The Anatomy of Day Traders Juhani Linnainmaa University of California, Los Angeles This version: June, 2003 First version: December, 2002 ËÌÊ Ì This paper examines the complete trading records of all day traders in Finland. A typical day trader is a male in his late 30s, who lives in the metropolitan area and trades in larger quantities than an investor in a sizematched control group even after ignoring day trades. These traders day-trade stocks that grab their attention, that they own, or that they have day-traded before. They pay close attention to the state of the limit order book, are very active near the end of the trading session, and are strongly deterred by losses. Day traders do not earn better returns than investors in the control group. Their realized returns from day trades are high, but these returns are not representative of overall performance because of their strong reluctance to realize losses. Day traders have attracted a significant amount of attention in the popular press. A search of the LexisNexis TM Academic service reports over 2,500 articles on day traders. A popular Internet bookstore lists over 100 titles for aspiring day traders, including at least one murder mystery, Stephen W. Frey s The Day Trader, whichthenew York Times (February 10, 2002) calls fast-paced. This interest has not been matched in academic journals. A similar search on day trading finds a single citation, and that work deals with the performance of technical trading rules at the daily level, not day trading in the sense we understand it today (see Landingham, 1980). This is not because of a lack of interest, but rather a lack of data. Barber and Odean (2001b, pp. 51) point out Contact information: Juhani Linnainmaa, juhani.linnainmaa@anderson.ucla.edu, Tel. (310) 825 8160. I wish to thank Mark Grinblatt, Matti Keloharju, Michael Brennan, and Monika Piazzesi for many suggestions on how to improve this paper. Special thanks are due to Matti Keloharju for his comments and help with the FCSD registry. I gratefully acknowledge the financial support provided by the Graduate School of Finance and Financial Accounting, the Foundation for the Development of Finnish Securities Markets, the OKOBANK Group Research Foundation, and the Foundation of Jenny and Antti Wihuri. Henri Bergström from the Finnish Central Securities Depository and Pekka Peiponen, Timo Kaski, and Jani Ahola from the Helsinki Exchanges provided data used in this study. 1
that little is known about their [day traders ] trading strategies, because firms that cater to day traders have been generally reluctant to provide access to the trading records of their clients. 1 We address this gap by examining the complete trading records of all individual investors engaged in day trading activity, along with complete limit order data for intraday analysis. These data offer a comprehensive look at the day trading phenomenon. We focus on the behavior and performance of day traders. For example, how often does a typical day trader turn over a portfolio? How does a day trader pick a stock to day-trade? How does he act in the market when executing a trade? Do day traders earn better returns than similar, non-day trading, investors? Do traders behavior change as their careers progress? These questions are important because of the degree of uncertainty surrounding day trading, and because of the possibility that day trading may increase stock market volatility (Campbell, Lettau, Malkiel, and Xu, 2001). Our results can be summarized as follows. Demographic Characteristics. A typical day trader is a man in his late 30s who lives in the metropolitan area and turns over his portfolio about once a month. Even after ignoring actual day trades, he trades more and hold stocks for a shorter time than investors in a size-matched control group. Stock Selection. Day traders tend to day-trade in stocks that (1) grab their attention (through excess returns during previous trading sessions), (2) they already own, or (3) they have day-traded before. Market volatility raises and trading losses in the same stock diminish the likelihood of day trading. Intraday Behavior. Day traders show a high overall level of activity and demand for liquidity at the opening and the close of the trading session. Day traders who are about to realize a loss from a day trade are very likely to take the loss at the very end of the trading session. We show that day traders try to imitate the behavior of other market participants when they execute trades; they buy (sell) after an uptick (downtick) and after a buyer-initiated (sellerinitiated) trade. They also pay attention to the depth of the book and react to changes in the bid-ask prices. Their decisions on passive or active limit orders depend strongly on the current state of the market and changes in the market. Performance. The average return from day trades is very high, but returns are not representative of overall performance because of day traders reluctance 1 A study that most closely resembles this paper is Harris and Schultz (1998). They use approximately three weeks worth of proprietary data from two brokerage firms that cater to SOES (Small Order Execution System of the Nasdaq) bandits to study these traders strategies and profitability of round-trip trades. Although these traders are day traders, their strategy is distinctive: to profit from stale quotes that arise in Nasdaq from fragmented order flow. Authors credit SOES bandits as a force that keep quotes of different dealers in line more cost-effectively than if dealers did this themselves, due to differences in incentives. Other studies on SOES bandits include Battalio, Hatch, and Jennings (1997), Harris and Schultz (1997), Kandel and Marx (1999), and Foucault, Röell, and Sandås (2003). These authors rely on indirect evidence, using data on maximum-sized SOES trades to examine bandits impact on the market. SOES activity declined significantly with Nasdaq reforms in 1997, indicating that the influence of SOES bandits reduced as well (see Barclay, Christie, Kandel, and Schultz, 1999). 2
to realize losses. Day traders overall level of performance during the 1998-2000 sample period does not differ from the control group before commissions. This suggests that day traders are not trading on superior information. Careers. Day traders become more confident and more aggressive as they continue to day-trade. They more often sell stocks that do not own and use more leverage in day trading. Trading losses play an important role in determining the fate of a day trader s career; the likelihood of quitting day trading increases with the extent of the current losses. I. Data and Demographic Characteristics The data come from the Helsinki Exchanges, Finland, which maintain a fully automated trading system based largely on an electronic limit order book. 2 These data provide the daily trading records of all individual investors (other investor groups are discarded) from January 1995 through May 2000, and complete limit order book data from November 1998 through May 2000. The first data set is the same as that used by Grinblatt and Keloharju (2001), including complete information on shareholdings and changes in shareholdings by each investor. It also includes demographic information, such as birth year, sex, and postal code. This data set is supplemented with the supervisory files kept by the Helsinki Exchanges, which shows all orders submitted to the market, and information on the status of orders (whether executed, amended, withdrawn, or expired). These data can be used to reconstruct the state of the limit order book for any time during a trading day. 3 The structure of the limit order data is similar to data sets used by Biais, Hillion, and Spatt (1995) and Gouriéroux, Jasiak, and LeFol (1999), but our cover a considerably longer period. A. Defining Day Traders and Control Group We define a day trader as an individual investor who makes a complete roundtrip trade during a single trading day, that is, an investor who buys and sells the same amount of the same stock on one day. Using this criteria, we select 7,686 investors of 413,645 households in the sample who meet this criterion. Similar to Barber and Odean (2002b), we constitute a size-matched sample of investors not classified as day traders. We include four times as many investors as in the group of day traders in this control group, because non-day traders are significantly less active traders (see below). Before selecting investors for the 2 Institutional features of the Helsinki Exchanges are discussed in detail in Booth, Lin, Martikainen, and Tse (2002). There were 154 stocks listed on the Helsinki Exchanges with a combined market value of 192.76 billion euros in late February 2000. 3 One limitation on the limit order data is that no separate time-stamp is given for the time of order withdrawals. We approximate this time-stamp by determining when each withdrawn order is about to cause a conflict in the book (i.e., it must already had been withdrawn). The robustness of this methodology was verified using data from a later time period for which the stamp is known. 3
