Aggregate Stock Market Fluctuations in a Natural Experiment

Driving out Speculators: Aggregate Stock Market Fluctuations in a Natural Experiment

Thummim Cho∗ London School of Economics

October 2018

Abstract

Does uninformed speculation generate short-term ﬂuctuations in the aggregate stock market? I test this idea in a unique setting from the pre-air-conditioning 1800s in which temperature shocks in Manhattan generated exogenous variation in the speculative participation at the NYSE. Using Manhattan weather shocks as instrumental variables, I show that speculative trade volume induces short-term stock market ﬂuctuations by generating aggregate stock price movements that tend to reverse on the next trading day.

∗Department of Finance, LSE, London, UK. Email: [email protected]. I especially thank John Campbell, Samuel Hanson, Jeremy Stein, and Adi Sunderam for their guidance and support. I thank Urim Cho, now at the Korea Environment Institute, who collaborated on idea generation as well as an earlier version of this paper. I also thank Christopher Anderson, Peter Blair, Vicente Cunat, Melissa Dell, Claudia Goldin, Larry Harris, Richard Hornbeck, Yosub Jung, Dyvia Kirti, Peter Koudijs (discussant), David Laibson, Owen Lamont, Dong Lou, Daniel Paravisini, Cameron Peng, Christopher Polk, Andrei Shleifer, Dimitri Vayanos, and seminar participants at Harvard Business School (ﬁnance), Harvard University (economic history), London School of Economics, and the 2016 AFA Annual Meeting for their helpful comments. I gratefully acknowledge the ﬁnancial support from the Hirtle Callaghan grant to Harvard. I thank the NYSE Archives team for its support during the data collection process. Dada Huang, Dian Jiao, Dongryeol Lee, and Michelle Namkoong provided excellent research assistance. 1 Introduction

The aggregate value of the U.S. stock market exhibits large short-term volatility, moving up or down by 0.8% in absolute value on an average trading day.1 What generates these short-term ﬂuctuations in the aggregate stock market?

Theory attributes short-term stock price movements to non-informational “liquidity” trades driven by sentiments, actual liquidity events, or hedging needs (Grossman and Miller, 1988). If the number of potential liquidity suppliers willing to absorb the non-informational trades is limited, the short-run supply curve for stocks slopes upward. In this case, ﬂuctuations in the non-informational buying or selling pressure generate price movements that subsequently reverse as more liquidity suppliers step in to restore the price to a normal level.

The non-informational-trade explanation for aggregate stock market fluctuations, however, has seldom been subjected to formal tests due to the difficulty of finding exogenous variation in the aggregate level of non-informational trades. The only empirical test was done by Campbell, Gross- man, and Wang (1993) under the assumption that non-informational trades show up as abnormal trade volume, but subsequent research has found abnormal volume to occur for other reasons as well (e.g., Wang, 1994; Kandel and Pearson, 1995). At the individual stock level, more tests point to non-informational trades moving individual stock prices. However, these do not imply that aggregate market fluctuations are similarly driven by non-informational trades since individual stock price movements due to non-informational trades can cancel one another out to yield zero aggregate price movement.2 Given this, can we confirm the theoretical explanation for short-term stock market fluctuations using more exogenous variation in aggregate non-informational trades?

The goal of this short article is to study aggregate stock market ﬂuctuations using a natural experiment. In the pre-air-conditioning 1800s, temperature shocks in Manhattan generated exogenous variation in non-informational trades in the aggregate stock market, presenting a rare opportunity to understand the extent to which short-term stock market ﬂuctuations are driven by non-informational trades.

1Based on the CRSP value-weighted index over the recent twenty years (1/1/1998-12/31/2017). 2The evidence on liquidity-driven ﬂuctuations in individual stock prices includes Harris and Gurel (1986), Shleifer (1986), Kumar and Lee (2006), Dorn, Hubermann, and Sengmueller (2008), Kaniel, Saar, and Titman (2008), Jvidkajer (2008), Focault, Sraer, and Thesmar (2011), and Peress and Schmidt (2018).

1 My empirical tests focus on 1888-1903, the period after the modernization of the stock market but before the introduction of air-conditioning and communications technologies that enabled investors to avoid the adverse effect of weather on trading.3 By this period, the New York Stock Exchange (NYSE) had already adopted (in 1871) the current market microstructure in which liquidity suppliers maintain a continuous market by exposing their balance sheet to intertemporal order imbalance. However, due to the lack of advanced communication technologies, most investors in this period participated in the daily stock market by visiting their brokerage houses in person. In addition, the lack of air conditioning technologies meant that hotter days of the summer discouraged investors with no valuable information about stocks from participating in the stock market.4 On the other hand, traders who supplied liquidity and investors with tradable information were less affected by weather, allowing me to interpret high temperature shocks as negative shocks to the fraction of non-informational trades in the market.

After presenting narrative evidence supporting the differential effect of weather on different types of investors (section 2), I show in section 3 that the stock market response to daily temperature shocks supports this interpretation: 1oF rise in Manhattan temperature reduced the total trade volume by 0.9% and increased the bid-ask spread by 0.19%p, signaling a reduction in uninformed investors in the stock market.5 Moreover, the reduction in trade volume due to hot temperature does not generate “pent-up” trades over the next ﬁve days, suggesting that investors “treated” by hot weather had transitory trading motives like speculative sentiments rather than more permanent needs like information or liquidity events, justifying the word “speculator” in the title.

Using temperature shocks as a proxy for the fraction of non-informational trades in the aggregate market—the key latent variable—I ﬁnd that the exogenous variation in non-informational trades has a large effect on aggregate stock market reversals (section 4). The probability of return reversal fell and the daily serial correlation in returns rose signiﬁcantly for the aggregate stock market as hot weather drove out speculative non-informational traders from the market. The magnitude of the effect was large: a 1% increase in total trade volume relative to the trailing 13-week average

3Data availability constrains me to begin my sample period in March 1888. 4The ﬁrst large-scale air conditioner was introduced to the world in April 1903, when I end my data for baseline analyses. Interestingly, the location of the ﬁrst air conditioner was the NYSE, highlighting the effect temperature had on stock trading. 5A high bid-ask spread signals a reduction in the fraction of uninformed investors under information asymmetry (Glosten and Milgrom, 1985), although it may simply signal a reduction in the arrival of any investors under the inventory-cost model (Roll, 1984).

2 due to an increase in speculative non-informational trades increased the probability of next-day return reversal by 0.59%-0.75% and lowered the daily serial correlation of returns by 49-93 basis points.

This paper documents the only known natural experiment on the non-informational-trade explanation for aggregate stock market fluctuations. Although forms of investor distraction at the aggregate level may occasionally occur (e.g., Super Bowl or World Cup Final), these are unlikely to generate a sufficiently large number of time series observations one would require in a study of aggregate stock market fluctuations.6 It is therefore important to store insights from this natural experiment in our knowledge base.

