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o r K in g r a p e r b e rie s An Investigation of Returns Conditional on Trading Performance J a m e s T. M o s e r a n d J a c k y C . S o W o rk in g P a p e rs S e rie s Is s u e s In F in a n c ia l R e g u la tio n R e s e a rc h D e p a rtm e n t F e d e ra l R e s e rv e B a n k o f C h ic a g o D e c e m b e r 1 9 9 2 (W P -9 2 -2 4 ) FEDERAL RESERVE B A N K O F CHICAGO November 30, 1992 Preliminary Draft Comments Welcome An Investigation of Returns Conditional on Trading Performance by James T. Moser Research Department Federal Reserve Bank of Chicago 230 S. LaSalle St. Chicago, IL 60604-1413 (312) 322-5769 and Jacky C. So Department of Finance and Operations Management School of Business Southern Illinois University at Edwardsville Edwardsville, IL 62026-1103 (618) 692-2638 Abstract The performance appraisal procedures of Henriksson and Merton (1981) and Cumby and Model (1987) are applied to the returns of large speculators in futures contracts. Fewer than ten percent of the trader sample demonstrate superior performance. The performance appraisal procedure is re-applied to the idiosyncratic portion of the returns of these investors. This test indicates that their superior performance cannot be attributed to the idiosyncratic portion of their returns. This suggests that superior performance, though infrequently obtained, can be attributed to superior forecasts of the systematic portion of returns. This is consistent with ability to accurately forecast risk premiums. I. Introduction This paper investigates the returns of large-position speculative traders to obtain evidence on the type of information which enables superior-return performance. Superior performance is determined using an appraisal procedure original with Merton (1981) and Henriksson and Merton (1981) and extended by Cumby and Modest (1987). This procedure does not depend on a model for equilibrium returns, relying instead on ordinal rankings of available investments. This independence from models of equilibrium returns enables subsequent consideration of the relationship between observed superior performance and equilibrium models for expected returns. Specifically, the idiosyncratic portion of the returns of traders achieving superior performance in total returns is appraised. Since idiosyncratic return components are orthogonal to systematic components, rejecting superior performance in the idiosyncratic portion attributes the superior performance to the systematic portion. This exercise provides insight into the type of information used by these investors to achieve superior returns. Superior performance attributable to systematic-return components is consistent with superior forecasts of risk premiums paired with an ability to exploit this insight We find that less than five percent of the large traders in our sample reliably produce superior returns. Of these, however, the performance of most is consistent with superior forecasts of risk premiums. This result has a bearing on econometric investigations of the predictability of risk premiums. If only a small proportion of traders can successfully predict risk premiums, then it is likely that the forces determining these equilibria are dynamic and complex. Given this, the frequency of econometric investigations which find no support for positive risk 1 premiums is not surprising.1 The investor-performance literature focuses on whether performance is conditional on trading category. Houthakker (1957) examines the forecasting ability of large and small traders. He finds that large speculators show definite evidence of forecasting skill and small traders do well by taking, in general, only long positions. Rockwell (1967) extends Houthakker’s study to consider a longer time period and more markets, finding that most profits made by large speculators can be attributed to their skill in forecasting price movements. Using the nonparametric procedure of Merton (1981) and Henriksson and Merton (1981), Chang (1985) documents that the superior forecasting ability of large speculators allows them to make higher returns. These returns are clustered within relatively few time periods suggesting that forecast ability may be conditional on certain market conditions. Hartzmark (1987) classifies