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Abstract Rational models claim “trading to learn” explains widespread excessive speculative trading and challenge behavioral explanations of excessive trading. We argue rational learning models do not explain speculative trading by studying day traders in Taiwan. Consistent with previous studies of learning, unprofitable day traders are more likely than profitable traders to quit. Consistent with models of overconfidence and biased learning (but not with rational learning), the aggregate performance of day traders is negative; 74% of day trading volume is generated by traders with a history of losses; and 97% of day traders are likely to lose money in future day trading. Received: March 4, 2019; Editorial decision: May 16, 2019 by Editor: Jeffrey Pontiff. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online. This paper contributes to a debate about whether individual investors trade excessively and, if so, why. Noting that psychologists find that people tend to be overconfident, several theoretical models of overconfidence show that, in a variety of theoretical settings, investors trade more actively if they are overconfident and thereby lower their utility (Odean 1998; Daniel, Hirshleifer, and Subrahmanyan 1998, 2001; Kyle and Wang 1997; Gervais and Odean 2001; Caballe and Sakovics 2003). A series of papers analyzing the trading records of individual investors report findings consistent with these models of investor overconfidence: in the year following stock trades, the stocks purchased by individual investors at a U.S. discount brokerage (1987–1993) underperform the stocks they sold (Odean 1999); unsophisticated Finnish investors underperform all other investors on the Helsinki Stock Exchange (1995–1996) (Grinblatt and Keloharju 2000); the portfolios of the most active investors at a U.S. discount brokerage (1991–1996) underperform those of less active investors (Barber and Odean 2000); and, in this same data set, women, who tend to exhibit less overconfidence than men in areas such as finance, trade less actively than men and reduce their returns less through active trading than do men (Barber and Odean 2001). Analyzing all stock trades by all investors on the Taiwan Stock Exchange from 1991 to 1995, Barber et al. (2009) find that after transactions costs active trading reduces the return of the aggregate individual investor portfolio by 3.8 percentage points a year, the equivalent of 2.2% of Taiwan’s gross domestic product (GDP). Glaser and Weber (2007) match survey data to trading records for individual investors and document investors-based scores of overconfidence correlate with trading activity. Biais et al. (2005) use an experimental asset market to document calibration-based overconfidence reduces trade performance, and Deaves, Luders, and Luo (2008) provide experimental evidence that calibration-based overconfidence induces additional trade.1 As many of these papers acknowledge, excessive trading could result for reasons other than overconfidence, such as a desire for entertainment, or from a combination of overconfidence and other motives. Grinblatt and Keloharju (2009) find that Finnish investors who get more speeding tickets trade more actively which they attribute to sensation seeking. Dorn and Sengmueller (2009) match survey responses and administrative records at a German broker and document investors who report enjoying gambling have twice the turnover rates of their peers. The introduction of a national lottery in Taiwan reduced trading on the Taiwan Stock Exchange by about one fourth (Barber et al. 2009; Gao and Lin 2014); Dorn, Dorn, and Sengmueller (2015) provide similar evidence using California, multistate U.S., and German lotteries. Linnainmaa (2010) argues that the underperformance of individual investors results from unmonitored limit orders. Rational learning models are offered as alternative explanations for excessive speculative trading (Mahani and Bernhardt 2007; Linnainmaa 2011; Seru, Shumway, and Stoffman (2010); Lubensky and Smith 2017). Mahani and Bernhardt (2007, p. 1334) write that their model indicates “Most inexperienced traders realize losses, conclude that they are unlikely to be skilled, and leave the markets; survivors expand their trades and make more profits. Learning produces the aggressive trading that is traditionally attributed to psychological biases.” Linnainmaa (2011) writes “When agents can learn about their abilities as active investors, they rationally ‘trade to learn’ even if they expect to lose from active investing…. a stylized learning model approximates household trading decision remarkably well.” Seru, Shumway, and Stoffman (2010, p. 733) conclude “an open question in the literature is why there is such high trading volume, particularly among seemingly uninformed individual investors. Our results indicate that such trading may be rational; investors may be aware that they will learn from experience and trade in order to learn.” While these papers do not dismiss behavioral motives for trade, they make the case that learning alone can explain why individuals engage in so much speculative trading. In these models, investors do not initially know their own abilities and rationally infer their abilities by observing their trading performance. Investors are aware that most speculators lose money, but believe that these losses are small compared to the profits of successful speculators. Thus, risk-averse investors rationally try speculation because they believe expected lifetime profits are positive. Unsuccessful investors conclude that they lack or are unable to acquire ability and quit trading speculatively; successful investors continue to speculate and make profits doing so. Gervais and Odean (2001) also develop a model in which investors with different abilities do not initially know their own ability (i.e., the precision of their information) and infer ability by observing their trading performance. In this model of biased learning, self-attribution bias leads investors to update more on successes than on failures. Thus, successful investors become overconfident and unsuccessful investors are slow to realize that they have low ability and to curtail their trading. The qualitative predictions of the rational learning model of Mahani and Bernhardt (2007) and the biased learning model of Gervais and Odean (2001) are the same. Investors increase their trading in response to successful trades and decrease their trading in response to unsuccessful trades. The difference in these models is in the speed with which investors respond to feedback. Biased traders learn slowly. We test the predictions of rational learning models by analyzing the performance of day traders in Taiwan. Using the complete transaction data for the Taiwan Stock Exchange over 15 years (1992 to 2006), we focus on individual investors who engage in day trading, the purchase and sale of the same stock within a day.2 We choose to study day traders because day trading is almost surely speculative behavior. Individual investors in general may trade speculatively, but they also trade to meet liquidity demands, manage taxes, and rebalance their portfolio allocations. Round-trip trades of the same stock in the same day are unlikely to be intended to address these needs. Previous tests of rational learning models of trading have primarily focused on confirming evidence; for example, do investors increase (decrease) trading in response to successful (unsuccessful) trades? Seru, Shumway, and Stoffman (2010) document unsuccessful Finnish speculators are more likely to stop trading and that some speculators get better at trading with experience. Campbell, Ramadorai, and Ranish (2014) document that previously successful Indian investors trade more aggressively. Linnainmaa (2011) finds that Finnish investors are more likely to increase trade size after successful trades and more likely to decrease trade size or quit trading after unsuccessful trades. Furthermore, the size and quitting effects are stronger early in an investor’s career, when his or her prior beliefs about ability are more diffuse. Using U.S. broker data, Nicolosi, Peng, and Zhu (2009) show that trade intensity increases following signals of strong performance. Analyzing data from the National Stock Exchange in India, De et al. (2010) document that investors increase trading in response to recent profits and that the sign of profits matters more than their magnitude. We, too, find evidence of learning among day traders. The majority of day traders quit relatively quickly (more than 75% of all day traders quit within 2 years), and poor performers are more likely to quit. These results are consistent with the models of both rational and biased learning. However, to properly test a model it is important to look for disconfirming evidence. We document behavior inconsistent with rational Bayesian learning as modeled by Mahani and Bernhardt (2007), Linnainmaa (2011), and Lubensky and Smith (2017) for two reasons. First, if the entry (and exit) of speculators is stable over time, then the sign of the expected lifetime profits of new speculators is the same as that of aggregate speculator profits. Therefore risk-averse (or risk-neutral) potential speculators with no special prior knowledge of their abilities should only “trade to learn” if aggregate speculator profits are positive.3 In fact, using complete data for the Taiwan market, the aggregate performance of day traders net of fees is negative in each of the 15 years that we study. A profit-maximizing risk-averse Bayesian investor would not enter a market if her expected lifetime profits were negative. Of course, a few investors with unusual abilities, such as extraordinary mathematical skills, might rationally anticipate becoming successful day traders. We do not dispute that it may be rational for some day traders to enter the market or that some learn rationally. However, we argue that entry and learning for the purpose of profits cannot explain a material portion of the observed day trading, because the vast majority of day traders have a history of losses, and traders with a history of losses generate most day trading. If most Taiwanese day traders undertake day trading because they believe day trading has positive lifetime expected profits, they are mistaken and overconfident. Conditional on that overconfidence, entry may look reasonable. But this behavior is consistent with the overconfidence theories, not with rational trading to learn. Second, though performance affects day trader persistence, many traders continue to day trade after extended periods of losses. In one analysis, we measure how past performance affects traders’ willingness to continue. Specifically, we sort traders based on the number of days they have engaged in day trading as of the end of the previous month and on the past profitability of their intraday trades net of trading costs. Previously unprofitable traders with 50 or more days of past day trading experience have a 95.3% probability of day trading again in the next 12 months, whereas previously profitable traders with 50 or more days of past day trading experience have a 96.4% probability of doing so. So experienced day traders with histories of losses not only persist in day trading but also do so at nearly the same rate as those who have been profitable. We also document that 97% of day traders and over 90% of day trading volume can be traced to investors who, based on their past experience and performance, are likely to lose money in future day trading. These figures include novice day traders who should expect to lose given the aggregate performance of day traders is negative. Perhaps more tellingly, 65% of day traders and 74% of day trading volume can be traced to investors with day trading experience and a history of losses. To reach these conclusions, we sort day traders into six groups based on their past experience. Within each experience group, we further partition investors based on whether their past profits net of trading costs are positive or negative. Thus, we are left with twelve groups based on the double-sort of past experience and past profitability. Among these twelve groups, only the profitable and most experienced investors predictably earn future profits net of trading costs. However, on average, these investors represent less than 3% of all day traders each day and less than 10% of