My test supports the theoretical prediction of Grossman and Miller (1988), suggests a larger magnitude of the role played by non-informational-trades than previously documented in Camp- bell, Grossman, and Wang (1993), and implies that similar evidence on individual stocks holds for the aggregate market. My result suggests that “noise” traders exist at the aggregate market level, not just for individual stocks (e.g., Shiller, 1984; De Long et al., 1990; Shleifer and Summers, 1990): speculative sentiments on individual stocks are positively correlated, generating aggregate sentiments that move the market. This is related to the ﬁnding that retail investors trade exhibit a systematic pattern (Lee, Shleifer, and Thaler, 1991; Jackson, 2003; Kumar and Lee, 2006; Bar- ber, Odean, and Zhu, 2009a,b; and Schmeling, 2009). Finally, this paper adds to the growing list of papers that use natural experiments from the past to test ﬁnance theories that cannot be easily tested in today’s settings (e.g., Benmelech, 2009; Koudijs, 2015, 2016; Braggion, Dwarkasing, and Moore, 2017; Koudijs, Salisbury, and Sran, 2018).

2 Historical Background and Data

Wall Street sweltered in the recurrence of extreme heat at the start of the new week. ... [T]he high altitude to which the temperature soared perceptibly reduced speculative participation in the stock market. (“Heat Cuts Down Volume: Soaring temperature reduces speculative participation in market,” Wall Street Journal, 16 Jun 1925)

6In contrast, I study weather shocks over 4,495 daily observations.

3 2.1 Weather and stock trading in New York: Late 19th to early 20th c.

The quote above captures the essence of the natural experiment I employ in this paper: extreme weather shocks in Manhattan used to “perceptibly” reduce speculative trades at the New York Stock Exchange (NYSE). In this subsection, I provide more color to stock trading in the 19th to early 20th century New York to highlight three features that make my empirical setting particularly attractive: (i) the stock market in this time period were sufﬁciently modernized to be able to shed light on today’s market; (ii) the identity of the market makers was more clear-cut than today’s market, making it easier to differentiate between the demanders and suppliers of liquidity, and (iii) weather shocks represent shocks to non-informational liquidity traders that demanded liquidity but not to market makers that supplied liquidity.

Market microstructure. To begin, the microstructure of the stock market was sufﬁciently modernized by late 1800s. Prior to 1871, the NYSE was a call market in which a given stock was traded only two times a day—in the morning and in the afternoon—through the intermediation of an auctioneer, which minimized the order imbalance problem present in today’s market. In 1871, however, the NYSE became a continuous market in which the “specialists” and other traders take balance sheet exposures to short-term price movements as they resolve the intertemporal order imbalance problem.

Liquidity suppliers, liquidity demanders. The identity of the liquidity suppliers was much clearer than today’s market since market liquidity at that time was provided almost exclusively by two types of traders that held the rights to trade directly at the exchange: specialists and room traders. The specialists, just like today, were obligated to provide liquidity to a set of stocks in addition to trading for their own account. Room traders were not obligated to provide liquidity but provided liquidity by betting on short-term ﬂuctuations (Selden, 1917).

Besides the specialists and room traders, there were two other important stock market participants: brokers and customers. Brokers held the right to trade stocks at the NYSE but could do so only as agents for their customers.7 Customers were the retail investors and institutional investors without the exchange membership. They placed orders with their brokers to trade stocks

7There was one other important membership at the exchange: capitalist. Capitalists were employees of large institutional investors who wished who wished to trade large shares without paying commissions. There are no records of capitalists acting as liquidity suppliers, although they may have contributed. See Selden (1917) for more details.

4 through letter, telegraph, and—more rarely—telephone (Selden, 1917; Beckert, 2003).8 However, updated information about the stock market was difﬁcult to attain except through automatic ticker machines, leading the majority of customers without ticker machines to observe stock price movements by visiting a “commission house” (brokerage house):9

Most such houses provided a “customers’ room” where quotations from all exchanges of which the house is a member are posted on a blackboard as fast as they come out on the tickers, and the principal newspapers and news services are kept on ﬁle (p.108 of Selden 1917).

Hot weather as aggregate shocks to non-informational trades. Hot weather in Manhattan generated aggregate shocks to non-informational liquidity demand since it discouraged customers—the potential non-informational traders—from visiting the commission houses. This meant less brokers executing customer orderes at the exchange:

A slim attendance in commission houses, and the absence of many brokers on the ﬂoor owing to the excessively high temperature, accounted for substantial reduction in the volume of deal- ings yesterday (“Score Further Gains in Market Generally Restrained by Heat,” Wall Street Journal, 20 Jun 1929).

On the other hand, heat did not generate shocks to liquidity supply since the traders at the exchange showed up to work regardless of weather conditions:

The heat had a good deal to do with keeping the market inactive, for it thinned out the attendance on the ﬂoor and left the traders who remained more inclined to make themselves comfortable on the seats surrounding the posts . . . (“Trading restricted,” Wall Street Journal, 23 Jun 1909).

That is, while these traders have retreated to seats at the posts or went back to their original seats with no orders from brokers to process, they maintained their physical presence at the exchange, ready to execute trades when brokers reappear.

Although the differential effect of weather shocks on liquidity demanders vs. suppliers is clear from the narrative evidence, interpreting weather shocks as non-informational-trade shocks also requires informed customers to be relatively unaffected by hot weather. Intuitively, this is likely

8One in every 300 persons had a telephone in 1890 (U.S. Census Bureau 1975). 9Approximately 1000 automatic ticker machines existed in bank and brokerage ofﬁces in New York as of 1880 (Donnan 2011).

5 to be true: investors with valuable information about a stock would not put their informational advantage at risk by delaying their trades. Indeed, in section 3, I show that the average bid- ask spread on stocks widens on hotter days, consistent with liquidity suppliers knowing that the composition of non-informational trades in the market falls on hotter days.

The issue of location and sample period. Among weather shocks in different locations, Man- hattan weather was most relevant since a bulk of NYSE trades originated from New York City. This is because investors in other cities were at a disadvantage in trading NYSE stocks. Long-distance automatic ticker service was unavailable until 1905, when the service was ﬁrst set up between New York and Philadelphia. Before then, it took brokerage houses in other cities an additional 15 minutes to receive market updates from New York, because the employees had to hand-copy the stock quotations received by Morse on manifold sheets (Tilghman 1961).10 Consistent with this evidence, I ﬁnd that NYSE trade volume responded uniquely to Manhattan temperature and not to temperature shocks in other cities (Table 4), as I discuss further in section 3.

Finally, what is the sample period over which weather shocks were most effective in driving out non-informational trades? The period before the introduction of large-scale air conditioning in April 1903 seems to be an obvious choice.11 As brokerage houses began installing air conditioning after that, the discouraging effect of hot weather on customers should have waned. In addition, transportation and communication technologies also improved signiﬁcantly in the early 1900s with the advent of the New York City subway system in 1904 and the spread of telephones in the early 1900s.12 In the Appendix A, I nonetheless show that the temperature effect on volume persists throughout the early 1900s albeit at a diminishing level.