control group, we exclude investors with fewer than two trades during the sample period, to match the same requirement implicitly imposed on day traders. Investors are matched primarily on the basis of their portfolio values at the beginning of 1999, and then according to the date they first traded. This sizematching works well. The average (median) day trader has a portfolio worth 148,538 (17,525) euros, and the average investor in the control group has a portfolio worth 141,086 (17,528) euros. Panel A of Figure 1 shows the number of day trading events and the fraction of trades originating from day traders (of all trades in the market) per month from January 1998 through May 2000. There are 48,661 day trading events, 1,023,562 trades from day traders, and 4,107,328 total trades. There is a significant increase in day trading activity in early 2000; over 55% of all day trading events took place during the first five months of year 2000. Overall activity of day traders during this period, as measured by fraction of trades, represents 12.46% of the total trades. That is, either the buyer or the seller (or both) in a trade is classified as a day trader. 4 The Lorenz curves in Panel B show that both trading and day trading events are concentrated in a small fraction of all stocks. For example, 71% (76%) of all trades (day trading events) between January 1998 and May 2000 took place in the most active decile of stocks. Their Gini coefficients are 80.6% and 85.8%, respectively. Day trading and trading in general are concentrated in the same stocks; the correlation between the proportion of trades and day trading events is 0.9. Panel C shows the number of new day traders entering and old day traders exiting the market per month between January 1998 and May 2000. We assume that a day trader has exited if he does not day-trade for one month, and does not start day trading again (thus, the number of day traders exiting in May 2000 is undefined). Taking this definition as a proxy for the actual exit rate, the number of day traders exiting the market was approximately equal to the number of day traders entering the market in March 2000. We report this figure only for descriptive purposes. When the actual time of exit is unknown, the upward bias increases with time. The importance of the day trading phenomenon becomes obvious in Panel C. In April 2000, over 1,000 individuals tried their luck in day trading (the population of Finland is approximately 5.2 million). The market index is reported for reference. For example, as of the end of 1999, a sharp increase in the market index coincided with a surge in the number of day traders. The contemporaneous monthly correlation from January 1999 through May 2000 between the return for the market index and the relative change in the number of day traders entering the market is 0.74 (p-value < 0.001). Although Figure 1 does not report this, some day traders had had very little investment experience before completing their first day trade. 318 (4.1%) of day traders had not traded at all before starting day trading at least as of January 4 Angel (2000) finds that, in spring 2000, 20% of new orders flowing to Nasdaq originated from firms that cater to day traders. 4
Panel A: Day Trading Activity 8,000 # Day Trading Events Fraction of Trades 6,000 # Day Trading Events 4,000 2,000 18% 15% 12% 9% Fraction of All Trades 0 6% 01/98 02/98 03/98 04/98 05/98 06/98 07/98 08/98 09/98 10/98 11/98 12/98 01/99 02/99 03/99 04/99 Month 05/99 06/99 07/99 08/99 09/99 10/99 11/99 12/99 01/00 02/00 03/00 04/00 05/00 Panel B: Number of Day Traders Entering and Exiting the Market 2,000 Entering # Day Traders 1,600 Exiting Market Index (01/02/1998 = 100) 1,200 800 400 220 192 164 136 108 Market Index 0 80 01/98 02/98 03/98 04/98 05/98 06/98 07/98 08/98 09/98 10/98 11/98 12/98 01/99 02/99 03/99 04/99 Month 05/99 06/99 07/99 08/99 09/99 10/99 11/99 12/99 01/00 02/00 03/00 04/00 05/00 Panel C: Concentration of All Trades in the Market and Day Trading Events 100% All Trades in the Market Day Trading Events 75% Cumulative Proportion of Trades / DT Events 50% 25% 0% 50% 60% 70% 80% 90% 100% Cumulative Proportion of Stocks Figure 1. Day Trading Activity and Its Concentration A day trading event is defined as a day an investor both purchases and sells the same amount of the same stock. Panel A shows the number of day trading events and the activity of day traders as a fraction of all trades in the market from January 1998 through May 2000. During this period, investors classified as day traders traded 1,023,562 times, and there were a total of 4,107,328 trades. Panel B shows the number of day traders entering and exiting the market. The dotted line is the level of the value-weighted and weight-constrained market index. A day trader is assumed to have exited if he does not day-trade in one month and does not start day trading again. Panel C reports Lorenz curves for day trading events and all trades. 1995 when the data starts. Of all the remaining day traders, 1,255 (16.3%) had traded for the first time no more than three months before. 5
Table I Sample Descriptive Statistics Descriptive statistics of demographic factors and investor characteristics are shown for day traders and investors in a size-matched control group. A day trader is defined as an investor who at least once during the sample period completes a round-trip trade during a single trading day. Panel A reports differences in sex, mother tongue, and whether the investor lives in the metropolitan area. Panels B and C report age and investor characteristics such as number of trades. Each investor is a single observation. The last column in Panel B reports z-values from the Mann-Whitney test for the difference between day traders and investors in the control group. Trade size and portfolio values are reported in thousands of euros. Holding period is calculated using the FIFO principle and reported in the number of days. Daily turnover is the capital-weighted average over the entire sample period. Portfolio values are as of January 1, 1999. For day traders, this table reports the number of trades and the average trade size separately for a sample excluding day trading events and for a sample consisting only of day trading events. Panel A: Distributions of Sex, Mother Tongue, and Metropolitan Area Day Control Traders Group z-value N 7,686 30,748 Women 16.2% 34.9% 31.7 Swedish speaking 6.1% 10.1% 10.7 Metropolitan 39.9% 33.5% 10.5 Panel B: Day Traders Percentiles z-value Mean 10% 25% 50% 75% 90% (DT CG) Age 41.5 25 31 39 52 60 34.8 # Days Active 67.2 10 20 42 85 150 112.3 Excluding DT Events # Trades 137.9 12 29 70 154 313 106.0 Trade Size 7.5 1.5 2.5 4.5 8.2 15.1 35.5 Holding Period 58.8 7.2 15.4 35.3 72.0 135.5 60.7 Only DT Events # Trades 24.0 2 2 5 15 47 10.0 Trade Size 15.1 1.7 3.2 6.3 13.5 31.9 55.7 Daily Turnover 10.1% 0.6% 1.4% 3.9% 11.0% 26.4% 79.2 Portfolio Value 148.5 1.6 5.0 17.5 62.2 194.0 0.0 #DTevents 7.1 1 1 2 5 15 Panel C: Control Group Percentiles Mean 10% 25% 50% 75% 90% Age 48.7 25 35 50 61 72 # Trades 16.0 2 3 6 15 36 Trade Size 6.2 0.7 1.4 2.8 5.9 12.1 Holding Period 167.7 23.0 50.3 112.5 224.0 384.2 Daily Turnover 4.6% 0.1% 0.2% 0.5% 1.7% 7.1% Portfolio Value 141.1 1.6 5.0 17.5 62.2 194.1 B. Demographics of Day Traders and Control Group Table I reports demographics and investor characteristics for both day traders and the control group. A typical day trader is younger, more often male, lives more often in the metropolitan area, and is less often Swedish speaking than an investor in the control group. 5 The median day trader is 39 years old, while the median investor in the control group is 50. All these differences are highly 5 Approximately 6% of the Finnish population speak Swedish as their native language. Karhunen and Keloharju (2001) document that Swedish speaking individuals in Finland are on average over three times wealthier than Finnish speaking individuals. 6
significant, and are consistent with the analysis of Odean (1999) and Barber and Odean (2001a) on sex, overconfidence, and decision to engage in online trading. 6 A comparison of investor characteristics shows that the day trading and control group investor categories are very different, even excluding trades related to the actual day trading events (i.e., a full round-trip during a trading day). This finding of higher activity is not surprising, and is consistent with Harris and Schultz (1998). Day traders also trade in larger quantities. This is especially true for trades related to day trading events: median trade sizes (in thousands of euros) are 2.83 for the control group, 4.53 for day traders excluding DT events, and 6.26 for day traders (only DT events). 72.38% of day traders trade in larger average trade sizes for DT events than for their other trades. The difference is highly significant with a t-value of 39.08. Day trader average holding periods (excluding day trading events) are considerably shorter than the average holding periods of investors in the control group. The median day trader holds shares on average for 35 trading days, while the median investor in the control group holds them for 113 trading days. 7 The capital-weighted average daily percentage turnover over a T -day period is defined as: 8 T t=1 Daily Turnover T = turnover t T t=1 position value t 1 + T t=1 turnover (1) t This measure shows that the median day trader turns the portfolio over once every 25th trading day, while the median investor in the control group does so once every ten months. Panel B of Table I also reports the number of day trading events for day traders (the number of round-trip trades completed during a single day) for day traders. Even though a considerable number of investors day-trade only once, one-quarter of day traders engage in at least 5 day trades, and the most active decile shows at least 15 day trading events. Given the size of the sample, this reveals a significant number of very active day traders. It can also be observed that day traders do not always use two trades to complete a round-trip within a single trading day; in fact, the average (median) day trader uses an average of 2.8 (2.3) trades, and the highest decile uses an average of at least four trades. We examine differences between day traders and investors in the control group in greater detail (full results not reported here). First, the concentration of day traders trading activity in liquid stocks is manifested in a difference in spreads for day traders and investors in the control group. The median 6 There is some variation in demographic and investor characteristics within day traders. Those who day-trade the most are younger and have smaller portfolios than the majority of day traders. These results are not reported for the reasons of space. 7 The perhaps surprisingly short holding period can be explained by the fact that we do not includes sales of stock acquired before 1995 because of the absence of data on purchase dates. Furthermore, holding periods are evaluated only on the basis of actual sales, not on stocks in the portfolio that are never sold during the period. 8 The reason for including turnover in the denominator is that some investors have so small (or zero) positions that the unstandardized measure would have a very large variance. 7