all day trading volume.4 Put differently, each day 97% of day traders can expect to lose money from trading and more than 90% of all day trading volume can be traced to investors who predictably lose money. These figures include novice day traders (defined as an investor with less than 10 days of day trading experience). When we exclude these novice investors, 65% of day traders and 74% of day trading volume can be traced to those with more than 10 days of day trading experience and a history of losses. Given the overwhelming lack of profitability of day traders and the persistence of trading in the face of losses, rational trading to learn cannot account for “high trading volume … among seemingly uninformed individual investors” (Seru, Shumway, and Stoffman 2010, p. 733). Economists have long debated whether investors with mistaken beliefs in asset markets can survive (Friedman 1953). Delong et al. (1991) demonstrate that investors with biased beliefs may earn higher returns from bearing more market risk and, as a result, survive in aggregate in equilibrium. However, in Taiwan, individual investors who day trade account for large fractions of trading volume and, in aggregate, significantly underperform the market. On average, day traders persist in trading in the face of losses while those who eventually quit are replaced by new day traders. These results indicate that overconfident traders or traders with nonpecuniary trading motives (e.g., entertainment or gambling) can represent a large fraction of the trading population over extended periods of time. 1. Learning by Speculators The suggestion that investors learn from experience is neither novel nor controversial.5 Learning is a ubiquitous feature of human experience. From a welfare and policy perspective, the question is not whether investors learn, but how well they learn. In this section we develop testable predications that emanate from a rational model of learning and highlight the predictions that would discriminate between rational and biased models of learning. Mahani and Bernhardt (2007) argue that rational Bayesian learning can explain several empirical regularities: cross-sectionally, most speculators lose money; large speculators outperform small speculators; past performance positively affects subsequent trade intensity; most new traders lose money and cease speculation; and performance shows persistence. With a view similar to Mahani and Bernhardt (2007), Linnainmaa (2011) develops a structural model of rational learning. Using trading data from Finland, he finds investors with poor performance are likely to quit and trading intensity increases following good performance. The “trading to learn” literature argues that investors rationally try their hands at speculation to make profits. These investors are not trading for entertainment nor are they risk-seeking. Consider a risk-neutral investor with a zero discount rate,6 no utility or disutility from the activity of trading, and no opportunity cost for his capital. At time t, he chooses to speculate if his expected lifetime profits from speculation are positive conditional on his information set at t, Ωt. Let t = 0, be the time at which an investor who has never speculated decides whether or not to do so. The rational investor will only speculate if E(Lifetime Profits|Ω0)>0 . Prior to acquiring speculation experience, the average investors’ unconditional expected lifetime profits from speculation are the average lifetime profits of other investors who undertake speculation. While any given investor’s conditional lifetime profits from speculation may be higher than average, the average investor who engages in speculation should expect to earn average lifetime profits. A person who is considering day trading (call him a prospective trader) is unlikely to know with precision the lifetime profits of existing day traders. The prospective trader may form beliefs based on a biased information set (e.g., what he hears from other traders or news in the market). Friends who trade may share successes and be reluctant to share less successful picks. This selective sharing may bias the beliefs of the prospective trader and cause him to be overconfident about his trading ability. In Section 5, we provide some support for this idea as we show new day traders enter the market following periods of strong market returns and strong aggregate day trader performance. If the speculative market is in equilibrium, that is, speculator profits and the numbers of speculators entering and leaving are stable, and if unsuccessful speculators exit the market faster than successful speculators, then the sign of the unconditional expected lifetime profits from speculation is the same as the sign of the average annual profit from speculation. To see this, consider a market in which N new speculators enter the market each year; n, 0 < n < N, new speculators either are skilled or have the ability to acquire skill (prior to entry the potential speculator cares about his lifetime expected profits, regardless of whether these result from innate skill or learning and, because we have assumed a zero discount rate, the timing of the profits is not important); N-n new speculators are unskilled with no ability to acquire skill. Unskilled speculators trade for 1 year, lose 1 dollar, and quit. Skilled speculators trade for Y > 1 years, earn a profit of S > 0 dollars each year, and quit (retire). Because skilled speculators stay in the market longer than unskilled speculators (i.e., Y > 1), skilled speculators account for a greater fraction of active speculators than of new speculators (i.e., Y*n / (Y*n + N - n ) > n/N). The unconditional expected lifetime profits of a new speculator are E(Lifetime Profits)=n*Y*SN−N−nN=n(Y*S+1)−NN. (1) The average expected profits of an active speculator in any year are Average Annual Profits=n*Y*S−(N−n)n*Y+(N−n)=n(Y*S+1)−NN+n*(Y−1). (2) Average annual profits, that is, aggregate annual profits divided by the number of all speculators trading in a year, are of the same sign but lower magnitude than expected lifetime profits. Thus, when average annual profits are negative, they provide an upper bound to the unconditional expected lifetime profits of a speculator. Furthermore, because skilled speculators stay in the market longer than unskilled (i.e., Y > 1), in equilibrium the proportion of speculators in the market at any time who have skill is greater than the unconditional probability that a new speculator has skill. Thus, if traders have rational prior beliefs about the unconditional expected lifetime profits from engaging in speculation (and are engaging in speculation for the purpose of earning lifetime profits), then the aggregate performance of speculators should be positive.7 This leads to our first null hypothesis: H1: The aggregate net performance of day traders is positive (nonnegative). The alternative is that the aggregate net performance of day traders is negative. This is consistent with traders holding biased prior beliefs about the unconditional expected lifetime profits from trying day trading. Once a trader engages in speculation, he begins to acquire feedback about his potential skill. In the rational learning models, unsuccessful traders quit trading after the accumulation of negative signals outweighs their positive initial prior beliefs about their ability. Gervais and Odean (2001) develop a model in which investors take too much credit for their success and thus, relative to a Bayesian, overweight successes when learning about their ability. In their model, too, successful investors have more ability than unsuccessful ones and investors respond to good performance by trading more aggressively. In contrast to the rational Bayesian model, their model can also explain persistent trading by previously unsuccessful traders; these traders put too much weight on successes and too little on failures when updating beliefs about their abilities. Consider a trader who began speculation believing he had positive expected lifetime profits. Given net positive feedback, he will continue to speculate; but at some threshold of negative feedback, he should quit. Consider a trader who began speculation believing he had negative expected lifetime profits. Entry was not a rational decision, and while there is a threshold of positive feedback at which it may be rational to continue trading, persistent trading in the face of losses is not consistent with the models of rational learning. If traders began speculation with the rational prior belief that their expected lifetime profits from speculation were positive, an econometrician could specify and calibrate a model of quitting behavior. The econometrician could estimate the probability of negative future profits conditional on trading histories and test whether traders quit at the point at which their trading histories forecast future losses. However, when traders begin speculation with negative expected lifetime profits from speculation, the point at which they should rationally quit speculation is before they even start, regardless of their learning process. When traders who should have negative priors continue to trade in the face of negative feedback, it is difficult to disentangle whether persistence is due to extremely biased priors or biased learning. We present evidence of remarkable trading persistence in the face of losses; for example, nearly three-fourths of day trading volume is generated by unsuccessful day traders with at least 10 days of day trading experience and, in an average month, only 9% of those day traders who have 400 or more days of day trading experience have earned positive lifetime intraday net returns. This perverse persistence might result from biased prior beliefs, biased learning, or both. However, as feedback grows, rational learning models predict that even speculators who began with positively biased priors should quit in the face of losses. H2: Experienced day traders with previous net losses will stop trading speculatively. Under Gervais and Odean’s biased learning model, it is possible for unsuccessful traders to become overconfident and, thus, more active traders, if their learning bias is sufficient. Thus, continuing to trade by experienced unprofitable day traders is contrary to the rational learning models but consistent with biased learning. 2. Data and Methods 2.1 Day traders and speculative trading Empirical tests of the learning models must identify traders who trade speculatively. Investors might reasonably trade to save (or consume), to rebalance their portfolios, or to reduce their tax liability. Thus, an important feature of our empirical strategy is to identify a clean sample of speculators. We do so by focusing on day trading on the Taiwan Stock Exchange. Day trading is the purchase and sale of the same stock by an investor on a day. We argue that these intraday trades are almost certainly speculative. Moreover, day trading is common and prevalent in Taiwan. We are not the first to study day trading, though the sample of day traders we study is much larger and the time series much longer than those in prior studies.8 The one exception to this generalization is Barber et al. (2014), who identify a small subset of day traders (less than 1% of the day trading population) that predictably earns profits. None of these prior studies used the empirical setting to test rational and biased models of learning, the focus of our investigation. 2.2 Taiwan market rules The Taiwan Stock Exchange (TSE) operates in a consolidated limit order book environment where only limit orders are accepted. During the regular trading session, from 9:00 a.m. to noon during most of our sample period, buy and sell orders can interact to determine the executed price subject to applicable automatching rules.9 Minimum tick sizes are set by the TSE and vary depending on the price of the security. Generally, orders are cleared using automatching rules one to two times every 90 seconds throughout the trading day. Orders are executed in strict price and time priority. An order entered into the system at an earlier time must be executed in full before an order at the same price entered at a later time is executed. Although market orders are not permitted, traders can submit aggressive price-limit orders to obtain matching priority. During our study period, there is a daily price limit of 7% in each direction and a trade-by-trade intraday price limit of two ticks from the previous trade price. Our analysis focuses on day trading, so transaction costs are an important consideration. The TSE caps commissions at 0.1425% of the value of a trade. Some brokers offer lower commissions for high-volume traders. Officials at brokerage firms and the TSE indicated to us that the largest commission discount offered is 50% (i.e., a commission of roughly 7 basis points [bps]); these same officials estimated the trade-weighted commission paid by market participants to be about 10 bps. We use the 10 bps when calculating returns net of fees. Taiwan also imposes a transaction tax on stock sales of 0.3%. 