Prior outcomes and risky choices by professional traders. Current draft: December Peter R. Locke* and. Steven C. Mann**

Transcription

1 Prior outcomes and risky choices by professional traders Current draft: December 2003 Peter R. Locke* and Steven C. Mann** *The George Washington University, Dept. of Finance, 2023 G Street, Washington, D.C., plocke@gwu.edu, phone ** The Neeley School of Business, Texas Christian University, TCU Box , Fort Worth, Texas s.mann@tcu.edu, phone (817) ; fax (817) We thank Chris Barry, Vassil Mihov, Richard Thaler, and Andy Waisburd, as well as seminar participants at the 2001 FMA meetings, the 2002 AFA meetings and TCU for helpful comments on a previous version of this paper titled, House money and overconfidence on the trading floor. Mann appreciates financial support from the Luther King Capital Management Center for Financial Studies. Locke thanks the George Washington University s School of Business and Public Management for summer research support.

2 Prior outcomes and risky choices by professional traders Abstract How is professional risk-taking influenced by prior results? We examine the impact of past gains or losses on subsequent futures traders activity. The evidence provides support for the Gervais and Odean (2001) model of overconfidence: we find little relationship between higher risk taking and unusual success among these traders. Also consistent with Gervais and Odean, successful traders exhibit a relatively stronger correlation of risk with prior income. We also find that experienced traders are relatively unlikely to take unusually high risks after a period of abnormally good profits. The results suggest that while success may inspire overconfidence, experience limits the impact.

3 This paper investigates the impact of prior results on the trading activity of a sample of professional futures traders. Irrational risk-taking following abnormal trading gains has been proposed as an explanation for various anomalous return, volume, and volatility relationships in securities markets, such as momentum and the equity premium. 1 This effect is typically framed in terms of the behavioral phenomenon of overconfidence. 2 For example, evidence of behavior consistent with overconfidence has been documented among retail investors (e.g., Barber and Odean 2000, 2001, 2002) who are presumably amateur traders. However, irrational behavior by amateurs may not be very important if rational behavior by market professionals limits the impact of irrationality. The rationality of market professionals is somewhat of an open question, and much of the general research on rationality with respect to the evaluation of prior outcomes is experimental. For example, Griffin and Tversky (1992) suggest that experts are more likely than others to exhibit the effects of overconfidence. 3 Haigh and List (2003) provide evidence that professional futures traders at the Chicago Board of Trade (CBOT) are more irrational than amateur (student) traders. Glaser, Langer and Weber (2003) also find that professional traders are overconfident compared to novices (MBA students). On the other hand, List (2003, 2004) finds that experienced participants in the sports card memorabilia market are more rational than amateurs. The prevalence of behavioral phenomena among financial professionals in their occupations, rather than in experiments, has not been fully explored. The remainder of the paper is organized as follows. Section 1 briefly describes the relationship of behavior to financial markets. Section 2 describes the floor-trading 1

4 environment, and how certain behavioral problems may affect trader income, volume, and risk exposure. Section 3 describes our data in some detail and presents summary statistics. Section 4 presents results of tests for income, volume, and volatility effects consistent with trading behavior resulting from overconfidence. These results are presented in aggregate and in groups based on relative raw and risk-adjusted income. Section 5 concludes. 1. Behavior in financial markets In financial markets, success is generally required for survival, and irrationality is likely to be accompanied by significant attendant costs. Biais, Hilton, Mazurier and Pouget (2002) provide experimental support for such costs, finding that subjects who are deemed overconfident earn relatively low trading profits, a result also documented in experiments reported by Nelson, Bloomfield, Hales and Libby (2001). Gervais and Odean (2001) predict that experience and learning will tend to eliminate the harmful effects of overconfidence. They develop a microstructure model with an informed but overconfident trader. The overconfidence bias, coupled with early success (from the informational advantage), leads to increased risk taking relative to a normal trader (or an unsuccessful trader), but individual overconfidence disappears over time as traders learn their true abilities. If this model holds, experienced professional traders should exhibit little or no evidence of overconfidence. 4 The Gervais and Odean model may have implications for the market effects of retail traders, whose documented seemingly irrational behavior has the potential to generate inefficiencies that can be arbitraged away by savvy, rational professionals. 2