percentage spread for day traders is 0.696%; the median spread for investors in the control group is 0.725% (difference significant with a z-value of 17.7 by the Mann-Whitney signed rank test). 9 This finding that day traders prefer to trade in more liquid stocks is consistent with the behavior of SOES bandits, as reported in Harris and Schultz (1998) and Foucault, Röell, and Sandås (2003). Second, day traders and investors in the control group have different types of order submission strategies (Linnainmaa, 2003)see. We measure order submission strategies by examining the placement of the limit order relative to the spread (outside, at, or inside), and whether the order is placed before the trading session begins (pre-open). 47.5% of day traders limit orders are placed inside the spread (i.e., they improve the spread). The corresponding figure is 38.6% for investors in the control group. These proportions are significantly different with a z-value of 28.6. Furthermore, investors in the control group favor placing orders before the exchange opens: 21.2% of their limit orders are of this type, compared to 6.4% for day traders. The independence of limit order submission strategies between day traders and investors in the control group is rejected with a χ 2 (3)-value of 17, 598. II. The Decision to Day-Trade How much do marketwide and stock-specific factors influence day traders decision to day-trade? Are day traders more likely to day-trade in stocks that have experienced large excess returns? Barber and Odean (2002a) find individual investors seem to chase the action by trading on salient news. 10 Figure 2 plots cumulative excess returns over the previous five trading sessions before a day trading event, conditional on both ownership and strategy (buy first, sell later / sell first, buy later). If the investor day-trades a stock he does not own, cumulative excess returns through the previous day s close are significantly higher than if the investor owns the stock. This finding is consistent with the attention hypothesis of Barber and Odean (2002a). Also, an investor who first sells a stock and later buys it back is drawn by stocks that have appreciated more than those that the investor is betting to rise in value. This is consistent with research finding that individual investors are 9 Spreads are measured by calculating the average spread for each stock-day and then the median spread over all trades for day traders and investors in the control group. We use stock-day spreads instead of actual realized spreads to ensure that differences in non-stockspecific trading behavior do not affect the results. For reference, the actual median spread paid (earned) by a day trader is 0.513% (0.568%) and the median spread paid (earned) by an investor in the control group is 0.564% (0.632%). These differences are similar to the results obtained using stock-specific spreads. 10 Froot, Scharfstein, and Stein (1992) note the literature offers two reasons for trading with short horizons: (1) money managers need to prove their skills, and (2) speculators who, in the fear of future credit constraints, do not wish to tie up their money in long-horizon investments. It is also possible that a day trader tries to act as a market maker. Because individuals pay commissions and financial institutions do not, it is unlikely that any equilibrium would support their existence. Furthermore, individuals are likely to be in an information disadvantage (Schultz, 2003). 8
Cumulative Excess Return (%) 8% 6% 4% 2% 0% Buy First, Does Not Own Buy First, Owns Sell First, Does Not Own Sell First, Owns -2% -5-4 -3-2 -1 Trading Day Relative To Day Trading Event Figure 2. Cumulative Excess Returns on Stock Selected for Day Trading, Conditional on Strategy and Ownership For each day trading event for which the strategy is identified (buy first, sell later / sell first, buy later), the cumulative excess return on the stock traded over the previous five trading sessions is calculated. The darker line indicates the investor owned the stock he day traded at t =0. The lighter line indicates the investor did not own the stock. The solid line indicates the investor first bought the stock; the dashed line indicates the investor first sold the stock. contrarians (e.g., Grinblatt and Keloharju, 2000). We use a multivariate logistic regression to simultaneously account for different factors affecting day trader decisions. The dependent variable takes the value of one if a day trader day-trades and zero otherwise. For each investor, we include in the analysis daily observations of all stocks, even if the investor does not trade in that stock. A stock enters the sample when the investor first day-trades in it. Our purpose is to construct a sample of stocks the investor is familiar with. We assume the investor becomes familiar with a stock as he first day-trades it. This universe of stocks is an appropriate benchmark when the investor decides which stock to day trade. To keep the sample size manageable, we restrict the analysis to days when the investor traded or had traded the preceding day in any stock. The explanatory variables for stock i (with five daily lags) are: excess return conditional on ownership, dummy variables for investor (1) trading; (2) day trading; (3) generating a moderate trading loss (< 3%); and (4) generating a large trading loss ( 3%). 11 Working with investor holdings at the previous day s close, we include a dummy for ownership, and a paper return from the time of the purchase (set to zero if the investor does not own the stock). We also include event dummies (1)-(4) for all other stocks the investor is familiar with (i.e., has day traded). Finally, we control for the return on the market 11 Trading loss is defined as the intraday return due to trading for days when an investor buys (and possibly sells) a stock. 9
Table II Daily Analysis of Factors Affecting Day Trader Decision to Day-Trade Results of a multivariate logistic regression where the dependent variable takes the value of one if a day trader day trades in stock i and zero otherwise. The sample consists of daily observations of all stocks that the investor has previously day-traded. For stock i, the RHS of the regression includes (five daily lags) the excess return conditional on ownership, and four dummy variables for whether the investor (1) trades, (2) day trades, (3) generates a moderate trading loss (< 3%), and (4) generates a large trading loss ( 3%). These dummies are also included for all other stocks the investor is familiar with (e.g., whether the investor traded in any other stocks besides i at date t 3). Ownership is a dummy that takes the value of one if investor owns the stock at the previous close. Paper return is calculated as the unrealized return on stock i from the time of purchase. The model also includes an intercept (not reported). t-values are reported in parentheses. Variable Trading Day Category Variable t 1 t 2 t 3 t 4 t 5 Market Return 0.026 0.023 0.025 0.020 0.010 ( 11.4) ( 9.9) ( 10.7) (8.8) (4.3) Volatility 0.009 0.009 0.003 0.003 0.006 (13.1) (12.4) (4.2) (3.8) (8.4) Stock Used Excess Return 0.044 0.017 0.008 0.002 0.003 for (50.6) (23.4) (10.7) (2.0) (3.2) Day Trading Excess Return Own. 0.040 0.008 0.011 0.005 0.002 ( 27.8) ( 6.3) ( 8.1) ( 3.5) ( 1.2) Traded 0.454 0.536 0.354 0.312 0.367 (29.9) (32.0) (20.0) (17.2) (20.2) Day Traded 0.694 0.423 0.320 0.313 0.352 (40.4) (21.8) (15.4) (14.5) (16.1) Trading Loss, Low 0.016 0.062 0.095 0.130 0.105 ( 0.8) (2.8) (4.0) (5.3) (4.2) Trading Loss, High 0.116 0.105 0.108 0.072 0.192 ( 3.6) ( 2.8) ( 2.7) ( 1.7) ( 4.4) Other Stocks Traded 1.074 0.232 0.213 0.231 0.249 ( 91.3) ( 18.9) ( 17.2) ( 18.5) ( 20.1) Day Traded 0.699 0.375 0.285 0.288 0.276 (51.3) (26.3) (19.6) (19.7) (19.0) Trading Loss, Low 0.032 0.019 0.015 0.004 0.019 ( 1.9) ( 1.1) ( 0.9) (0.3) (1.1) Trading Loss, High 0.012 0.029 0.050 0.005 0.048 (0.5) ( 1.1) (1.9) (0.2) (1.8) Ownership Ownership 0.420 (44.6) Min(Paper Return, 0) 0.020 ( 48.3) Max(Paper Return, 0) 0.002 (12.5) Model N 2,012,543 Summary Block χ 2 78,393.0 Pseudo-R 2 13.9% index (m t ) and market volatility (m 2 t ). The estimated coefficients are shown in Table II. At short lags, market volatility, trading activity in the same stock, and the stock s excess return have a significantly positive impact on the likelihood to day trade. A strong relationship between ownership and excess returns persists; an investor is more likely to day trade in a stock that he owns. In these cases, the excess return is not as significant a determinant. For example, at day t 1, the effect of excess returns is only 0.003 (0.044 0.040 without rounding) if the investor owns the stock. 10
If the investor owns the stock, the unrealized return (paper gain or loss) is important. Day traders choose to day-trade in stocks that they have paper losses in. There is also evidence that the likelihood of day trading also increases with paper gains. In other words, day traders choose to day-trade in stocks that have been good investments. Although this type of behavior could be evidence of irrationality (because of tax considerations), this effect is economically less significant than the impact of paper losses (0.002 vs. 0.020). Large trading losses in the same stock reduce the likelihood of day trading; interestingly, for moderate losses at lags from t 3tot 5, the coefficients are positive. This could indicate that day traders are not permanently intimidated by such losses. A comparison of day trading and loss coefficients shows that losses do not seem to be as important as the act of day trading itself. Furthermore, trading losses in other stocks seem to make little difference. III. Intraday Trading Behavior To analyze the intraday trading behavior of day traders, we use limit order data to recreate the limit order book and combine this information with transaction records of day traders and investors in the control group. 12 This allows us to directly observe whether an investor initiated trade or supplied liquidity to the market. More generally, the data let us to determine what the limit order book looks like at the time each order is submitted. A. Activity, Liquidity, and Buy-Sell Ratios During a Trading Day We categorize trades into three groups on the basis of type: (1) trades originating from the control group, (2) trades that are part of a day trader s day trade, and (3) trades that originate from a day trader but are not part of a day trade. We divide the trading day into five-minute intervals and calculate trading activity, the supply of liquidity (passive versus active orders), and buy-sell ratios for each interval as follows: 13 Activity = Supply of Liquidity = Buy-Sell Ratio = #trades total # trades over all periods # passive trades #trades # buys # buys + # sells (2) (3) (4) 12 See Appendix for description of the matching procedure. 13 There are no designated market makers on the HEX. All liquidity is supplied by market participants. A limit order is called passive if it is not immediately executed and active otherwise. There are no market orders; an investor wishing to trade in larger quantity than is available at the best price level must submit separate active limit orders at each price level. 11