the data of reporting large traders as commercial firms (hedge positions predominate) and noncommercial firms (speculative positions predominate). He finds that a small number of large commercial firms made excess profits and their profits generally arose from short positions. He concludes however, that speculators in futures markets do not earn significant profits and that hedgers do not suffer significant losses. Thus, previous researchers investigate the performance of aggregated trader positions. This paper investigates the performance of individual traders based on their actual trading activity. Our approach is motivated by an interest in exploring the nature of information 1 For references of recent papers finding no risk premiums see Gallant, Rossi, and Tauchen (1992). 2 which can be used to obtain superior performance. In Section n, we develop the method of classifying traders based on their performance. Section HI analyses the idiosyncratic portions of the returns obtained by traders realizing superior performance. Section IV concludes the paper. II. Designation of Superior Traders A. Test procedure We begin with an identification of traders obtaining superior trading ability. Merton (1981) and Henriksson and Merton (1981) develop a conditional probability method to assess forecasting ability. Merton demonstrates a necessary condition for superior forecasting ability: the sum of the probabilities of being on the right side of the market, conditional on realized price changes, must exceed one. Chang (1985), Cumby and Modest (1987), Hartzmark (1990), Weiner and Philips (1992) and So (1992) apply the method to study commodity futures, foreign exchange rate prediction, and currency futures. This procedure is briefly reviewed below. Define percentage changes in futures prices from time t-1 to time t as rt. Before taking a long or short position, a speculator either predicts that r,>0 or that rt<0. Define yt as the forecast variable, its value is 1 if the speculator correctly predicts an increase in price and 0 if the speculator correctly predicts a decrease in price. The probabilities for yt conditional on correctly forecasting prices are: 3 P (1 ,0 = prob[yt = 1 I rt > 0] (1) P(0,t) = prob[yt = 0 | rt < 0 ] w here P (l,t) is the conditional probability o f a correct forecast given that the price goes up and P(0,t) is the conditional probability o f a correct forecast given that the price goes down. Henriksson and M erton show that under the null hypothesis o f no forecast ability, this sum is distributed hypergeom etric, as follows: N *2 n -n, n l) J "■J \ W, Pin, | N v N, n ) = (2) w here n t is the num ber of correct forecasts given rt<0; n is the num ber of tim es the forecaster predicts rt<0; N , is the num ber of observations where rt<0; N 2 is the num ber o f observations w here rt>0; and the num ber of observations, N, is Nj + N2. These counts can be illustrated by classifying them as follows: Realized Price Changes Futures Position Down or No Change Up Total Long N2-n+n! N,-n, N-n Short n-ni n. n Total n2 N, N 4 Dividing the diagonal elem ents of this table by their respective row totals gives the conditional probabilities of correct forecasts. The expectation of the sum o f these conditional probabilities under the null of no forecast ability is unity. The H -M test o f perform ance considers this null. W hen the sample size is large, the hypergeom etric distribution is approxim ated by the normal distribution. Obtaining the mean and variance allow s z tests to be perform ed, the com ponent statistics for these tests are com puted as follows: nNl (3) ~a T a2(n,) nN^N-NJQf-n) (4) N \ N - 1) Cumby and M odest (1987) point out that the H-M test lacks pow er against the alternative and is valid only if returns are independent over time; in particular, this presum ption of independence is violated when superior perform ance is obtained through use of technical trading methods. To address this issue, their regression-based procedure is also used in this study. Their procedure em ploys a regression of the observed changes of futures prices on a constant and an indicator variable, as in the follow ing specification: (5) The indicator variable, Iit, is unity if trader i ’s position at tim e t is long and zero otherwise. 