5 Daniel and Titman (1999) show how market anomalies associated with overconfident investors may be exploited. They attribute the persistence of these exploitable anomalies to a lack of adaptive efficiency. Daniel and Titman build directly on Daniel et al. (1998), who model investor overconfidence in a multi-security economy. Overconfidence in these models has a continuing effect on relative market prices and leads to profitable bottom feeding strategies. 5 In this paper we examine the impact of prior outcomes on risk taking among a sample of professional futures floor traders. These individuals trade on the floor of a futures exchange, executing trades primarily for their personal accounts. They directly benefit from their trading, and presumably would be directly harmed by any behavioral abnormalities, perhaps in a more observable manner (to themselves and to the econometrician) than would retail investors. Our data set allows direct measurement of professional trading activity, rather than inferential assessments (from aggregate data), and eliminates the multifaceted problem of the interpretation of retail trading. In particular, the traders in our sample have homogeneous trading horizons, in contrast to the investor data employed by Odean (1999); the degree to which traders have widely different investment horizons potentially muddles the interpretation of earlier empirical results. Another advantage of using futures traders in behavioral analysis is the symmetric nature of short and long positions. Short and long positions have equal risk and equal liquidity, since neither has an initial value and there are no short sale restrictions. We address the remaining issue of the latent period of evaluation, by examining multiple time frames. Across these various potential evaluation time periods we find no evidence consistent with trader overconfidence. 3

6 Our results show that, in a variety of tests controlling for market and idiosyncratic factors, futures floor traders as a group do not exhibit abnormal risk-taking subsequent to abnormal trading gains. If anything, these traders subsequently take less risky positions when their recent income is higher, and increase their risk exposure subsequent to losses, and the findings are robust to various evaluation periods. Our evidence on the effect of prior outcomes on risk taking is consistent with Coval and Shumway (2001), who find increased risk-taking by losers on the Chicago Board of Trade. We thus find little evidence of overconfident behavior among these experienced professional traders. When we examine the cross-sectional characteristics of traders, we find evidence that success and experience are related to trading activity, particularly risktaking. We interpret the evidence in this paper as consistent with an (at most) initial overconfidence that evolves into rationality a manner much as that suggested by Gervais and Odean. The Gervais and Odean model implies that success by skilled but overconfident traders will lead to higher trading volume and lower risk-adjusted performance in the short run, but an increase in risk-adjusted performance over time. For less skilled traders who lose early on, there is no prediction of subsequent overconfidence or underconfidence, and such traders ought to fail at some point. Consistent with the implications of the Gervais and Odean model, we do not find evidence of pervasive overconfidence in our sample of professional traders. However, cross-sectional results indicate that successful (on a risk-adjusted basis) traders have a stronger correlation of risk taking with prior incomes. 6 4

7 2. Floor traders, risk and overconfidence Futures floor traders interact in a dynamic bilateral auction market. A member or leaseholder on the futures exchange may trade for a proprietary account or execute trades for others. There is no obligation by the member or leaseholder to be on the exchange floor, to be in any particular trading pit, or to actively bid, offer, or trade. During trade negotiations, the bid or offer to trade is theoretically only good while the words are in the mouth of the trader. Earlier evidence suggests that floor traders by and large act as market makers when executing trades for their personal accounts; see, for example, Silber (1984), Kuserk and Locke (1993) or Manaster and Mann (1996). Floor traders take on positions expecting to profit from price movements. Kuserk and Locke (1993) and Manaster and Mann (1996) show that floor traders on average earn a small amount on each roundtrip undertaken. However, Manaster and Mann (1999) find that the majority of trader income is due to timing (as opposed to the bid-ask spread), and Locke and Mann (2003) show that only about 60% of trades result in positive revenue. The mean profit per contract is low, around one tick (minimum price change) or less, while the mean absolute value of profit per contract for gains and losses is about five ticks. There are many large losses and large gains on the trading floor. Thus, floor traders take considerable risk when undertaking a trade, and are inadequately described as the order-matching mechanical operatives of the microstructure literature with linear price schedules. The speculative nature of their trading makes these traders ideal subjects for the study of behavior related to trading and risk. How can prior outcomes affect floor trader strategies? One possibility is if traders assign excessive weight to their own abilities when things go their way by chance, which 5