Panel A: Activity 8% Fraction of Trades 6% 4% 2% Control Group Day Traders (Non-RT) Day Traders (RT) 0% 1030 1045 1100 1115 1130 1145 1200 1215 1230 1245 1300 1315 1330 1345 1400 1415 1430 Time of Day 1445 1500 1515 1530 1545 1600 1615 1630 1645 1700 1715 Panel B: Supply of Liquidity 70% Fraction of Passive Orders 60% 50% 40% Control Group Day Traders (Non-RT) Day Traders (RT) 1030 1045 1100 1115 1130 1145 1200 1215 1230 1245 1300 1315 1330 1345 1400 1415 1430 Time of Day 1445 1500 1515 1530 1545 1600 1615 1630 1645 1700 1715 Panel C: Buy-Sell Ratio 60% Buy-Sell Ratio 50% 40% 30% Control Group Day Traders (Non-RT) Day Traders (RT) 1030 1045 1100 1115 1130 1145 1200 1215 1230 1245 1300 1315 1330 1345 1400 1415 1430 Time of Day 1445 1500 1515 1530 1545 1600 1615 1630 1645 1700 1715 Figure 3. Intraday Trading Activity, Supply of Liquidity, and Buy-Sell Ratios for Day Traders and Control Group This figure plots average intraday trading activity (Panel A), supply of liquidity (Panel B), and buy-sell ratios (Panel C) of day traders and investors in the control group. Trades of day traders are divided into two exclusive groups: (1) trades originating from day traders that are part of roundtrip trading (i.e., day trading event) and (2) other trades. Trading day is divided into five-minute intervals, and time of the day is shown on x-axis. These statistics are plotted in Figure 3. Table III shows daily totals and statistics for the opening call that takes place at 10:10a.m. Panel A of Figure 3 shows that in all categories trading is concentrated near the opening and the close. Day traders (round-tripping or not), however, are significantly more active during intervals immediately before the close than investors in the control group. Panel B shows that day traders engaged in round-trip trading are more aggressive in their demand for liquidity near the close. Day traders appear to start to use active orders only when they are running out of time. Investors 12
Table III Intraday Trading Activity, Supply of Liquidity, and Buy-Sell Ratios Similar to the graphical presentation in Figure 3, this table shows (1) the intraday trading activity (N), (2) the supply of liquidity (Supp.), and (3) buy-sell ratios (B-S) of day traders and investors in the control group. Trades of day traders are divided into two exclusive groups: (1) trades originating from day traders that are part of round-trip trading (RT) and (2) other trades (Non-RT). Statistics are given for the opening call and for the first and last 15 minutes of the continuous trading session. Control Group Day Traders (Non-RT) Day Traders (RT) Time N Supp. B-S N Supp. B-S N Supp. B-S Open 1.6 53.6 51.0 0.7 50.6 47.1 0.4 58.0 64.5 10:30 6.2 58.6 48.5 4.0 49.1 48.8 4.0 42.6 58.7 10:35 3.0 52.0 52.2 2.7 47.9 50.4 2.8 49.9 59.9 10:40 2.2 52.5 50.8 2.1 51.3 50.9 2.3 52.3 57.1 17:15 0.9 58.8 50.8 1.7 53.8 50.8 2.1 50.4 31.3 17:20 1.0 62.0 52.2 2.0 54.2 51.3 2.6 48.0 31.4 17:25 1.4 68.9 50.3 3.1 56.4 52.5 4.3 46.3 30.9 Total 52.6 51.1 55.6 49.9 57.1 47.9 z-values (Non-RT z-values (RT vs. Control Group) vs. Non-RT) Time N Supp. B-S N Supp. B-S Open 3.3 2.2 2.8 0.9 3.4 8.0 10:30 7.7 14.6 0.5 0.0 9.2 14.1 10:35 0.9 4.7 2.0 0.2 2.5 11.2 10:40 0.2 1.1 0.1 0.8 1.0 6.6 17:15 2.1 3.4 0.0 1.4 3.4 19.6 17:20 2.8 5.5 0.6 2.2 6.8 22.1 17:25 4.2 10.8 1.9 4.7 14.2 30.4 Total 19.3 7.7 11.0 14.1 in the control group by contrast become a significant source of liquidity to the market near the end of the trading session. Table III shows that differences in the supply of liquidity are highly significant among all three groups. Day traders are net suppliers of liquidity, which means they effectively frequently act as market makers, not only as speculators betting on the direction of the price movement. This directly suggests that day trader behavior differs from the behavior SOES bandits, who initiate their positions through SOES with market orders but dispose of them using limit orders on Instinet or SelectNet (Harris and Schultz, 1998). In fact, the behavior of day traders indicates that day traders are more like dealers than bandits (see Foucault, Röell, and Sandås, 2003, p. 29). Panel C of Figure 3 shows that day traders engaged in intraday trading behave asymmetrically with respect to trading strategies. 14 During the first five-minute period of the continuous trading session, 58.73% of trades originating from day traders (round-trip) are buys. During the opening call the figure is 64.50%. As the trading session progresses, the buy-sell ratio decreases monotonically. In the very last interval, the buy-sell ratio is 30.88%. The timing of 14 Table V shows that day traders prefer to first purchase and then sell stock when they engage in complete round-trip trades. The net effect on the market is that there is more sell pressure toward the end of the day. 13
Panel A: Activity 8.00% 6.00% No Loss Loss 4.00% 2.00% 0.00% 103000 104500 110000 111500 113000 114500 120000 121500 123000 124500 130000 131500 133000 134500 140000 141500 143000 144500 150000 151500 153000 154500 160000 161500 163000 164500 170000 171500 Panel B: Supply of Liquidity 70.00% 60.00% 50.00% 40.00% No Loss Loss 30.00% 103000 104500 110000 111500 113000 114500 120000 121500 123000 124500 130000 131500 133000 134500 140000 141500 143000 144500 150000 151500 153000 154500 160000 161500 163000 164500 170000 171500 Figure 4. Intraday Trading Activity and Supply of Liquidity, Conditional on Loss The analysis of Figure 3 (except for buy-sell ratios) is repeated by comparing behavior of day traders on days they are day trading, conditional on realizing a loss (gross return strictly smaller than zero). buys and sells seems to be unimportant for day traders when they are not day trading. Figure 4 repeats the analysis for round-tripping day traders, conditional on realizing a loss. We define a loss as a gross return strictly lower than zero. Panel A shows that after very closely trailing the no loss category for the early part of the day, day traders who are about to realize a loss become significantly more active approximately half an hour before the session ends. Panel B shows that investors who are about to realize a loss revert more quickly to active orders than when realizing a gain. Although the last result could be affected by confusion between cause and consequence (i.e., a trader might realize a loss because of demanding liquidity from the market, rather than demand liquidity from the market because he is about to realize a loss), the intraday variation is not explained by this argument. Investors who are about to realize a loss become gradually more impatient and shift to the use of active orders. B. Intraday Analysis of Trade Execution Is a day trader more likely to buy after another buyer has demanded liquidity from the market, and is a day trader more likely to submit a passive order when he wants to trade in larger quantities? To investigate questions such as these, we specify two multivariate regressions: (1) in a sample consisting of all buys 14
and sells where the day trader demands liquidity, wr set the dependent variable to one for buys and zero for sells and (2) in a sample consisting of buys (sells), we set the dependent variable to one if the day trader demands liquidity. As explanatory variables, we include trading activity (measured as logarithm of the sum of number of orders and number of trades); logarithm of the time since the previous trade (following Dufour and Engle, 2000); the logarithmic difference between ask and bid prices (spread); and changes in the size of the spread, the midpoint of the spread, and the bid and ask depths. We calculate the depth of the book at bid and ask sides at a 2.5% interval from the midpoint of the spread (i.e., if the spread midpoint is 10e, the buy depth is defined as the total volume outstanding on the interval [9.75, 10]). Changes are measured by comparing the state of the book five minutes before the trade and immediately before the trade. For the previous five transactions, we include dummy variables to capture whether the trade is an up- or downtick and whether it is buyeror seller-initiated. 15 We include separate dummies to capture cases where all previous five trades are either buyer- or seller-initiated. The second regression also includes logarithm of order value as an explanatory variable. The Columns (a) in Table IV present the results for the buy vs. sell decision. Dummies for previous ticks and trade initiator show that day traders follow momentum in their intraday trading; they are more likely to buy when the price has risen and sell when the price has dropped, as well as buy (sell) when the previous trade was initiated by a buyer (seller). This intraday momentum should not be confused with the conventional definition of the dependence of buys and sells on past (longer term) price movements. The direction of a trade is more important than whether the trade generates an up- or downtick. At one trade lag, for example, coefficients for the uptick and the buyer-initiated trade dummies are 0.06 and 0.56, respectively. Furthermore, these effects are asymmetric; an uptick does not increase the propensity to buy as strongly as the downtick reduces it. The change in the midpoint of the spread during the past five minutes is insignificant, suggesting that transaction time variables better capture the factor that drives day trader decisions. Increase in the volume at the bid (ask) side of the book increases (reduces) the propensity to buy. This also indicates that day traders attempt to trade in the same direction as the incoming order flow. The coefficient of the percentage spread shows that day traders are more likely to buy when the spread is wide. Columns (b) and (c) of Table IV analyze the choice between active and passive orders, conditional on whether the order is a buy or sell. 16 For passive orders, we look at the state of the book at the time an order is submitted (i.e., when the investor enters the passive order in the book) instead of the time of 15 Trades can also also occur in the upstairs market as prenegotiated trades, which ensures that some 10% of trades in the sample are neither buyer- nor seller-initiated (Linnainmaa, 2003). 16 Bae, Jang, and Park (2002) analyze the submission of limit and market orders on the NYSE and find that liquidity is provided when the spread and the order size are large. Griffiths, Smith, Turnbull, and White (2000) and Ranaldo (2002) study the determinants of order aggressiveness. Our analysis differs significantly from theirs in that we focus on a specific group of investors. 15
