Survival of Overconfidence in Currency Markets

Survival of Overconfidence in Currency Markets Thomas Oberlechner1 Webster University Vienna Carol Osler2,* Brandeis International Business School 1 Thomas Oberlechner, Webster University Vienna, Department of Psychology, Berchtoldgasse 1, A-1220 Vienna, Austria, Email: [email protected] 2 Carol Osler, Brandeis International Business School, Brandeis University, Mailstop 32, 415 South Street, Waltham, MA 02454, USA, Email: [email protected] * Corresponding author Acknowledgments: The authors gratefully acknowledge helpful comments from Steve Cecchetti, Blake LeBaron, Lukas Menkhoff, Dagfinn Rime, Paroma Sanyal, Robert Shiller, David Simon, and Hanno Ulmer, as well as seminar participants at the Expertise in Context Conference in Berlin, the University of Hannover, Queens University Belfast, the LIEP group at Harvard University, Norges Bank, and the Federal Reserve Bank of New York. Also, we acknowledge with thanks each foreign exchange professional who took the time to fill out the survey. We gratefully acknowledge financial support for this research from Hottinger & Partner and the Austrian Science Fund (Schroedinger Scholarship #J2219 and #J1955-SOZ). Survival of Overconfidence in Currency Markets This paper tests the influential hypothesis, typically attributed to Friedman (1953), that irrational traders will be driven out of financial markets by trading losses. The paper’s main finding is that overconfident currency dealers are not driven out of the market. Dealers with extensive experience are neither more nor less overconfident than their junior colleagues. We set the stage for this investigation by providing evidence that currency dealers display two forms of overconfidence: they underestimate uncertainty and they overestimate their professional success. This is notable since dealers face strong incentives to accuracy, have access to comprehensive information, and have extensive experience. [Key words: Overconfidence, imperfect rationality, behavioral, exchange rates, foreign exchange, survival of imperfect rationality. JEL classifications: G14, G15, F31.] I. Introduction This paper tests whether imperfect rationality survives in financial markets, an issue that is central to the debate between neoclassical and behavioral economics. According to the neoclassical view, most famously articulated by Friedman (1953), irrational traders will buy assets at high prices and sell them at low prices, thus incurring trading losses that ultimately drive them out of the market. Since extensive evidence now exists for the presence of imperfect rationality in financial markets (Hirshleifer (2001); Daniel et al. (2002)), this argument provides an important justification for maintaining an exclusive focus on rational agents: If irrational traders are eventually forced to cease trading, then imperfect rationality may have at most a transient influence on prices. Nonetheless, empirical research on this question is at best rare and perhaps nonexistent. The evidence presented here suggests that one form of imperfect rationality, 2 overconfidence, does survive in financial markets and may in fact be unaffected by trading experience. We focus on the world’s biggest market, the foreign exchange market, and on the agents that set the prices in that market, the dealers. We first provide evidence that currency dealers are indeed overconfident, on average, as logically required for this investigation. Consistent with evidence for other financial-market agents (see, for example, Glaser and Weber (2007)), the dealers display two forms of overconfidence: they underestimate uncertainty and they overestimate their own abilities. We test whether overconfidence survives the rigors of the marketplace by comparing overconfidence across dealers with differing levels of experience. We find that experienced and inexperienced currency dealers are equally overconfident. This robust result holds for both dimensions of overconfidence; it holds whether we measure experience by years of trading, age, or institutional rank; and it holds for different types of dealers. The literature suggests a number of reasons why overconfidence might survive in financial markets. Overconfident traders might make more money because they take on more risk and thus earn higher returns (De Long et al. (1991); Hirshleifer and Luo (2001)). They might make more money because their cognitive performance – and hence their ability to spot profitable trading opportunities – is enhanced by illusions of success (Taylor and Brown (1988)). Overconfident traders might be more successful even without making more money if their overconfidence inspires superiors and customers to regard them highly (Trivers (1985)). Finally, overconfidence might not enhance success per se but it might instead be necessary for dealers to persist in this stressful, high-stakes profession (Oberlechner (2004); Oberlechner and Nimgade (2005)). 3 Our finding that overconfidence survives among currency traders has potential relevance for issues in both international economics and microstructure. At the intersection of those two, for example, we find the puzzle of excessive real and nominal exchange-rate volatility under floating exchange rates (Flood and Rose (1995)). Theoretical work by Odean (1998) suggests that overconfident agents are likely to trade more and that this excess trading could foster excess volatility. Deaves et al. (2003) and Glaser and Weber (2007) confirm empirically that overconfident agents do trade more than others. The survival of overconfidence among currency traders could also explain the profitability of trend-following technical strategies in currency markets (Menkhoff and Taylor (2007)), since overconfidence can be the source of trending and trend reversals (Daniel et al. (1998)). The forward bias puzzle – meaning the substantial average risk-adjusted returns one can expect from holding high-interest currencies – is another foreign-exchange anomaly that may be related to the survival of overconfidence. Decades of effort to trace this puzzle to time-varying premiums for volatility risk have had at best mixed success (Engel (1996)). An important alternative explanation involves imperfect rationality, for which substantial evidence has long existed (Goodman (1979); MacDonald (2000)). This evidence indicates that professional exchange-rate forecasts are biased, inefficient, incompatible across horizons, and less accurate than the naïve forecast of no change. As shown in Burnside et al. (2010), overconfidence could be responsible for some of the forecasts’ shortcomings as well as the overall inverse relationship between exchange-rate changes and interest differentials. When studying the rationality of economic agents it is important to have an objective basis for choice among the infinitude of potential departures from perfect rationality. Otherwise, deviations from rationality could be tailor-made to explain each anomaly, leaving the overall 4 hypothesis of imperfect rationality essentially impossible to disprove. Our objective basis for choice is the large body of evidence for overconfidence from the disciplines of psychology and economics. The widespread human tendency towards overconfidence was noted as early as the mid-1960s (Oskamp (1965)) and is by now one of the strongest findings in the psychology of judgment and cognition. In the world of asset management, overconfidence has been identified among defined contribution pension plan members (Bhandari and Deaves (2006)), pension-plan decision makers (Gort et al. (2008)), individual online brokerage investors (Glaser and Weber (2007), (2009)), and financial planners (van de Venter and Michayluk (2008)). More broadly, overconfidence has been identified in settings ranging from corporate investment decisions to medical diagnosis to driving skills (Malmendier and Tate (2005); Hoffrage (2004) and Alicke and Govorun (2005) provide recent surveys). We are not alone, of course, in relying on evidence from psychology to provide a scientific basis for the study