8 may be viewed as an example of overconfidence. Consider again Gervais and Odean (2001), whose overconfident traders initially over-adjust their priors when the truth corresponds to their signal, attributing too much of their success to their own skill. For the floor traders we are analyzing, this could mean that after observing a set of signals such as a flurry of communication by certain brokers with their customers, and then trading successfully, the traders may feel emboldened to increase their position upon observing similar signals again, whereas, in fact, these signals are simply noise. Thus, a period of relatively high income, which can be interpreted as confirmation of a signal, could be followed by an inordinate increase in trading activity and an increase in the volatility of trading income. However, if traders are simply mistaken, and are irrationally reacting to recent success, then subsequent relative success will come only by chance. A resulting increase in the volatility of the trader s income would be due to the signal being noisier than suspected by the trader, suggesting that prior relative success was only spuriously correlated with price innovations. In the Gervais and Odean (2001) model, traders suffering from overconfidence evolve from somewhat rational but noisy, to overconfident, and finally after discovering their true abilities back to rational. Their model predicts that overconfidence is a trait that will be exhibited mostly by unseasoned traders with greater inherent abilities, because (in their model) losses are not discounted and wins are overvalued. Traders with greater abilities are more likely to be successful, and thus build up some overconfidence, until they are made aware of their true abilities and outgrow the overconfidence. There is likely to be a significant difference between seasoned, successful floor traders, who should know their abilities, and traders who have not yet 6

9 completed their learning, or whose declining account balances are leading them toward alternate occupations. One major methodological problem in testing for evidence of overconfidence is determining the relevant evaluation period. 7 It is, in fact, a situational parameter. The experimental literature includes the assumption of very short horizons, within a fixed trading period such as an evening or half an evening. The literature that makes inferences from price and volume trading behavior (e.g., Daniel and Titman, 1999) examines much longer horizons. Bernartzi and Thaler (1995) discuss the critical nature of the evaluation period for the behavioral phenomenon of myopic loss realization aversion. Given these issues with the evaluation period, we employ a variety of time frames, although all of our evaluation periods are much shorter than a year to reflect the high trading frequency exhibited by our subjects. Our results are consistent across these various assumed evaluation periods. In addition, we encounter an interesting behavioral accounting issue in testing for effects of prior gains on subsequent trading. At any point in time in our sample, the results of previous trading consist of two elements: realized income and unrealized income (marking-to-market). Since behavioral effects are typically viewed in terms of realized results, we are mainly interested in focusing on future trading as a function of completed past trading results. However, unrealized potential income can also be measured throughout the day. We are able to distinguish incremental behavior by categorizing each trader s position at any time not only as a function of realized (past) gains and losses, but also on the basis of the intraday marking-to-market of any existing position. A trader may have executed a number of trades and accrued a large amount of 7

10 money (i.e., realized large gains), but simultaneously be deep in the hole with a large unrealized loss. Similarly, a trader may have amassed significant realized losses, but have large unrealized gains (or even further losses). Realized gains and losses both have the potential to affect subsequent activity through behavioral abnormalities. However, unrealized gains or losses are accompanied by existing positions, which are mechanically correlated with subsequent activity. If traders include unrealized gains or losses in their wealth evaluation, then subsequent activity, potentially affected by changes in wealth, can be both mechanically and theoretically affected by existing positions. We recognize the role of existing positions in our experimental design by providing cross-sections of trader activity across combinations of realized and unrealized changes in wealth. 3. Data and methodology The data consist of transaction records for 334 active traders in four futures pits on the Chicago Mercantile Exchange (CME) for There were 560 traders who executed at least one contract for their personal account in these pits, but most of these are transient (the selection procedure is described in 3.1 below). The transaction records are provided via the generosity of the Commodity Futures Trading Commission. The data include masked (but unique) trader identification, the price and quantity bought or sold, and the time (to the minute) that the trade occurred. We examine the four highestvolume currency and agricultural contracts traded on the CME: the Deutsche mark (mark), Swiss franc (franc), live cattle (cattle), and pork bellies (bellies). Each trader on the floor, upon completing a trade, fills in by hand a set of information on the trade. 8