Table IV Intraday Analysis of Factors Influencing Day Trader Decision to Trade Limit order book data is matched with transaction records of day traders to analyze the impact of market microstructure variables on day traders buy/sell decision (Columns a) and decision to use active versus passive order (Columns b and c). In Columns a, the sample is limited to cases where the investor is demanding liquidity from the market and the dependent variable takes the value of one if the investor buys. In Columns b (c), the sample consists of all buys (sells), and the dependent variables takes the value of one if the investor demands liquidity. Activity is defined as logarithm of the number of new orders and trades in the stock during the past five minute period. Last Trade is defined as logarithm of the time from the previous trade (in seconds + 1). Spread is the log-difference between best ask and bid prices. Change in Spread is the percentage change in the size of the spread during the past five minute period. Change in Mid Quote is the log-difference between the midpoint of the spread immediately before the trade and the midpoint five minutes earlier. Change in Bid Depth (Ask Depth) is calculated as the change in the volume outstanding in the book within 2.5% interval from the midpoint of the spread during the past five minute period. Uptick i j (Downtick i j ) takes the value of one if trade i j takes place at a higher (lower) price than trade i j 1. Buyer-Initiated i j (Seller-Initiated i j ) takes the value of one if trade i j is initiated by the buyer (seller). Buyer-Initiated all (Seller-Initiated all ) takes the value of one if all previous five trades are initiated by the buyer (seller). Logarithm of the order value is included as an additional explanatory variable in Columns b and c. All regressions also include time dummies for all 30-minute periods except for the one from noon to 12:30p.m. and an intercept (not reported). Dependent Variable (a) Buy vs. Sell (b) Market vs. (c) Market vs. formarketorders Limit(Buys) Limit(Sells) Variable Coeff. t-value Coeff. t-value Coeff. t-value Activity 0.105 26.1 0.102 26.3 0.137 34.2 Last Trade 0.016 7.3 0.184 72.4 0.191 76.7 Spread 2.582 7.9 12.829 38.8 16.006 45.0 Change in Spread 0.004 2.8 0.021 13.9 0.025 14.5 Change in Mid Quote 0.050 0.1 6.039 15.5 4.478 10.3 Change in Bid Depth 0.224 42.5 0.071 15.8 0.105 21.3 Change in Ask Depth 0.193 37.0 0.093 20.8 0.060 12.3 Uptick i 1 0.060 5.3 0.010 1.0 0.036 3.2 Uptick i 2 0.045 3.9 0.006 0.6 0.048 4.3 Uptick i 3 0.027 2.3 0.021 2.1 0.041 3.7 Uptick i 4 0.000 0.0 0.022 2.1 0.051 4.6 Uptick i 5 0.041 3.5 0.043 4.1 0.021 1.9 Downtick i 1 0.219 19.4 0.054 4.8 0.134 13.4 Downtick i 2 0.099 8.6 0.032 2.9 0.052 5.0 Downtick i 3 0.055 4.7 0.049 4.4 0.042 4.0 Downtick i 4 0.019 1.6 0.051 4.6 0.022 2.1 Downtick i 5 0.028 2.5 0.002 0.2 0.028 2.6 Buyer Initiated i 1 0.560 38.9 0.409 31.9 0.062 4.6 Buyer Initiated i 2 0.145 10.0 0.086 6.5 0.061 4.4 Buyer Initiated i 3 0.110 7.5 0.020 1.5 0.144 10.5 Buyer Initiated i 4 0.085 5.8 0.039 2.9 0.146 10.7 Buyer Initiated i 5 0.109 7.8 0.036 2.8 0.259 19.6 Buyer Initiated all 0.118 7.8 0.045 3.3 0.071 4.7 Seller Initiated i 1 0.659 44.9 0.086 6.2 0.532 39.8 Seller Initiated i 2 0.175 11.9 0.092 6.6 0.136 10.0 Seller Initiated i 3 0.095 6.4 0.138 9.9 0.011 0.8 Seller Initiated i 4 0.063 4.3 0.195 14.6 0.024 1.8 Seller Initiated i 5 0.081 5.7 0.047 3.7 0.102 7.6 Seller Initiated all 0.094 5.8 0.100 6.0 0.018 1.3 Ln(Order Value) 0.174 56.4 0.265 84.1 N 301,204 321,904 328,866 Block χ 2 51,551.9 25,366.3 41,099.7 Pseudo-R 2 12.3% 5.7% 9.1% 16
the trade. (A potential problem with the analysis of passive orders is that the sample consists only of orders that are ultimately executed; e.g., orders that are put further away from the spread are less likely to get executed (see, e.g., Handa and Schwartz, 1996; Lo, MacKinlay, and Zhang, 2002). Thus, the sample is not representative of order submission strategies. We see no reason to believe this filtration would bias analysis of the differences between active and passive orders.) Changes in the depth of the book and initiator coefficients show that when day traders demand liquidity, they are trying to go with the flow more than when they are supplying liquidity. For example, if the day trader buys after a buyer-initiated trade, he is more likely to dosousingamarketorderratherthan a limit order. Changes in the depth of the book also show that when investors demand liquidity, they base their decisions more heavily on the behavior of other market participants (incoming order flow). Negative coefficients on the time since last trade and trading activity show that a day trader is more likely to supply liquidity when there has been more activity in the stock (i.e., the probability of execution is higher). Order size, spread, and change in the spread show that day traders are supplying liquidity when they (1) want to trade in larger quantities, (2) are facing wider spreads, and (3) when the spread has worsened. The converse is more important: Day traders supply liquidity when it is valued the most, thus improving market quality. This finding is not sufficient to conclude that the overall impact on market quality is positive. For example, it could be that day traders high demand for liquidity near the open and the close disrupt the price discovery process and add unnecessary volatility. The same asymmetry between buys and sells is apparent in Columns (b) and (c). First, the overall explanatory power of the model (judging by the pseudo- R 2 statistic) is higher for sells. Second, individual coefficients indicate stronger relationships, e.g., the trade size is unimportant for buys but highly significant for sells. Overall, the results in Table IV suggests that market microstructure considerations are more important for an investor wishing to sell. 17 IV. Performance of Day Traders Are day traders able to take advantage of minute price movements? Or do they day-trade because they have superior information, at least compared to similar investors? If day trading is driven by these factors, day traders would be expected to outperform the control group that never day-trades. To see whether this is the case, we analyze rates of return. First, we study 17 A potential explanation for the asymmetry between buys and sells is that the sell transaction is most often the trade that realizes the return. An investor buying a stock may believe the trade will generate enough return to dilute the importance of the spread and the intraday timing of the transaction. When the investor is selling the stock, the price taken from the market is directly reflected in the return. 17
Table V Realized Returns from Day Trading Events A day trading event is defined as a day an investor both buys and sells stock i. Average gross returns assuming no commissions and taking the value of buys as capital are partitioned by strategy (buy first, sell later / sell first, buy later) and stock ownership (owns the stock / does not own). F -value is from analysis of variance of the means. Strategy Ownership N Mean Median s.e. Buy First No 19,817 1.50% 1.21% 0.16% Buy First Yes 7,417 1.20% 0.90% 0.22% Sell First No 6,425 0.79% 0.72% 0.26% Sell First Yes 5,019 2.18% 1.72% 0.30% F -value 88.21 Total 38,678 1.41% 1.13% 0.11% p-value < 0.001 the returns day traders realize from day trades. While the realized returns are highly positive, this appears to be a consequence of the fact that day traders are reluctant to realize losses. Second, we compare the overall performance of day traders and the control group. Their performance records do not differ significantly. Finally, we show that neither group seems to have stock selection skills. A. Day Traders Day Trades Our investigation of the returns that day traders realize from day trades reveal that returns are high because of a strong reluctance to sell losers. 18 The hypothesis that day traders have information places a testable restriction on the profitability of day trades; if day trading is nothing more than investor exploitation of private signals, returns should be largely independent of ownership, strategy, and amount of leverage. We classify each day trading event according to whether an investor owns the stock he day trades and whether he (1) first buys and later sells or (2) first sells and later buys the stock. 19 Finland is different from many other markets in that some (online) brokerage firms allow intraday short-selling without a requirement to borrow the stock or to post additional capital. Table V reports the gross rate of return that day traders realize from full round-trips, and frequencies of different strategies. In 70.4% of all events, an investor first buys a stock and later sells it. This finding could be particular to the period under study (which represents a bull market), and not necessarily an indication of a reluctance to assume short positions that could result in 18 Odean (1998) and Grinblatt and Keloharju (2001) offer empirical evidence. At a theoretical level, the disposition effect is proposed in Shefrin and Statman (1985), based on the prospect theory of Kahneman and Tversky (1979). Shefrin and Statman augment prospect theory with mental accounting, regret aversion, and self-control to describe a general tendency to sell winners and to hold losers. 19 It is not possible to classify all events based on strategy because of an ambiguity in the sequence of trades within a trading day when trading records and limit order data do not match each other. This results in a loss of 13,517 observations, or 28.9% of the sample. 18
unbounded losses. 20 A large share (32%) of day trading activity takes place in stocks that the investor owns. Day traders earn very high returns, 1.41%, on full round-trips (no commissions are assumed; for full round-trips, k commissions would reduce estimates by 2k). These returns, which are similar to the findings in Schlarbaum, Lewellen, and Lease (1978), would appear high even if traders paid, say, 0.25% in trading commissions. Schlarbaum, Lewellen, and Lease (1978) hypothesize that investors have some target in mind, and when this target is reached, they sell the stock. Categorization of results according to strategy and ownership indicates that reluctance to realize losses plays a role. The third row in Table V shows that when an investor first sells a stock he does not own, he earns only 0.79% in comparison to 2.18% when he owns the stock. In the first case, the investor is constrained. He either has to be able to lend the stock, or he has to buy back the shares. In the latter case, the investor faces no constraint at all. This difference could indicate that when the investor is less likely to be able to keep a losing position, he also displays more modest returns. 21 There is evidence of reluctance to realize losses, in the relationship between leverage and returns. An investor might be forced to close a position if he is highly leveraged (except when the investor sells something he owns). A major online brokerage firm in Finland determines investors allowed trading positions based on their (1) shareholdings and (2) balances kept in the broker s account. Because we do not have data on the second component, we proxy for overall leverage as follows: ( ) Trading Capitalt Leverage t =ln (5) Position Value t 1 when defined (i.e., the investor must have holdings at t 1). Trading capital is the value of buys, or the value of sells if the investor is known to sell first. The position value is the value of shareholdings at the close on day t 1. We form deciles based on this variable and calculate mean day trading event return for each category. Figure 5 shows that leverage has an almost monotonic impact on day trading event returns. Starting from an impressive return in excess of 2.5%, the return 20 There is evidence in the research to support the reluctance hypothesis. For example, Almazan, Brown, Carlson, and Chapman (2001) find that only 10% of mutual fund managers who are allowed to take short positions actually do so. In unreported analysis, we find that the relative frequency of the sell first, buy later strategy remains about the same over the entire sample period and that it is in fact below average in the start of the downturn in May 2000. This suggests that reluctance to assume short positions is the cause, not the market conditions. 21 In unreported work, we examine the returns from partial day trades (where the investor reverses at least 50% of the position accumulated during the trading day). We find the same pattern in returns across strategy and ownership categories but at a significantly lower overall level. This could be interpreted as evidence that day traders do partial day trades when things go awry. 19