To summarize, in the pre-air-conditioning period before April 1903, hot weather in Manhat- tan generated exogenous variation in the composition of NYSE investors by driving out non- informational trades from the market but leaving the informed investors and liquidity suppliers relatively unaffected. Although I do not take a strong stance on the nature of the non-informational trades, I provide evidence in section 3 that these trades are likely to reﬂect uninformed speculation,

10Furthermore, banks and ﬁnancial services have long had high concentration near NYSE on Wall Street (Longcore and Rees 1996). 11In fact, it was in the NYSE building that the world’s ﬁrst large-ever air conditioning was installed, highlighting the crucial effect temperature had on stock trading (Buchanan, 2013). 12The number of telephones growing at an annual rate of approximately 20% from 1900 to 1910 based on numbers provided by U.S. Census Bureau (1975).

6 justifying the title of this article.

2.2 Daily stock market and weather data

For daily aggregate stock returns, I use the series constructed by Schwert (1990) based on the Dow Jones composite portfolio for the period 2/16/1885-12/31/1925.13 For daily aggregate trade volume, I use the NYSE trading volume downloaded from the NYSE website for the period 1/1/1888- 12/31/1925.14 To remove low-frequency movements in aggregate trade volume, I subtract a moving average from the log of trade volume (Schwert, 1989; Campbell, Grossman, and Wang, 1993; and Chen, Hong, and Stein, 2001).15 The moving average is computed using trade volumes on the same day of the week over the previous 13 weeks (one quarter), thereby accounting for lower trade volume on Fridays and Saturdays. This gives daily detrended volume from 4/1/1888 to 12/31/2017.16

I collect daily Manhattan weather data for the period 1/1/1869-12/31/2017 from the National Climatic Data Center (NCDC). I use midpoint temperature (in oF ), precipitation (in inches), and snow (in inches) observed at the New York Central Park.17 It is crucial to control for seasonality since trade volume tends to be lower in the summer, when temperature tends to be the highest (Hong and Yu, 2009). I control for seasonality by including 120 seasonality dummies in all my analyses (approximately one for each sequence of 3 days for a given year).

To delve deeper into the nature of the weather-induced aggregate volume shocks, I use unique data on daily high and low prices on individual stocks for the summers (June-August) of 1888-1902

13The stocks in the Dow Jones composite portfolio in the late 1800s were the largest stocks listed at the NYSE. For my supplementary analysis of the period 1/1/1926 through 12/31/2017, I use the value-weighted stock returns constructed by the Center for Research in Security Prices (CRSP). 14The NYSE data contain 4 instances in which two volume observations have the same date, and in those cases, I average the two numbers. None of the dates, however, are in the period of interest (4/1/1888-3/31/1903). For my supplementary analysis of the period 1/1/1926 through 12/31/2017, I use the total trade volume of all domestic common stocks from the CRSP. 15I use trade volume instead of turnover (volume divided by shares outstanding) since the number of shares outstanding is unavailable in the pre-1903 period. However, I conﬁrm using the CRSP data (1926-2017) that the division by shares outstanding has little effect on the daily detrended volume measure I use. 16The NYSE opened on Saturday until September 1952. My results are robust to the choice of moving average. I try trailing 26-week and 52-week moving averages, with or without the day-of-week speciﬁcation, and obtain similar results in my analyses. 17Available on the NCDC website http://www.ncdc.noaa.gov/data-access/land-based-station-data. The station ID is USW00094728 for the New York Central Park data. Missing values for precipitation and snow are assumed to be zero, and unfortunately, relative level is unavailable until mid 1950s.

7 collected from the Commercial and Financial Chronicle.18 I use the data to compute the fraction of idle stocks and to estimate the cross-sectional average bid-ask spread using the method of Corwin and Schultz (2012).19

To study short-term ﬂuctuations in the aggregate stock market, I use two measures of daily stock market reversal as the dependent variable: the binary event that that the stock return changes the sign on the next trading day (1 (rt+1 · rt < 0)) and the time-varying serial correlation. The conditional serial correlation on day t is estimated as the realized one-day serial correlation in returns over the preceding week.

2.3 Summary statistics

Merging the individual datasets gives daily stock market and weather data beginning in April 1888. I focus on the period 4/1/1888-3/31/1903 prior to the introduction of large-scale air conditioning, but my results are robust to including additional years in the early 20th century. Table 1 describes the key variables. Trade volume and the fraction of idle stocks both exhibit some autocorrelation even over 5 days, so I use Newey-West standard errors with 10 lags when those variables are used as the dependent variable. The mean of conditional serial correlation is negative, contrary to the a near-zero unconditional serial correlation (not reported), which reﬂects that conditional serial correlation and return are not independent.20

3 Manhattan Temperature and Non-informational Trades

This section presents a bundle of evidence that temperature shocks in Manhattan proxy the reduction in aggregate non-informational trades, the latent variable of interest in this paper. As summa-

18I focus on the summer period with the largest weather effects to reduce the data collection effort. The hard copies of the Chronicle are unavailable for June 1894 and June 1-24 of 1898, which are excluded from the data. 19This method uses daily high and low prices of a given stock for two consecutive trading days. I estimate two spreads for stock i on day t, one using days t − 1 and t and the other using days t and t + 1, and take the average of the two spreads. I then take the cross-sectional average across all stocks on day t. 20 To see this, write a simple return process with time-varying serial correlation as rt+1 = ρtrt + t+1 where t+1 is i.i.d. In this case, the unconditional autocovariance is Cov (ρtrt, rt), which can be zero despite E [ρt] < 0 if ρt and rt are dependent. The unconditional autocorrelation equals E [ρ] under independence since 2 2 then Cov (ρtrt, rt) /V ar (rt) = E [ρt] E rt − E [rt] /V ar (rt) = E [ρt].

8 rized in Table 3, the direction of the effect that weather has on trade volume, the fraction of idle stocks, bid-ask spread, and “pent-up” trades suggest that the investors “treated” by adverse weather shocks are likely to be the informed investors with transitory trading motives such as speculative sentiments.

3.1 Lower trade volume on hotter days

The ﬁrst step to establishing weather shocks as aggregate shocks to non-informational trades is to examine if they affect aggregate trade volume. Hence, I use daily regression over 4/1/1888- 3/31/1903 to test if Manhattan weather affects the aggregate NYSE trade volume. Since the effect of temperature depends on the season of the year, I use temperature interacted with three dummy variables for summer (Jun-Aug), winter (Dec-Feb), and spring/fall. To prevent seasonality in both trade volume and temperature from generating spurious results, I include 3-day seasonal ﬁxed effects as mentioned earlier. Finally, I add volatility estimated from GARCH(1,2) as an additional determinant of volume.