11 Clerks input these data into a trade-matching algorithm. The algorithm assigns an imputed execution time for the trade consistent with recorded prices and the sequence of other trades. 3.1 Trader inclusion criteria Motivated by the open nature of the trading arena, we follow a trader screening process to select a subset of active individuals. In each of these pits there appear transient traders, trading a few contracts for their personal account one or two days out of the sample, or trading a small amount more frequently. For example, brokers (traders who are mainly executing trades for others) may make mistakes, and then absorb the trade and its offset into an error account, which in our data would appear as a small amount of proprietary trading. The filter we use selects all traders who traded ten or more contracts for their personal account on at least five or more days, in order to avoid contamination of results via inclusion of casual or error traders. For our one year of data, this filter provides a sample consisting of 109 mark traders, 88 franc traders, 99 cattle traders, and 38 pork belly traders. These traders account for over 95% of the proprietary trading for these markets. 3.2 Fundamental data We generate a set of fundamental trader data for our empirical analysis. Traders typically end the day flat with no net position in the contract (see Kuserk and Locke, 1993). Our analysis begins by building daily histories for each trader starting from an assumed flat position. 8 We calculate the time series of minute-by-minute trader 9

12 positions, the values of the position in terms of its mark-to-market (unrealized gain/loss), and cumulative realized gains/losses. At any point in time, a trader s total gain or loss consists of the realized gains or losses and the unrealized (mark-to-market) gains or losses on a current position. Preliminary analysis reveals that traders rarely offset a position completely during a day. Instead, a trader may take on a large position, or build a large position, and then work the position down slowly, buying and selling during the work-down. To calculate trading profits associated with a trade, we use an average-cost accounting method, explained below. We consider a trade to be completed every time a trader s inventory declines in absolute value, or when he/she buys and sells futures in the same minute. This includes times when his/her position may be eliminated by going from long to zero, may switch from long to short, or simply may involve a position reduction by going from long to less long. Similar completions would reduce the (absolute) size of short positions, which, since these are intraday futures trades, are perfectly symmetrical (for accounting purposes) to long positions. At each time that the trader completes a trade, we calculate the income earned on the trade and the number of contracts that have been offset. The income from a trade is the revenue from the offset of the trade less the average cost of the trade. Revenue and average cost are positive (negative) for trades offset by purchasing (selling). Needless to say, the income from a trade may be positive or negative. To mark a trader s position to market, we generate the volume-weighted average pit price for each minute and form a sequence of minute-by-minute settlement prices. For daily income statistics, traders are marked-to-market at the end of the day, and this final daily mark is added to the sum of their daily tally, though it is not included in the trade- 10

13 by-trade analysis. We also examine the risk-taking behavior of these traders. Overconfidence in the Gervais-Odean sense implies increased risk taking after a trader has earned an above-average amount of income. Our measure of risk is based on worstcase scenarios, using the trading history. Since we are able to mark each trader to market continuously, we can observe maximum potential losses (maximum unrealized losses) over any time frame. We use ex post Value at Risk ( VaR ) measures based on trader maximum absolute potential losses for time intervals on a daily basis. Table 1 presents summary statistics for the traders in the four CME pits for the full year 1995, reporting distributions for trading volume, income, and risk. The upper panel presents summary statistics across traders for the entire sample. For example, the median income of the 109 mark traders is $57,305. For pork bellies, the median income is $88,603. The lower half of Table 1 focuses on weekly success rankings. The data reported for quintile 1, for example, are the weekly statistics for traders ranked in the top 20% for that week. Thus, the top traders in Swiss francs had a median income of $22,622 per week; the similar statistic for pork bellies is $10,156. Corresponding to these incomes are measures of risk. For Table 1, we define the VaR for each trader as the minimum (largest negative) marking to market during a week. Thus, the average weekly income for the top quintile for cattle is $7,331, which the traders earn while risking, on average, $2,601. For the mark, the top 20% of traders ranked on weekly income have a median ex post VaR of $8,792. Note that while incomes decline monotonically, since this is our ranking characteristic, the VaRs do not. For the first four quintiles, VaRs decline with income. For the fifth quintile, the value at 11

14 risk is actually higher than the fourth, and for all but cattle the median VaR is higher for the fifth quintile than the first quintile. We also calculate a measure of return for the traders, assuming that the VaR corresponds to a capital requirement in an economic sense. In addition to this risk-based capital, we figure a seat charge for a trader based on a seat price of $0.5M, a rough estimate of the cost of a CME seat in We charge the seat price and VaR at 12% per year and calculate risk-adjusted returns as income less the risk charge and seat lease charge, divided by the VaR. These returns are also listed in Table 1 and are in the range of 2% to 6%, albeit negative for some of the lower quintiles. 4. Behavioral analysis In this section we document the degree of heterogeneity in our sample, in particular comparing relative success to the activity level of the trader. Key predictions of the Gervais and Odean (2001) model are, first, that successful traders are more likely to be overconfident, and second, that seasoned traders will exhibit less overconfidence because they discover their true abilities over time, after some initial overconfidence. Gervais and Odean show that because these traders are overconfident and highly skilled, they outperform less highly skilled traders to a greater degree than would be the case if they were not overconfident. Though our data are limited to one year, we are able to make some inferences based on the relative success of our traders, as well as the trading of new entrants. We examine trader income stability by grouping traders according to value added (income). To establish a measure of stability, we first group traders into quintiles based 12