2.3 Trades data and descriptive statistics We use a unique and remarkably complete data set, which contains the entire transaction data, underlying order data, and the identity of each trader on the Taiwan Stock Exchange (TSE). With these data, we provide a comprehensive accounting of the profitability of day traders during the period 1992 through 2006. The trade data include the date and time of the transaction, a stock identifier, order type (buy or sell -- cash or margin), transaction price, number of shares, a broker code, and the identity of the trader. In total, the data set contains 3.7 billion purchase (or sale) transactions with a value of $NT 310 trillion (approximately $10 trillion US).10 The trader code allows us to broadly categorize traders as individuals, corporations, dealers, foreign investors, and mutual funds. The majority of investors (by value and number) are individual investors. Corporations include Taiwan corporations and government-owned firms (e.g., in December 2000 the government-owned Post, Banking, and Insurance Services held over $NT 213 billion in Taiwanese stock).11 Dealers include Taiwanese financial institutions such as Fubon Securities, Pacific Securities, and Grand Cathay Securities. Foreign investors are primarily foreign banks, insurance companies, securities firms, and mutual funds. During our sample period, the largest foreign investors are Fidelity Investments, Scudder Kemper, and Schroder Investment Management. Mutual funds are domestic mutual funds, the largest of which is ABN-AMRO Asset Management, with $NT 82 billion invested in Taiwanese stocks in December 2000. We define day trading as the purchase and sale, in any order, of the same stock on the same day by an investor. Specifically, if an investor buys and sells the same stock on the same day, we calculate the number of shares bought (Sb), the number of shares sold (Ss), the average purchase price (Pb), and the average sales price (Ps). The value of day trading is defined as half of the total value of sales and purchases (½*Pb*min(Sb,Ss)+ ½*Ps*min(Sb,Ss)). Over our sample period, aggregate day trading accounts for more than 19% of the total dollar value of aggregate trading volume. Virtually all day trading can be traced to individual investors. In the average month, individual investors account for over 99% of all day traders (and 95% of day trading volume). Individuals and corporations are free to short sell, though dealers, mutual funds, and foreigners are prohibited from doing so on the TSE. These short sale restrictions might partially explain the tendency for day trading to concentrate among individual investors. In contrast to U.S. markets, dealers are not active providers of liquidity. TSE rules state that dealers are required to efficiently adjust the demand and supply in the market depending on the market situation, and ensure that the formation of fair price and its sound operation are not harmed, yet dealers do not face specific penalties for failing to meet this requirement. Dealer trades emanate from their proprietary trading activity. Based on our discussions with dealers in the TSE, the majority of this proprietary trading is not necessarily intended to provide liquidity. Chae and Wang (2003) also report that TSE dealers are not net providers of liquidity. In the remainder of the paper, we focus on individual investors. In Figure 1, we plot day trading (round-trip trades of the same stock by the same investor on the same day) as a percentage of total trading volume and the number of individuals who day trade by month. While day trading was somewhat less prevalent in the early part of our sample period, the share of volume traced to day trading has been consistently around 20% of total trading volume from 1995 to 2006. In the average month, almost 140,000 individuals day trade.12 With an adult population of about 16 million (total population about 22 million), this means just shy of 1% of the adult population day trades in the average month. In terms of both a percentage of total trading volume and numbers of traders, day trading is an equilibrium feature of the Taiwan stock exchange with no apparent trend over the period 1997 through 2006. Most day traders do not trade on many days. For example, in the average year a day trader will trade on 42.9 days and executes round-trip day trades on 12.9 days; the median day trader trades on only 18.9 days and day trades on 3.1 days. (See Table A1 of the Online Appendix for more details about the distribution of day trader activity by year.) Because of this skewed distribution of day trading activity, in many analyses we focus on day traders with a history of day trading. Figure 1 Open in new tabDownload slide Day trading as a percentage of total volume and number of individual day traders The figure presents the 12-month moving average for (1) the number of individual investors who engage in day trading and (2) day trading as a percentage of total trading volume. Figure 1 Open in new tabDownload slide Day trading as a percentage of total volume and number of individual day traders The figure presents the 12-month moving average for (1) the number of individual investors who engage in day trading and (2) day trading as a percentage of total trading volume. Table 1 Gross and net abnormal intraday returns from day trading, 1992 to 2006 . Gross . Net . . . . α (%) . t-stat . α (%) . t-stat . Beta . R-sq . All years −0.070 −10.20 −0.239 −34.78 0.26 43% 1992 0.018 0.57 −0.091 −2.91 0.37 49% 1993 −0.089 −3.40 −0.206 −7.80 0.33 59% 1994 −0.119 −5.03 −0.275 −11.65 0.32 58% 1995 −0.047 −2.18 −0.221 −10.23 0.24 45% 1996 −0.088 −4.90 −0.245 −13.58 0.26 48% 1997 −0.089 −3.27 −0.271 −10.00 0.26 39% 1998 −0.067 −3.13 −0.256 −11.99 0.21 43% 1999 −0.053 −1.91 −0.224 −8.04 0.25 42% 2000 −0.007 −0.18 −0.190 −5.23 0.23 36% 2001 −0.088 −2.43 −0.279 −7.68 0.24 37% 2002 −0.104 −3.47 −0.289 −9.67 0.23 39% 2003 −0.100 −4.39 −0.280 −12.34 0.22 38% 2004 −0.062 −2.51 −0.244 −9.90 0.22 39% 2005 −0.087 −5.00 −0.280 −16.23 0.28 41% 2006 −0.089 −4.07 −0.277 −12.82 0.26 38% . Gross . Net . . . . α (%) . t-stat . α (%) . t-stat . Beta . R-sq . All years −0.070 −10.20 −0.239 −34.78 0.26 43% 1992 0.018 0.57 −0.091 −2.91 0.37 49% 1993 −0.089 −3.40 −0.206 −7.80 0.33 59% 1994 −0.119 −5.03 −0.275 −11.65 0.32 58% 1995 −0.047 −2.18 −0.221 −10.23 0.24 45% 1996 −0.088 −4.90 −0.245 −13.58 0.26 48% 1997 −0.089 −3.27 −0.271 −10.00 0.26 39% 1998 −0.067 −3.13 −0.256 −11.99 0.21 43% 1999 −0.053 −1.91 −0.224 −8.04 0.25 42% 2000 −0.007 −0.18 −0.190 −5.23 0.23 36% 2001 −0.088 −2.43 −0.279 −7.68 0.24 37% 2002 −0.104 −3.47 −0.289 −9.67 0.23 39% 2003 −0.100 −4.39 −0.280 −12.34 0.22 38% 2004 −0.062 −2.51 −0.244 −9.90 0.22 39% 2005 −0.087 −5.00 −0.280 −16.23 0.28 41% 2006 −0.089 −4.07 −0.277 −12.82 0.26 38% This table presents the daily percentage alpha from aggregate day trading of day traders. Day traders are defined as any trader who places a round-tip day trade in month t. Day trading is defined as round-trip trades by the same stock, investor, and day. In month t, all trades of day traders are included in the analysis. The alphas are estimated using the following regression of daily returns: (Rpt-Rft)=αp+βp(Rmt-Rft)+εpt, where Rpt, Rmt, and Rft are the portfolio return, market return, and risk-free return (respectively). The gross day trading return is calculated from daily round-trip trades plus the intraday returns on open trades; an open trade is a trade made during the day that results in an outstanding position at the close of the day. The net day trading return assumes a 10 bps round-trip commission and a 30 bps transaction tax on sales. Open in new tab Table 1 Gross and net abnormal intraday returns from day trading, 1992 to 2006 . Gross . Net . . . . α (%) . t-stat . α (%) . t-stat . Beta . R-sq . All years −0.070 −10.20 −0.239 −34.78 0.26 43% 1992 0.018 0.57 −0.091 −2.91 0.37 49% 1993 −0.089 −3.40 −0.206 −7.80 0.33 59% 1994 −0.119 −5.03 −0.275 −11.65 0.32 58% 1995 −0.047 −2.18 −0.221 −10.23 0.24 45% 1996 −0.088 −4.90 −0.245 −13.58 0.26 48% 1997 −0.089 −3.27 −0.271 −10.00 0.26 39% 1998 −0.067 −3.13 −0.256 −11.99 0.21 43% 1999 −0.053 −1.91 −0.224 −8.04 0.25 42% 2000 −0.007 −0.18 −0.190 −5.23 0.23 36% 2001 −0.088 −2.43 −0.279 −7.68 0.24 37% 2002 −0.104 −3.47 −0.289 −9.67 0.23 39% 2003 −0.100 −4.39 −0.280 −12.34 0.22 38% 2004 −0.062 −2.51 −0.244 −9.90 0.22 39% 2005 −0.087 −5.00 −0.280 −16.23 0.28 41% 2006 −0.089 −4.07 −0.277 −12.82 0.26 38% . Gross . Net . . . . α (%) . t-stat . α (%) . t-stat . Beta . R-sq . All years −0.070 −10.20 −0.239 −34.78 0.26 43% 1992 0.018 0.57 −0.091 −2.91 0.37 49% 1993 −0.089 −3.40 −0.206 −7.80 0.33 59% 1994 −0.119 −5.03 −0.275 −11.65 0.32 58% 1995 −0.047 −2.18 −0.221 −10.23 0.24 45% 1996 −0.088 −4.90 −0.245 −13.58 0.26 48% 1997 −0.089 −3.27 −0.271 −10.00 0.26 39% 1998 −0.067 −3.13 −0.256 −11.99 0.21 43% 1999 −0.053 −1.91 −0.224 −8.04 0.25 42% 2000 −0.007 −0.18 −0.190 −5.23 0.23 36% 2001 −0.088 −2.43 −0.279 −7.68 0.24 37% 2002 −0.104 −3.47 −0.289 −9.67 0.23 39% 2003 −0.100 −4.39 −0.280 −12.34 0.22 38% 2004 −0.062 −2.51 −0.244 −9.90 0.22 39% 2005 −0.087 −5.00 −0.280 −16.23 0.28 41% 2006 −0.089 −4.07 −0.277 −12.82 0.26 38% This table presents the daily percentage alpha from aggregate day trading of day traders. Day traders are defined as any trader who places a round-tip day trade in month t. Day trading is defined as round-trip trades by the same stock, investor, and day. In month t, all trades of day traders are included in the analysis. The alphas are estimated using the following regression of daily returns: (Rpt-Rft)=αp+βp(Rmt-Rft)+εpt, where Rpt, Rmt, and Rft are the portfolio return, market return, and risk-free return (respectively). The gross day trading return is calculated from daily round-trip trades plus the intraday returns on open trades; an open trade is a trade made during the day that results in an outstanding position at the close of the day. The net day trading return assumes a 10 bps round-trip commission and a 30 bps transaction tax on sales. Open in new tab 2.4 Performance measurement Our primary performance measurement focuses on the intraday profits of all trades made by day traders and on trade-weighted intraday returns. This analysis focuses on returns on the day that positions are opened. In Section 4.3, we also analyze the event time profitability of purchases and sales over longer holding periods to ensure the inferences we draw from the analysis of intraday profits are accurate. We calculate the intraday returns to day trading, by identifying all trades made by day traders (i.e., traders who had at least one round-trip trade that day). We calculate the profits on round-trip day trades and other position opening trades that remain open at the close of the trading day. The other trades are either purchases to open a long position or sales that open a short position. The profits for trades that lead to an open position at the end of the trading day are calculated relative to closing prices on the date of the trade (i.e., mark-to-market at the day’s closing price). To calculate the daily return earned by a day trader, we sum the proceeds from stocks sold to close long positions and bought to close short positions opened that day (or their mark-to-market equivalent at the close of the trading day) and divide by the cost of initiating those positions (i.e., the value of stocks bought or sold short at the time of the purchase or sale). We refer to this return as the gross intraday return from day trading. To calculate the net intraday return to day trading, we assume a 5 commission on purchases, a 5 bps commission on sales, and a 30 bps transaction tax on sales. (See the appendix for details.) We calculate a trader’s past intraday returns to see whether quitting is sensitive to past performance. When calculating these