5 Thus, separate regressions are run for each trader, regressing their m onthly returns on indicator variables determ ined by their net m onthly positions. If speculators have superior forecasting ability, the coefficient o f the indicator variable w ill reliably differ from zero. As pointed out by W einer and Phillips (1992), the regression-based tests have the draw back o f assum ing the norm ality o f forecast errors. B. D ata set H artzm ark (1986,1987,1991) describes a data set consisting o f the daily trading positions of large-position speculators and hedgers. W e use this data for the period July 1, 1978 through D ecem ber 31, 1981. The data set, prepared by the CFTC, classifies speculators as traders having no long positions in the corresponding cash m arket. From this data w e construct a data set o f daily positions held by speculators. This data includes date, traderidentification code, num ber of long and short positions, and contract m onth. M atching these positions with prices, we com pute daily returns realized by speculators. Traders frequently have no position on dates within the sample. T he perform ance evaluation techniques em ployed here interpret positions taken and cannot evaluate no-trade decisions. To avoid this problem , positions are evaluated on a m onthly basis. Thus, m onthly returns are com puted by com pounding the daily returns o f each trader and net speculative positions are constructed by netting their long and short positions. Thus, w e study trading perform ance during each month of the sam ple period. This adaptation o f the test procedure requires investigation. A M onte Carlo analysis o f the adaptation was conducted using the Cum by-M odest procedure. For cases w here as few as five o f the thirty positions within each evaluation period were, by construction, superior, 6 77% of the coefficient t statistics exceeded the 5% level. W hen ten o f thirty positions were constructed as superior, 99% o f the coefficient t statistics exceeded the 5% level. Finally, w hen no superior positions were constructed, 11% of the coefficient t statistics exceeded the 5% level. Thus, com bining daily positions slightly overstates the actual num ber o f traders achieving superior perform ance.2 Four heavily traded contracts are used in this study: the Chicago B oard o f Trade (CBT) wheat; the CBT U.S. Treasury bond market; the Chicago M ercantile Exchange (CM E) pork bellies market; the CM E feeder cattle market. C. Results Table 1 provides the results from the H-M method. The table lists item s for each trader in the sam ple by identification number. Identification codes are distinct for each contract; that is, trader 1 in the w heat contract is not trader 1 in the bond contract. T he listed items are: N „ N2, n, nt, and the com puted sums of conditional probabilities for superior performance. Superior perform ance is evidenced when the sum of conditional probabilities exceeds unity, a one-tail test. Plus signs indicate significance levels for superior perform ance. Two pluses (++) for the five percent level and one (+) for the ten percent level. N egative signs indicate significance levels for inferior perform ance. Two negatives (—) for the five percent level and one (-) for the ten percent level. O f the 120 traders exam ined, superior perform ance is indicated for four traders at the 10% level or better. For the w heat subsample, trader 23 dem onstrates superior perform ance at the 10% level, correctly predicting six declines and one increase. Traders 15 and 26 of the pork contract are reliably superior at the 2 Appendix A describes this Monte Carlo evaluation in more detail. 7 10% level. One cattle-contract trader demonstrates superior performance at the 5% level. A lso, in passing, five traders dem onstrate inferior perform ance at the 10% level or better. T he evidence suggests taking positions opposite those taken by these traders reliably produces superior perform ance. Table 2 reports results from the Cum by-M odest approach. Reported fo r each trader are the coefficients on position-indicator variables, the regression t statistic for the null o f a zero coefficient, and its significance probability. Superior perform ance is indicated w hen the regression coefficient differs from zero, a two-tail test. To distinguish these results from the one-tailed