Hot weather in Manhattan strongly reduced NYSE trade volume (Table 2). A one-degree- Fahrenheit rise in Manhattan temperature in the summer reduced aggregate stock trade volume by −0.9% in the summer, consistent with the narrative evidence that the stock market was less active on hotter days (columns (1)-(4)). Temperature in other seasons and rain mattered less for trade volume, although the magnitude of the effect of rain was large (−2.3% drop in trade volume for every inch of rain). Depending on the speciﬁcation, snow had a more signiﬁcant effect on trade volume, with the volume dropping by −2.7 to −2.8% for every inch of snow (columns (1)-(2)). Volume was higher during more volatile times, and controlling for volatility seems to reduce the noise caused by residuals (comparing columns (3) and (4)).

I also investigate the temperature effect on volume for different intervals of temperature: T ∈ (−∞, 15], T ∈ [15, 20),..., T ∈ [80, 85), and T ∈ (85, ∞) (the interval T ∈ [60, 65) excluded from the regression to form a baseline interval).21 Compared to the stock market with the baseline temperature interval, the aggregate volume falls by −26.7% on days with midpoint temperature above 85oF and −18.1% on days with temperature of 80 − 85oF (column (5)). This large

21I select this interval as the baseline based on the evidence that the optimal indoor temperature is around 70oF (Seppanen, Fisk, and Lei, 2006).

9 temperature effect on volume diminishes over the intermediate temperature values but appears to re-emerge for extremely low temperature (−10.2% volume drop on days with temperature below 15oF ), although this magnitude appears sensitive to the choice of controls (columns (5)-(8)). ?? visualizes the temperature effect on trade volume.

3.2 Backing up causality: A horse race against temperatures in other cities

Since weather shocks are exogenous, the temperature effect on volume is likely to be causal. How- ever, to ensure that it is not driven by spurious reasons, I show that temperatures in other cities had little effect on NYSE trade volume. I do this by repeating the trade volume regression to run a horse race between Manhattan temperature and temperature in seven other cities (Cambridge, MA; Concordia, KS; Jacksonville, FL; San Diego, CA; Oxford, Great Britain; and Sydney, Australia).22

Table 4 shows that controlling for temperature in Manhattan, temperature in other cities have no statistically significant effect on NYSE trade volume. Even temperature in Cambridge, which has a 79% correlation with Manhattan temperature, fails to survive the horse race. In all specifications, the coefficient on Manhattan temperature remains assuringly stable, suggesting that Manhattan weather mattered uniquely for NYSE investors. This result strengthens the causal interpretation of the temperature-volume relationship.

3.3 The nature of the weather-induced changes in trade volume

Previous analysis shows that temperature shocks in Manhattan generated exogenous variation in the aggregate stock trade volume. Furthermore, narrative evidence in Section 2 suggests that this variation in trade volume is due to the variation in the stock market participation by uninformed traders. Does data support this interpretation?

To put more structure to this discussion, it is useful to consider the data-generating process for each variable of interest. First, the theoretical prediction is that reversals in aggregate stock returns which lead to short-term ﬂuctuations are caused by aggregate (correlated) non-informational

22Cambridge and Sydney have some missing temperature values during the time period, reducing the number of observations in the regression.

10 trades: agg agg reversalt+1 = β0 + β1N.I.tradet + t+1. (1)

On the other hand, aggregate trade volume can be driven by both non-informational trades and informed trades:

agg agg agg volumet = b0 + b1N.I.tradet + b2I.tradet + et. (2)

Hence, under the assumption of Campbell, Grossman, and Wang (1993) that b1 > 0 and b2 ≈ 0, abnormal trade volume is a noisy proxy for non-informational trades, which justiﬁes putting trade volume in place of non-informational trades in eq. (1).

In comparison, my approach is to use exogenous shocks to non-informational trades caused by temperature variation in Manhattan:

agg NI NI NI NI N.I.trade = γ + γ Tt + ω where γ > 0; t 0 1 t 1 (3) agg I I I I I.tradet = γ0 + γ1 Tt + ωt where γ1 = 0.

I The goal in this section, then, is to provide evidence that γ1 = 0 (temperature does not affect informed investors) and to understand the nature of the non-informational trades affected by temperature.

To begin, I study the cross-sectional average bid-ask spread estimated from the high and low prices of individual stocks (Corwin and Schultz, 2012). Since market makers facing asymmetric information lowers the bid-ask spread in the presence of non-informational trades and raises in the presence of informed investors (Glosten and Milgrom, 1985), a proxy for reduction in non- informational trades should predict a rise in the bid-ask spread.

Table 5 suggests that high Manhattan temperature reduces the level of non-informational trades from the market and causes market makers to increase the bid-ask spread, suggesting that in eq. NI I (3) γ1 > 0 and γ1 ≈ 0 in (columns (1)-(2)). The magnitude is economically large, with a one- degree-Fahrenheit rise in Manhattan temperature in the summer raising average bid-ask spread by 19 basis points (see also Figure 2). In contrast, the bid-ask spread does not fall signiﬁcantly with trade volume, and the magnitude of the estimated effect is also small: a 100% increase in aggregate trade volume is associated with a 19 basis point fall in the bid-ask spread (column (3)).

11 This suggests that variation in aggregate trade volume is driven by both non-informational and informational trades (b2 6= 0 in eq. (3)).

Although the evidence from bid-ask spreads point to the temperature effect on non-informational trades, this interpretaton hinges on the importance of information asymmetry in market making. Under the inventory-cost model alone (Roll, 1984), the bid-ask spread is not helpful is distinguishing between different types of investors since the inventory cost would increase with the reduction in any investors, which likely lengthens the holding period of market makers.

Next, I check whether the effect of temperature appears in individual stock price data. Although this particular analysis is not particularly helpful in distinguishing between different channels for the temperature effect, it provides further evidence for the temperature effect on stock trading. I ﬁnd that the fraction of stocks with no buy or sell transaction—another measure of stock market inactivity—rises with temperature (columns (4)-(5) of Table 5). As for the magnitude, a one- degree-Fahrenheit rise in Manhattan temperature in the summer leads to a 19 basis point increase in the fraction of idle stocks. The fraction of idle stocks falls with trade volume as expected, suggesting that the dependent variable is correctly measured (column (6)).

Finally, I ask whether the non-informational traders affected by weather shocks intertemporally substitute their trade needs to a future date—i.e., whether these non-informational traders were driven by short-lived speculative sentiments or by more permanent needs like liquidity events or hedging needs. Table 6 show that while temperature reduces trade volume contemporaneously, it does not predict an increased level of trade volume in the next 5 trading days. The absence of temperature-induced “pent-up” trades is striking given the strong contemporaneous temperature- volume relationship and offers perhaps the strongest evidence that the identiﬁed temperature- induced reduction is trade volume is not due to investors with valuable information, hedging needs, or liquidity events but by those with short-lived motives like sentiments.