returns, we do not market adjust. We believe that when evaluating their past performance day traders are unlikely to market adjust because of their short holding periods and the low market betas of their portfolios. When evaluating future performance, we do adjust for market returns because an obvious alternative to day trading would be to hold the market portfolio. Market adjusting does not qualitatively change our findings. It is important to include both round-trip and one-sided position-opening trades to measure the performance of day trading. Focusing on round-trip trades only would yield a biased measure of performance if investors sell winners and hold losers (i.e., exhibit the disposition effect). For example, assume some day traders randomly buy and sell (random traders), whereas others close only winning investments while riding losers (disposition traders). Were we to analyze only the profits of intraday round-trip trades, it is clear that the disposition traders would have better intraday round-trip returns than the random traders merely because they postpone closing losing positions. The disposition effect is prevalent among Taiwanese investors and among day traders elsewhere,13 so including both round-trip and other trades when analyzing performance is an important step. 3. Evidence Consistent with Both Rational and Behavioral Learning Models We begin by estimating the survival rate of day traders. Our trading data starts in 1992. To reasonably ensure that we are analyzing new day traders, we restrict our analysis to those who begin day trading after 1992. In this analysis, we define a day trader as an investor who has day traded for at least 10 days and designate the first month when they hit the minimum 10-day threshold as their entry month. Our data ends in 2006 and thus is right-censored. We consider a trader to have quit day trading if we observe no day trading for 12 consecutive months. As a result of this requirement, we do not analyze day traders who begin day trading in 2006, because we cannot reliably observe whether they have quit. Figure 2 presents a 5-year Kaplan-Meier survival function for the day trader sample defined above. For many of these traders, day trading is a persistent activity. Only 2.5% drop out within 1 month, while survival rates at 1, 2, and 3 years are 44%, 24%, and 15%, respectively. Figure 2 Open in new tabDownload slide Day trader survival function Observations are monthly. Entry in month 0 is defined as the month when a day trader has 10 or more days of day trading. Quitting (the failure event) is defined as the first month in which we observe no day trading in 12 consecutive months. Figure 2 Open in new tabDownload slide Day trader survival function Observations are monthly. Entry in month 0 is defined as the month when a day trader has 10 or more days of day trading. Quitting (the failure event) is defined as the first month in which we observe no day trading in 12 consecutive months. To test whether magnitude of past profitability affects the decision to quit day trading, we estimate the following Cox proportional hazard rate model, h(t,x) = h0(t)e{XB}, (3) where X is a matrix of independent variables, B is a vector of coefficient estimates, h0(t) is the baseline hazard rate (i.e., the hazard rate when all covariates are equal to zero), and h(t,x) is the hazard rate conditional on a set of covariates (x) at time t. In our application, a trader becomes at risk of quitting once he begins day trading. Again, we restrict our analysis to day traders who have day traded for a minimum of 10 days. To assess the impact of past performance on quitting, we use net intraday returns. To estimate the impact of past returns on the propensity to quit day trading, we construct a series of 26 dummy variables corresponding to the following ranges in basis points of performance net of trading costs: (-∞, -90], (-90, -85], … , (25, ∞). (Figure A1 of the Online Appendix shows the percentage of observations with the dummy variable equal to one in each return bin.) When estimating the Cox proportional hazard rate model, we set the range (0, 5 bps] as the default category and include the remaining 25 dummy variables as covariates in our estimation. As control variables we include measures of past day trading activity: the log of the number of days with day trading activity, the log of the number of days since a trader’s first day trade, and the log of the total volume of day trading. In the event history analysis, all independent variables are updated monthly. Figure 3 presents the results of this analysis. The horizontal axis of the figure represents net intraday return categories, while the vertical axis represents the hazard rate relative to the omitted profit category (net intraday return in the interval (0, 0.05]). As predicted by the learning models, the net intraday return is negatively related to the hazard rate. More profitable day traders are less likely to quit.14 Figure 3 Open in new tabDownload slide Hazard ratio for quitting day trading conditional on past performance, 1993–2005 Observations are monthly and exclude traders who day traded in 1992 or started in 2006. Entry in month 0 is defined as the month when a day trader has 10 or more days of day trading. Quitting (the failure event) is defined as the first month in which we observe no day trading in 12 consecutive months. The figure reports the hazard ratio for quitting (solid line) and the 95% confidence interval (dashed lines) for different return categories relative to the default category of (0,5] basis points (bps) where the hazard ratio is equal to one by construction. Mean net intraday return range is the investor's average daily return on days with trades from the first month of day trading to the end of the prior month. Figure 3 Open in new tabDownload slide Hazard ratio for quitting day trading conditional on past performance, 1993–2005 Observations are monthly and exclude traders who day traded in 1992 or started in 2006. Entry in month 0 is defined as the month when a day trader has 10 or more days of day trading. Quitting (the failure event) is defined as the first month in which we observe no day trading in 12 consecutive months. The figure reports the hazard ratio for quitting (solid line) and the 95% confidence interval (dashed lines) for different return categories relative to the default category of (0,5] basis points (bps) where the hazard ratio is equal to one by construction. Mean net intraday return range is the investor's average daily return on days with trades from the first month of day trading to the end of the prior month. However, the effect is not linear. The propensity to quit is relatively insensitive to differences past net intraday returns in the -30 bps to 30 bps range. Traders with past net intraday returns in the (30 bps, infinity) range are more likely to quit than those with returns in the -30 bps to 30 bps range, though not as likely as traders with more negative returns. In the domain of negative returns, the propensity to quit is quite sensitive to the magnitudes. For example, consider the impact on hazard rates of moving across four equidistant profit categories: (0, 0,05], (−0.30, −0.25], (−0.60, −0.55] and (−0.90, −0.85]. The first move, from just profitable to the low range of losses increases the hazard rate six percentage points (from 1.00 to 1.06); the second move, from the low range of losses to midrange losses, increases the hazard rate by an additional 30 percentage points (from 1.06 to 1.36), the third move, from the midrange of losses to a high range increases the hazard rate by an additional 36 percentage points (from 1.36 to 1.72). In summary, these analyses provide evidence that traders do learn about their own ability by trading. Those who profit are less likely to quit, though the effect is most pronounced for those with steep losses. 4. Evidence Inconsistent with Rational Learning Models To this point, we find evidence consistent with both the rational and behavioral learning models of investor behavior. Poor performers are more likely to quit day trading. This evidence indicates learning is an important feature of financial markets. In this section, we argue that rational learning does not explain behavior of the large population of speculative investors for three reasons: aggregate performance is negative, experienced speculators lose money, and unprofitable speculators persist. 4.1 Aggregate performance is negative To evaluate the performance of day traders relative to their opportunity cost of holding the market portfolio, we estimate abnormal returns by regressing the portfolio excess return (portfolio return less the risk-free rate, Rpt-Rft ) on the excess return on a value-weighted market index (market return less the risk-free rate, Rmt-Rft ): Rpt-Rft=α+βRmt-Rft+ϵpt (4) We construct our own market index using market capitalization from the Taiwan Economic Journal (TEJ) and individual stock returns calculated from the TSE data. The intercept of this regression ( α ) is our measure of abnormal returns. Our goal is to estimate the aggregate performance of day traders so we identify any investor who day trades in month t and analyze the performance of all trades the investor makes in month t. We include all trades because only analyzing round-trip trades imparts a serious positive bias in the calculation of returns. As discussed above, investors are more likely to sell winning rather than losing investments (the disposition effect). As a result, a sale following a purchase is more likely if the returns following the purchase are good rather than bad. Thus, this disposition effect yields a positively biased portrait of returns if we analyze only round-trip trades. The analysis weights investors by the investments they make and thus represents the aggregate performance of day traders. In sum, there are two reasons that including all trades in the month of day trading might positively bias our performance analysis. First, because of the disposition effect, day traders are more likely to close profitable positions. Thus, months in which we observe day trading are more likely to be profitable months. Second, it is possible that good investment performance leads to day trading (i.e., reverse causation). (In subsequent analyses, we identify day traders ex ante to avoid these issues.) We are not concerned by these biases in this preliminary analysis, because we document poor performance in aggregate. In Table 1, we present the gross and net performance of all day traders from a calendar time regression of daily aggregate day trading returns on daily market returns. In the second column of Table 1, we present the gross abnormal intraday returns of day traders. On average, day traders lose 7 bps on their day trading before costs (t=-10.2). In the fourth column we see that trading costs more than triple the losses to 23.9 bps per day. Moreover, we observe reliably negative gross and net performance in all years but 1992, when gross returns are indistinguishable from zero but net returns are reliably negative.15 We estimate the total dollar value of day trader losses by multiplying the dollar value of trades that open positions on day t by the alpha (intercept) and day t residual from the regression of Equation (4). In the average year, aggregate gross losses are NT$13.5 billion and net losses are NT$33.7 billion, which corresponds to 0.14% and 0.35% of GDP, respectively.16 We also divide the aggregate losses by the number of traders in each year to obtain an average annual loss per trader, which is NT$30,239 before and NT$73,065 after fees; these represent 2.9% and 6.9% of the mean household income in Taiwan. (See Tables A3–A5 of Online Appendix for the details of these calculations.) Table 3 Day trader performance conditional on prior year's day trading experience and profitability # days of day trading experience in previous year . Gross . Net . . . Mean number of traders per day . Mean daily number of trades per trader . Day trades / all trades (%) . Share of all day trading by volume (%) . α (%) . t-stat . α (%) . t-stat . Beta . R-sq . A. Previously profitable day traders 0 d ≤ X < 5 d −0.066 −7.64 −0.140 −16.26 0.33 46% 14,936 3.43 9.73 7.81 6 d ≤ X < 10 d 0.001 0.18 −0.107 −14.57 0.29 46% 2,110 5.58 18.90 2.12 11 d ≤ X < 20 d 0.053 7.75 −0.070 −10.32 0.27 47% 1,976 6.84 22.53 2.50 21 d ≤ X < 40 d 0.120 19.33 −0.019 −3.14 0.24 47% 1,732 8.85 26.34 2.90 41 d ≤ X < 80 