tests of the H M m ethod, w e denote significance levels as follows: * for the 10% level and ** for the 5% level. Table 2 results are generally consistent w ith those o f Table 1. D ifferences between the tables can be attributed to the higher pow er o f the regression technique. The regression method detects superior perform ance by three additional traders: bond trader 15 and cattle traders 11 and 16. In total, Table 2 indicates superior perform ance for five traders at the ten percent level or better. As previously noted, this test procedure relies on norm ality of the residuals. T he appropriateness of this reliance was investigated. W e w ere unable to reject the null that the accum ulated return series are norm ally distributed. In addition, we exam ined estim ates of the kurtosis of these return series for evidence o f non norm ality. The extent of these kurtosis estim ates does not w arrant rejection o f a norm al return distribution.3 T he small num ber o f traders dem onstrating superior perform ance is consistent w ith 3 H artzm ark (1988) indicates that the daily returns o f his sam ple exhibit excess kurtosis. Our rejection o f this hypothesis is consistent with evidence that returns over longer periods appear m ore norm ally distributed than do returns from shorter periods. 8 previous research. H artzm ark finds superior perform ance for 46% of his large trader sample. H e regards this as small. Cumby and M odest (1987) find evidence o f superior forecasting in five firm s in their sam ple o f seven foreign-exchange advisory services. R estricting their sam ple to a consistent tim e period, as w e do in this paper, reduces their num ber of superior forecasters to two. III. Analysis of the Source of Superior Performance A. D ecom position of returns Position returns are categorized as systematic E[Rtlam] and idiosyncratic Rt - E[Rtlam] using the expected-return m odel of Ross (1976). A pplying the M erton procedure to the idiosyncratic portion of these returns enables us to determine the likelihood that individual traders can predict either (or both) the systematic portion o f return or the idiosyncratic portion. Since the previous classification of traders found evidence of superior perform ance, the results o f this test allow us to conclude w hether superior perform ance is based on the ability to predict system atic or idiosyncratic returns. The Arbitrage Pricing M odel of Ross (1976) is em ployed to estim ate expected return com ponents. Chen, Roll and Ross (1986) em ploy specific factors in their specification for the APT. W e adopt this specification which is denoted as follows: r. - rft = bxUIt + b2E[It] + b J P t + b4UTS, + bsURP, + \ E P t + c. (6) w here UIj is unexpected inflation, E[IJ is expected inflation, YPt is growth in industrial production, U TSt is the m aturity spread between long-term and short-term default-free rates of interest, URPt is the spread between high and low rated corporate bonds, and EPt is the equity 9 risk prem ium . Equity data are m onthly returns obtained from the C R SP tapes. Equity returns are m atched with m acroeconom ic data obtained from M oney M arket Surveys. The sam ple period is July, 1978 through D ecem ber, 1981, corresponding to the sam ple period o f the large-trader data set. Table 3 reports the results for this specification. R esults are not surprising. The m aturity spread is positively related to returns for the bond contract. Returns on w heat contracts are related to industrial production. The equity prem ium enters significantly for all but the pork contract. The significance of the coefficient on equity risk prem ium s contrasts w ith the em pirical results of D usak (1973), but conform s with the predictions o f equilibrium return m odels such as the consum ption beta m odel of Richard and Sundaresan (1981). Ehrhardt, Jordan and W alkling (1987) em ploy the A PT to obtain evidence o f risk prem ium s in futures contracts. T hey reject the K eynes-Hicks hypothesis based on exam ination of coefficients on extracted factor loadings from the returns o f 16 futures contracts over an 85m onth sam ple period, 1977 through 1980. O ur use o f the A PT differs. W e partition returns into their systematic and idiosyncratic portions in order to investigate the source o f superior perform