As a side note, the reduction is trade volume also does not appear to be driven by weather interfering with the arrival of public news, which is not explicitly considered in the model of trade volume in eq. (3). For one, there is no known record that the distribution of the daily Wall Street Journal and weekly Commercial and Financial Chronicles—the main sources of stock market information at the time—was interrupted by Manhattan weather. Furthermore, I ﬁnd that the absolute value of the return does not change predictably on hot days in Manhattan, implying

12 that the extent to which information generates returns is not related to weather conditions.

In summary, I ﬁnd that hot weather (i) discourages some investors from participating in the stock market, (ii) increases the average bid-ask spread on stocks, (iii) does not generate pent-up trades in the future, and (iv) is not driven by slower arrival of public information. This, along with the narrative evidence in section 2, suggests that hot weather lowers the aggregate level of non-informational trades driven by short-lived motives such as speculative sentiments.

4 Explaining Short-term Stock Market Fluctuations

Now I arrive at the main test of this paper: does exogenous variation in non-informational trades reduce aggregate stock market fluctuations? Since both narrative (section 2) and quantitative (section 3) evidence shows that Manhattan temperature shocks generated exogenous variation in the aggregate level of non-informational trades, I use these temperature shocks as a proxy for aggregate non-informational trades. For the left-hand side, I use two measures of short-run fluctuations in the aggregate stock market: probability of next-day return reversal and time-varying serial correlation in daily returns.23 Since the composition of investors and information flow may change on weekend (Chordia, Roll, and Subrahmanyam, 2002), I include dummy variables for Friday and Saturday in most of the specifications.24

Table 7 reports the results. Before I exploit exogenous temperature variation, I examine the effect of trade volume on aggregate short-term return reversals (columns (1)-(2)). Panel A shows that more trade volume increases the probability of a reversal in aggregate stock returns, but the magnitude is small: the reversal probability falls by only 3.7% for a 100% increase in the trade volume relative to an average trading day. Furthermore, trade volume does not have a significant association with the estimated serial correlation in daily returns. The result is similar irrespective of controlling for volatility, which remains insignificant in both panels and are therefore excluded in other specifications.

Next, I use weather shocks as a proxy for non-informational trades to analyze how non-informational

23I use reversal rather than volatility as the dependent variable since reversal is the more theoretically relevant measure (Grossman and Miller 1988; Campbell, Grossman, and Wang, 1993). 24NYSE was open on Saturday until 1952.

13 trades measured with less noise affect aggregate reversals. Columns (3)-(4) of Panel A show that on hot days, the probability of reversal in the aggregate stock market return falls signiﬁcantly, suggesting that driving out non-informational traders reduces short-term ﬂuctuations. The magnitude is also large with the probability of market return reversal falling by 66 basis point for every one-degree-Fahrenheit rise in Manhattan temperature in the summer and the probability falling by more than 10 percentage points in total on hot or cold days relative to other days.

I also try the instrumenting trade approach. Unlike traditional instrumental-variables (IV) analyses, non-informational trades remain the latent variable of interest here, but instrumenting aggregate trade volume using weather shocks allows me to interpret the magnitude of the effect in units of volume. Columns (5)-(9) show that the probability of aggregate return reversal falls by 59-75 percentage points when the level of non-informational trades rises by 100% relative to a normal trading day, highlighting the important role they play in generating aggregate market reversals. It is important to note, however, that this magnitude corresponds to the local treatment effect; if only the least informed investors (i.e. those with least valuable information) were by adverse weather conditions, the effect each of them has on the reduction of return reversals would be large.

Serial correlation in the aggregate market returns tells a consistent story (Panel B). Serial correlation increases significantly on hot summer days, with one-degree-Fahrenheit rise in Manhattan temperature in the summer raising the autocorrelation coefficient by 0.009 with the result of return autocorrelation rising by 0.196 on days with midpoint temperature above 85oF . (columns (3)-(4)). The instrumental-variable approach suggests that the autocorrelation coefficient falls by 0.49-0.93 when the level of non-informational trades rises by 100% relative to a normal trading day.

These results point to the important role non-informational trades play in generating short-term stock market ﬂuctuations. This together with the evidence in the previous section suggest that investors are driven by correlated, uninformed sentiments that lead them to trade different stocks in the same direction, shifting the demand curve for the aggregate stock market.

14 5 Conclusion

In this paper, I exploit exogenous variation in speculative non-informational trades to show that they generate short-term aggregate stock price movements. Since my test setting in the late 19th century features the modern form of market making, it can be used to conduct natural experiments on other theories on liquidity and sentiments at the aggregate or individual stock level.

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18 Table 1: Descriptive Statistics

The table reports summary statistics on the key variables used in this paper for the period 4/1/1888-3/31/1903. Return reversal is the binary event that that the stock return changes the sign on the next trading day (1 (rt+1 · rt < 0)). Serial correlation on day t is estimated as the one-day serial correlation in returns from day t−7 to t+1 (one week, including holidays). Serial correlation is estimated Daily bid-ask spread is estimated using the method of Corwin and Schultz (2012) assuming constant expected bid-ask spread for each day across different stocks.

Partial Autocorrelation N Mean Median Stdev 5% 95% 1 5 10 (1) (2) (3) (4) (5) (6) (7) (8) (9) Return (%) 4495 0.03 0.05 0.9 -1.31 1.36 -0.01 0.05 -0.01 Trade Volume 4495 0.01 0 0.51 -0.81 0.86 0.75 0.05 0.01 Volatility 4495 0.83 0.77 0.31 0.5 1.39 0.85 0.17 0.04 Return Reversal (%) 4495 49.5 0 50 0 100 -0.01 0.01 0.01 Conditional Serial Correlation 4495 -0.17 -0.19 0.4 -0.76 0.46 0.52 0 -0.01 Idle Stocks (%) 1270 0.32 0.32 0.11 0.15 0.5 0.67 0.1 0.06 Estimated Bid-Ask Spread (%) 1269 0.57 0.57 0.08 0.46 0.7 0.8 0.03 0.03 Temperature T (degrees F) 4495 53.33 54 17.64 24.5 79.5 0.93 0.12 0.02 T (Summer Only) 1154 73.54 73.5 6.1 64 83 0.63 0.03 0.04 Snow (inches) 4495 0.05 0 0.45 0 0 0.03 0.01 0.02 Rain (inches) 4495 0.12 0 0.34 0 0.74 0.04 -0.01 -0.02

19 Table 2: The Temperature Effect on Daily NYSE Trade Volume

The table studies the effect of Manhattan weather on the aggregate trade volume at the New York Stock Exchange (NYSE). The regression uses daily trade volume and weather data from 4/1/1888 to 3/31/1903, which is prior to the introduction of large-scale air conditioning. Daily midpoint temperature T (oF ), snow (inches), and rain ( inches) are measured in Manhattan. Column (5) includes all intermediate temperature intervals except T ∈ (60, 65], but the coefﬁcients on some of the intervals are not reported. Trade volume is measured in percentage. Volatility is 10 times the conditional standard deviation of returns estimated from GARCH(1,2). In the parentheses are standard errors adjusted for serial correlation in the error term (Newey-West with 10 lags). ***, **, and * indicate 1%, 5%, and 10% signiﬁcance levels.