15 on their first week s income ranking. We form a four-week moving average of weekly average ranks for the traders in each of these quintiles for every week in the year, which we depict in Figure 1. While there are obvious occasional jumps, there is evidence of broad stability in the group rankings. The traders who are ranked in the highest quintile in the beginning of the year for the most part remain there (on average as a group), with only infrequent departures. Also observe in this graph that pork belly traders exhibit more volatility in the group rankings than do traders in the other three contracts. 9 While informative regarding group rank stability, the graph obscures substantial volatility in individual trader rankings, as even the most successful traders have bad weeks. This graphical depiction suggests that the traders in the lower quintiles have only limited staying power, in the sense that they persist in earning relatively low incomes, which may not be covering the costs of trading. To investigate this instability, we examine the tenure of the traders in our sample, based on their annual income quintile. Table 2 presents means and medians for weekly income, the number of trading days (out of a possible 252), tenure (the difference, in terms of number of trading days, between the first and last trading day that a trader is observed), and trading intensity (trading days/tenure) for traders in each quintile. The distributional statistics reported in Table 2 show that traders in the top quintile in each pit (with the exception of bellies) earn a substantially higher trading income than traders in the second quintile. For the mark and cattle, the top quintile earns on average three times the second quintile s average income. For the franc and pork bellies this multiple is about two. When we look at trader tenure, we see that the traders in each quintile trade for a large number of the possible trading days, with similar tenure for traders in the top three 13

16 quintiles. In addition to the number of days traded, we consider steadfastness in the pit, which we measure by trading intensity. This is potentially interesting because traders may wander from pit to pit, or have other things to do, and there is no constraint on their trading behavior. The intensity numbers show that traders in the top three quintiles for each contract are similar in their intensity, around 70-90%. Traders in the lower two quintiles trade less than 50% of the time, or on about half of the days during the year between their first and last days of trading. Our conclusion from this analysis is that we may compare the most successful traders to traders with lesser success and be somewhat confident that these groups are not arbitrarily different, but rather are persistently different Risk taking and prior outcomes In this section, we analyze trader activity in an attempt to identify evidence of an increased risk appetite subsequent to abnormal trading gains. In order to minimize any possible bias introduced by intraday patterns, we examine each trader each day at the same time. For each day, for each trader, we calculate the daily income earned up to the observation time and the mark-to-market at the time of the observation. We report results derived from taking a snapshot at the end of the third hour of trading, and examining risk taking and other trading statistics in the fourth hour. We have replicated this analysis for alternative times of the trading day, obtaining qualitatively similar results. The empirical question is whether prior losses or gains changes in wealth - have an impact on subsequent trader activity. At any time during a day, the change in a trader s wealth up to that time is comprised of both realized income and the current mark- 14

17 to-market of the trader s position (potential but unrealized income). However, some component of subsequent activity is mechanically related to any existing position associated with marking-to-market, at least partially because traders tend to eliminate positions by the end of the day. Therefore, we decompose the change in trader wealth into realized and unrealized components at every point in time. For purposes of comparison across traders, we normalize gains and losses. For each trader, we rank into quintiles each day s realized gains through the third hour of trading and the day s unrealized gains (mark-to-market) at the end of the third hour of trading, which results in 25 categories combinations of realized gains and mark-tomarket for each trader (a trader trading 200 days would have 8 trader-day entries in each of the 25 categories, 8 would be the days of highest realized and unrealized income, 8 would be the days of lowest realized and unrealized income, with the other 184 days falling into the 23 other categories). Particular observations from across traders are then combined based on these categories. For example, the 1/25 of a trader s days that have the highest third-hour mark-to-market and the highest realized income are combined with the corresponding 1/25 of days for the other traders. The goal is to collect those days when traders have extraordinary gains by their own standards and examine trader behavior in those circumstances. We examine risk-taking and income in the hour immediately following the evaluation period. We measure risk-taking by the trader s maximum potential loss during that hour. This is the largest, in absolute value, negative mark-to-market. While this exposure may or may not result in a realized loss, at the time of the exposure measurement, an immediate closing out of the trader s position would result in 15