of imperfect rationality (see, e.g., Barber and Odean (2000), (2001); Daniel et al. (1998); Biais et al. (2005)). We focus on two important dimensions of overconfidence: hubris and miscalibration. Hubris refers to the tendency to overestimate one’s own success (Alicke and Govorun (2005); Camerer and Lovallo (1999); Roll (1986)). Miscalibration refers to the tendency to overestimate the precision of one’s information (Lichtenstein et al. (1977); Soll and Klayman (2004)); its name refers to the way perceived probabilities are poorly calibrated to true probabilities. Our sample of North American currency dealers brings several strengths to the analysis of imperfect rationality in finance. First, dealers are the agents who actually set prices; many studies in behavioral finance focus on amateurs, whose influence on the market might be limited. Second, dealers face intense financial incentives for accuracy: dealers’ annual bonuses, which typically reach $100,000 and often exceed $1 million, are largely determined by their personal 5 trading profits and the penalties for losses can include the loss of a job. Third, dealers are experts in their field who get daily practice and are provided by their employers with comprehensive information resources. Finally, the extent of the dealers’ experience varies widely: some are trainees while others have over twenty-five years of experience and have the title of Treasurer. The paper is structured as follows. Section II, which follows, summarizes academic perspectives on the survival of overconfidence in financial markets. Section III outlines the structure of the foreign exchange market and describes our data. Section IV provides evidence that dealers tend towards miscalibration and hubris. Section V presents the evidence for our main finding, specifically that overconfident dealers are not driven out of the market. Section VI concludes. II. Overconfidence and the Survival of Imperfect Rationality By now, most economists assume that departures from rationality exist in financial markets. Nonetheless, they often doubt that these departures compromise financial market performance. The view is that even if “investors are irrational …, they [may be] met in the market by rational arbitrageurs who eliminate their influences on prices” (Shleifer (2000), p. 2), an argument often expressed in terms of a “rational marginal agent.” The present study examines whether overconfidence, as one form of imperfect rationality, survives among the market participants most likely to serve as marginal agents. Foreign exchange dealers set the price in almost every currency transaction of meaningful size and they undertake speculative and arbitrage trades with substantial resources at their disposal. If overconfidence survives within 6 this group then, given limits to arbitrage, there may not be sufficient rational marginal agents for the market to achieve and maintain efficient prices.1 Skepticism about the survival of imperfect rationality is often based on Friedman’s (1953) depiction of how trading losses could drive imperfectly rational traders out of business. Though Friedman’s analysis did not cite a specific form of imperfect rationality, it could logically be expected to apply to overconfidence. Biais et al. (2005) find a direct empirical relation between miscalibration and reduced trading performance. The connection could operate through excess trading which in turn can result from either miscalibration (Odean (1998)) and or hubris (Glaser and Weber (2007)). Skepticism about the survival of imperfect rationality is also sometimes based on a set of related ideas about cognitive performance: “(i) that people, through repetition, will learn their way out of biases; (ii) that experts in a field, such as traders in an investment bank, will make fewer errors; and (iii) that with more powerful incentives, the effects [of cognitive biases] disappear” (Barberis and Thaler (2003)). While it seems logical that experience, expertise, and incentives will overcome irrational tendencies, the evidence for all three points is mixed at best. For example, studies show that experience sometimes reduces forecasting accuracy (Staël von Holstein (1972); Glaser et al. (2005)) and raises overconfidence (Bradley (1981)). With respect to expertise, a few studies find that it reduces miscalibration (Keren (1987); List (2003); Murphy and Winkler (1984)), but most studies find that it has no effect (Chen et al. (2007); Lichtenstein et al. (1977)). Likewise, financial incentives appear to attenuate some biases (e.g., Laury and Holt (2005)) but they do not eliminate miscalibration (Fischhoff et al. (1977); Sieber (1974)). 1 We note that when there is positive-feedback trading, as there is in currency markets (Osler (2009)), the presumption that rational arbitrageurs eliminate departures from the efficient price is incorrect (De Long et al. (1990)). 7 The finance literature suggests a number of reasons why overconfident agents might actually survive. De Long et al. (1991) argue that overconfident traders hold riskier assets than others and thus earn higher average returns. Kyle and Wang (1997) show that overconfident individuals involved in bilateral negotiations can survive because other participants compete less aggressively. The trading strategies of overconfident traders may help them exploit the mispricing caused by liquidity and noise traders (Hirshleifer and Luo (2001)). Wang (2001) shows, in a theoretical setting, that in markets with high fundamental volatility both underconfident and extremely overconfident agents are driven out while modestly overconfident traders ultimately dominate. Overconfidence may also enhance success and promote trader survival through a number of psychological channels. Overconfidence could support trading success because it enhances cognitive abilities (Greenwald (1980)) and it could support non-trading skills such as organizational capability and leadership because it promotes self-esteem (Taylor and Brown (1988)). Overconfidence may also speed professional advancement by inflating others’ opinions about oneself (Trivers (1985); Bénabou and Tirole (2002)). Finally, overconfidence fosters persistence, an essential trait in a profession where setbacks occur daily (Felson (1984)). “Confidence in his abilities and efficacy can help the individual undertake more ambitious goals and persist in the face of adversity” (Bénabou and Tirole (2002), p. 872). Currency dealers concur. According to a trading manager at a top-ten institution interviewed by the authors, “If you are not that self-confident, you are not going to be a good trader.” Dealers may self select for overconfidence through a "sleep-well-at-night" effect: those that can handle the stress sleep well at night while the others switch careers. 8 As this summary indicates, the disciplines of both psychology and economics provide conflicting theoretical and empirical predictions about the survival of imperfect rationality in financial markets. Identifying which predictions are correct requires empirical tests. III. Market Overview and Data Trading in the foreign exchange market, the world’s largest by any measure, averages roughly $4.0 trillion per day (Bank for International Settlements (2010)). Dealing banks stand ready to provide instant liquidity to hedge funds, mutual funds, and other asset managers; corporations that buy and sell goods internationally; central banks; and other “end-user” institutions. In this predominantly wholesale market, the dealers are involved in almost every significant currency trade. The interdealer market, in which banks trade with each other, by itself represents almost half of total trading (Bank for International Settlements (2007)), and the rest of trading almost invariably involves customer-bank transactions. A typical dealing room includes salespeople, interbank traders, and proprietary traders. Salespeople manage the bank’s relationship with customers. Interbank dealers use the interbank market to manage inventory accumulated in customer trades, to speculate, and to