(1) (2) (3) (4) (5) (6) (7) (8) T × Summer -0.915∗∗∗ -0.913∗∗∗ -0.913∗∗∗ -0.927∗∗ (0.350) (0.350) (0.350) (0.363) T × SpringF all 0.023 (0.210) T × W inter -0.050 (0.236) 1(T > 85) -26.674∗∗ -24.184∗∗ -24.183∗∗ -23.811∗ (12.506) (12.328) (12.328) (14.111) 1(80 < T ≤ 85) -18.111∗∗∗ -16.142∗∗∗ -16.141∗∗∗ -16.233∗∗∗ (6.252) (5.773) (5.772) (5.908) 1(75 < T ≤ 80) -4.605 -2.413 -2.413 -3.192 (5.524) (4.899) (4.898) (4.962) 1(70 < T ≤ 75) -6.031 -3.401 -3.400 -3.584 (4.176) (3.385) (3.385) (3.408) 1(65 < T ≤ 70) -0.377 (3.536) 1(15 < T ≤ 20) 2.603 (9.637) 1(T ≤ 15) -10.233 -4.406 -4.489 -4.392 (13.161) (11.736) (11.394) (11.216) Snow -2.674 -2.865∗ -2.878 -2.860∗ (1.713) (1.717) (1.779) (1.722) Rain -2.345 -2.273 (2.209) (2.193) Volatility 1.514∗∗∗ 1.517∗∗∗ 1.516∗∗∗ 1.550∗∗∗ 1.532∗∗∗ 1.531∗∗∗ (0.504) (0.502) (0.502) (0.506) (0.505) (0.505) Seasonal ﬁxed effect Yes Yes Yes Yes Yes Yes Yes Yes Observations 4,495 4,495 4,495 4,495 4,495 4,495 4,495 4,495

20 Table 3: The Identity of Investors Treated by Temperature: Evidence from Market-based Indicators

The table describes the effect that an increase in the size of investors in each category has on various market-based indicators. “Pent-up trades” refer to trades that occur on future dates when the investors in each category are prevented from trading today.

Trade Bid-ask Spread Pent-up Idle Stocks Volume Glosten-Milgrom (1985) Roll (1984) Trades Informed investors ↑↓↑↓ Yes Uninformed investors - Short-lived speculative ↑↓↓↓ No sentiments - Other liquidity reasons ↑↓↓↓ Yes (hedging, liquidity event, etc.)

Table 4: NYSE Trade Volume Responds Only to Manhattan Temperature

The table shows that controlling for temperature in Manhattan, temperature in other cities did not affect the aggregate trade volume at the New York Stock Exchange (NYSE). The regression uses daily trade volume and weather data from 4/1/1888 to 3/31/1903, which is prior to the introduction of large-scale air conditioning. T denotes the temperature in Manhattan (in oF ). The other cities are Cambridge, MA (“MA”); Concordia, KS (“KS”), Jacksonville, FL (“FL”), San Diego, CA (“CA”); Oxford, Great Britain (“GBR”); and Sydney, Australia (“AUS”). The differences in the number of observations is caused by missing temperature values in some of those cities. Trade volume is measured in percentage change from the moving average on the same day of the week for the last 13 weeks (one quarter). Volatility is 10 times the conditional standard deviation of returns estimated from GARCH(1,2). In the parentheses are standard errors adjusted for serial correlation in the error term (Newey-West with 10 lags). ***, **, and * indicate 1%, 5%, and 10% signiﬁcance levels.

(1) (2) (3) (4) (5) (6) T × Summer -0.983∗∗ -0.871∗∗ -0.961∗∗∗ -0.862∗∗ -0.958∗∗∗ -0.905∗∗∗ (0.492) (0.348) (0.349) (0.351) (0.354) (0.350)

TMA × Summer 0.076 (0.480)

TKS × Summer -0.348 (0.350) ∗ TFL × Summer 1.395 (0.818)

TCA × Summer 1.270 (1.039)

TGBR × Summer 0.653 (0.685)

TAUS × Summer 0.743 (0.719) Volatility 1.498∗∗∗ 1.521∗∗∗ 1.488∗∗∗ 1.474∗∗∗ 1.482∗∗∗ 1.533∗∗∗ (0.505) (0.503) (0.499) (0.501) (0.505) (0.505) Seasonal ﬁxed effect Yes Yes Yes Yes Yes Yes Observations 4,472 4,495 4,495 4,495 4,495 4,493 Correlation in summer temperature .79 .23 .2 .11 .19 -.15

21 Table 5: The Nature of Weather-induced Changes in Trade Volume Inferred from Bid-ask Spread and the Fraction of Idle Stocks

The table shows that hot weather in Manhattan increased the average bid-ask spread on stocks (in %) and the fraction of idle stocks (in %) during the pre-air-conditioning era of the modern stock market with data availability (4/1/1888- 3/31/1903). The individual stock price data used in the analyses are digitized from the Commercial and Financial Chronicle for the summer periods only. The hard copies of the Chronicle are unavailable for June 1894 and June 1-24 of 1898, which are excluded from the data. The bid-ask spread is estimated according to Corwin and Schultz (2012). Volatility is 10 times the conditional standard deviation of returns estimated from GARCH(1,2). In the parentheses are standard errors adjusted for serial correlation in the error term (Newey-West with 10 lags). ***, **, and * indicate 1%, 5%, and 10% signiﬁcance levels.

Bid-ask Spread (%) Idle Stocks (%) (1) (2) (3) (4) (5) (6) T × Summer 0.187∗∗∗ 0.194∗∗∗ (0.051) (0.070) 1(T > 85) 4.429∗∗∗ 6.856∗∗∗ (1.600) (2.402) 1(80 < T ≤ 85) 3.339∗∗∗ 4.365∗∗∗ (0.825) (1.247) 1(75 < T ≤ 80) 1.537∗∗ 1.102 (0.681) (1.106) 1(70 < T ≤ 75) 0.251 -0.098 (0.563) (0.835) Trade volume -0.190 -10.615∗∗∗ (0.749) (1.049) Volatility 1.074∗∗∗ 1.074∗∗∗ 1.075∗∗∗ -0.484∗∗∗ -0.488∗∗∗ -0.250∗ (0.103) (0.101) (0.111) (0.143) (0.141) (0.131) Seasonal ﬁxed effect Yes Yes Yes Yes Yes Yes Observations 1,269 1,269 1,269 1,270 1,270 1,270

22 Table 6: No “Pent-up” Trades After Temperature Shocks

The table shows that there the fall in trade volume due to hot temperature does not generate “pent-up” trade over the next five trading days, suggesting that the temperature-induced fall in trade volume reflects trades based on short-lived motives such as sentiments. Trade volume is in %, and the analysis focuses on the pre-air-conditioning era of the modern stock market with data availability (4/1/1888-3/31/1903). In the parentheses are standard errors adjusted for serial correlation in the error term (Newey-West with 10 lags). ***, **, and * indicate 1%, 5%, and 10% significance levels.