18 approximately this loss. Across all trader-days in each cell, we calculate the median subsequent-hour (hour 4) risk exposure and median income. These medians across trader-days are presented in Table 3, aggregated across all contracts (panel A) as well as for individual contracts (panel B). Table 3 also reports medians for realized income and the mark-to-market. There are 25 divisions or cells in Table 3, each representing a combination of mark-to-market ranking and realized income ranking by trader-day quintiles. In each cell we report the median of the classifying variables (realized gains and unrealized gains), and median income and risk in the succeeding period. Panel A of Table 3 presents activity statistics aggregated across all contracts. The first column in each cell presents median realized gains through hour 3. For example, the first cell of the first column contains median realized gains for the days when traders had the highest realized gains. Reading down the column, the median incomes (from $2,033 to $2,062) represent median income for mark-to-market ranks from high to low, holding constant the realized income. Realized income does not appear to be related to the endof-period mark-to-market, with the exception of the middle quintile median mark-tomarket, which appears associated with lower median prior income. The third column within each cell presents subsequent median income, and the fourth column presents subsequent median risk taking. Subsequent income appears related to the mark-to-market going into the period, although looking at all cells the relationship is not always monotonic. A reasonable prior would be that subsequent value at risk increases as the markto-market falls from the first rank to the fifth. In other words, if the trading period begins with a high positive mark-to-market, then the subsequent largest negative mark would not 16

19 be expected to be particularly large. However, this is clearly not the case. As expected, traders in the fifth mark-to-market quintile (the early losers) exhibit the highest subsequent value at risk. But both the first (winners) and fifth (losers) mark-to-market quintiles generally show the highest subsequent value at risk, especially compared to the middle mark-to-market quintile. This table suggests that extreme markings to market (very high or very low) predict subsequent extreme risk taking, i.e., relatively large potential losses. It is easy to see how this result could be due to day-specific factors. Days with an exogenous, unpredicted shock to volatility, for example, could easily lead to increased variability in the mark-to-market. This corresponds with the raised risk at the first and fifth mark-tomarket quintiles, which is generally true across contracts and previous incomes. Since this day-specific factor confounds the inference problem, we adjust our subsequent tests for variation in daily trading environments. We test for significant patterns in risk taking based on realized income and marking-to-market. Prior to performing the tests, we apply two normalizations to the data. The first accounts for trader-specific behavior, and the second accounts for dayspecific pit-based risk factors. We calculate each trader s risk for the subsequent hour each day in terms of standard deviations from that trader s mean exposure during that hour across the entire year. For the day-specific risk factor we calculate a market risk measure for each day, based on activity prior to the measurement time. We first form the cross-sectional distribution of trader VaRs for the evaluation period each day. We then define the raw market risk for that day as the 75 th percentile from this distribution, so that 25% of the 17

20 traders have a larger potential loss than this exposure for that day. Finally we normalize the raw market risk, forming standard deviations of market risk from the mean market risk across the entire year. We adjust each trader s subsequent VaR by this day-specific factor. We subtract the day-specific risk factor from the individual trader s VaR in the subsequent period, providing an excess risk metric scaled in differences of standard deviations, which allows us to aggregate across traders and days. If a trader s risk taking was above normal subsequent to evaluation, but the market was also more than normally volatile, then these would essentially offset, leaving the risk for the trader that day rather normal. Positive values for this excess risk metric indicate extra risk taking, controlling for market conditions, while negative values indicate less risk. We examine excess risk metrics across all 25 realized income and mark-to-market categories, calculating means and t-statistics to test the null hypothesis of zero mean for each particular cell. If the mean excess risk is negative, then traders are taking less risk for that combination of income and marking-to-market, on average. If the difference is positive, then traders are taking more risk for that combination. Table 4 reports these means along with t-statistics testing whether these tendencies are significantly different from zero. The five-by-five matrix reported in Table 4 provides a rich level of information. For enhanced clarity and clearer inference, it is useful to examine the matrix corners, where traders had extreme realized and unrealized gains. 18