d 0.197 35.39 0.035 6.34 0.21 46% 1,455 11.85 33.36 3.20 80 d ≤ X 0.333 72.65 0.118 26.03 0.17 45% 1,724 25.78 50.52 6.61 B. Previously unprofitable day traders 0 d ≤ X < 5 d −0.139 −16.10 −0.213 −24.60 0.33 46% 46,078 3.31 8.95 20.55 6 d ≤ X < 10 d −0.167 −20.75 −0.270 −33.60 0.31 47% 9,468 4.86 18.52 6.81 11 d ≤ X < 20 d −0.171 −21.98 −0.289 −37.26 0.31 47% 10,335 5.67 23.99 8.77 21 d ≤ X < 40 d −0.171 −23.05 −0.310 −41.83 0.30 48% 10,308 6.82 30.47 10.47 41 d ≤ X < 80 d −0.166 −23.71 −0.332 −47.56 0.28 49% 9,184 8.53 37.81 11.34 80 d ≤ X −0.132 −21.88 −0.348 −57.90 0.25 50% 9,639 13.72 50.72 16.91 # days of day trading experience in previous year . Gross . Net . . . Mean number of traders per day . Mean daily number of trades per trader . Day trades / all trades (%) . Share of all day trading by volume (%) . α (%) . t-stat . α (%) . t-stat . Beta . R-sq . A. Previously profitable day traders 0 d ≤ X < 5 d −0.066 −7.64 −0.140 −16.26 0.33 46% 14,936 3.43 9.73 7.81 6 d ≤ X < 10 d 0.001 0.18 −0.107 −14.57 0.29 46% 2,110 5.58 18.90 2.12 11 d ≤ X < 20 d 0.053 7.75 −0.070 −10.32 0.27 47% 1,976 6.84 22.53 2.50 21 d ≤ X < 40 d 0.120 19.33 −0.019 −3.14 0.24 47% 1,732 8.85 26.34 2.90 41 d ≤ X < 80 d 0.197 35.39 0.035 6.34 0.21 46% 1,455 11.85 33.36 3.20 80 d ≤ X 0.333 72.65 0.118 26.03 0.17 45% 1,724 25.78 50.52 6.61 B. Previously unprofitable day traders 0 d ≤ X < 5 d −0.139 −16.10 −0.213 −24.60 0.33 46% 46,078 3.31 8.95 20.55 6 d ≤ X < 10 d −0.167 −20.75 −0.270 −33.60 0.31 47% 9,468 4.86 18.52 6.81 11 d ≤ X < 20 d −0.171 −21.98 −0.289 −37.26 0.31 47% 10,335 5.67 23.99 8.77 21 d ≤ X < 40 d −0.171 −23.05 −0.310 −41.83 0.30 48% 10,308 6.82 30.47 10.47 41 d ≤ X < 80 d −0.166 −23.71 −0.332 −47.56 0.28 49% 9,184 8.53 37.81 11.34 80 d ≤ X −0.132 −21.88 −0.348 −57.90 0.25 50% 9,639 13.72 50.72 16.91 Each day we sort traders who executed a round-trip trade that day into groups based upon how many days they engaged in day trading and whether their intraday returns were profitable during the previous 365 days. The alphas are estimated using the following regression of intraday daily returns: (Rpt - Rft) = αp + βp(Rmt - Rft) + εpt, where Rpt, Rmt, and Rft are the portfolio return, market return, and risk-free return (respectively). The gross day trading return is calculated from daily round-trip trades plus the intraday returns on open trades; an open trade is a trade made during the day that results in an outstanding position at the close of the day. The net day trading return assumes a 10 bps round-trip commission and a 30 bps transaction tax on sales. “Mean daily number of trades per trader” is the average number of trades per day for the group divided by the average number of traders in the group. “Day trade / all trade” is the fraction of the group’s trading that is round-trip day trades. “Share of all day trading by volume” presents the share of all day trading accounted for by each group. Open in new tab Table 3 Day trader performance conditional on prior year's day trading experience and profitability # days of day trading experience in previous year . Gross . Net . . . Mean number of traders per day . Mean daily number of trades per trader . Day trades / all trades (%) . Share of all day trading by volume (%) . α (%) . t-stat . α (%) . t-stat . Beta . R-sq . A. Previously profitable day traders 0 d ≤ X < 5 d −0.066 −7.64 −0.140 −16.26 0.33 46% 14,936 3.43 9.73 7.81 6 d ≤ X < 10 d 0.001 0.18 −0.107 −14.57 0.29 46% 2,110 5.58 18.90 2.12 11 d ≤ X < 20 d 0.053 7.75 −0.070 −10.32 0.27 47% 1,976 6.84 22.53 2.50 21 d ≤ X < 40 d 0.120 19.33 −0.019 −3.14 0.24 47% 1,732 8.85 26.34 2.90 41 d ≤ X < 80 d 0.197 35.39 0.035 6.34 0.21 46% 1,455 11.85 33.36 3.20 80 d ≤ X 0.333 72.65 0.118 26.03 0.17 45% 1,724 25.78 50.52 6.61 B. Previously unprofitable day traders 0 d ≤ X < 5 d −0.139 −16.10 −0.213 −24.60 0.33 46% 46,078 3.31 8.95 20.55 6 d ≤ X < 10 d −0.167 −20.75 −0.270 −33.60 0.31 47% 9,468 4.86 18.52 6.81 11 d ≤ X < 20 d −0.171 −21.98 −0.289 −37.26 0.31 47% 10,335 5.67 23.99 8.77 21 d ≤ X < 40 d −0.171 −23.05 −0.310 −41.83 0.30 48% 10,308 6.82 30.47 10.47 41 d ≤ X < 80 d −0.166 −23.71 −0.332 −47.56 0.28 49% 9,184 8.53 37.81 11.34 80 d ≤ X −0.132 −21.88 −0.348 −57.90 0.25 50% 9,639 13.72 50.72 16.91 # days of day trading experience in previous year . Gross . Net . . . Mean number of traders per day . Mean daily number of trades per trader . Day trades / all trades (%) . Share of all day trading by volume (%) . α (%) . t-stat . α (%) . t-stat . Beta . R-sq . A. Previously profitable day traders 0 d ≤ X < 5 d −0.066 −7.64 −0.140 −16.26 0.33 46% 14,936 3.43 9.73 7.81 6 d ≤ X < 10 d 0.001 0.18 −0.107 −14.57 0.29 46% 2,110 5.58 18.90 2.12 11 d ≤ X < 20 d 0.053 7.75 −0.070 −10.32 0.27 47% 1,976 6.84 22.53 2.50 21 d ≤ X < 40 d 0.120 19.33 −0.019 −3.14 0.24 47% 1,732 8.85 26.34 2.90 41 d ≤ X < 80 d 0.197 35.39 0.035 6.34 0.21 46% 1,455 11.85 33.36 3.20 80 d ≤ X 0.333 72.65 0.118 26.03 0.17 45% 1,724 25.78 50.52 6.61 B. Previously unprofitable day traders 0 d ≤ X < 5 d −0.139 −16.10 −0.213 −24.60 0.33 46% 46,078 3.31 8.95 20.55 6 d ≤ X < 10 d −0.167 −20.75 −0.270 −33.60 0.31 47% 9,468 4.86 18.52 6.81 11 d ≤ X < 20 d −0.171 −21.98 −0.289 −37.26 0.31 47% 10,335 5.67 23.99 8.77 21 d ≤ X < 40 d −0.171 −23.05 −0.310 −41.83 0.30 48% 10,308 6.82 30.47 10.47 41 d ≤ X < 80 d −0.166 −23.71 −0.332 −47.56 0.28 49% 9,184 8.53 37.81 11.34 80 d ≤ X −0.132 −21.88 −0.348 −57.90 0.25 50% 9,639 13.72 50.72 16.91 Each day we sort traders who executed a round-trip trade that day into groups based upon how many days they engaged in day trading and whether their intraday returns were profitable during the previous 365 days. The alphas are estimated using the following regression of intraday daily returns: (Rpt - Rft) = αp + βp(Rmt - Rft) + εpt, where Rpt, Rmt, and Rft are the portfolio return, market return, and risk-free return (respectively). The gross day trading return is calculated from daily round-trip trades plus the intraday returns on open trades; an open trade is a trade made during the day that results in an outstanding position at the close of the day. The net day trading return assumes a 10 bps round-trip commission and a 30 bps transaction tax on sales. “Mean daily number of trades per trader” is the average number of trades per day for the group divided by the average number of traders in the group. “Day trade / all trade” is the fraction of the group’s trading that is round-trip day trades. “Share of all day trading by volume” presents the share of all day trading accounted for by each group. Open in new tab In aggregate, day trading is a losing proposition; day trading is an industry that consistently and reliably loses money. From an industrial organization perspective, it is difficult to understand how such an industry survives. For people to knowingly day trade, most must either be overconfident about their prospects of success or derive nonfinancial utility from the activity and knowingly suffer losses as a result. Finally, the poor aggregate performance of day trading is not consistent with the learning model of Mahani and Bernhardt (2007). In their model, novice speculators lose while the experienced profit, but aggregate performance should be positive and represent the equilibrium return to day trading. We discuss this issue in detail and explicitly test rational learning models after presenting results on cross-sectional variation in performance. 4.2 Experienced day traders continue to lose money A central feature of the learning model is the observation that bad traders quit. This raises two natural questions. First, do traders with a long history of losses continue to trade? Second, what fraction of day trading can we trace to traders with a history of losses? Do traders with a long history of losses continue to trade? To investigate the relation between experience, past performance, and continued trading we categorize day traders into groups based upon past day trading experience and whether or not they have been profitable. Each month from 1993 to 2005, we sort traders based on the number of days they have engaged in day trading and on the cumulative profitability of their past intraday trades as of the end of the previous month. To have an accurate measure of day trading experience, we exclude traders who day traded in 1992. We exclude traders with fewer than 10 days of past day trading experience and sort the remaining traders into those with 10 to 49 days, 50 to 99 days, 100 to 199 days, 200 to 399 days, and 400 or more days of day trading experience. We further partition these experience groups into those with positive cumulative past intraday profits and those with negative or zero cumulative past intraday profits. We then measure the propensity for traders in each experience/profitability group to stop day trading for 1 month or for 12 consecutive months. Table 2, panel A, reports the rate at which traders stop day trading for at least 1 month. Not surprisingly, traders with less experience are more likely to stop. For example, 41.98% of profitable traders and 43.19% unprofitable traders with 10 to 49 days of experience stop trading for at least 1 month, whereas only 7.58% of profitable traders and 9.30% of unprofitable traders with 400 or more days of experience do so. As predicted by both rational and behavioral learning models, unprofitable traders are more likely to stop trading than profitable traders. Across the five experience bins, the unprofitable traders quit at rates ranging from 1.21 to 2.73 percentage points higher than profitable traders. What is more surprising is that the magnitude of the differences in the quitting rates of profitable and unprofitable traders, though statistically significant, is tiny. Table 2 Quitting day trading conditional on experience and past profitability Experience (X) partition . Unprofitable traders . Profitable traders . Difference in means (%) . t-statistic (difference in means) . Mean (%) . N . Mean (%) . N . A. Percentage of day traders who day trade in month t-1 but do not day trade in month t 10 d ≤ X < 50 d 43.19 5,578,277 41.98 540,228 1.21 12.85 50 d ≤ X < 100 d 29.82 2,460,476 27.08 154,435 2.73 15.52 100 d ≤ X < 200 d 22.47 2,018,002 20.06 123,009 2.41 12.40 200 d ≤ X < 400 d 15.95 1,344,396 13.67 90,711 2.28 10.56 400 d ≤ X 9.30 832,988 7.58 81,713 1.72 8.45 B. Percentage of day traders who day trade in month t-1, but not in months t to t+11 10 d ≤ X < 50 d 11.73 5,578,277 11.41 540,228 0.33 6.12 50 d ≤ X < 100 d 6.55 2,460,476 5.43 154,435 1.12 16.27 100 d ≤ X < 200 d 4.62 2,018,002 3.65 123,009 0.98 15.26 200 d ≤ X < 400 d 3.24 1,344,396 2.43 90,711 0.81 13.30 400 d ≤ X 2.05 832,988 1.58 81,713 0.47 8.84 Experience (X) partition . Unprofitable traders . Profitable traders . Difference in means (%) . t-statistic (difference in means) . Mean (%) . N . Mean (%) . N . A. Percentage of day traders who day trade in month t-1 but do not day trade in month t 10 d ≤ X < 50 d 43.19 5,578,277 41.98 540,228 1.21 12.85 50 d ≤ X < 100 d 29.82 2,460,476 27.08 154,435 2.73 15.52 100 d ≤ X < 200 d 22.47 2,018,002 20.06 123,009 2.41 12.40 200 d ≤ X < 400 d 15.95 1,344,396 13.67 90,711 2.28 10.56 400 d ≤ X 9.30 832,988 7.58 81,713 1.72 8.45 B. Percentage of day traders who day trade in month t-1, but not in months t to t+11 10 d ≤ X < 50 d 11.73 5,578,277 11.41 540,228 0.33 6.12 50 d ≤ X < 100 d 6.55 2,460,476 5.43 154,435 1.12 16.27 100 d ≤ X < 200 d 4.62 2,018,002 3.65 123,009 0.98 15.26 200 d ≤ X < 400 d 3.24 1,344,396 2.43 90,711 0.81 13.30 400 d ≤ X 2.05 832,988 1.58 81,713 0.47 8.84 Day trading is defined as round-trip trades by the same stock, investor, and day. Only traders with 10 or more days of day trading experience are included. In panel A, we present the percentage of traders who day trade in month t-1, but not in month t. In panel B, we present percentage of traders who day trade in month t-1, but not in months t through t+11 We sort traders on experience (rows) and profitability (columns). Experience is the number of previous days on which a trader has day traded through month t-1. Profitable day traders are those with mean daily intraday returns that are positive from the first month in which they make an intraday roundtrip trade through month t-1. The analyses begin in 1993 and exclude traders who day traded in 1992. N is the number of trader/month observations. Standard error estimates are based on clusters by investor. Open in new tab Table 2 Quitting day trading conditional on