Tradevolt+1 Tradevolt+2 Tradevolt+3 Tradevolt+4 Tradevolt+5 (1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

Tt × Summer -0.036 -0.078 -0.125 -0.048 0.019 (0.306) (0.317) (0.334) (0.353) (0.349)

Tradevold 0.049 0.095 0.141 0.053 -0.020 (0.394) (0.372) (0.355) (0.370) (0.389) ∗∗∗ ∗∗∗ Tt+1 × Summer -0.830 -0.814 (0.312) (0.305) ∗∗∗ ∗∗∗ Tt+2 × Summer -0.898 -0.849 (0.328) (0.289) ∗∗ ∗∗∗ Tt+3 × Summer -0.881 -0.823 (0.349) (0.294) ∗∗ ∗∗∗ Tt+4 × Summer -0.874 -0.869 (0.361) (0.327) ∗∗ ∗∗ Tt+5 × Summer -0.878 -0.879 (0.365) (0.352) Seasonal ﬁxed effect Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Observations 4,495 4,495 4,495 4,495 4,495 4,495 4,495 4,495 4,495 4,495 IV using Tt × Summer

23 Table 7: Explaining Daily Reversals in Aggregate Stock Market Returns

The table shows that non-informational trades instrumented or proxied by Manhattan weather shocks generated reversals in the aggregate stock market returns in the pre-air-conditioning era of the modern stock market with data availability (4/1/1888-3/31/1903). Return reversal is the binary event that that the stock return changes the sign on the next trading day (1 (rt+1 · rt < 0)). Serial correlation on day t is estimated as the one-day serial correlation in returns from day t − 7 to t + 1 (one week, including holidays). All weather variables are measured in Manhattan. Midpoint temperature T is measured in oF . Temperature bins used as instruments are the ﬁve bins listed below. Volatility is 10 times the conditional standard deviation of returns estimated from GARCH(1,2). Weekend dummies are dummy variables for Friday and Saturday. In the parentheses are standard errors adjusted for serial correlation in the error term (Newey-West with 10 lags). ***, **, and * indicate 1%, 5%, and 10% signiﬁcance levels.

OLS 2SLS (1) (2) (3) (4) (5) (6) (7) (8) (9) Panel A. Probability of next-day reversal in returns (%) Trade volume 0.037** 0.035** 0.037** 0.037** 0.753** 0.738** 0.681** 0.632** 0.591** (0.015) (0.015) (0.016) (0.016) (0.340) (0.335) (0.310) (0.274) (0.259) Volatility 0.333 (0.239) T × Summer -0.664** (0.258) 1(T > 85) -12.496 (9.287) 1(80 < T ≤ 85) -9.599** (4.651) 1(75 < T ≤ 80) -4.483 (3.538) 1(70 < T ≤ 75) -4.175 (3.122) 1(T ≤ 15) -15.363* (8.162)

Panel B. Serial correlation in returns Trade volume 0.011 0.014 0.025 0.024 -0.931** -0.934** -0.783** -0.556* -0.491* (0.017) (0.017) (0.018) (0.018) (0.438) (0.440) (0.356) (0.316) (0.278) Volatility -0.004 (0.003) T × Summer 0.009*** (0.002) 1(T > 85) 0.196* (0.105) 1(80 < T ≤ 85) 0.081** (0.038) 1(75 < T ≤ 80) 0.074** (0.030) 1(70 < T ≤ 75) 0.048** (0.024) 1(T ≤ 15) 0.102 (0.070) Seasonal ﬁxed effect No No Yes Yes Yes Yes Yes Yes Yes Weekend dummies Yes Yes Yes Yes Yes No Yes Yes Yes Observations 4,495 4,495 4,495 4,495 4,495 4,495 4,495 4,495 4,495 Instrumental variables Summer temperature Temperature bins Snow

24 fzr.Tevria asidct 0 ofiec interval. confidence 60-65 10% The the indicate coefficients. of bars these are vertical era generated snow The pre-air-conditioning that and regression zero. the rain, volatility, the of during effects, in days fixed controls hotter Seasonal additional on as (4/1/1888-3/31/1903). decreased availability used data %) with (in market volume stock trade modern NYSE that shows figure The iue1: Figure eprtr feto grgt rd oueb eprtr Interval Temperature by Volume Trade Aggregate on Effect Temperature

NYSE Trade Volume (%)

-40 -20 0 20

-15 15-20 Manhattan Temperature(degreesFahrenheit) 20-25 25-30 30-35 35-40

25 40-45 45-50 50-55 55-60 60-65 65-70 70-75 75-80 o F 80-85 i sue stebaseline the as used is bin 85+ oaiiy an nw n ekn ume Fia n audy r sda diinlcnrl nteregression the in controls pre- additional as the 60-65 used during effects, The interval. are fixed days confidence Saturday) Seasonal coefficients. hotter and these on (4/1/1888-3/31/1903). (Friday generated availability reversals dummies data that short-term weekend with and less market snow, featured stock rain, market modern volatility, stock the of aggregate era the air-conditioning that show figures The in controls additional 1898, as of used 1-24 are 60-65 June snow The and interval. and 1894 confidence rain, coefficients. 10% June volatility, these Chronicle indicate for effects, generated unavailable Financial fixed are and that Seasonal Chronicle Commercial regression during data. the the the the summers of from from copies the digitized excluded individual hard are of are The The (1)-(6) days which only. columns hotter (4/1/1888-3/31/1903). periods for availability on summer analyses data increased the the with for %) in market used (in stock data stocks modern price on the stock spread of bid-ask era average pre-air-conditioning the the that shows figure The iue3: Figure iue3.Poaiiyo etdyRtr eeslFgr b eilCreaini al Returns Daily in Correlation Serial 3b. Figure Reversal Return Next-day of Probability 3a. Figure

Probability of Return Reversal (%) 2: Figure -30 -20 -10 0 10 20 30

eprtr feto grgt tc aktRvra yTmeaueInterval Temperature by Reversal Market Stock Aggregate on Effect Temperature -15 Manhattan Temperature(degreesFahrenheit) 15-20

20-25 Interval Temperature by Spread Bid-ask Average on Effect Temperature 25-30 30-35 Average Bid-ask Spread (%) 35-40 -10 -5 0 5 40-45 45-50 50-55 50-55 55-60 Manhattan Temperature(degreesFahrenheit) 60-65 65-70 55-60 o

F 70-75

i sue stebsln fzr.Tevria asidct 10% indicate bars vertical The zero. of baseline the as used is bin 75-80 80-85 60-65 85+ 26

o 65-70 F

Serial Correlation in Returns bars vertical The zero. of baseline the as used is bin -.3 -.2 -.1 0 .1 .2 .3 70-75 -15 Manhattan Temperature(degreesFahrenheit) 15-20 20-25 75-80 25-30 30-35 35-40 80-85 40-45 45-50 50-55 85+ 55-60 60-65 65-70 70-75 75-80 80-85 85+ A Appendix