do arbitrage. Proprietary traders – usually interbank dealers with extensive experience – speculate with the bank’s own funds in foreign exchange and other assets. (Foreign exchange market structure is described more fully in Osler (2009).) Our analysis of overconfidence is based on the results of a survey distributed on June 25, 2002 to all foreign exchange dealing banks in North America. North American dealers, in aggregate, account for almost one fifth of world-wide trading (Bank for International Settlements (2007)). Of the 1,080 questionnaires sent out, 416 were completed, an overall return rate of 38.5 percent; this compares favorably with return rates of other surveys of foreign exchange 9 professionals, which are sometimes in single digits (Cheung and Chinn (2001)). In aggregate, the North American dealers in our study have vast trading capacity: the sum of their daily position limits is at least $30 billion.2 Participating institutions include a number of prominent banks with familiar names, which we label “top-tier banks.” Appendix A lists the membership criteria for this group. Research based on survey data has become fairly standard in the analysis of exchange rates (e.g., Frankel and Froot (1987); MacDonald (2000); Cheung and Chinn (2001); Menkhoff (2001)). This acceptance reflects, in part, an acknowledgment that carefully structured surveys provide no incentive to distort the truth. Further, evidence indicates that our results would be unchanged even with financial incentives for accuracy (Fischhoff et al. (1977); Sieber (1974)). The survey first assessed a number of personal and professional attributes, from which we draw the following portrait of participating dealers (see Table 1). About half of them work in New York City, and most work in the spot market. The participants primarily trade U.S. dollars against the euro, the yen, and the Canadian dollar, with smaller concentrations trading U.S. dollars against British pound and Swiss franc; a few trade other currency pairs. Though a majority of our participants trade in the interbank market, sizable portions work in sales (32 percent) or serve as proprietary traders (20 percent). Many dealers have multiple functions. Over one in five of the salespeople are female, while only one in thirteen interbank and proprietary traders are female. [Table 1 near here] Since our study focuses on the effects of experience on overconfidence, it is essential that the dealers in our sample represent a wide range of experience. The Trainees in our sample have 2 The aggregate limit figure is based on dealer responses when asked to locate their position limit on a list with five ranges: $0 -$10 million, $11-$25 million, $26-$50 million, $51-$100 million, and over $100 million. 10 spent just over one year on a trading floor, on average, and are in their mid-twenties; the Junior Traders average four years of trading experience and are typically in their early thirties; the Senior Traders average twelve years of experience and are typically in their late thirties; the dealers in the Head Trader/Treasurers category average 17 years of experience and are typically over forty. Across all dealers, years of trading experience ranges up to thirty. IV. Existence of Overconfidence This section sets the stage for our main result by providing evidence that currency dealers tend towards miscalibration and hubris. Readers willing to accept this conclusion can move direction to Section V, which concerns the survival of these two tendencies. A. Miscalibration Existing evidence that people overestimate the precision of their information largely comes from experiments in which individuals provide 90-percent confidence intervals for general knowledge questions such as “How many miles is it from Paris to Tokyo?” (Lichtenstein et al. (1977)). Under perfect rationality, 10 percent of these confidence intervals would exclude the correct answer, but that share is typically above 50 percent among experimental subjects (Nofsinger (2007)). Our survey took a similar approach but tailored the questions to measure financial-market calibration. Each trader was asked to “enter today’s exchange rates of the Euro, the Japanese Yen, the British Pound, the Swiss Franc, and the Canadian Dollar against the U.S. Dollar. Then give your personal forecasts of these exchange rates on December 1, 2002 and on June 1, 2003. For each currency, give your actual forecast and the lower and the upper limit of a range within which you expect these rates to be with a certainty of 90%.” 11 1. Confidence intervals: Standard tests The standard test for miscalibration involves comparing the share of confidence intervals that exclude the correct answer to ten percent, the true share under the null hypothesis of no overconfidence. We first examine the confidence intervals of proprietary traders, who regularly keep positions open for a month or more. Since the horizons of other traders are shorter, proprietary traders might be better calibrated than salespeople or interbank traders. We focus on the dealers’ five most actively traded currency pairs (“currencies” for brevity), identifying them by the market’s standard 3-letter abbreviations: euro-dollar (EUR), dollar-yen (JPY), sterlingdollar (GBP), dollar-Swiss franc (CHF), and dollar-Canadian dollar (CAD). Consistent with the literature, the share of the proprietary traders’ confidence intervals excluding the realized exchange rate at the end of the forecast horizon exceeds ten percent for all ten of the tests associated with our proprietary traders (five currencies, two forecast horizons). As shown in Table 2, Panel A, the share of December confidence intervals excluding the realized rate ranges from 25 for GBP to 44 percent for CHF; for the June forecasts the share ranges from 44 to 92 percent. The possibility that these results reflect overconfidence is also supported by the fact that the share of June intervals excluding the realized rate is consistently higher than the corresponding share of December intervals. Indeed, the average share for June intervals, 70.7 percent, is roughly double the share for December intervals, 35.2 percent. This pattern is predicted by the robust finding that overconfidence rises with task difficulty (e.g., Lichtenstein et al. (1977); Pulford and Colman (1997); Dittrich et al. (2005)). To examine whether proprietary traders are indeed better calibrated than other traders we carry out the same test for all traders. As anticipated, the share of forecast intervals excluding the 12 realized rate is generally higher for all traders than for proprietary traders. Nonetheless, the average difference between the relevant shares for proprietary traders and all traders is quite small, at 4.6 percentage points. This is consistent with evidence in the literature that miscalibration responds only modestly to financial incentives (Fischhoff et al. (1977); Sieber (1974)). It may also reflect the importance to all dealers of having a “view” about exchange rates. Some customers base trading decisions on these views and good forecasting increases one’s chance of becoming a proprietary trader, considered a plum job. These results, while striking, cannot persuasively demonstrate overconfidence because the placement of the dealers’ confidence intervals depends on their point forecasts, which have two notable shortcomings. First, the point forecasts themselves may be inaccurate, since studies consistently show that professional forecasters could improve their accuracy by adopting the naïve forecast of no change (MacDonald (2000)). Second, the point forecasts are probably not generated independently, since traders often discuss their views with others. We isolate the influence of confidence-interval width by re-aligning each interval relative to the rate prevailing when each dealer submits the survey, maintaining proportionate distances of confidence-interval endpoints above and below. The share of confidence intervals excluding realized rates generally declines after this realignment, suggesting that our dealers’ point forecasts, like