21 The results are summarized below: Table 4 summary Abnormal risk (t-stat in parentheses) for traders with abnormally: Large unrealized gains Large unrealized losses Large realized gains (-8.2) (4.5) Large realized losses (9.7) (21.7) The results indicate that abnormal gains are associated with declining subsequent risk, and that losses (abnormally low gains) are associated with increased risk-taking. Examining the first column in Table 4 (highest realized gains) in more detail, the t- statistics are overwhelmingly negative and significant, except for extremely low markingto-market positions. Recall that extremely low marking-to-market (large unrealized loss) naturally leads to expectations of higher subsequent risk (potential loss). Thus, looking across the fifth row of each subsection, we see that as realized gains fall from high to low, the marking-to-market rank is held low, and there is significantly higher risk in many instances. The only other indication of significantly higher subsequent risk taking is for the lowest realized income those observations where traders lost the most relative to their own income distribution. In addition to the measure of risk in terms of dollars, we also examine the position held in the subsequent period by each trader. Some may consider this measure to be more direct, since it reflects only the trader s actions rather than a combination of actions and price movement. Since traders are able to trade continuously, and should be able to avoid large losses by exiting positions early, we consider both to be direct measures of exposure. For this analysis, the absolute size of the trader s maximum position (either 19

22 short or long) is calculated each day for the hour after the observation time, and then normalized into standard deviations as above for risk. A similar day-specific position factor is again used to adjust the individual standard deviations. Table 5 reports these statistics, which are summarized below for the corners of the five-by-five matrix: Table 5 summary Abnormal position ( t in parentheses) for traders with abnormally: Large unrealized gains Large unrealized losses Large realized gains (-2.7) (3.5) Large realized losses (3.4) (9.4) The results complement those of Table 4. Higher ex ante income is associated with significantly smaller subsequent position taking. Looking in more detail at Table 5, we see that many instances of the fifth level of marking-to-market are positive, but the pattern is not the same as for risk. There are far fewer instances of significantly positive abnormal positions than there are abnormal risks. Again, there is no evidence of overconfidence. On the other hand, there is evidence that losses are associated with increased subsequent risk taking, consistent with evidence from the Chicago Board of Trade documented by Coval and Shumway (2001). 4.2 Experience, success and unusual risk taking The Gervais and Odean (2001) model implies that the observed effects of overconfidence vary across traders on the basis of success and experience. The model predicts that the traders most likely to exhibit overconfidence (in the short run) are highly skilled traders. Unskilled traders are less likely to be successful, hence are less likely to 20

23 become overconfident: they rarely get a chance due to poor skill. The model also implies a reduction in overconfidence as traders gain experience and learn to distinguish their abilities from otherwise random successes. We examine these implications by isolating the individual decisions from market factors. Table 6 reports differences in abnormal risk taking (as previously defined for Tables 3, 4, and 5) between the most successful traders (highest quintile) and the least successful traders (quintiles 4 and 5). Table 6 shows that the most successful traders take comparatively more risk after winning than do the less successful traders. Below we summarize the results of Table 6 for the matrix corners: Table 6 summary The difference between the abnormal risk metrics for the best traders and the worst traders ( t in parentheses) when the traders have abnormally: Large unrealized gains Large Unrealized losses Large realized gains (3.1) (0.6) Large realized losses (4.1) (-2.1) As the corners of the Table 6 matrix show, the best traders take on more risk when ahead and less risk when behind, relative to the worst traders. Thus, even though the traders generally take less risk when ahead, these success-dependent results show some consistency with the Gervais and Odean result that overconfident traders are successful. One interpretation of these results, reconciling Table 6 with Table 5, is that overall the overconfidence has been tempered (perhaps due to long term success, as with Gervais and Odean) and yet, relatively speaking, the successful traders are more likely to 21

24 exhibit a positive correlation between prior gains and subsequent risk-taking than are the less successful traders. 4.3 Longer-horizon effects As described above, the time frame for evaluating past trading and its effect on current behavior is ad hoc, opening the possibility of a search within any set of data for some look-back time frame that would generate empirical results showing increased risk taking after abnormal income. Such a search is properly constrained by the institutional setting in which the data are generated. In our case, the futures trading pit suggests a relatively brief evaluation period, consistent with the intraday time frame of most positions taken by the traders on the floor. Nonetheless, we expand the analysis to consider day-to-day effects. In this sense, traders could be considering good days versus bad days, making these evaluations overnight, and taking on excess risk the next trading day after a good day. To examine this possibility, we use look-back periods ranging from one to five trading days, allowing for various potential evaluations so as to provide a robust search for evidence where prior gains or losses might influence risk taking. We measure the tendency to take abnormal risk for each trader (i) via a regression coefficient from model (1): VaR (i) t = α ik + β ik [abnormal gains over past K days prior to t] + ε ikt (1) We estimate model (1) for five different prior profitability periods, examining gains over the prior k days, where k = 1, 2, 3, 4, or 5. We use non-overlapping 22

