Why have the returns to technical analysis decreased?

Journal of Economics and Business 56 (2004) 159–176

Why have the returns to technical analysis decreased? Willis V. Kidd, B. Wade Brorsen∗ Department of Agricultural Economics, Oklahoma State University, 414 Agriculture Hall, Stillwater, OK 74078-6026, USA Received 13 August 2002; received in revised form 28 July 2003; accepted 22 August 2003

Abstract Returns to managed futures funds and Commodity Trading Advisors (CTAs) have decreased dramatically. Funds overwhelmingly use technical analysis. This research determines if structural change in futures price movements could explain the reduced fund returns. Bootstrap tests are used to test significance of a change in statistics related to daily returns, close-to-open changes, breakaway gaps, and serial correlation. Several statistics have changed across a broad range of commodities. Lower price volatility is the most likely explanation of the lower returns from technical analysis. The structural changes likely caused the decreased returns rather than increased technical trading causing the structural changes. © 2004 Elsevier Inc. All rights reserved. JEL classification: G13 Keywords: Bootstrap; Managed futures; Technical analysis

1. Introduction During the 1980s and early 1990s, investment in managed futures grew quickly. In recent years however, futures fund returns have decreased and the value of assets invested in managed futures has stagnated along with returns (Pendley & Zurla, 2002). Fig. 1 shows the Barclay Commodity Trading Advisor Index versus time and shows a steady trend of decreasing returns during the past 20 years. The causes of this decrease in fund performance are not fully known. Two possible explanations for the decrease are (a) decreased market ∗

Corresponding author. Tel.: +1-405-744-6836; fax: +1-405-744-8210. E-mail address: [email protected] (B.W. Brorsen).

0148-6195/$ – see front matter © 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jeconbus.2003.08.001

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Fig. 1. Barclay CTA index annual percentage returns by year. Source: The Barclay Group (2002).

volatility (and therefore profit opportunities) and (b) price distortion caused by the growth of the industry. Certainly there must have been changes in the distribution of futures prices in order for returns to have decreased so dramatically.1 This naturally leads to the research question, “What structural changes have occurred in futures price movements?” Knowing the way futures price distributions have changed will help explain why futures fund returns have decreased. Most financial participants are at least superficially interested in the return characteristics of managed futures funds and Commodity Trading Advisors. Technically traded managed futures funds rely almost exclusively on past prices to generate buy and sell signals. Accordingly positive returns to these funds require weak-form inefficiency of the markets. Therefore, the return attributes of managed futures funds are of high interest not only to investors but also to regulators, investment advisors, and policy makers. Research is needed to determine the ways in which the market has changed, thereby allowing technical traders to adjust trading systems to account for these changes. Most previous studies of returns to managed futures funds focus on the predictability of returns (e.g., Brorsen & Townsend, 2002; Schwager, 1996), factors that increase returns (e.g., Irwin & Brorsen, 1987), and if an increase in the trading volume of managed futures funds decreases returns (e.g., Brorsen & Irwin, 1987; Holt & Irwin, 2000). Some authors have examined the profitability of technical trading (e.g., Brock, Lakonishok, & LeBaron 1992; Lukac & Brorsen, 1990; Osler & Chang, 1995), and Boyd and Brorsen (1992) used simulated technical trading profits to see which price statistics are correlated with technical returns, but no authors have examined possible causes of the recent decrease in returns to technical analysis. Furthermore, many authors have examined the distribution (e.g., Gordon, 1985; Mandelbrot, 1963) and dependence (e.g., Gordon, 1985; Mann & Heifner, 1976) of futures price changes. The few studies that have evaluated a possible change in price distributions and dependence are limited in statistical techniques and commodities tested. 1 Indeed there have been many charges that trading by the funds has distorted prices. But the evidence in support of these charges is still inconclusive (Brorsen & Irwin 1987; Commodity Futures Trading Commission 2002; Holt & Irwin 2000).

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Although not backed by formal significance tests, Hudson, Leuthold, and Sarassoro (1987) suggest that price changes have become more normal over time. No research has comprehensively studied a change in daily return characteristics. This research directly tests the hypothesis that a structural change in futures price fluctuations has occurred that may have affected the profitability of managed futures and technical analysis. Bootstrap resampling techniques are used to test for evidence of a structural change in the distribution of futures prices because futures prices are known to be nonnormally distributed and they must not be independent for there to be positive returns to technical analysis.

2. Evidence that technical trading returns have decreased The returns graphed in Fig. 1 are indicative of decreased technical trading returns, but they are an imperfect measure of technical trading returns. Therefore, we now provide some additional evidence regarding the changes in returns. The three issues considered are (i) some CTAs do not use technical analysis, (ii) returns are net of costs and include interest returns, and (iii) larger funds have reportedly reduced leverage. Mean returns before 1991 and from 1991 to 2001 are presented in Table 1 for various indices of Zurich Capital Markets. All of the five indices show a substantial decrease in Table 1 Annual continuous-time CTA and commodity pool trading return statistics before and after 1991 Item returnsa

CTA value-weighted CTA equal-weighted returnsa CTA trend-following returnsa Private poolsa Public fundsa Costs Interest (80%)d Trend-following standard deviatione Estimated gross returns