those of most professional forecasters, are less accurate than the no-change forecast. Nonetheless, the results do not challenge our previous inference that dealers tend to underestimate uncertainty. As shown in Table 2, Panel A, the share of intervals excluding the realized rate remains significantly higher than ten percent for nine of our ten currency-horizon pairs. Further, the excess over ten percent 13 remains economically meaningful; the average share across the five currencies is 26.3 for December forecasts and 66.0 for June forecasts. We test the statistical significance of these realigned confidence intervals by noting that, under the null hypothesis of no overconfidence, each interval represents a Bernoulli trial where p=0.10 is the probability of excluding the realized rate. If n is the number of intervals submitted, the share of realigned intervals excluding the realized rate has a binomial distribution with mean np and standard deviation np(1-p). Since n is reasonably large, this can be approximated by the corresponding normal distribution. In these tests, all but one of the ten shares is significantly different from 10 percent at standard significance levels. [Table 2 near here] Overconfidence is also suggested by the inaccuracy of dealer forecasts relative to the nochange forecast. The conclusion that they lack accuracy is supported by a formal statistical analysis showing that the dealers’ average RMSE typically exceeds twice the RMSE of the nochange forecasts and the dealers’ average directional accuracy, at 51 percent, is not statistically better than a coin toss (for details see Oberlechner and Osler (2009)). Since the more accurate no-change forecast is always available free on the dealers’ computer screens, it is striking that none of them submitted point forecasts within a few basis points of it. Bradley’s (1981) research suggests this choice may be another manifestation of miscalibration. That study examines the responses of novices and experts to questions for which subjects had only an even chance of providing the correct answer. Though subjects’ claimed expertise was unrelated to correctness, by construction, their willingness to admit ignorance was inversely related to claimed expertise. 14 2. Confidence intervals: Comparison against benchmarks Since rational forecasts are not necessarily accurate ones, the foregoing results could be unrelated to miscalibration. Suppose, for example, that dealers rationally anticipated low volatility during the forecast horizon but realized volatility was high. In this case the confidence intervals would tend to exclude realized rates, as occurs in our data, despite being rational. Instead of comparing confidence intervals to realized outcomes, we next compare the dealers’ confidence-interval widths to the widths implied by rational volatility forecasts. We forecast volatility using GARCH models of exchange-rate returns at different horizons.3 Dealers completing the survey in July evidently had to forecast over longer time horizons (four and ten months) than those completing the survey in October (one and seven months). Surveys were submitted in July, August, September, and October, so we create GARCH models of historical non-overlapping returns measured over all the relevant forecast time horizons: 1, 2, 3, and 4 months for December forecasts; 7, 8, 9, and 10 months for June forecasts. Each sample ends in the associated survey-completion month, so each model’s final variance estimate is an out-of-sample forecast of volatility for the associated forecast time interval. Dealers’ access to real-time market information might enhance their forecasting ability relative to the crude AR(1) of our GARCH models, so we shrink the GARCH variance forecasts before converting them to confidence intervals. By how much should they be reduced? Our earlier evidence suggests that dealers do not have special forecasting power at horizons of a 3 The data, which come from Datastream, begin in 1970 for EUR, GBP, and CHF, and in 1978 for JPY and CAD. In every case we first tried a GARCH(1,1) model. This converged (in Stata) in 26 of 40 cases. If this failed, we tried a GARCH(1,2) model (converged in ten cases), a GARCH(2,2) model (converged in three cases), and finally an ARCH(1) model. 15 month or more, but Evans and Lyons (2005) show that by incorporating order-flow data they can reduce one-month forecast variances by up to 15.7 percent. We therefore assume conservatively that dealers forecast returns as well as Evans and Lyons and reduce the GARCH-based variance forecasts by 15.7 percent. From these adjusted forecast variances we calculate 90-percent confidence intervals using the fact that the 90-percent confidence interval for a normal distribution equals 3.29 times the standard deviation. If our proprietary traders are well-calibrated, then about half of their confidence intervals should be narrower than the GARCH benchmark. Instead, they are almost all narrower than the benchmark (Table 2, Panel B). This finding is robust to three methodological modifications: broadening our focus to include all traders; considering only traders at top-tier institutions; and basing the benchmark confidence-interval widths on the unconditional rather than the conditional distribution of returns.4 To evaluate the statistical significance of these results, we take the null hypothesis to be no miscalibration and view each interval as the outcome of a Bernoulli trial in which too-wide and too-narrow have equal probability. The number of too-narrow confidence intervals under the null thus has a binomial distribution with p = 0.5 and n ≡ nfcm is the number of responding traders for a given forecast date f, currency c, and survey completion month m (e.g., nDEJ = 262 for December 1 forecasts for the euro submitted in July). Since our samples are reasonably large and p is not extreme, the distribution is well approximated as normal with mean pnfcm and variance p(1-p)nfcm. Our results are highly significant, with all marginal significance levels below 0.0001. These test statistics do not provide a direct measure of the share of traders who are overconfident, but back-of-the-envelope calculations suggest that the share is fairly high. As a 4 The results using the unconditional distribution, unreported to save space, are available upon request. 16 baseline, suppose that there are no underconfident dealers, so all dealers are either wellcalibrated or overconfident. Suppose likewise that half of well-calibrated dealers choose toonarrow confidence intervals. In this case, the 94.5 percent share of too-narrow intervals among our 355 EUR forecasts for December would be observed only if 90 percent of dealers were overconfident. If we adopt the more generous assumption that the share of too-narrow intervals from well-calibrated dealers had only a 5 percent likelihood of occurring by chance, the implied share of overconfident dealers declines only to 88 percent. As a further robustness test we construct benchmark confidence intervals from option implied volatilities. These are sampled at the end of the associated survey-completion months (e.g., for July forecasts we used implied volatilities from the last trading day in July) and are adjusted for maturity. They are not reduced to allow for the possibility that our dealers have an advantage in forecasting exchange rates because implied volatilities are independent of any trend in the underlying asset. As shown in Table 2, Panel C, a large and statistically significant majority of the confidence intervals provided by the dealers are again smaller than the benchmarks. These tests so far assume that survey participants decide the width of their confidence intervals independently from other participants. In our final test, we evaluate statistical significance under the alternative assumption that interval widths are not generated independently. To do this we bootstrap the distribution of confidence intervals assuming that the confidence-interval width for each dealer, CIi, is the sum of a shared component, CIS, and an ~ ~ idiosyncratic component, d i : CIi = CI S + d i . Appendix B describes the methodology in detail. The results, shown in Table 2, Panel D, again indicate that our survey participants are 17 significantly overconfident. The null hypothesis of rationality is rejected at the five percent level or better for nine of ten tests and at the ten percent level in one remaining test. B. Hubris So far we have provided evidence that currency traders tend to overestimate the precision of their information. We next provide evidence that dealers also tend to overrate their personal success. Survey participants were asked: “How successful do you see yourself as a foreign exchange trader?” The top rank of 7 was assigned to “Much more successful than other foreign exchange traders;” the bottom rank of 1 was assigned to “Much less successful than other foreign exchange traders”; “Average” was assigned to the middle rank of 4. All categories of the sevenstep rating scale were individually labeled. The participants’ immediate superiors (i.e., head traders or chief dealers) were also asked to rate their subordinates. The superiors were specifically instructed to compare subordinates to others with similar responsibilities at the same institutional rank, since such specificity is shown in the organizational literature to increase discriminative ratings and to reduce judgment errors among supervisors (Locklear et al. (1989)).5 The superiors rated their subordinates along three dimensions: “Overall Contribution to the Organization,” “Trading Profits,” and “Trading Potential.” Traders’ Overall Contributions to the Organization were comprehensively defined to include trading profits and broader factors such as the support of other traders and the completion of tasks for the whole group (Borman and Motowidlo (1993)). Overall Contribution thus matches the overall success rating requested of the traders themselves. Trading Profits is self-explanatory. Trading Potential was defined as the degree to which traders have the personal making of successful traders in their trading area; head traders were specifically instructed to 5 For example, without position-specific standards, supervisors may show an unwanted tendency to rate workers better the higher their rank (Brandstätter (1970)). 18 separate trading potential from realized profits. The three ratings are highly correlated, with bilateral correlation coefficients ranging from 0.58 to 0.72. Our currency market professionals give themselves an average rank of 5.06, or “better than average,” with standard error of 0.05 (Table 3). In all, three quarters of traders perceive themselves as more successful than average (ratings 5, 6, or 7), a share that is roughly fourteen times the share of dealers perceiving themselves as below average. [Table 3 near here] Though these shares seem extreme, there is at least one reason why they could conceivably be realistic: most of our dealers work at top-tier institutions. If this explains our result then traders at lower-tier institutions should generally rate themselves below average, but the average self-rating of traders at lower-tier banks, 4.86, is only slightly below the average selfrating of traders at top-tier banks, 5.20, and remains significantly higher than the benchmark for no hubris, 4.0. As noted earlier, these results are consistent with extensive evidence for the “better-thanaverage effect” (Alicke and Govorun (2005)), as the common tendency towards hubris is often labeled. Among traders, this apparent bias could reflect traders choosing favorable yardsticks when rating themselves. Rather than rate themselves against their current competitors, for example, they might rate themselves against every trader with whom they ever worked, including those that failed and dropped out of the profession. Alternatively, traders might assign different weights to the various skills that are involved in trading, with higher weights assigned to the skills at which they excel. Whatever traders were thinking, it is still statistically implausible for three-quarters of a large sample of individuals to be above average overall. 19 To evaluate the statistical significance of these results, we undertake a bootstrap test of the null hypothesis of no hubris. We assume the superiors’ ratings represent the true distribution of ratings within rank and responsibility classes (which is less restrictive than the assumption that superiors correctly rated individual traders.) Only two of the twelve rank-responsibility categories – senior interbank traders and senior salespeople – include sufficient individuals to generate a meaningfully powerful test. Fortunately, these two categories include 70 percent of the dealers with both superior and subordinate ratings. For each rank-responsibility category we create 1,000 sets of k ratings, where kI =78 is the number of senior interbank traders and kS = 94 is the number of senior salespeople. Each rating is drawn at random (with replacement) from the associated sample of superiors’ ratings. For each set of simulated ratings we calculate the share that are above average, and the distribution of these simulated shares is compared with the corresponding observed share from that rank-responsibility category. Note that the tests are biased towards accepting the null because the supervisors themselves tended to rate their subordinates better-than-average. Average supervisors' ratings (standard errors) are 4.6 (0.09), 4.5 (0.09), and 4.9 (0.08) for the Overall Contribution, Trading Profits, and Trading Potential dimensions, respectively. [Table 4 near here] The tests unambiguously reject the null hypothesis of no overconfidence (Table 4). In our baseline test, which uses the Overall Contribution rating by superiors, none of the 1,000 sets of simulated ratings for senior interbank traders had a share of above-average ratings as high as the observed share of 77.5; indeed, the highest simulated share was 66.2. Similarly, none of the sets of simulated ratings for senior interbank traders had a share of below-average ratings as low as 20 the observed fraction of 5.6. Our conclusions are not changed if the superiors' ratings for Trading Profitability or Trading Potential replace their ratings for Overall Contribution. V. Survival of Overconfidence So far this paper has presented evidence that currency dealers display two widespread human tendencies: they underestimate uncertainty and they overestimate their abilities. This is notable since dealers face strong incentives to be accurate, have access to comprehensive information, and get frequent practice forecasting and assessing their personal trading competence.6 These results set the stage for the paper’s central question: Is overconfidence driven out of the foreign exchange market? Overconfidence could disappear if individual dealers become well-calibrated in response to frequent feedback or strong incentives for accuracy. Alternatively, it could disappear if overconfident dealers are fired or leave the profession voluntarily. This section presents evidence that overconfidence is not driven out of the market. We organize our analysis around two testable implications of the hypothesis that imperfect rationality will not survive: • Absolute rationality: The most experienced dealers are not overconfident at all. • Relative rationality: Overconfidence is moderated by experience. For this analysis we need measures of each individual’s overconfidence. Our measure of individual miscalibration focuses on the extent to which a dealer’s confidence intervals fall short of its value under rationality, taking the rational value to be the width calculated from our GARCH analysis. We first calculate the ratio between the width of each confidence interval and the relevant GARCH width. As before, we distinguish dealers according to the month in which 6 Profitability, for example, is measured daily and every month each dealer and boss sign statements to show they agree on the figure. 