ance. B. Perform ance analysis o f the idiosyncratic portion of returns Subtracting the system atic portion o f returns obtained from the specification sum m arized in the previous subsection from total returns produces the idiosyncratic com ponents of these returns. The contract positions o f traders obtaining superior returns are m erged w ith the idiosyncratic return sam ple to obtain the idiosyncratic returns realized by m em bers o f the superior-trader subsample. B y construction, these are orthogonal to the 10 systematic return com ponents. Thus, rejecting superior perform ance for the idiosyncratic portion im plies that superior perform ance is based on forecasts of the system atic portion which can be interpreted as the risk premium. This, in turn, im plies that superior return perform ance can be obtained by placing positions based on forecasts rooted in an equilibrium m odel of returns. Table 4 contains results from this analysis. Panel A reports results from re-applying the M erton procedure to the idiosyncratic portion of superior trader returns. The results suggest that the superior perform ance of these traders cannot be attributed to the idiosyncratic portion of their returns. Panel B indicates that at the ten percent confidence level, two of six traders obtained superior perform ance from the idiosyncratic portion of their returns. This evidence suggests that superior perform ance is more often based on predictions o f the systematic com ponent of returns. The possibility that trading perform ance is time dependent w as exam ined. Tim e dependence suggests that trading perform ance m ight be tied to a single m acroeconom ic variable. For exam ple, suppose a trader’s perform ance was based on recognition o f the im pact of the 1978-79 oil price shock on futures prices, then we would expect the dates of their superior perform ance to be clum ped within this interval. To check this possibility, we graphed the incidences of returns for the superior-perform ance traders. For m ost o f the traders dem onstrating superior perform ance, the incidences of their superior trades appears approxim ately uniform over the sam ple period. This indicates that trading perform ance is not clumped as m ight be expected w hen perform ance is tied to a single indicator. The one exception is w heat trader 23, see Figure 1. The superior perform ance of that trader appears to 11 com e after mid-1979.4 These results indicate that superior perform ance is obtained when traders can accurately predict the system atic portion o f returns. Follow ing the A PT fram ework, evidence o f accurate predictions o f system atic returns im plies accuracy in predictions o f risk prem ium s. IV. Conclusion The perform ance o f a sam ple o f large speculators in four futures contracts is investigated using the perform ance-appraisal procedures o f H enriksson and M erton (1981) and Cum by and M odest (1987). W e find that superior perform ance w ithin this sam ple is not frequently realized. This is consistent with previous analysis o f the perform ance o f futures traders. Futures returns are then decom posed into their system atic and idiosyncratic com ponents following the Arbitrage Pricing M odel o f Ross (1976) using the Chen, Roll and Ross (1983) specification. W e com pute the idiosyncratic portion o f the returns o f each trader dem onstrating superior perform ance. R e-application of the perform ance appraisal procedures indicates that superior perform ance is generally attributable to the system atic return com ponent. The results cannot be explained as violations o f the norm ality assum ption; and in m ost cases, superior return perform ance is not tim e dependent. This result suggests that superior perform ance, when obtained, is likely to be based on predictions o f risk prem ium s. 4 G raphs of return incidences for each o f the superior-perform ance traders are available on request. 