experience and past profitability Experience (X) partition . Unprofitable traders . Profitable traders . Difference in means (%) . t-statistic (difference in means) . Mean (%) . N . Mean (%) . N . A. Percentage of day traders who day trade in month t-1 but do not day trade in month t 10 d ≤ X < 50 d 43.19 5,578,277 41.98 540,228 1.21 12.85 50 d ≤ X < 100 d 29.82 2,460,476 27.08 154,435 2.73 15.52 100 d ≤ X < 200 d 22.47 2,018,002 20.06 123,009 2.41 12.40 200 d ≤ X < 400 d 15.95 1,344,396 13.67 90,711 2.28 10.56 400 d ≤ X 9.30 832,988 7.58 81,713 1.72 8.45 B. Percentage of day traders who day trade in month t-1, but not in months t to t+11 10 d ≤ X < 50 d 11.73 5,578,277 11.41 540,228 0.33 6.12 50 d ≤ X < 100 d 6.55 2,460,476 5.43 154,435 1.12 16.27 100 d ≤ X < 200 d 4.62 2,018,002 3.65 123,009 0.98 15.26 200 d ≤ X < 400 d 3.24 1,344,396 2.43 90,711 0.81 13.30 400 d ≤ X 2.05 832,988 1.58 81,713 0.47 8.84 Experience (X) partition . Unprofitable traders . Profitable traders . Difference in means (%) . t-statistic (difference in means) . Mean (%) . N . Mean (%) . N . A. Percentage of day traders who day trade in month t-1 but do not day trade in month t 10 d ≤ X < 50 d 43.19 5,578,277 41.98 540,228 1.21 12.85 50 d ≤ X < 100 d 29.82 2,460,476 27.08 154,435 2.73 15.52 100 d ≤ X < 200 d 22.47 2,018,002 20.06 123,009 2.41 12.40 200 d ≤ X < 400 d 15.95 1,344,396 13.67 90,711 2.28 10.56 400 d ≤ X 9.30 832,988 7.58 81,713 1.72 8.45 B. Percentage of day traders who day trade in month t-1, but not in months t to t+11 10 d ≤ X < 50 d 11.73 5,578,277 11.41 540,228 0.33 6.12 50 d ≤ X < 100 d 6.55 2,460,476 5.43 154,435 1.12 16.27 100 d ≤ X < 200 d 4.62 2,018,002 3.65 123,009 0.98 15.26 200 d ≤ X < 400 d 3.24 1,344,396 2.43 90,711 0.81 13.30 400 d ≤ X 2.05 832,988 1.58 81,713 0.47 8.84 Day trading is defined as round-trip trades by the same stock, investor, and day. Only traders with 10 or more days of day trading experience are included. In panel A, we present the percentage of traders who day trade in month t-1, but not in month t. In panel B, we present percentage of traders who day trade in month t-1, but not in months t through t+11 We sort traders on experience (rows) and profitability (columns). Experience is the number of previous days on which a trader has day traded through month t-1. Profitable day traders are those with mean daily intraday returns that are positive from the first month in which they make an intraday roundtrip trade through month t-1. The analyses begin in 1993 and exclude traders who day traded in 1992. N is the number of trader/month observations. Standard error estimates are based on clusters by investor. Open in new tab Table 2, panel B, reports the rates at which traders stop day trading for at least 12 consecutive months. Naturally, these rates are lower than those for stopping for a month, but a similar pattern emerges like in panel A. For example, 5.43% of profitable traders and 6.55% of unprofitable traders with 10 to 49 days of experience stop trading for at least 12 months. Of traders who have day traded 400 or more days, profitable traders have a 1.58% probability of quitting for 12 or more months and unprofitable traders have a 2.05% probability quitting. Using Columns 2–5 and the last four rows of panel B, one can calculate that all previously unprofitable traders with 50 or more days of past day trading experience have a 95.3% probability of day trading again in the next 12 months, whereas previously profitable traders with similar experience have a 96.4% probability doing so. What fraction of day trading can we trace to traders with a history of losses? To answer this question, each month we sort traders who day trade that month into three groups: novice day traders (traders with 1 to 9 days of day trading experience), unprofitable day traders (traders with 10 or more days of day trading experience and negative or zero life time net intraday profits prior to the month of sorting), and profitable day traders (traders with 10 or more days of day trading experience and positive life time net intraday profits prior to the month of sorting). Figure 4 graphs the relative sizes of these three groups from 1995 through 2006 when measured by number of traders (Figure 4A) and trading volume in dollars (Figure 4B). Throughout this 12-year period the fraction of profitable day traders is consistently about 5%. The fraction of unprofitable traders grows to over two-thirds as more and more novice day traders are reclassified as profitable or unprofitable. As one would expect, profitable and unprofitable day traders account for proportionately more trading volume than novice day traders. In aggregate over the post-1995 sample period, unprofitable traders account for 74% of trading volume (65% of day traders) and in the last several years of the sample they consistently account for about 80% of trading volume. Figure 4 Open in new tabDownload slide Day trading by novice, profitable, and unprofitable day traders Novice day traders are those with less than 10 days of day trading. Figure 4 Open in new tabDownload slide Day trading by novice, profitable, and unprofitable day traders Novice day traders are those with less than 10 days of day trading. Thus, most day traders are unprofitable, previously unprofitable traders generate most day trading, and previously unprofitable day traders with considerable experience persist at day trading at almost the same high rate as profitable experienced day traders. These observations are not consistent with models of rational learning. We sort day trader based on past profitability and experience. A reasonable concern is that if these sorts are not good indicators of future performance, traders might reasonably ignore them. However, as we demonstrate in the next section, sorting day traders on experience and past profitability is remarkably effective at forecasting their future performance. 4.3 Event time analysis and the persistence of performance So far, we have considered only intraday returns. This is appropriate given our focus on day trading. However, not all positions initiated by day traders are closed the day they are opened. Do day traders earn profits on positions that they hold beyond the close of trading? We address this question with an event time analysis of returns subsequent to purchases and sales. On each day (event day t=0), we sort traders who executed a round-trip trade that day on profitability and day trading experience over the last 365 calendar days (t-1 to t-365). Profitable traders earn a cumulative intraday net profit over the previous year that are positive, and unprofitable traders earn negative or zero profits. Experience bins are based on number of days of day trading during the previous 365 days with low experience (0–5 days), exp. 2 (6–10), exp. 3 (11–20), exp. 4 (21–40), exp. 5 (41–80), and hi exp. (> 80). Thus, each day trader falls into 1 of 12 groups that represent the independent sorting into two profit groups and six experience groups. To assess the profitability of trades for each group, we aggregate all purchases on event day t=0 for each group. We calculate the market-adjusted abnormal return on event day t=0 weighted by the value of stocks bought using the purchase prices and closing prices to calculate the intraday return. This step provides us with one buy return for event day t=0 for each calendar day during our sample period. We then calculate the mean market-adjusted abnormal return across all days over our sample period, MA0buy . For subsequent event days (t=1,10), we weight daily stock returns by the value of purchases on t=0. There is a similar calculation for the sales of each group. Finally, we calculate the cumulative (market-adjusted) abnormal return on stocks bought less the cumulative (market-adjusted) abnormal return on stocks sold as: CARt=∑τ=0tMAτbuy-MAτsell. (5) Figure 5 displays the results for a 10 trading day event horizon. The most striking results in the graph are (1) regardless of experience, traders with past profits outperform those with past losses, (2) for traders with positive past profits, cumulative abnormal returns increase with experience, and (3) profitable traders with more than 40 days of day trading experience in the last year earn more than enough to cover 40 bps of round-trip transaction costs. Most of this profit is earned on the day of the transaction. We do not estimate standard errors in this analysis given the well-known problems in calculating standard errors with cross-sectionally correlated observations (i.e., many traders are active in the same period). Instead, we turn to a calendar-time approach to assess statistical significance. Figure 5 Open in new tabDownload slide Cumulative abnormal returns in event time conditional on past profitability and experience, 1993–2005 On event day t=0, traders who day trade that day are sorted based on net profitability of intraday trades and day trading experience over previous year (t-1 to t-365). On the horizontal axis, labels mark the beginning of the event day, the time of trade for event day 0 and the prior day close for all other event days. Profitable (unprofitable) traders are those with cumulative intraday net profits over the previous 365 calendar days that are positive (negative or zero). Experience bins are based on number of days of day trading during the previous 365 days with low experience (0–5), exp. 2 (6–10), exp 3 (11–20), exp 4 (21–40), exp 5 (41–80), and hi exp ( > 80). CARs, cumulative abnormal returns. Figure 5 Open in new tabDownload slide Cumulative abnormal returns in event time conditional on past profitability and experience, 1993–2005 On event day t=0, traders who day trade that day are sorted based on net profitability of intraday trades and day trading experience over previous year (t-1 to t-365). On the horizontal axis, labels mark the beginning of the event day, the time of trade for event day 0 and the prior day close for all other event days. Profitable (unprofitable) traders are those with cumulative intraday net profits over the previous 365 calendar days that are positive (negative or zero). Experience bins are based on number of days of day trading during the previous 365 days with low experience (0–5), exp. 2 (6–10), exp 3 (11–20), exp 4 (21–40), exp 5 (41–80), and hi exp ( > 80). CARs, cumulative abnormal returns. Specifically, we calculate the gross and net intraday abnormal returns like in Table 1. We partition day traders daily using the same criteria as for Figure 5. Table 3 reports results. As in Table 1, these results are based on daily calendar time regressions. Thus, we assume that each day—but not each trader or each security—is a separate independent observation. The reader may notice that many of the reported t-statistics are quite large. For example, we reject the null hypothesis that the alpha of the net returns of previously unprofitable day traders with more than 80 days of experience is 0 with a t-statistic of -57.90. This may strike some readers as a remarkably large t-statistic for a sample of only 3,728 observations. However, the aggregate performance of this group of day traders is remarkably persistent. An alternative, nonparametric, approach to testing the performance of this group of traders is to employ a binomial test. Previously unprofitable day traders with more than 80 days of experience, earn positive aggregate net returns on only 920 out of 3,728 days. For p = .5, the probability of 920 or fewer successes in 3,728 trials is less than 6.2 × 10-220. In Table 3, we see that (1) regardless of experience, traders with past profits outperform those with past losses, (2) for traders with positive past profits, cumulative abnormal returns increase with experience, and (3) profitable traders with more than 40 days of day trading experience in the last year earn more than enough to cover their transaction costs. These results confirm that an extensive history of profitability is a strong predictor of future profitable. Moreover, the most profitable and experienced traders trade more frequently than other groups, consistent with the models of rational learning. For example, the most profitable and experienced traders average 25.8 trades per day, almost twice the frequency of trading we observe in other groups. But this is a pyrrhic victory for rational models because in the wake of these profitable traders are many traders who predictably lose money. In the last column of Table 3, we