Table A1: Determinants of Daily NYSE Trade Volume: Other Sample Periods

The table studies the effect of Manhattan weather on the aggregate stock market volume for different sample periods. Stock market volume is the total New York Stock Exchange (NYSE) volume for the period until 1925 and the total trade volume for all three major exchanges (NYSE, NASDAQ, AMEX)—subject to availability—for the period from 1926. Daily midpoint temperature T (oF ), snow (inches), and rain ( inches) are measured in Manhattan. Trade volume is measured in percentage change from the moving average on the same day of the week for the last 13 weeks (one quarter). Volatility is 10 times the conditional standard deviation of returns estimated from GARCH(1,2). In the parentheses are standard errors adjusted for serial correlation in the error term (Newey-West with 10 lags). ***, **, and * indicate 1%, 5%, and 10% signiﬁcance levels.

Expanding Sample during 1888m4-1925m12 Later Period (1) (2) (3) (4) (5) (6) (7) (8) T × Summer -0.866∗∗∗ -0.560∗ -0.575∗∗ -0.709∗∗∗ -0.646∗∗∗ -0.067 -0.054 (0.325) (0.305) (0.279) (0.262) (0.238) (0.237) (0.080) 1(T > 85) -21.970∗∗∗ (8.272) 1(80 < T ≤ 85) -9.540∗∗ (4.267) 1(75 < T ≤ 80) -6.928∗∗ (2.928) 1(70 < T ≤ 75) -4.638∗∗ (2.010) 1(T ≤ 15) -7.430 (5.811) Snow -2.135 -0.841 -1.098 -1.076 -0.944 -0.943 -0.117 -0.969∗∗ (1.463) (1.247) (1.270) (1.097) (0.951) (0.951) (0.552) (0.395) Volatility 1.306∗∗∗ 1.657∗∗∗ 1.817∗∗∗ 1.864∗∗∗ 1.699∗∗∗ 1.698∗∗∗ 0.833∗∗∗ 0.613∗∗∗ (0.482) (0.424) (0.428) (0.383) (0.356) (0.358) (0.244) (0.104) Seasonal ﬁxed effect Yes Yes Yes Yes Yes Yes Yes Yes Observations 5,320 6,818 8,200 9,687 11,188 11,188 9,936 14,347 Sample period 1888m4 1888m4 1888m4 1888m4 1888m4 1888m4 1926m1 1961m1 -1905m12 -1910m12 -1915m12 -1920m12 -1925m12 -1925m12 -1960m12 -2017m12

27 Table A2: Explaining the Probability of Aggregate Stock Market Reversal: Other Sample Periods

The table shows the ability of Manhattan weather shocks to generated reversals in the aggregate stock market returns for different sample periods. Reversal is measured by the binary event that that the stock return changes the sign on the next trading day (1 (rt+1 · rt < 0)). All weather variables are measured in Manhattan. Midpoint temperature T is measured in oF . Temperature bins used as instruments are the ﬁve bins listed below. Volatility is 10 times the conditional standard deviation of returns estimated from GARCH(1,2). Weekend dummies are dummy variables for Friday and Saturday. In the parentheses are standard errors adjusted for serial correlation in the error term (Newey- West with 10 lags). ***, **, and * indicate 1%, 5%, and 10% signiﬁcance levels.

Expanding Sample during 1888m4-1925m12 Later Period (1) (2) (3) (4) (5) (6) (7) (8) Trade volume 0.039∗∗∗ 0.042∗∗∗ 0.042∗∗∗ 0.034∗∗∗ 0.038∗∗∗ 0.037∗∗∗ 0.005 -0.003 (0.014) (0.012) (0.011) (0.010) (0.010) (0.010) (0.013) (0.021) T × Summer -0.416∗ -0.314 -0.235 -0.252 -0.166 -0.277 -0.131 (0.235) (0.210) (0.192) (0.178) (0.166) (0.180) (0.155) 1(T > 85) -8.972 (6.352) 1(80 < T ≤ 85) -1.477 (3.161) 1(75 < T ≤ 80) -0.183 (2.236) 1(70 < T ≤ 75) -0.550 (1.942) 1(T ≤ 15) -12.289∗∗ (4.954) Seasonal ﬁxed effect Yes Yes Yes Yes Yes Yes Yes Yes Weekend dummies Yes Yes Yes Yes Yes Yes Yes Yes Observations 5,320 6,818 8,200 9,687 11,188 11,188 9,936 14,347 Sample period 1888m4 1888m4 1888m4 1888m4 1888m4 1888m4 1926m1 1961m1 -1905m12 -1910m12 -1915m12 -1920m12 -1925m12 1925m12 -1960m12 -2017m12

28 Table A3: Explaining the Serial Correlation in Aggregate Stock Market Returns: Other Sam- ple Periods

The table shows the ability of Manhattan weather shocks to generated reversals in the aggregate stock market returns for different sample periods. Serial correlation on day t is estimated as the one-day serial correlation in returns from day t − 7 to t + 1 (one week, including holidays). All weather variables are measured in Manhattan. Midpoint temperature T is measured in oF . Temperature bins used as instruments are the ﬁve bins listed below. Volatility is 10 times the conditional standard deviation of returns estimated from GARCH(1,2). Weekend dummies are dummy variables for Friday and Saturday. In the parentheses are standard errors adjusted for serial correlation in the error term (Newey-West with 10 lags). ***, **, and * indicate 1%, 5%, and 10% signiﬁcance levels.

Expanding Sample during 1888m4-1925m12 Later Period (1) (2) (3) (4) (5) (6) (7) (8) Trade volume 0.020 0.004 -0.006 -0.007 -0.014 -0.015 -0.037∗∗∗ -0.083∗∗∗ (0.016) (0.014) (0.012) (0.011) (0.011) (0.011) (0.014) (0.028) T × Summer 0.007∗∗∗ 0.006∗∗∗ 0.003 0.004∗∗ 0.003 0.001 -0.000 (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) 1(T > 85) 0.056 (0.062) 1(80 < T ≤ 85) -0.010 (0.029) 1(75 < T ≤ 80) 0.018 (0.022) 1(70 < T ≤ 75) 0.018 (0.017) 1(T ≤ 15) 0.071 (0.046) Seasonal ﬁxed effect Yes Yes Yes Yes Yes Yes Yes Yes Weekend dummies Yes Yes Yes Yes Yes Yes Yes Yes Observations 5,320 6,818 8,200 9,687 11,188 11,188 9,935 14,346 Sample period 1888m4 1888m4 1888m4 1888m4 1888m4 1888m4 1926m1 1961m1 -1905m12 -1910m12 -1915m12 -1920m12 -1925m12 1925m12 -1960m12 -2017m12