21 they submitted the survey. For dealer i’s confidence interval for currency c at forecast date f, wicf, G G is the appropriate GARCH width for that dealer’s surveythis ratio is Rcfi ≡ wcfi / wcfm , where wcfm completion month. Since each dealer provided up to ten confidence intervals, we take the average of the submitted ratios, Ri. (The correlation between the dealers’ average December and average June ratios is a strong 0.82, so little information is lost by combining intervals.) Dealer i’s miscalibration, Mi, is then defined as the gap between unity and this average: Mi ≡ 1- Ri. For well-calibrated individuals Mi is near zero and could be slightly negative; for overconfident individuals Mi ranges upwards to a maximum of one. To measure each trader’s hubris we take the difference between the trader’s rating of his/her own performance, PiOwn, and the superior’s Overall Contribution rating, PiSup: Hi ≡ PiOwn PiSup. 7 For agents who are not overconfident Hi will be zero; like miscalibration, Hi rises with overconfidence. Note that this measure is not available for lower-tier banks because superiors’ ratings were only solicited from top-tier banks. To ensure robustness we measure experience three ways: years spent trading, age, and institutional rank. For years spent trading we create three categories: 0-8 years, 9-14 years, and 15 or more years. For age we create four categories: 30 and under, 31-35, 36-40, and over forty. For rank we create three categories: Trainees and Junior Traders, Senior Traders, and Head Dealers/Treasurers. It might be natural to assume that miscalibration and hubris are closely related. Indeed, Gervais and Odean (2001) describe how, in theory, hubris could be the source of miscalibration. Nonetheless, the correlation between our dealers’ miscalibration and their hubris, -0.18, is not only economically small but significantly negative. A weak relation between these two 7 This measure effectively assumes that superiors’ ratings are more accurate than those of their subordinates 22 dimensions of overconfidence is consistent with results from other relevant studies (Deaves et al. (2003); Régner et al. (2004); Glaser and Weber (2007)). A. Absolute rationality: Are the most experienced dealers overconfident? If imperfect rationality is driven out of the market, the most experienced traders will display zero overconfidence. Table 5, which reports the averages of measured miscalibration and hubris for dealers in different experience categories, provides no support for absolute rationality. Table 5, Panel A shows that average miscalibration is statistically significant among the most experienced dealers no matter how we measure experience. Among dealers with 15 or more years of trading experience, confidence intervals are 58 percent smaller, on average, than they would be under the null hypothesis that dealers are all well-calibrated (t-statistic 28.1). Confidence intervals among dealers over 40 years old are on average 59 percent smaller than implied by the null (t-statistic 29.8); confidence intervals among Head Traders/Treasurers are on average over 40 percent smaller (t-statistic 2.9). Hubris is also economically and statistically strong for experienced dealers, as shown in Table 5, Panel B. For dealers with 15 or more years of experience, hubris averages 0.65 (tstatistic 2.2). This represents a substantial distortion of their performance ratings, as it covers over a quarter of the gap between the superior’s average performance rating for this group, which is 4.5, and the highest possible rating, which is seven. Average hubris is 0.46 for dealers over 40 years old (t-statistic 2.1), which implies that this group inflates their performance rating almost 20 percent of the way towards ideal performance, on average. Average hubris is 1.13 for Head Traders and Treasurers, which implies that these individuals inflate their performance rating almost half-way to ideal performance. [Table 5 near here] 23 As discussed in Section IV, the incentives to overcome miscalibration are strongest for proprietary traders, so this group provides a stronger test of whether experienced traders are overconfident (Table 5, Panel C). The miscalibration and hubris measures for this group provide no evidence for dealer rationality, however. Among the most experienced proprietary traders, both miscalibration and hubris are statistically and economically significant. (Note that, to conserve statistical power, we create fewer age categories when analyzing proprietary traders; we do not use “rank” to measure experience since almost all proprietary traders have the rank of Senior Trader or higher.) For robustness we also examine miscalibration among the most experienced dealers at top-tier banks (as noted earlier, the hubris measures apply only to top-tier banks). These dealers are likely to have greater influence over market prices than other dealers because they have larger position limits and more customers. A comparison of results for top-tier banks (Table 5, Panel D) and for all banks (Table 5, Panel A) indicates that there is no difference between the most experienced dealers at top- and lower-tier banks. Our conclusion that the most experienced dealers tend to be overconfident is also sustained if we focus exclusively on the currencies that dealers trade most actively.8 B. Relative rationality: Is overconfidence moderated by experience? Overconfidence could be moderated by experience even if it doesn’t disappear with experience. The moderation hypothesis is not supported by our comparison of overconfidence levels across dealers with varying experience. When experience is measured in terms of years spent trading, the miscalibration estimates are almost identical for dealers at all experience levels at 0.59, 0.58, and 0.58 for the traders with least experience, intermediate experience, and greatest 8 Results of this robustness test are available upon request. 24 experience, respectively (Table 5, Panel A). When experience is measured by age, the miscalibration estimates vary more but the variation is non-monotonic. Estimated miscalibration averages 0.59 for the two youngest groups, 0.52 for traders in their late 30s, and once again 0.59 for traders over forty. Moreover, the differences across experience groups are again insignificant. When experience is measured by rank, the point estimates of miscalibration decline modestly with rising rank – from 0.65 to 0.57 to 0.42 – but once again the differences are insignificant. As shown in Table 5, Panel B, the hubris measures provide similarly scant support for the hypothesis that overconfidence declines with experience; indeed, this evidence suggests weakly that hubris rises with experience. When experience is measured by years spent trading, average hubris is 0.50, 0.47, and 0.65 for traders with the least experience, intermediate experience, and greatest experience, respectively, though the differences across groups are insignificant. When experience is measured by age or rank, however, the evidence that hubris rises with experience is a bit stronger. For both these experience measures, average hubris is insignificant for the least experienced traders and it is significant – and higher – for all other groups. The evidence for the hypothesis that hubris rises with experience is weakened, however, by the insignificance of differences in hubris across experience categories. Research has revealed that that overconfidence rises with experience and expertise in various settings (Staël von Holstein (1972); Glaser et al. (2005)). Most notably, for this paper, overconfidence rises with expertise when maximum achievable accuracy is extremely low, as in exchange-rate forecasting (Bradley (1981)). The hypothesis that overconfidence is moderated by experience likewise receives no support if the sample is restricted to proprietary traders (Table 5, Panel C) or to dealers at top-tier banks (Table 5, Panel D). 