3.0% Gross Return from a Round-Trip (%) 2.5% 2.0% 1.5% 1.0% 0.5% 0.0% Low 2 3 4 5 6 7 8 9 High Leverage (Deciles) Figure 5. Impact of Leverage on Day Trading Event Returns Amount of leverage is proxied by logarithm of the trading capital divided by portfolio value at yesterday s close, ignoring cases where the investor does own any shares. Mean gross returns of day trading events are calculated for each deciles formed on the basis of the leverage variable. The dashed line shows the 95% confidence interval around the mean. drops to approximately 0.5% when leverage becomes high. This is consistent with a conclusion that investors are unwilling to realize losses. If possible, they prefer to hold on to their losing trades. 22 B. Measuring Returns We investigate differences in the overall performance of day traders and the control group by comparing their daily capital-weighted average total returns. We also decompose this return into the rate of return earned on stocks held in the portfolio and the gain from intraday trading (e.g., if an investor buys stock, we call the change from purchase price to the close the intraday return). We calculate returns as capital-weighted averages to account for investors timevarying market participation; more weight is given to periods the investor is more highly invested in the market. We define trading, position, and total profits as follows: 22 In unreported work, we find that day traders are less likely to close their positions when the stock price moves against them. We proxy for a day trader s intention to day-trade by focusing on days he buys a stock and does not sell it after day trading in it at least once during the previous five trading sessions. The stock on average depreciates by 0.93% to the close on these days, while the change in value for buys that are not surrounded by day trading events is not significantly different from zero. 20
Π trading = max[buy volume sell volume, 0] P t max[sell volume buy volume, 0] P t 1 + value of sells value of buys (6) Π position = r t (n t 1 sell volume) P t 1 (7) Π total = Π trading +Π position (8) where P is the stock price at the close (t for today and t 1foryesterday),r is the stock s return from close to close, and n is number of shares held. In calculating the trading profit (6), we first record the gain from the trade to the close for buys and the gain from the previous close to the time of trade (i.e., the price at which the trade takes place) for sells. Then, we adjust the profit for the cash flows generated by the buys and sells. This definition of trading profit captures the effect of trading activity (including day trading activity) on performance; Barber and Odean (2000) attribute this difference to the spread. Our definition of the position profit (7) is the gain on shares held from close to close. The total profit (8) is the sum of these two components. We define the amount of capital (C) requiredto generatethe profit asfollows: C trading = value of buys + max(sell volume buy volume, 0) P t 1 (9) C position = (n t 1 sell volume) P t 1 (10) C total = C trading + C position (11) For Equation (9), we assume that buys precede sells. If the sell volume is higher than the buy volume (i.e., the investor is selling shares from the portfolio), we adjust capital by the price at the previous close (c t 1 ) times the sell volume exceeding the buy volume. The capital required by the position (10) is simply the value of shares at t 1, after subtracting shares that were possibly sold at t. The total capital (11) is the sum of the capital used in trading and the capital needed to uphold the position. By these definitions, the average capital-weighted total return over aperiodoft days can be calculated by taking the sum over all I stocks: I T i=1 t=1 r total = Π total,i,t I T i=1 t=1 C total,i,t (12) Table VI demonstrates the calculation of returns for three examples. 23 21
Table VI Example of Measuring Returns Three examples of calculation of capital-weighted average total return and its components are shown. In example 1, an investor buys 100 shares (with an average price of 1050/100 = 10.5). In example 2, the investor sells 100 shares, and in example 3, the investor buys 100 shares and sells 200 shares. Example (1) (2) (3) Yesterday s Close (P t 1) 10.0 10.5 11.0 Today s Close (P t) 10.5 11.0 10.0 Position Yesterday (n t 1) 500 600 500 Buy Volume 100 0 100 Sell Volume 0 100 200 Value of Buys 1,025 0 1,050 Value of Sells 0 1,100 2,200 + Value of Buys at t 1,050 0 0 Value of Sells at t 1 0 1,050 1,100 + Cash-Flow from Sells 0 1,100 2,200 Cash-Flow from Buys 1,025 0 1,050 = Trading Profit (Π trading ) 25 50 50 Position Profit (Π position) 250 250 300 Total Profit (Π total ) 275 300 250 + Value of Buys 1,025 0 1,050 + Net Sells 0 1,050 1,100 = Trading Capital (C trading ) 1,025 1,050 2,150 Position Capital (C position) 5,000 5,250 3,300 Total Capital (C total ) 6,025 6,300 5,450 Trading Component 0.4% 0.8% 0.9% Position Component 4.1% 4.0% 5.5% Total Return 4.6% 4.8% 4.6% C. Evaluating Performance Table VII reports capital-weighted trading, position, and total return estimates for day traders and the control group. Total return is reported (1) without commissions (Panel C), and (2) assuming that the commission per trade is 10 euros and 0.25% of the value of the trade (Panel D). This assumption of commissions is based on the lowest rate advertised by a major online brokerage firm in Finland at the time. A comparison of total returns shows that before commissions, day traders perform no better but no worse than investors in the control group. The average daily total returns for day traders are 0.093% compared to 0.102% for the control group, not significantly different. After assuming 10 euros plus 0.25% commission, the control group generates a significantly higher total return (0.095%) than the day traders (0.057%). This suggests that day traders are not trading on superior information. This finding is important because it shows that day traders, unlike devoted SOES bandits, are unable to earn returns that would justify their existence (Harris and Schultz, 1998). 23 In calculating returns, we ignore days when the investor appears to have a negative position. This decision does not affect the results because there are few such observations, but is consistent with the treatment in Grinblatt and Keloharju (2001). 22
Table VII Comparison of Performance of Day Traders and Control Group This table reports the capital-weighted average total return, the trading component, and the position component of the total return separately for day traders and the control group. All returns are reported in basis points. Means and medians reported in this table are calculated across investors. The total return is reported (1) without commissions and (2) assuming that commission per trade is 10 euros and 0.25% of the trade value. The position return is the rate of return an investor earns on stocks held in the portfolio from close to close. t-value (z-value from the Mann-Whitney test) reports the difference in means (in mean ranks) between day traders and investors in the control group. Panel A: Trading Component (No Commissions) Day Traders Control Group Mann- Period Mean Median s.e. Mean Median s.e. t-value Whitney z 1998 / I 2.43 0.00 0.38 0.03 0.00 0.11 6.3 25.6 1998 / II 2.65 0.00 0.36 0.17 0.00 0.07 6.8 23.7 1999 / I 2.36 0.03 0.39 1.00 0.00 0.19 3.2 24.9 1999 / II 1.74 0.60 0.91 4.50 0.00 0.53 5.9 34.9 2000 / I 3.87 0.87 0.59 0.81 0.00 0.26 4.8 27.7 All 3.68 1.10 0.44 0.82 0.01 0.24 9.0 40.0 Panel B: Position Component 1998 / I 24.20 20.73 0.33 26.00 22.49 0.15 4.9 8.5 1998 / II 10.67 0.00 0.70 3.69 5.74 0.34 9.0 11.3 1999 / I 14.73 13.03 0.31 13.59 12.07 0.16 3.2 3.5 1999 / II 47.37 40.22 0.65 44.32 37.81 0.32 4.2 5.5 2000 / I 17.90 13.23 0.50 9.73 6.56 0.26 14.5 22.2 All 5.61 9.45 0.38 11.02 10.45 0.19 12.7 13.5 Panel C: Total Return (No Commissions) 1998 / I 26.63 22.31 0.52 25.97 22.60 0.19 1.2 2.5 1998 / II 13.32 2.18 0.80 3.87 5.75 0.35 10.9 14.5 1999 / I 17.09 14.46 0.50 14.59 12.30 0.26 4.4 11.1 1999 / II 49.11 44.29 1.12 39.82 38.38 0.63 7.2 11.1 2000 / I 14.03 10.81 0.76 8.92 6.26 0.37 6.0 13.8 All 9.28 12.40 0.57 10.20 10.70 0.31 1.4 1.8 Panel D: Total Return (10 Euros per Trade + 0.25% of Trade Value) 1998 / I 25.16 21.58 0.51 25.65 22.49 0.19 0.9 4.9 1998 / II 11.41 1.01 0.79 3.53 5.87 0.35 9.1 12.4 1999 / I 15.26 13.67 0.50 14.14 12.18 0.26 2.0 6.8 1999 / II 46.72 42.32 1.13 39.15 38.14 0.64 5.8 8.4 2000 / I 18.38 13.25 0.77 9.58 6.56 0.37 10.4 20.5 All 5.66 10.58 0.58 9.50 10.46 0.32 5.8 9.2 Consists of only the first five months of year 2000. The performance records of the two investor categories vary across subperiods. Day traders perform better from late 1998 through the end of 1999, but during the peak of day trading in early 2000, their performance is significantly worse. These losses are weighted more heavily than earlier gains, because day traders were more heavily invested in the market during this period. The extent of the increase in their trading activity becomes apparent when we compare total returns with and without commissions. In early 1999, the difference in mean total returns without and with commissions for day traders is only 1.8 basis points (0.171% 0.153%), compared to 4.4 bps a year later. The position component of returns indicates that the reason for the poorer returns in early 2000 is the return day traders earn on their portfolios. 23