12 Appendix A M onte Carlo Analysis of Accum ulating Returns Thirty norm ally-distributed, iid, returns were generated for each evaluation period. For each evaluation period a fraction, a , of these returns were restricted to be positive. For exam ple, with a = 1/6, the first five returns o f the evaluation period were positive. For returns 1 through 5, the generation process w as repeated until five positive returns were obtained. The rem aining returns, the fraction 1-a, were then generated w ithout this restriction. This procedure assures that a given num ber o f returns w ill be positive. H owever, the underlying distribution of all returns within the evaluation period is the same. This generation process was repeated for 120 evaluation periods for each o f 100 traders. The Cum by-M odest perform ance appraisal procedure was then applied to these samples. Results are reported in the text. As a sensitivity check, the procedure was re-applied for various com binations o f mean and variance com binations governing the return-generation process. The procedure appears to be robust for mean-variance com binations such as observed during our sample period. 13 B ib lio g rap h y Chang, Eric C. (1985): "Returns to Speculators and the Theory o f N orm al Backw ardation," Journal of Finance 40, p. 193-208. Chen, Nai-fu, R ichard Roll and Stephen A. Ross (1983): "Econom ic Forces and the Stock M arket," Journal of Business 59, p. 383-403. Cum by, Robert E. and D avid M. M odest (1987): "Testing for M arket Tim ing Ability," Journal of Financial Economics 19, p. 169-189. D usak, K atherine (1973): "Futures Trading and Investor Returns: An Investigation o f Com m odity M arket R isk Prem ium s," Journal of Political Economy 81, pp. 1387-1406. Ehrhardt, M ichael, Jam es Jordan, and Ralph W alkling (1987): "An A pplication o f A rbitrage Theory to Futures M arkets: Tests of N orm al Backw ardation." Journal of Futures Markets 7, pp.21-34. G allant, Ronald, Peter Rossi and G eorge Tauchen (1992): "Stock Prices and V olum e " Review of Financial Studies 5, p. 199-242. H artzm ark, M ichael L. (1986): "The Effects of Changing M argin Levels on Futures M arket Activity, the C om position of Traders in the M arket, and Price Perform ance" Journal of Business 59, p. s l4 7 -s l8 0 . Hartzm ark, M ichael L. (1987): "Returns to Individual Traders o f Futures: A ggregate R esults," Journal of Political Economy 95, pp. 1292-1306. H artzm ark, M ichael L. (1990): "Luck V ersus Forecast A bility: D eterm inants o f Trader Perform ance in Futures M arkets," w orking paper, April. H enriksson, R oy D. and R obert C. M erton (1981): "On M arket Tim ing and Investm ent 14 Performance, II: Statistical Procedures for Evaluating Forecasting Skills," Journal o f Business 54, p. 513-533. H outhakker, H endrik S. (1957): "Can Speculators Forecast Prices?" Review of Economics and Statistics 39, p. 143-151. M erton, Robert C. (1981): "On M arket Tim ing and Investm ent Perform ance, I: An Equilibrium Theory of Value for M arket Forecasts," Journal of Business 54, p. 363406. Richard, S. F. and M. Sundaresan (1981): "A Continuous Tim e Equilibrium M odel o f Forward Prices and Futures Prices in a M ultigood Econom y," Journal of Financial Economics 9, p. 347-371. Rockwell, Charles S. (1967): "Profits, Normal Backw ardation, and Forecasting in Com m odity Futures," Ph.D. dissertation, U niversity of California, Berkeley. Ross, Stephen A. (1976): "The Arbitrage Theory of Capital A sset Pricing." Journal of Economic Theory 13, p. 341-360. So, Jacky C. (1987): "Commodity Futures Risk Prem ium and U nstable System atic Risk," Journal of Futures Markets 7, pp. 311-326. So, Jacky C. (1992): "Speculative Behavior of Com m ercial Banks." Paper presented at the Fourth Annual PA C A P meetings. W einer, Robert and Gordon Philips (1991): "W inners and Losers in Forward M arkets: A M icro-D ata T est of N orm al Backwardation." Paper presented at the 1992 m eetings of the A m erican Finance Association. 15 Figure 1 TRA D ER 23 O F W HEAT CO N TRACT 0.25 -r Oct-78 Oct-78 Feb-79 Oct-79 16 Oct-79 Dec-79 Table 1 Sum of Estimated Conditional Probability of Correct Forecasts Trader 1 2 3 4 5 Nl 42 121 45 80 64 85 30 32 26 45 30 17 75 115 5 38 71 58 65 85 34 34 14 26 7 28 62 124 19 40 117 26 20 102 ii 51 119 42 34 35 42 74 27 62 12 66 13 14 15 16 17 18 19 7 6 7 8 9 10 20 21 22 23 24 25 26 27 28 29 30 n2 100 108 63 59 114 29 35 8 34 10 37 57 117 22 24 ______________ Bond____________ Wheat____________ P n n n2 P N, n, n. 42 20 0.99 59 59 30 63 0.95 41 0.92 77 0.95 46 59 27 66 82 66 33 1.13 55 79 46 0.96 97 57 1.01 28 27 17 31 1.09 1.04 33 20 69 1.04 58 55 31 27 14 25 13 29 1.01 26 1.11 31 17 0.95 39 29 