see that only 9.81% (3.20%+6.61%) of day trading volume is generated by predictably profitable day traders despite the fact that they trade more frequently than other investor groups. From Column 8, we can calculate that these predictably profitable traders constitute less than 3% of all day traders active on an average day. 5. New Day Trader Entry We argue that it is not rational for the average investor who begins day trading to believe doing so will be profitable. Furthermore, it is not rational for the average day trader who is motivated by profits to continue to trade actively despite a history of poor performance. Of course, if an investor mistakenly believes that day trading has positive expected lifetime profits, entry may be rational conditional on that mistaken belief. But it is not rational for hundreds of thousands of investors to have materially mistaken beliefs. We believe that many investors begin day trading because they are overconfident in their ability to earn profits day trading. We conjecture that two factors might influence beliefs and the entry decisions of new day traders (and the beliefs and decisions of existing traders who continue trading): recent market returns and recent day trader returns. Strong market returns may attract the attention of and increase the overconfidence of investors. Statman, Thorley, and Vorkink (2006) document that across countries, volume increases following strong market returns; they attribute increased volume to increase overconfidence consistent with the theoretical predictions of Gervais and Odean (2001). Potential day traders may also, mistakenly,17 believe that day trading profits are highly correlated with market returns. Thus, strong recent market returns may lead to increased day trader entry, because (1) investors are paying more attention to the market, (2) investor overconfidence increases with strong market returns, and (3) investors may believe that strong market returns are indicative of strong day trading opportunities. Recent day trader performance may also influence entry decisions because potential day traders learn of the recent successes of others and decide to try day trading themselves. Han and Hirshleifer (2016) argue this social transmission channel can explain investors’ willingness to invest in active strategies. We thus expect the aggregate performance of day traders will also draw new entrants into the market above and beyond general market returns. To test these conjectures, we estimate the following time-series regression using 712 weekly observations: NDt=a+∑τ=t-1t-12bτRmτ+∑τ=t-1t-12cτDPτ+dt+μdow+μmth+et. (6) NDt is the number of new day traders in week t; Rmt is the value-weighted Taiwan market return for week t; and DPt is the aggregate performance of day traders in week t. We standardize these variables to facilitate the interpretation of regression results. New day traders (NDt) are traders who execute a round-trip day on day t but never did so prior to day t. We drop the first year (1992) from this analysis, because we would misidentify many 1992 day traders as new. Day trader performance (DPt) is measured as the residual from a univariate regression of weekly day trader performance on the weekly market return (and is thus orthogonal to market returns). As controls we include fixed effects for the number of trading days in the week ( μdow ) and calendar month ( μmth ) and a time trend (t); results are not sensitive to the inclusion of these control variables. To address concerns regarding serial correlation, we estimate these regressions using Newey-West correction assuming six lags.18 In addition to analyzing the entry of new day traders, we estimate two analogous regressions where the independent variable is either the number of repeat day traders (day traders who trade on day t and traded prior to day t, RPt) or the ratio of new day traders to total day traders on day t, NDt/(NDt+ RPt). The six graphs of Figure 6 present the key results of this regression. Each column of the figure presents two graphs, one for the 12 estimated coefficients on the lagged market return (top graph) and one for 12 estimated coefficients on the lagged performance of day traders (bottom panel). The three columns of the figure represent the three regressions where the independent variable is alternatively new day traders (blue lines in left column), repeat day traders (red lines in middle column), or the ratio of new to all day traders (green lines in right column). Figure 6 Open in new tabDownload slide The effect of market returns and day trader performance on day trading activity The figure depicts the results of three regressions using weekly observations from 1993 to 2006. The left column (blue lines, labeled “New Day Traders”) presents the key results of the following regression in two graphs: NDt=a+∑τ=t-1t-12bτRmτ+∑τ=t-1t-12cτDPτ+dt+μdow+μmth+et where ND t is the number of new day traders in week t, R mt is the value-weighted Taiwan market return for week t, and DPt is the aggregate performance of day traders in week t. We standardize these variables to facilitate the interpretation of regression results. The top graph plots the estimated coefficients on lagged market returns, and the bottom graph plots the estimated coefficients on lagged day trader performance. As controls we include fixed effects for the number of trading days in the week (μdow) and calendar month (μmth) and a time trend (t). Standard errors are calculated using Newey-West correction assuming six lags. The center column (red lines, labeled “Repeat Day Traders”) presents the key results of a similar regression with repeat day traders (RDt) as the dependent variable. The right column (green lines, labeled “Ratio of New to All Day Traders”) presents the key results of a similar regression with the ratio of new to all day traders as the dependent variables, NDt/(NDt + RDt). Figure 6 Open in new tabDownload slide The effect of market returns and day trader performance on day trading activity The figure depicts the results of three regressions using weekly observations from 1993 to 2006. The left column (blue lines, labeled “New Day Traders”) presents the key results of the following regression in two graphs: NDt=a+∑τ=t-1t-12bτRmτ+∑τ=t-1t-12cτDPτ+dt+μdow+μmth+et where ND t is the number of new day traders in week t, R mt is the value-weighted Taiwan market return for week t, and DPt is the aggregate performance of day traders in week t. We standardize these variables to facilitate the interpretation of regression results. The top graph plots the estimated coefficients on lagged market returns, and the bottom graph plots the estimated coefficients on lagged day trader performance. As controls we include fixed effects for the number of trading days in the week (μdow) and calendar month (μmth) and a time trend (t). Standard errors are calculated using Newey-West correction assuming six lags. The center column (red lines, labeled “Repeat Day Traders”) presents the key results of a similar regression with repeat day traders (RDt) as the dependent variable. The right column (green lines, labeled “Ratio of New to All Day Traders”) presents the key results of a similar regression with the ratio of new to all day traders as the dependent variables, NDt/(NDt + RDt). New day trader entry and repeat day trader activity are positively correlated with both recent market returns and recent aggregate day trader performance. The influence of recent market returns on entry and repeat activity is more persistent than that of recent aggregate day trader performance. However, at a lag of only 1 week, aggregate day trader performance is more influential than market returns (i.e., the coefficient at a 1-week lag of Day trader performance is greater than the coefficient at a 1-week lag of Market returns). This suggests that if lagged aggregate day trader performance is influencing new entry and repeat activity through social channels, those channels focus on very recent performance. This is consistent with day traders bragging to others about their most recent successes. 6. Discussion Our data are remarkably well suited for testing models of rational learning such as Mahani and Bernhardt (2007). Mahani and Bernhardt (2007, p. 1317) write that their “prototypical novice speculator is the Japanese hairdresser Kiyoshi Wakino” who day trades between giving haircuts. We observe the day trading of hundreds of thousands of investors over a 17-year period. And while our day traders are Taiwanese and certainly not all hairdressers, it is probable that—like Kiyoshi Wakino—many of our novice day traders pursue trading in addition to, if not during, a regular job. Despite the size and appropriateness of our data, our results do not support the rational learning models. In Mahani and Bernhardt’s model, day trading is, in aggregate, profitable because skilled day traders are able to take advantage of the insensitivity of liquidity traders to price and the willingness of competitive market-makers to forego a profit. In Taiwan, day traders, in aggregate, lose money. It is not rational for a risk-averse investor with no special claim to superior ability to undertake day trading in hopes of discovering that he is amongst the chosen few. Furthermore, it is not rational for day traders who have incurred persistent losses to continue day trading for the purpose of learning about their ability. So why do investors take up day trading and why do so many persist in the face of losses? We consider three broadly defined answers to this question. First, it could be the case that day traders do not have standard risk-averse preferences; they may be risk-seeking or, as suggested by Kumar (2009), attracted to investments with highly skewed investments, such as lotteries, that have negative expected payoffs but a small probability of a large payoff. However, the day trading profits that we document are similar in magnitude to, and far less prevalent than, the losses. Unlike lottery winners, day traders must succeed on repeated gambles in order to achieve overall success. Such repeated gambles do not tend to generate highly skewed distributions. Furthermore, daily day trading returns have a negative mean, and yet lower variance and less right-hand skewness than the average returns of Taiwanese stocks. Define the annual day trading return as the sum of the returns earned on each day of day trading. For traders with a minimum of ten days of day trading, the skewness of the annual return is −0.22 (i.e., modestly negatively skewed). In contrast, when we calculate the skewness of annual returns across individual stocks listed on the TSE from 1981 to 2009, the coefficient of skewness is positive in all but 1 year and averages 2.36. Thus, a risk or lottery seeker could better maximize his utility, with far less effort, by simply buying and holding a single volatile stock. Second, day traders may be overconfident in their prior beliefs about their abilities and biased in the way they learn. Several papers (e.g., Odean 1998, 1999; Barber and Odean 2000, 2001) argue that overconfidence causes investors to trade more than is in their own best interest. Overconfident day traders may simply be bearing losses that they did not anticipate. While novice day traders undoubtedly realize that other day traders lose money, stories of successful day traders may circulate in nonrepresentative proportions, thus giving the impression that success is more frequent than it is. Once investors undertake day trading, their prior overconfidence may be reinforced through biased learning as in Gervais and Odean (2001). Furthermore, day traders who earn gross profits but net losses may not fully consider trading costs when assessing their own ability. Third, day traders may trade for nonfinancial motivations including entertainment, a taste for gambling, and the desire to impress others (see, e.g., Grinblatt and Keloharju 2009). Some investors may enjoy the process of day trading so much that they are willing to persist in the face of regular losses. Some investors may be attracted to the casino like qualities of day trading with its frequent bets, wins, and losses.19 Some investors may choose to day trade in hopes of impressing others.20 We are unable to explicitly test whether day traders are motivated by overconfidence rather than the desire for entertainment, gambling, or to impress others. Nor is there reason to believe that overconfidence and nonfinancial