25 The results of this section suggest consistently that overconfident traders are not driven out of currency markets. Despite many years of trading, experienced dealers still tend to overestimate the precision of their information and to overestimate their own abilities. VI. Concluding Observations This paper tests whether overconfident traders are driven out of the foreign exchange market. Friedman famously claimed that imperfectly rational traders will be driven out of financial markets by trading losses (1953), a claim that has been influential because it supports the assumption of trader rationality. Nonetheless, this claim has rarely, if ever, been tested. We examine whether overconfidence, a well-documented form of imperfect rationality, survives among those who set prices in the world’s largest financial market. We set the stage for this analysis by providing evidence that currency dealers, like most people, display two types of overconfidence; they tend to overestimate the precision of their information (miscalibration) and they tend to overestimate their professional success (hubris). We then analyze how overconfidence varies across foreign exchange dealers with different amounts of experience. The results indicate that even the most experienced dealers are strongly overconfident and that they are just as overconfident as their junior colleagues. These conclusions are remarkably robust. They hold for both types of overconfidence; they hold regardless of whether we measure experience by years spent trading, age, or institutional rank; they hold for proprietary traders, who get the most experience forecasting at our horizons, as well as other traders; and they hold for traders at the most prestigious dealing banks. Future research could constructively examine the mechanism(s) through which dealer overconfidence survives. Among the many hypotheses worth exploring, we highlight three: 26 Overconfidence, by fostering persistence and a tolerance for adversity, might enable dealers to sustain a career with intense competition and frequent setbacks; overconfidence, by leading others to have inflated opinions of one’s success, might increase one’s likelihood of promotion within an organization; overconfidence, by enhancing cognitive facility, might enhance dealers’ ability to identify profitable trading opportunities. 27 References Alicke, M. D., and O. 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The 26 banks in this category were defined as institutions included in at least one of the following lists: (i) membership in the New York Foreign Exchange Committee in 2001 and/or 2002; (ii) the top 10 institutions of the Best Provider of Foreign Exchange Services Overall annual ranking published by Global Investor Magazine in March 2001 and/or March 2002; (iii) the top 10 institutions of the Global Top 50 Foreign Exchange Market Companies by estimated market share annual ranking published by Euromoney Magazine in May 2001; (iv) the top 10 institutions of the annual Best Bank Overall for Foreign Exchange Dealing ranking published by Foreign Exchange Week in December 2001; (v) the top 10 institutions in the annual ranking of banks’ foreign exchange revenues 2001 published by Foreign Exchange Week in December 2001. North American trading floors of the resulting 26 institutions were contacted and invited to participate in the study. Twenty-one of these trading floors agreed to participate fully, resulting in an institutional participation rate of 81 percent of the leading market participants. Of 551 questionnaires sent to these 21 trading floors, 326 were returned, an individual questionnaire return rate of 60 percent. Lower Tier: Other foreign exchange dealing banks in North America. These are defined as all other foreign exchange banking institutions in the U.S. and in Canada listed in Societé Générale's Dealer Directory (Nicolson (2002)). Foreign exchange traders at these institutions were sent questionnaires by mail. Of 529 questionnaires sent to banks in this group, 90 were returned, resulting in a questionnaire return rate of 17 percent for this group. 35 Appendix B: Testing significance under null that confidence-interval widths are not independent This appendix describes the bootstrap procedure used to identify the distribution of confidence intervals under the assumption that dealer’s confidence interval widths are not independent. Specifically, it is assumed that each dealer’s confidence-interval width, CIi, is the ~ ~ sum of a shared component, CIS, and an idiosyncratic component, d i : CIi = CI S + d i . The bootstrap simulations are done separately for each combination of forecast date f and currency c. Within each f-c combination we work separately with each forecast submission month m, since any shared component would likely differ across surveys submitted in different months. For concreteness we illustrate our methodology with the December 1, 2002 confidence intervals for euro submitted in July of 2002. S To determine the shared variance components, VDec , Euro , July , we first sample (with replacement) 1,000 values from our GARCH model’s fitted variances for the four-month returns, V Dec , Euro , July . We assume (as in previous tests) that dealers can use order-flow information to reduce the forecast variance by the full 15.7 percent estimated by Evans and Lyons (2005). We then calculate the associated 90-percent confidence interval widths: CISDec,Euro,July = S 3.29 (1 − 0.157)VDec , Euro , July . To find the idiosyncratic component of a simulated confidence interval width, ~i d Dec , Euro , July , we first calculate the differences between each dealer’s originally-submitted proportionate confidence-interval width and the mean proportionate width across all dealers for a given forecast submission month: diDec,Euro,July = widthDec,Euro,July - meanwidthDec,Euro,July. We then sample (with replacement) nDec,Euro,July of the original differences for each of the 1,000 elements 36 of V Dec , Euro , July to create the nDec,Euro,July simulated widths for that survey completion month: ~i ~ S CI iDec,Euro,July = CI Dec , Euro , July + d Dec , Euro , July . We then sample a second time (with replacement) from the relevant fitted variances to create a set of 1,000 “true” variances, VTDec,Euro,July, and associated true rational confidence T interval widths: CITDec,Euro,July = 3.29 (1 − 0.157)VDec , Euro , July . We repeat this procedure for the December 1 forecasts submitted in August, September, and October. This provides a set of 1,000 “periods.” For each period there are four true confidence-interval widths, one for each survey-completion month and four sets of idiosyncratic confidence-interval widths. For each period we calculate how many of the simulated dealer widths are smaller than their associated true width. We then express the total as a share of the number of simulated widths for that forecast date and currency, nDec,Euro = ∑ n Dec , Euro ,m . The m distribution of these shares is taken to be the true distribution of shares under the null hypothesis that individuals’ estimated confidence interval widths are unbiased but correlated with each other to the extent that they share the same mean on a period-by-period basis. We note that this test implicitly assumes that estimated and actual confidence interval widths are uncorrelated, which we accept because it favors the hypothesis of no overconfidence and because anything else would necessarily involve arbitrary assumptions that would make it difficult to interpret the results. 