47 28 1.07 39 19 42 1.12 1.01 50 40 26 46 42 32 1.09 35 45 26 1.03 1.12 32 14 19 13 26 1.05 31 75 33 0.97 33 27 44 21 0.7392 32 0.97 43 58 53 25 1.10 1 3 0.67 62 0.8465 68 28 70 49 0.95 36 24 50 53 1.09 113 68 1.00 46 21 32 45 1.07 44 41 21 25 1.07 43 44 0.93 34 67 34 1.07 65 37 57 0.91 88 1.09 55 35 13 29 22 1.07 29 12 32 0.91 36 37 16 0.92 21 34 1.04 10 0.96 53 75 79 8 1.02 74 3 60 76 39 0.91 30 0.94 16 0.93 27 18 31 18 7 6 54 0.821.46+ 59 37 29 35 22 54 42 1.13 57 79 1.06 23 51 0.95 109 93 108 58 0.99 52 108 0.99 86 63 97 59 1.09 0.94 27 16 1.16 51 53 58 27 36 16 54 34 52 1.16 30 0.91 121 84 120 58 0.95 117 68 0.98 26 54 15 47 29 1.03 47 1.09 ________________ Pork___________ _______________Cattle P N, n n n2 N, n2 n, ni 45 51 59 29 1.06 31 19 26 17 34 1.14 12 67 27 43 26 36 25 48 20 37 27 1.05 60 56 70 36 4 14 11 32 18 8 1.00 33 33 24 14 4 2 18 16 9 0.99 15 24 21 11 33 16 0.89 17 16 13 14 24 0.94 24 49 40 46 33 26 21 40 0.99 48 3 20 71 19 51 54 41 32 46 29 1.01 36 50 19 34 32 17 1.18 40 38 18 31 27 52 24 32 18 1.08 22 31 28 10 44 16 0.99 67 21 40 29 28 48 18 26 35 28 35 51 48 0.93 17 12 22 16 25 47 39 37 10 0.99 34 9 51 10 50 31 29 1.19+ 25 16 0.88 10 48 18 5 18 17 7 54 64 24 30 0.87 47 28 38 50 34 32 30 26 26 12 0.86 38 20 14 16 30 19 37 35 0.87 35 45 31 23 1.21 27 35 20 10 33 15 22 14 2 1 28 9 13 5 1.10 32 42 40 35 31 15 47 20 0.95 12 12 17 13 6 0.92 48 25 25 34 12 24 16 39 35 15 0.85 30 28 9 16 46 19 13 1.10 47 57 14 8 14 1.14+ 42 44 8 5 38 34 12 11 19 0.73- 22 45 29 8 22 14 14 23 12 17 7 0.99 13 0 0 16 69 45 11 0 0 0.00 21 17 18 39 10 1.10 43 40 19 P 1.07 1.10 0.99 1.08 0.98 1.23 1.04 1.02 1.09 1.06 1.18 1.10 1.33” 0.91 0.94 1.15 1.01 1.17 0.89 1.10 1.12 0.88 1.03 0.99 0.93 0.790.91 0.66 1.12 0.94 Notes: n} is the number of correct forecasts given rt<0; n is the number of times the forecaster predicts rt<0; Nj is the number of observations where rt<0; N2 is the number of observations where rt>0; and the number of observations, N, is Nj + N2. Significance levels are for the hypothesis that sum of the conditional probabilities, P, exceed unity. Significance levels for the null of superior performance are indicated as follows: + 10% level and ++ 5% level. Significance levels for the null of inferior performance are indicated as follows: - 10% level and —5% level. 17 Table 2 Regression Tests of Forecasting Ability Trader 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 B 0.29 -0.01 0.18 0.63 -0.62 0.74 -0.35 -0.29 0.80 -0.75 -0.77 -0.14 0.12 Wheat t Stat. -0.43 -0.01 0.25 1.02 -0.85 0.77 -0.59 -0.51 1.24 -0.43 - 1.02 -0.25 0 .11 0.05 0.03 0.31 0.99 -0.34 -0.29 1.61 -0.60 -0.49 0.11 0.11 0.03 1.50 -0.04 2.72 0.05 -0.09 -0.02 -0.12 0.89 0.05 0.81 -0.05 2.69** 0.09 -0.13 -0.04 -0.11 1.05 0.11 0.21 0.76 1.13 0.68 P>ltl 0.67 0.99 0.81 0.31 0.40 0.45 0.56 0.61 0.22 0.67 0.31 0.81 0.91 0.96 0.50 0.11 0.55 0.63 0.92 0.96 0.43 0.96 0.02 0.93 0.90 0.97 0.91 0.30 0.83 0.26 6 -0.50 -0.53 -0.31 -0.09 0.51 -0.85 -0.20 1.11 -0.05 0.19 -1.32 0.43 -0.44 0.37 1.64 -0.23 -0.67 0.52 0.44 0.16 0.01 -0.15 0.14 0.13 0.20 0.23 -0.32 -0.90 0.15 -0.01 Bond t Stat. -0.99 -0.83 -0.92 -0.09 1.38 -0.93 -0.25 1.45 -0.09 0.27 - 1 .86* 0.80 -1.42 0.50 2.31** -0.40 -1.18 0.42 0.75 0.32 0.03 -0.12 0.39 0.37 0.80 0.82 -0.78 -1.60 0.55 -0.02 P>ltl 0.32 0.41 0.36 0.93 0.17 0.36 0.80 0.15 0.93 0.79 0.07 0.43 0.16 0.62 B 0.47 1.08 3.06 -0.64 0.45 0.44 -0.65 0.51 0.30 0.81 0.68 0.46 0.75 0.97 0.90 0.70 0.71 0.43 0.41 0.44 0.41 0.58 0.99 0.12 0.74 0.71 0.86 0.73 0.71 0.82 0.58 0.18 -3.58 1.50 0.00 0.68 0.00 0.00 0.33 0.74 0.70 -1.26 -0.75 4.80 -1.87 0.37 -1.18 -0.13 2.25 1.23 0.69 0.24 0.22 P>ltl 0.74 0.33 0.55 1.35 0.45 -0.93 -0.53 1.60 -0.88 0.36 -0.75 -0.05 1.99** 0.30 0.58 -0.35 -0.41 1.32 0.82 -2.31* 0.83 1.68 0.02 Pork t Stat. 0.33 0.96 1.60 -0.34 0.38 0.17 -0.35 0.38 0.66 -0.95 -1.13 1.94 2.22 B 0.49 0.51 -0.02 -0.15 0.30 0.46 -1.05 0.49 0.09 0.49 2.00 Cattle t Stat. 0.59 1.01 -0.05 -0.27 0.29 0.33 -1.07 0.32 0.16 0.58 2.40” P>ltl 0.56 0.32 0.96 0.78 0.77 0.75 0.29 0.75 0.88 0.56 0.02 0.66 0.50 1.00 0.32 0.35 0.60 2.01 2.62“ 0.17 -0.46 1.67* 0.78 1.07 -0.44 0.01 0.12 0.38 0.72 0.46 0.96 0.05 0.77 0.56 0.73 0.14 -0.23 1.92 1.94 24.54 -0.37 0.91 0.99 1.82 -0.23 0.68 0.02 0.19 0.42 0.06 0.41 -1.30 -1.03 1.31 -3.22 0.31 -1.06 1.10 0.91 0.64 -0.40 0.03 -0.76 -1.45 1.58 -1.36 0.50 -1.75* 0.87 0.65 0.10 0.44 0.29 0.66 0.28 0.37 0.52 0.69 0.98 0.45 0.15 0.12 0.19 0.62 0.08 Significance levels are for the null that the regression coefficient differs from zero. These are indicated as follows: * at the 10% level and ** at the 5% level. 