motivations are mutually exclusive. Quite to the contrary, entertainment, gambling, and the desire to impress others are all likely to be more attractive reasons to trade if one is overconfident about one’s likelihood of success. In Mahani and Bernhardt's model, “all speculators are made worse off if some speculators are slightly overconfident” (p. 1315). Our results are consistent with this prediction. If heavy day traders persist in trading due to overconfidence, then that overconfidence is detracting from their own welfare and that of other speculators. The welfare of the heavy traders themselves is diminished because, on average, they earn net losses; the welfare of other speculators is diminished because, on average, heavy traders earn gross profits thereby reducing the average returns of other investors. The beneficiaries of this overconfidence are brokerage firms—through commissions—and the government—through the transaction tax. 7. Conclusion We test predictions of models of learning by rational traders and find clear evidence that the decision to continue day trading is influenced by their previous day trading returns. Nevertheless, rational models of learning do not explain all or even most day trading. Only the most experienced previously profitable day traders—less than 3% of active day traders on an average day--earn predictably positive net returns, and yet most experienced unprofitable day traders continue to trade and continue to reap losses. Nearly 3/4ths of day trading can be traced to traders with a history of losses. Persistent trading in the face of losses is inconsistent with models of rational learning. So, too, is the decision to try day trading when ex ante expected lifetime profits are negative. For prospective day traders, “trading to learn” is slow learning. This paper was previously titled “Do day traders rationally learn about their ability?” We are grateful to the Taiwan Stock Exchange for providing the data used in this study. Barber appreciates the National Science Council of Taiwan for underwriting a visit to Taipei, where Timothy Lin (Yuanta Core Pacific Securities) and Keh Hsiao Lin (Taiwan Securities) organized excellent overviews of their trading operations. We have benefited from the comments of seminar participants at Cal Tech, Columbia University, HKUST, Peking University, PUC Rio de Janeiro, Santa Clara University, Texas A&M, University of Ghent, University of Illinois, University of Oregon, University of Utah, University of Virginia, USC, UT-Austin, and Washington University. Ke Zhang thanks the National Natural Science Foundation for research support [grants 71720107001 and U1811462]. Appendix: Details of Return and Profit Calculations We calculate the intraday return from day trading on day t for a particular group (g) of investors weighted by the value of investors’ trades: rgt=∑i∑j(SijtL− BijtL) +(SijtS− BijtS)∑i∑j(BijtL− SijtL) (A1) where B and S denote the value of buys and sells (with superscripts L and S for long and short transactions, respectively) on day t in stock i by investor j. For long positions, the sales value (SijtL) is the value based on the actual transaction price or the closing price if the long position is not closed out prior to the end of trading. For short positions, the purchase value (BijtS) is the value based on the actual transaction price or the closing price if the short position is not closed out prior to the end of trading. The numerator in Equation (A1) is the intraday gross profit of trader i on day t. Consider a concrete example where an investor buys a stock for $100 and sells later in the day for $102. On the same day, the investor shorts a stock (the same stock or a different stock) for $100 and later covers the short with a purchase at $97. The investor makes profits of $5 = (102-100) + (100-97). We scale the dollar profits by the total value of the opening positions, $200 = $100 + $100. Thus, we assume the investor put $200 of capital at risk and earned an intraday return of $5/$200 = 2.5%. This is an accurate representation of the returns if the investor trades in parallel (i.e., both positions are open at the same time). For investors who trade sequentially, we correctly calculate dollar profits of $5, but the capital at risk would be $100 rather than $200 as the $100 would be deployed sequentially. Thus, we always estimate the correct sign of returns, but for day traders who trade sequentially our return estimates are biased toward zero. In addition, we do not know the extent to which traders use leverage, which would increase the magnitude of returns for both gains and losses, but again the sign of the gains and losses would be the same as those in our calculations. In summary, the sign of the day trading returns that we calculate is accurate, though the magnitudes may differ because of sequential trading or the use of leverage. When we calculate net returns and net profits, we deduct a 5 bps commission for all trades (10 bps round-trip commission) and a 30 bps transaction tax for sales. Put differently, buys cost 5 bps (Cb) and sells cost 35 bps (Cs). We also increase the capital requirements to reflect the total cost of the opening positions: rgtnet=∑i∑jSijtL-BijtL+SijtS-BijtS-cbBijtL+BijtS-csSijtL+SijtS∑i∑jBijtL+SijtS+cbBijtL+csSijtS. (A2) Continuing our example from above, the net return for the trader would be (102−100) + (100−97)−0.0005(100+97) − 0.0035(102+100)(100+100)+0.0002*100+0.0035* 100=4.19200.40=2.09% Note the net return (2.09%) is roughly 40 bps (the total round-trip trading costs of 10 bps in commissions and 30 bps in transaction tax) less than the gross return (2.50%). The shortfall is slightly greater than 40 bps, because we also increase the capital required to open the positions. The numerator in Equation (A2) is the intraday net profit of trader i on day t. Footnotes 1 Several papers document individual investors in the United States earn strong returns immediately following their trades (Barber, Odean, and Zhu 2008; Kaniel, Saar, and Titman 2008; Kelley and Tetlock 2013). Barber, Odean, and Zhu (2008) document poor returns (reversals) at longer horizons using a 20-year data set derived from TAQ; Kaniel et al. (2008) and Kelley and Tetlock (2013) use data sets with more limited time series and fail to find evidence of poor returns at longer horizons. 2 Throughout the paper we define day trading as the purchase and sale of the same stock on the same day by the same investor. In some analyses in the paper, we restrict our analysis to day traders who engage in day trading for at least 10 days (i.e., we filter out occasional day traders). In the analysis of investor performance, we include all trades because only analyzing round-trip trades imparts a serious positive bias in the calculation of returns. Specifically, investors are more likely to sell winning rather than losing investments (the disposition effect). As a result, a sale following a purchase is more likely if the returns following the purchase are good rather than bad. Thus, the disposition effect yields a positively biased portrait of returns if we analyze only round-trip trades. 3 In rational learning models, as well as Gervais and Odean (2001), the unconditional lifetime profit from trying trading is positive. 4 Because highly experienced profitable day traders trade more actively than others, they are overrepresented when measured on a daily basis. Employing a different methodology, Barber et al. (2014) estimate that less than 1% of individuals who day trade over the course of a year are predictably profitable. 5 A number of papers, including those of Feng and Seasholes (2005), Seru, Shumway, and Stoffman (2010), Nicolosi, Peng, and Zhu (2009), Chiang et al. (2011), Choi et al. (2009), De, Gondhi, and Pochiraju (2010), and Strahilevitz, Odean, and Barber (2011), document investor learning in various forms. 6 Risk-averse investors and those with high discount rates require a higher threshold of expected lifetime profits before choosing to enter the market because of the uncertainty of profits and the likelihood that losses will be incurred earlier than gains. 7 In the overlapping generations model of Mahani and Bernhardt (2007), the expected aggregate profits of all speculators and expected lifetime profits of an individual speculator are positive (because skilled speculators have informative signals and liquidity traders are willing to lose money trading with speculators). Thus, it is rational in their model for a risk-neutral speculator who does not know his skill level to enter the market. 8 Harris and Schultz (1998) study SOES bandits at two brokers. Garvy and Murphy (2002, 2005) analyze 15 and 1,386 day traders at one U.S. broker. Seasholes and Wu (2007) analyze the trades of ten active traders on the Shanghai Stock Exchange. Linnainmaa (2003) analyzes 7,686 Finnish day traders. Kuo and Lin (2013) analyze the performance of day traders on the Taiwan futures market in 2007–2008. 9 Trading also occurred on Saturdays during most of our sample period. Before December 1997, Saturday trading occurred from 9:00 to 11:00. From January to March 1998, stocks were traded on the second and the fourth Saturday in each month only. From April 1998 to December 2000, Saturday trading occurred from 9 am to noon. From 2001 on, trading has not occurred on Saturday. 10 The mean TWD/USD exchange rate from 1992 to 2006 was 30.54, with a low of 24.65 and a high of 35.01. 11 Many corporations are small firms that are majority or wholly owned by an individual. Thus, the corporate category of trader also includes thousands of individual investors who trade under the label of corporation. 12 Most of the 140,000 individuals who day trade in a month do not do so for all months of the year. Analyzing these same data, Barber et al. (2014) estimate that approximately 450,000 individuals day trade in a typical year. 13 Barber et al. (2007) and Linnainmaa (2005) document, respectively, that individual Taiwanese investors and Finnish day traders exhibit the disposition effect. 14 The relation between profits and the propensity to quit is similar regardless of whether we include control variables. However, the control variables are all reliably related to hazard ratios at the 1% significance level. Traders with more days of day trading experience are less likely to quit; a 1-standard-deviation increase in the log of number of days of past day trading reduces the base case hazard rate to 0.43. Day traders who have been trading longer are more likely to quit; a 1-standard-deviation in the log of the number of days since a trader’s first day trade increases the hazard rate to 1.24. Heavy day traders are more likely to quit; a 1-standard-deviation increase in the log of past day trading volume increases the hazard rate to 1.11. 15 We perform an identical analysis of the trades in month t placed by individual investors who do not day trade in month t. They perform worse before costs losing -12.8 bps per day (t=-14.5), but better after costs because they do not trade as frequently (losing -19.0 bps per day, t=-21.7). See Online Appendix Table A2. 16 This is less than the 2.2% of GDP figure reported by Barber et al. (2009) for three reasons. First, they analyze the trading of all individual investors (not just day traders). Second, the majority of individual losses occur after the first day of trade. Third, day traders perform better than other individuals. 17 As reported in Table 1, the beta of aggregate day trading returns is only 0.26. 18 We also estimate models including twelve lags of the dependent variable and find qualitatively similar results for new day traders and repeat day traders. 19 Kumar (2009) shows a correlation between the propensity to gamble and the types of investment decisions U.S. investors make. Barber et al. (2009) document that the introduction of a National Lottery in Taiwan coincided with a significant drop in trading volume on the Taiwan Stock Exchange. Grinblatt and Keloharju (2009) document that investors prone to sensation seeking trade more frequently. 20 Several papers argue that investment decisions are influenced by social concerns (e.g., Barber, Heath, and Odean 2003; Statman 2004; Hong and Kacperczyk 2009). References Barber B. M. , Heath C. , Odean T. . 2003 . 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The Review of Asset Pricing Studies – Oxford University Press
Published: Feb 1, 2020
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