37 Table 1: Characteristics of survey respondents The table provides descriptive information concerning the 416 respondents to a June 2002 survey of North American currency market professionals. Note: totals may exceed 100% because some individuals fit multiple categories. Location New York City 53% U.S. non-NYC 33% Canada 14% Product Spot 73% Forward 33% Derivatives 23% Money Market 6% Function Interbank Trader 59% Salesperson 32% Proprietary Trader 20% Rank Treas./Head Trader 12% Senior Trader 75% Junior Trader 12% Trainee 1% Age Over 40 36-40 31-35 26-30 Less than 26 Currency Focus EUR/USD 61% USD/JPY 42% USD/CAD 39% GDP/USD 30% USD/CHF 20% USD vs. Other 20% EUR/JPY 11% EUR/GBP 11% EUR/CHF 8% EUR vs. Other 10% 30% 27% 27% 13% 3% 38 Table 2: Confidence intervals are too narrow Ninety-percent confidence intervals for exchange rates on December 1, 2002 and June 1, 2003 were submitted by North American currency market professionals in response to a survey distributed in June of 2002. Panel A shows the share of confidence-intervals widths that exclude the realized exchange rate. Under the null hypothesis of no miscalibration and independence the true share is 10%. For “realigned confidence intervals,” end-points are aligned relative to the exchange rate on the day the survey was completed rather than dealers’ point forecasts. Panels B and C show the share of confidence-intervals widths that exceed objective benchmarks. Under the null the share is 50%. In Panel B this benchmark is based on GARCH variance estimates. In Panel C the benchmark is based on option implied volatilities. Under the null the shares have a binomial distribution with p = 0.10 (Panel A) or p = 0.5 (Panels B and C). Panel D bootstraps the statistical significance of fractions from Panel B assuming that interval widths are not generated independently. * means 5% significance; ** means 1% significance. EUR JPY GBP A. Share of confidence intervals excluding realized exchange rates Proprietary traders December 1 forecast 35.2 35.7 25.4 June 1 forecast 87.9 47.7 43.8 All traders December 1 forecast 29.3 45.1 33.7 June 1 forecast 94.6 48.5 45.9 All traders: Realigned confidence intervals December 1 forecast 13.8 38.1** 22.4** June 1 forecast 98.8** 18.7** 20.3** B. Percent of intervals narrower than GARCH estimates Proprietary traders December 1 forecast 93.7** 90.7** 98.1** June 1 forecast 92.8** 96.3** 98.1** All traders December 1 forecast 94.9** 92.5** 99.1** June 1 forecast 95.2** 99.7** 98.8** All traders at top-tier banks December 1 forecast 97.1** 92.1** 99.2** June 1 forecast 95.6** 100.0** 99.6** 39 CHF CAD 35.9 82.0 43.9 92.1 34.0 93.8 54.7 95.8 14.7* 94.3** 42.5** 97.7** 96.9** 99.0** 64.7** 85.3** 98.5** 99.1** 70.2** 93.7** 99.6** 99.6** 71.9** 93.4** C. Percent of intervals narrower than estimates from option implied volatilities Proprietary traders December 1 forecast 94.6** 91.6** 93.3** 94.9** June 1 forecast 97.3** 92.5** 97.1** 95.9** All traders December 1 forecast 97.7** 95.1** 97.6** 96.9** June 1 forecast 99.2** 95.1** 98.8** 98.2** All traders at top-tier banks December 1 forecast 98.2** 95.5** 97.7** 98.4** June 1 forecast 99.6** 95.1** 99.2** 99.2** D. GARCH benchmarks with variance forecasts that are not independent All traders December 1 forecast 94.9** 92.5** 99.1** 98.5** June 1 forecast 95.2* 99.7** 98.8** 99.1** 40 97.1** 94.1** 97.9** 97.9** 98.4 ** 98.0** 70.2 93.7* Table 3: Most traders rate themselves professionally above-average The table shows self-assessments of personal success submitted by North American currency market professionals as part of a survey distributed in June of 2002. Participants rated their own professional success on a scale of 1 = far below average to 7 = far above average, with 4 = average. "Top-tier" traders work for "Top-tier" banks. All traders Top-tier traders Other traders 5.06 (0.05) 5.20 (0.06) 4.86 (0.11) Share above average (5, 6, 7) 73.6 74.9 68.9 Share below average (1, 2, 3) 5.4 4.5 8.9 Number of participants 401 311 90 Average self-rating (Standard error) 41 Table 4: Bootstrap tests of hubris The table shows the marginal significance of the share of North American currency market professionals rating themselves above average. Their superiors were asked to rate them on the same scale, with respect to three dimensions of success: Overall Contribution, Trading Profits, and Trading Potential. Distribution of traders’ share under the null of no hubris is bootstrapped from superiors’ ratings. Values of 0.000 indicate that the most extreme simulated share was less extreme than the observed share. Observed share Bootstrapped marginal significance levels Overall Contribution Trading Profits Trading Potential Senior interbank traders Above average (5, 6, 7) 77.5 0.000 0.000 0.003 Below average (1, 2, 3) 5.6 0.000 0.000 0.003 Above average (5, 6, 7) 76.7 0.009 0.000 0.014 Below average (1, 2, 3) 5.6 0.001 0.001 0.000 Senior salespersons 42 Table 5: Overconfidence unrelated to experience The table shows average overconfidence for currency dealers with different levels of experience. A dealer’s miscalibration is measured as the average percent gap between the width of his/her confidence intervals and GARCH-based benchmarks. A dealer’s hubris is measured as the gap between his/her self-rating of performance and the superior’s Overall Contribution rating. “Hubris share” is average hubris as a percent of the gap between 7, the highest possible rating, and the superior’s average rating for the group. All measures are zero for perfectly calibrated individuals and rise with overconfidence. 5A: Miscalibration, all traders Experience = years trading Miscalibration t-statistic Number obs. 0-8 yrs vs. … 9 – 14 yrs vs. … Experience = age Miscalibration t-statistic Number obs. Under 30 yrs vs. … 31 – 35 yrs vs. … 36 – 40 yrs vs. … 0-8 9 - 14 0.59 0.58 22.53 27.80 106 102 t-statistics for differences across groups 0.27 ≤ 30 31 - 35 0.60 0.58 16.68 24.72 56 96 t-statistics for differences across groups 0.51 15 0.58 28.06 107 0.09 -0.21 36 - 40 41 + 0.52 8.35 95 0.59 29.83 103 1.15 0.92 0.28 -0.34 -1.10 Trainees, Senior Head Traders, Jr. Traders Traders Treasurers Miscalibration 0.65 0.57 0.42 t-statistic 17.69 41.66 2.85 Number obs. 49 257 38 t-statistics for differences across groups Trainee and Jr. Trader vs. … 1.93 1.48 Senior Trader vs. … 1.01 Experience = rank 43 Table 5B: Hubris, all traders Experience = years trading Hubris t-statistic Hubris share Number obs. 0-8 yrs vs. … 9 – 14 yrs vs. … 0-8 0.50 2.25 9 - 14 0.47 2.81 15 0.65 2.19 0.14 0.22 0.26 57 76 t-statistics for differences across groups 0.09 51 -0.40 -0.51 Experience = age ≤ 30 31 - 35 36 - 40 41 + Hubris t-statistic Hubris share Number obs. 0.23 0.94 0.64 3.70 0.57 2.37 0.46 2.06 0.10 0.27 0.27 0.19 61 60 -0.98 0.24 -0.69 0.64 0.33 Under 30 yrs vs. … 31 – 35 yrs vs. … 36 – 40 yrs vs. … Experience = rank Hubris t-statistic Hubris share Number obs. 47 73 t-statistics for differences across groups -1.36 Trainees, Jr. Traders 0.41 1.52 Senior Traders 0.45 3.72 Head Traders, Treasurers 1.13 2.06 0.15 0.18 0.45 41 183 t-statistics for differences across groups Trainee and Jr. Trader vs. … -0.12 Senior Trader vs. … 44 15 -1.17 -1.21 5C: Miscalibration and hubris for traders by functional responsibility Function Overconfidence t-statistic Number obs. Sales vs. … Interbank vs. … Experience = years trading Overconfidence t-statistic Number obs. 0 - 7 yrs vs. … 8 – 15 yrs vs. … Miscalibration InterProprieta Sales Sales bank ry 0.64 0.55 0.50 0.16 34.64 15.53 14.05 0.81 108 174 64 72 t-statistics for differences across groups 2.23 3.35 1.04 Proprietary traders only Hubris Interbank 0.57 3.68 127 -1.65 -2.70 -1.35 0-8 0-8 9 - 14 15 + 0.47 0.53 0.52 0.78 6.21 7.82 10.24 2.50 22 11 28 17 t-statistics for differences across group -0.68 -0.55 0.23 0.83 3.54 9 1.09 2.21 11 -0.13 -0.53 -0.47 9 - 14 15 + Proprieta ry 0.92 4.58 39 Experience = age ≤ 35 ≤ 35 > 35 Overconfidence t-statistic Number obs. 0.50 0.51 0.94 7.86 11.56 3.42 25 38 19 t-statistics for differences across group -0.13 0.90 3.02 20 35-and-under vs. … > 35 45 0.09 5D: Miscalibration at top-tier banks Experience = years trading Miscalibration t-statistic Number obs. 0-8 yrs vs. … 9 – 14 yrs vs. … Experience = age Miscalibration t-statistic Number obs. Under 30 yrs vs. … 31 – 35 yrs vs. … 36 – 40 yrs vs. … 0-8 9 - 14 15 0.58 0.58 0.62 20.22 25.56 24.42 95 83 65 t-statistics for differences across groups -0.16 -1.09 -1.05 ≤ 30 31 - 35 36 - 40 41 + 0.60 0.58 0.58 15.16 22.77 19.86 51 83 66 t-statistics for differences across groups 0.46 0.32 -0.15 0.60 25.78 72 Trainees, Senior Head Traders, Jr. Traders Traders Treasurers Miscalibration 0.64 0.57 0.52 t-statistic 15.13 33.20 90.28 Number obs. 42 175 23 t-statistics for differences across groups Trainee and Jr. Trader vs. … 1.43 1.62 Senior Trader vs. … 0.83 Experience = rank 46 -0.06 -0.71 -0.50