Table VIII Own Benchmark-Adjusted Position Returns This table shows a modified version of the Grinblatt and Titman (1993) own benchmark measure. The realized capital-weighted average position return is compared to the capital weighted average position return an investor would have earned had he held the same portfolio as one month earlier. Average returns are calculated over days when the investor is both (1) currently invested and (2) has a non-zero lagged portfolio to avoid effects of market timing. Returns are reported in basis points. It is required that the investor is invested in the market for at least a month. Day Traders Control Group Mann- Period Mean Median s.e. Mean Median s.e. t-value Whitney z 1998 / I 1.17 0.25 0.25 0.06 0.00 0.11 4.5 5.2 1998 / II 6.63 2.79 0.39 4.28 0.83 0.16 5.6 9.9 1999 / I 1.39 0.67 0.27 2.61 1.13 0.14 4.1 8.8 1999 / II 3.13 0.93 0.30 1.28 0.10 0.09 5.9 8.8 2000 / I 1.05 0.33 0.60 0.70 0.01 0.20 0.6 1.8 All 0.85 0.51 0.37 0.30 0.09 0.09 1.4 6.0 Consists of only the first five months of year 2000. The overall returns are driven largely by the position component, but the trading returns of day traders are consistently better than those earned by the control group. This could reflect the fact thatdaytradersaremorelikelyto sell stocks when they have appreciated from the previous close; 60.72% of all day trader sells take place at a price higher than the previous close compared to 59.51% for the control group (results not tabulated here). The difference of 121 bps is highly significant with a z-value of 10.3. If a day trader sells a stock after it has appreciated in value from the previous close, the resulting gain is recorded as a short-term (trading) profit. If an investor in the control group keeps the stock in the same situation, the resulting gain will be recorded as a position profit. It is possible that day traders may show similar performance to the control group and yet possess superior information, if they take less risk than the control group. To evaluate this proposition, we estimate the own benchmark adjusted measure of Grinblatt and Titman (1993). For each investor, we calculate the realized capital-weighted average total return and the return the investor would have earned had he held the portfolio he owned one month earlier. We assume an investor changes the position at each close without paying commissions. We require that the investor is both (1) currently invested in the market and (2) holder of a non-zero lagged portfolio to eliminate the effects of market timing. The estimates are reported in Table VIII. For the entire sample, the average day trader (investor in the control group) was approximately 0.9 bps (0.3 bps) worse off each day with his new portfolio. The difference between investor categories is highly significant with a t-value of 6.8. Like the results on total returns, this result militates against a conclusion that day traders have better stock picking skills than the control group. 24 24 In unreported work, we examine whether this result could be explained by increasing day trader risk aversion. We compare the number of investors switching to a strictly inferior portfolio (higher volatility, lower returns) to the number of day traders switching to a strictly 24
Table IX Day Trading Returns at Different Career Points This table shows the average rate of return day traders earn at three different career points. Returns are defined as follows: the return from the first day trade, the return from the last day trade, and the capital-weighted average return from all other day trades. Only investors who day traded on at least three different dates are included. Career Point Mean s.e. Median N First Day Trade 1.94% 0.11% 1.33% 3041 Other Day Trades 1.58% 0.06% 1.24% 3041 F -value 19.02 Last Day Trade 1.18% 0.08% 0.96% 3041 p-value < 0.001 V. Careers Why do day traders stop day trading, and what are their careers from the first day trade to the last like? Does their trading behavior remain similar throughout their careers, or are there systematic changes? For example, conditional on staying in the market, do day traders start to take on more risk? This section examines these questions. A. Comparison of Returns and Decision to Quit We have shown that trading losses have little effect on day trader selection of stock to trade. It is conceivable that losses still have a greater impact on day traders careers. A sufficiently large loss, or the accumulation of smaller losses, might persuade a day trader to exit the market. We look at this relationship in two ways. First, we compare returns day traders earn during different points in their careers. Second, we use a logistic regression to show that there is a monotonic relation between contemporary trading loss and the likelihood of exit. Table IX shows the gross returns investors earn on their first, last, and (on average) all other day trades. The sample is limited to day traders who day traded at least on three separate dates. The average day trader earns 1.94% on his first day trade, 1.58% on trades between the first and the last, and 1.18% on the last day trade. The mean returns differ significantly from each other, suggesting that there may be a relationship between returns and careers. Note that the aggregate gross returns from day trading are relatively constant over time (not reported). This means that the result in Table IX is unlikely to be due to careers coinciding with a downturn in the market. We examine the relationship between returns and the decision to quit by investigating to what extent cumulative trading returns help to explain day traders decision to exit. An investor enters the sample as he makes his first superior portfolio (lower volatility, higher returns). During the sample period, 37.39% of day traders were able to switch into a superior portfolio compared to 42.45% of the control group. This difference is highly significant with a t-value of 5.0; providing additional evidence to support the claim that day traders do not have superior information or skills than the control group. 25
day trade and exits the sample when he trades for the last time. The last trade is not required to be a day trade. Each day the investor trades constitutes a separate observation. The dependent variable takes the value of one if investor has day traded for the last time (including the day of the last day trade). We include all trading days after the last day trade to account for the possibility that day traders are reluctant to realize losses. If they are, the loss that makes them quit the market is not necessarily generated through a day trade but rather through a non-day trading event that was intended as a day trade. As explanatory variables, we include monthly dummies for all months starting with January 1998, a dummy for a day trading event, and dummies for the size of the cumulative trading loss. The results are shown in Table X. Block χ 2 indicates that the day trading event dummy and cumulative trading loss dummies help to predict the decision to cease day trading. For all cumulative trading loss dummies except the smallest (between 1% and 0%), losses significantly increase the likelihood that the day trader will no longer day-trade. The finding that small trading losses do not persuade an investor to quit is consistent with the results in Table II. The likelihood that the day trader will quit increases with the extent of the cumulative trading loss. This can be confirmed by running a linear regression b i =â + ˆb i + ε i, where b i is the ith loss coefficient in the model. The likelihood of exit increases significantly with the extent of loss with a t-value of 4.9. Together, these findings show that losses are a very important determinant of a day trader s decision to quit day trading. In unreported work, we find that day traders who are starting out (those making their first day trades) are more sensitive to small losses than day traders later in their careers. These results are not tabulated for the sake of brevity. B. Changes in Behavior Table XI reports results on whether a day trader changes his behavior as he stays in the market. We calculate the proportion of the most aggressive strategy (No Ownership, Sell First), trade size relative to the first day trading event, and amount of leverage. Panel A includes all day traders. Panel B restricts the sample to day traders who day-traded at least ten times. Panel B is included to illustrate that a survival bias does not affect the results. That is, it is not that less aggressive investors never day-trade more than, say, three times. The results show that day traders grow more confident or more aggressive as they remain in the market. First, they switch to more aggressive strategies. In Panel B, in only 8.1% of first day trade events does the day trader sell a stock he does not own; this proportion doubles by the fifth day trade. Second, day traders begin to make larger trades. For example, the median tenth day trade is over 50% larger than the first day trade. Third, estimates of the amount of leverage show that the results prevail not only because day traders become wealthier or invest more into the market, but also because they trade in larger quantities relative to their portfolios. 26