25 observations. We varied the starting date, and obtained similar results to those reported. In addition, we examine variation across traders in abnormal risk taking by estimating a second regression, model (2), with the first-pass regression slope estimate for each trader (β i ) from model (1) as the dependent variable, using trader relative success and experience (days trading in the sample period) as explanatory variables: β ik = α k + δ k [success (i)] + φ k [days trading in year(i)] + w ik (2) Table 7 reports analysis for inter-day tests for this relationship. These results show that experience appears to reduce even further the tendency to take abnormal risk subsequent to making abnormal profits. The coefficients on gains, similar to the findings in Table 5, are all significantly negative. In model (2), the relationship of risk to past gains is regressed against success and the amount of trading. The coefficient on the number of trading days is negative for all five evaluation periods, but only significantly so for the three-day period. Together, these results offer little support for the view that professional traders are subject to an overconfidence bias. This is comforting, since these traders are functioning as market makers, filling an important role in the hedging and speculative trading by commercial traders. Due to their role as dealers, if these traders were burdened by trading biases it would affect not only on their own profitability but also the trading of many other individuals. 23

26 5. Discussion and Conclusions Trader overconfidence is often cited as a potential explanation for certain otherwise anomalous price dynamics. However, one implication of Gervais and Odean (2001) is that overconfidence dissipates with experience, a process that should be particularly evident among seasoned professional traders. Professional guidelines refer time and again to the benefits of disciplined trading, which one could interpret to mean trading without emotional baggage such as overconfidence. For example, Locke and Mann (2003) find that disciplined trading is related to future success. In contrast with the implications of overconfident trading, this paper s evidence indicates that professional floor traders do not increase risk taking subsequent to unusual gains. Overall, we find no evidence that these traders are overconfident. If this group of CME traders is experienced (a likely assumption), then our results are broadly consistent with the Gervais and Odean model. Our evidence also supports the Gervais and Odean implication that successful traders express themselves with relatively greater confidence based on prior revenues. We find that the most successful traders have a stronger correlation of risk with prior income than less successful traders. We also provide evidence that trader experience appears to play an important role traders with more experience are less likely to take more risk after a period of abnormally good profits than are their less experienced counterparts. The robustness of our evidence on experience is limited, however, because our data are restricted to one year of trading. An interesting, ambitious follow-up would be to examine trader entrants over a multiple-year evaluation period so as to more 24

27 precisely distinguish success from experience in empirical investigation of the Gervais- Odean learning hypothesis. 25

28 Notes 1 See Daniel, Hirshleifer, and Subrahmanyam (1998, 2001). 2 Overconfidence may take many forms, but one example is irrationality in a Bayesian model, under- or over-valuing priors. Another behavioral phenomenon which has connotations for prior results and risky choices is the house money effect of Thaler and Johnson (1990). 3 Griffin and Tversky (1992) find that overconfidence may be associated with positive but weak signals, while under-confidence arises from strong, negative signals. 4 Overconfidence is not necessarily incompatible with success in all settings. Bernardo and Welch (2001) examine overconfidence in an economy where entrepreneurs compete. In the equilibrium, overconfident entrepreneurs survive because while they are more likely to take risky projects, those projects also have higher expected returns. 5 Additional background is provided in reviews of behavioral literature related to finance by Shiller (2000), Hirshleifer (2001), and Shefrin (1999). 6 Coval, Hirshleifer and Shumway (2001) provide evidence on the persistence of success among retail investors. 7 The evaluation period is the interval of time for which prior results have an impact on subsequent behavior. 8 Traders may trade for their personal account off the floor, by sending in orders, or while on the floor, by assigning a trade to another trader. Both of these instances would not show up in our data as trades for the trader, and yet would affect the trader s inventory. We thus assume the overnight flat position for traders and proceed to build intraday histories. 26

29 9 Individual rank time series are interesting also, though graphically overwhelming. There are occasional jumps from rank 1 to rank 5, which we interpret as evidence of significant risk taking by the highest income traders. 10 This corresponds to the findings in Coval, Hirshleifer and Shumway (2001) regarding the persistence of retail investor success. 27

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