still find positive relations between rainy days, turnover and trading profits Alternative measures of trading behaviors In previous sections, we use turnover rate as our measure for trading volume. The advantage is that it measures the trading volume relative to the number of stock outstanding. We find consistent results if we use trading value as the alternative measure. Internet Appendix D presents the results Alternative cut-points of the measures of the rainy day As discussed in Tables 2 and 3, we find that individual traders tend to allocate more attention to the top 20% highest rain ratio days than in other days. We re-examine our results based on the cut-points of top 30%, 40%, and 50% rain ratio. We find consistent results and report them in Internet Appendix E and F. 5. Conclusion The existing theoretical models predict that investors benefit from attention allocation to the stock market. However, the empirical evidence of the link between individual investor attention and their investment performance is rather limited due to both identification challenge and data availability. Our study adds to the literature by using local weather as exogenous shocks to establish a causal link between attention allocation to the stock market and individual investor performances. We take advantage of a brokerage branch level dataset that contains the entire trading record of individual and institutional investors in Taiwan. We find that retail 26

29 investors allocate more attention to the stock market on rainy days. This rainy day effect on investor attention is verified by a larger retail trading volume, more Google search volume on stock symbols, and lower stock return co-movement. When paying more attention to the stock market on rainy days, individual investors earn more trading profits. This finding supports the notion that attention allocation benefits the investment performance and provide support to the implications of the existing models. We also find that the rainy day effect is not mainly driven by mood or skewness preference as we find the results still hold for both low risk and low skewness subsamples. The rainy day effect does not affect the institutional investors whose job is to trade irrespective of weather, reassuring our interpretation. Finally, our results are robust to alternative proxies for the attention shocks, attention measures, and alternative econometrics setups. 27

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