Table X Impact of Losses on Day Trader Decision to Leave the Market This table shows the results from an analysis of how losses affect a day trader s decision to quit. A day trader enters the sample as he makes his first day trade and leaves the sample as he trades (not necessarily a day trade) for the last time. Each day the investor trades is a single observation. The dependent variable in the multivariate logistic regression is set to one when investor has day traded for the last time (including that day), and zero for all days before this. Day Trade is a dummy that takes the value of one if investor day-trades. Cumulative trading loss is calculated by dividing trading profit (6) up to current day by trading capital (9). This cumulative trading loss is partitioned into 11 categories with dummy variables. An intercept and monthly dummies for all months starting with January 1998 are also included (not reported). Block χ 2 and Change in Pseudo-R 2 report how the model changes as variables other than the intercept and monthly dummies are added. Variable Coefficient t-value Day Trade 1.18 87.5 Cumulative Trading Loss [ 1%, 0%) 0.07 8.2 [ 2%, 1%) 0.29 16.0 [ 3%, 2%) 0.55 17.8 [ 4%, 3%) 0.63 13.0 [ 5%, 4%) 0.83 12.2 [ 6%, 5%) 0.88 9.5 [ 7%, 6%) 1.34 9.8 Model Summary [ 8%, 7%) 0.83 5.0 N 294,493 [ 9%, 8%) 1.01 5.7 Pseudo-R 2 4.8% [ 10%, 9%) 0.93 4.3 Block χ 2 (12) 7,584.3 < 10% 1.27 9.2 Change in Pseudo-R 2 2.8% VI. Conclusions The daily trading records of 7,686 investors classified as day traders, with complete limit order data for an intraday analysis of their trading behavior, allow an investigation of behavior and performance of day traders. Analysis of the factors that influence how day traders pick a stock to daytrade, indicates they day-trade in stocks that they either already own, have day traded before, or that have experienced high excess returns during previous trading sessions. Day traders concentrate their trading near the market opening and close. Because they prefer to first purchase and later sell, the net buy-sell ratio for round-tripping day traders decreases monotonically during the day. Day traders who are about to realize a loss from a round-trip do so very late in the trading session. An intraday analysis of trade execution shows that day traders attempt to go with the flow; they buy (sell) after an uptick (downtick) and after a buyer-initiated (seller-initiated) trade. They pay close attention to changes in the bid and ask prices and depth of the book, and are conscious of the spread. An analysis of the decision between active and passive limit orders reveals that day traders are more likely to submit liquidity when it is valued the most; the likelihood of a passive order increases with trade size and spread. The performance of day traders does not significantly differ from performance of a size-matched control group. It is thus unlikely that day traders are exploiting private signals or are engaged in profitable market making. A potential explanation for day trader failure to achieve superior returns is their 27
Table XI Changes in Behavior over Day Traders Careers Day traders careers are partitioned into eleven dates: (1) first ten day trading event days and (2) a single category that includes all day trading days larger than ten. Frequencies of the the most aggressive strategy ( No Ownership, Sell First ), size of each day trade relative to the first day trading event, and the amount of leverage (see Equation (5)) are calculated for each date. Mean, standard error (s.e.), and median (Md) are reported. Panel A includes all day traders. Panel B restricts the sample to day traders with at least ten trading day events to control for possible survival bias. Panel A: All Day Trading Events No Ownership, Size Relative to Sell First First Event Leverage Event Prop. s.e. Mean s.e. Md Mean s.e. Md N 1 7.2% 0.3% 1.03 0.01 1.00 1.33 0.02 1.41 8,355 2 9.6% 0.5% 1.88 0.07 1.04 1.16 0.03 1.28 4,688 3 11.2% 0.7% 2.10 0.07 1.13 1.07 0.03 1.10 3,362 4 12.5% 0.7% 2.33 0.11 1.18 0.98 0.03 1.00 2,787 5 14.7% 0.9% 2.49 0.14 1.28 0.90 0.04 0.94 2,296 6 15.3% 0.9% 2.70 0.13 1.31 0.86 0.04 0.91 2,012 7 16.5% 1.0% 2.87 0.16 1.35 0.83 0.04 0.91 1,746 8 16.5% 1.1% 2.93 0.19 1.34 0.84 0.05 0.89 1,565 9 15.1% 1.1% 3.08 0.24 1.35 0.83 0.05 0.82 1,426 10 16.5% 1.2% 2.90 0.23 1.44 0.84 0.05 0.91 1,267 > 10 22.2% 0.3% 3.82 0.06 1.57 0.59 0.01 0.81 24,868 Panel B: Sample Restricted to Day Traders with # Day Trading Events 10 No Ownership, Size Relative to Sell First First Event Leverage Event Prop. s.e. Mean s.e. Md Mean s.e. Md N 1 8.1% 0.9% 1.01 0.01 1.00 0.86 0.05 0.97 1,195 2 12.0% 1.1% 1.87 0.08 1.09 0.80 0.05 0.81 1,219 3 12.9% 1.1% 2.17 0.09 1.23 0.78 0.05 0.85 1,236 4 12.5% 1.1% 2.53 0.20 1.29 0.76 0.05 0.85 1,267 5 14.2% 1.2% 2.55 0.20 1.29 0.80 0.05 0.81 1,258 6 16.1% 1.2% 2.89 0.18 1.39 0.78 0.05 0.84 1,283 7 16.9% 1.2% 2.92 0.19 1.39 0.81 0.05 0.90 1,278 8 17.0% 1.2% 2.96 0.19 1.38 0.81 0.05 0.88 1,277 9 15.1% 1.2% 3.01 0.24 1.38 0.82 0.05 0.82 1,300 10 16.5% 1.2% 2.90 0.23 1.44 0.84 0.05 0.91 1,267 > 10 22.2% 0.3% 3.82 0.06 1.57 0.59 0.01 0.81 24,868 tendency to hold on to losers, and perhaps consequently to exhibit poor stock selection skill. This paper also demonstrates that trading losses influence day traders decision to quit the market. A day trader earns the highest return from his first day trade and the lowest from his last trade. Moreover, the likelihood of exiting increases with the extent of the current trading loss. Finally, conditional on remaining in the market, day traders become more confident and aggressive as their careers progress; they more often sell stocks that they do not own, trade in larger sizes, and become more highly leveraged. The decision to try day trading again after successful first day trade resembles the behavior of problem gamblers. Turner, Littman-Sharp, Zengeneh, and Spence (2003, pp. 3) find that problem gamblers were significantly more likely than non-problem gamblers to have experienced a win the first time they gambled. A number of potentially fruitful research avenues are not explored in this 28
paper. Barber and Odean (2001b) and Campbell, Lettau, Malkiel, and Xu (2001), point to day trading as a possible explanation for increased idiosyncratic volatility. We might ask whether day traders stabilize a market because they are net suppliers of liquidity, or destabilize the market because of the strategies they employ, or perhaps because of their demand for liquidity near the open and the close? 25 It would also be interesting to examine how the bear market that started in 2000 affected day trader behavior, as well as what type of day trader remained in the market. Appendix: Matching Data Sets Much of the analysis relies on a matching procedure that combines two data sets: (1) the Finnish Central Securities Registry, which includes the daily trading records of all investors, and (2) limit order data, which provide information on all orders and trades for the underlying market, the Helsinki Exchanges. We create a match separately for each day and each stock. If there is only a single transaction during a day, the trading record data will include two entries (one for the buyer and one for the seller), which can be directly matched to the trade. If there is more than one transaction, as usually is the case, the matching procedure is as follows. Table XII provides examples. In the first stage, we identify trades that have a unique price/volume combination, and thus can be identified with certainty. For example, trade number 1 in the limit order data is unique because no other trade took place at price 10.00 and had a volume of 100 shares. This can be directly matched with two trading record entries, numbers 1 and 15 (negative volume indicates a sell). By the same principle, all entries in the limit order data except for entries 4, 8, and 9 can be matched using the trading record data. In the second stage, the results from this initial match for the entire sample can be used to assess the brokers different investors use the most. Using this information, we determine whether there are trades that are unique with respect to broker; that is, there are no two or more trades than have the same price, volume, and broker, and only one investor with a potentially potentially matching trading record (correct price and volume), has been determined to use this broker. For example, three of the remaining trades took place at 10.20 and had a volume of 150 shares. These trades have brokers 3, 4, and 1 as the buyer, respectively, and there are three possible investors, 3, 5, and 7. After the match in stage 1, it can be determined that investor 5 is using broker 3. This leads us to match trade number 8 (investor 5 who uses broker 3) with trade 4 (a trade 25 The literature documents that SOES bandits do not have an adverse effect on the market (Battalio, Hatch, and Jennings, 1997; Foucault, Röell, and Sandås, 2003). Yet SOES bandits use a very distinctive day trading strategy that is closer to arbitrage than it is to speculation. Hence, the question whether the increase in day trading activity near the end of the millennium affected volatility remains. 29
Table XII Example of Matching of Trading Records and Limit Order Data This table shows a hypothetical example of matching trading record data and limit order data for a single stock on a single day. There are 10 trades and 20 trading record entries (10 for the buyers and 10 for the sellers). In the first stage of the matching, trades with unique volume/price combinations are identified and matched with corresponding trading record entries. In the second stage, this initial match over the entire sample is used to infer which broker each investor uses the most. This information is used to match trades that appear to be unique with respect to volume, price, and broker. In the third stage, ambiguous cases are matched by randomly selecting a trading record entry with the correct price and volume, and a preference for the correct broker is given. Column match stage displays at which stage the trading record entry is combined with the limit order data entry. Trading Record Data Limit Order Data Match Broker Match Stage # Inv. Size Pri. Stage Size Pri. Buy Sell Buy Sell 1 1 100 10.00 1 100 10.00 1 2 1 1 2 1 1,000 10.10 1 200 10.00 2 3 1 1 3 1 300 10.20 1 100 10.20 3 3 1 1 4 2 125 10.25 1 150 10.20 3 2 2 3 5 3 150 10.20 3 1,000 10.10 1 1 1 1 6 4 200 10.00 1 300 10.20 1 2 1 1 7 5 100 10.20 1 125 10.25 1 2 1 1 8 5 150 10.20 2 150 10.20 4 3 3 3 9 6 100 10.10 1 150 10.20 1 2 3 3 10 7 150 10.20 3 100 10.10 1 2 1 1 11 8 1,000 10.10 1 12 9 100 10.20 1 13 9 200 10.00 1 14 10 150 10.20 3 15 10 100 10.00 1 16 11 125 10.25 1 17 12 300 10.20 1 18 13 150 10.20 3 19 14 100 10.10 1 20 14 150 10.20 3 with broker 3 as the buyer). 26 In the third stage, we match the remaining cases. For each trade that has not been matched in the previous two stages, we randomly draw an unmatched trading record entry with the correct price and volume. For each trade, trading records that have correct price, volume, and broker are preferred over records that only have correct price and volume. For example, on the sell side, both investors 10 and 14 are known to use broker 2 as a result of the match in the first stage. They are potential sellers in the trades 4, 8, and 9 who have brokers 2, 3, and 2 as the seller, respectively. Hence, we randomly match trading record entries 14 (investor 10) and 20 (investor 14) with trades 4 and 9 (both have broker 2 as the seller). After this, only trading record entry 18 remains to be matched with the trade 8. Similarly, on the buy side, either investor 3 or 7 could be the buyer in either trade 8 or 9, because the broker these investors are using has not been identified. We randomly match these trading record entries with trades. The matching process described allows us to match 74.8% of all trading 26 In the actual matching process, we use the entire sample to determine the brokers each investor uses. Here, for the sake of clarity, we use only data given in Table XII. 30
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