18 Table 3 APT Estimates of Futures Returns Futures Contract a b. h2 b3 b, bj b6 R2 DW 0.0090 (0.77) 0.0139 (1.16) 0.0049 (0.40) 0.0037 (0.33) 0.0129 (1.06) 2.7421 (0.78) 1.9533 (0.54) 2.1303 (0.59) 2.8897 (0.84) 2.4784 (0 .68) -5.4560 (-1.34) -5.5135 (-1.31) -3.2186 (-0.76) -2.6110 (-0.65) -3.8690 (-0-91) 2.3016 (2.07) 2.2336 (1.95) 1.4348 (1.25) 2.2377 (2.05) 2.1907 ( 1 .88) 0.2983 (0.34) 0.7115 (0.78) -0.2484 (-0.27) -0.2101 (-0.24) 0.4815 (0.52) 0.2207 (0.28) 0.6697 (0.81) -0.1367 (-0-17) -0.1857 (-0.24) 0.4398 (0.53) 0.2898 (1.39) 0.3676 (1.70) 0.5497 (2.54) 0.4900 (2.38) 0.4192 (1.91) 0.20 2.33 0.21 2.53 0.21 2.01 0.26 2.23 0.21 2.42 -0.0035 ( 1 .0 1 ) 0.0094 (2.67) 0.0053 (1.64) 0.0037 (0.69) -0.9944 (-1 .02 ) 0.1549 (0.15) -0.9593 (-0.99) -0.9422 (-0.58) 0.1189 (0.09) -1.0652 (-0.87) 0.7881 (0.70) 0.6747 (0.36) 0.1219 (0.17) -0.1186 (-0.35) -0.0840 (-0.27) 0.8318 (1.62) 1.2808 (5.51) 1.6564 (6.22 ) 1.2501 (5.15) 1.0881 (2 .68) 0.3779 (1.83) 0.7422 (3.07) 0.3536 (1.60) 0.2504 (0 .68) -0.0600 (-1 . 10 ) -0.0007 (-0.0 1 ) -0.1278 (-2 .2 1 ) -0.1855 (-1.92) 0.89 2.17 0.87 1.77 0.87 2.30 0.65 1.73 0.0122 4.7035 (1.42) (1.82) 0.0039 2.7007 (0.43) (0.94) 0.0021 4.3005 (0.23) (1.57) 0.0066 3.1083 (0.64) (i.oi) 0.0053 2.3203 (0.50) (0.73) -0.0032 2.6284 (0.34) (0.93) -0.0046 1.9542 (0.47) (0.67) -2.1316 (-0.71) -6.4791 (-2.06) -5.8067 (-1.82) -5.9407 (-1 .66) -5.0943 (-1.39) -6.6416 (-2 .02) -7.1932 (-2 .1 1 ) 0.9382 (1.15) 0.2637 (0.31) 0.3097 (0.36) -0.2895 (-0.30) -0.4492 (-0.45) -0.2933 (-0.33) -0.4169 (-0.45) 0.8926 (138) -0.2246 (-0.33) 0.1519 (0 .22 ) 0.2229 (0.29) 0.1213 (0.15) 0.1942 (0.27) 0.2656 (0.36) 0.9236 (1.57) -0.1956 (-0.32) 0.2312 (0.37) 0.3562 (0.51) 0.2483 (0.34) 0.2604 (0.40) 0.2818 (0.42) 0.3836 (2.51) 0.4539 (2.81) 0.5201 (3.17) 0.6228 (3.39) 0.5476 (2.90) 0.6897 (4.07) 0.6047 (3.45) 0.27 1.50 0.29 1.79 0.31 1.59 0.29 1.87 0.23 1.80 0.38 2.00 0.33 1.77 0.0018 (0.08) -0.0060 (-0.26) -0.0137 (-0.57) -0.0173 (-0.67) -0.0135 (-0.45) -1.3024 (-0.16) -7.2354 (-0.89) -10.042 (-1.19) -13.013 (-1.45) -16.227 (-1.56) 1.0206 (0.47) 2.3630 (1.06) 2.0324 (0.89) 3.1358 (1.28) 3.2292 (1.14) -0.0403 (-0 .02) -0.8891 (-0.51) -0.7683 (-0.42) -0.9934 (-0.51) -1.5365 (-0 .68) 0.0689 (-0.04) -0.7969 (-0.50) -0.4841 (-0.29) -0.8241 (-0.47) -1.1751 (-0.58) 0.6779 (1.64) 0.4649 ( 1 .1 1 ) 0.7147 (1.65) 0.5696 (1.23) 0.3209 (0.60) 0.11 2.03 0.10 2.36 0.13 2.15 0.14 1.94 0.11 1.83 Wheat M arch M ay July S eptem ber D ecem ber Treasury Bond M arch June S eptem ber D ecem ber Cattle January contract missing M arch A p ril M ay A ugust S eptem ber O ctober N ovem ber Pork February M arch M ay July A ugust 8.7761 (1.27) 5.3345 (0.76) 3.9837 (0.55) 2.2837 (0.30) 0.6046 (0.07) (t statistics in parentheses) 19 Table 4 Performance Analysis of Nonsystematic Portion of Returns Conditional on a Superior Evaluation of Total Return Performance Panel A Henrikkson and Merton Procedure Trader 23 15 26 13 Contract Wheat Pork Pork Cattle n Ni n2 10 7 9 4 34 8 22 8 8 49 7 17 1*1 1 p 0.56 29 4 4 1.02 1.07 1.08 Notes: nj is the number of correct forecasts given rt<0; n is the number of times the forecaster predicts rt<0; Nx is the number of observations where rt<0; N2 is the number of observations where rt>0; and the number of observations, N, is Nt + N2. Significance levels are for the hypothesis that sum of the conditional probabilities, P, exceed unity. Significance levels for the null of superior performance are indicated as follows: + 10% level and ++ 5% level. Significance levels for the null of inferior performance are indicated as follows: - 10% level and -- 5% level. Panel B Cumby and Modest Procedure ru Trader Contract Wheat 23 Bond 15 Pork 20 11 Cattle Cattle 13 Cattle 16 n -0.33 -0.07 0.28 -0.21 0.05 0.53 = a o; + a , A t Stat. -1.60 -0.54 1.84* -1.39 0.40 3.42*’ + e i, (5) P>|t| 0.13 0.59 0.07 0.17 0.69 0.01 Significance levels are for the null that the regression coefficient differs from zero. These are indicated as follows: * at the 10% level and ** at the 5% level. 20
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