1990 and before

1991–2001

14.65 22.56 15.01 37.70 9.30 19.20b 6.75 8.05 21.72f

9.32 7.65 8.64 9.41 4.60 10.00c 3.80 7.54 16.57g

a The source is the indices of Zurich Captial Markets (2002). The returns are calculated as the natural logarithm of the ending index value minus the natural logarithm of the initial value divided by the number of years. b The source is Brorsen and Irwin (1987). The costs are for public funds. c The source is Brorsen (1998). The costs are for Commodity Trading Advisors. d Averages of the annualized returns for 1-year US treasury bills by Federal Reserve Bank of St. Louis reported and then converted to a continuous-time return. e The standard deviation of monthly returns was computed by year for each CTA that listed their trading system as trend-following, trend-identifier, or mechanical. The statistics reported are the simple average of these annual standard deviations. f Calculated using the CTA value-weighted return of 14.65 minus interest of 6.75 plus cost of 13.85. The cost number is calculated as the public fund cost of 19.20 minus the difference in CTA value weighted returns and public fund returns (14.65 − 9.30 = 5.35) and thus assumes the entire difference in CTA and public fund returns is due to differences in cost. g Calculated using the CTA value-weighted return of 9.32 minus interest of 3.80 plus cost of 10.00. The result of 15.52 is then multiplied by the ratio of standard deviations (8.05/7.54) to adjust for possible lower leverage in the more recent period, which gives the result of 16.57.

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returns. In particular, the CTA trend-following index shows a dropoff of over six percentage points. The other indices include some funds that either do not use technical trading systems or use a mixture of trading methods. Brorsen and Irwin (1987, p. 121) found that 13 of 21 advisors relied solely on computer-guided technical trading systems, but that only 2 of 21 used no objective technical analysis. Billingsley and Chance (1996) used a dataset that let the CTA self-describe their trading approach. Billingsley and Chance then classify 80% of their returns as being from technical trading, but they acknowledge that traders in their nontechnical category do rely partly on technical analysis. Data we obtained from CISDM (2000) classify the returns as 18.2% discretionary, 0.3% quantitative, 60.5% systematic, 17.4% trend-based, and 3.6% trend-identifier. Several of the CTAs we know that rely almost entirely on trend-following systems are classified as systematic in the CISDM database. Many of the discretionary traders also use trend-following systems based on both charts and computers. Thus, the broader indexes may be as representative of trend-following returns as the narrower indices. Another issue is that CTA and fund returns are reported net of costs and include interest returns. Costs have steadily declined over time (Table 1). Irwin and Brorsen (1985, p. 156) report annual cost of 19.2% for public funds (10.7% for commissions and 8.5% for management, incentive, and administrative costs). Brorsen (1998) finds costs of 10% per year using CTA data from 1994 (commissions 5.7%, administrative 2.5%, and incentive fee 19.9%). Our analysis2 of the CISDM (2000) CTA data show even lower costs of 7–8%. CTA data include some private pools, which may have lower cost than public funds. Part of the decrease in cost may be due to the public funds studied by Irwin and Brorsen (1985) having higher costs than the CTA’s studied by Brorsen (1998). The decline in interest rates can explain part of the decrease in net returns (Table 1). Irwin and Brorsen (1985) report that at that time about 80% of interest returns were earned by the funds with the remainder kept by the manager or general partner (a greater percent may now be returned to investors, but we conservatively assume 80% in both periods). The decline in interest received is nearly 3% per year, which is not enough to explain the decline in returns. A final issue to be addressed is that those in the industry have related to us that some of the larger funds may have adopted trading methods that accepted a lower return in order to get reduced risk. Brown, Goetzmann, and Park (1997) found that the more profitable CTA’s reduced the variability of their returns. The changes used to reduce risk could include reduced leverage, increased diversity in methods and markets, as well as risk management programs that scale out of volatile markets. Further, the reduced price volatility demonstrated here could also cause reduced volatility of returns. Average standard deviations across trend-following funds (Table 1) show a small decrease, but not anywhere near enough to explain the decrease in returns. There are numerous ways of estimating the decrease in gross trading returns. A conservative estimate of the decrease, computed in Table 1, is 5.15 percentage points. This estimate assumes all of the difference in public fund and CTA returns is due to differences in cost and it assumes all of the decreased standard deviation is due to reduced leverage. If

2

Based on commissions of 3.2%, administrative costs of 2.1%, and an incentive fee of 20.3%.

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Table 2 Return characteristics before and after 1991 for the two CTAs that were the largest before 1991 Fund

Statistic

Before 1991

1991 and later

Percent change (%)

One One Two Two

Annual mean Monthly S.D. Annual mean Monthly S.D.

24.48 6.63 16.32 8.31

4.56 4.63 8.64 5.94

−83 −30 −47 −28

Note. The calculations are based on the MAR/Laporte data (LaPorte). The returns are monthly logarithmic returns. The monthly standard deviations are the averages over years.

the full differences in cost are used, then the decrease in gross returns is 10.16 percentage points. A weakness of averages across funds is that the composition of traders changes and it does not put extra weight on the largest funds that are expected to have changed their trading practices. In terms of size, two funds operating in the early period clearly dominated the others. Returns and standard deviations for these two funds are reported in Table 2. Risk does show a substantial decline which supports the assertion that the larger funds changed their trading methods. But for both funds, the decline in trading returns was much greater than the decline in standard deviation. While a decline in risk may explain a portion of the decline in returns, it cannot explain all of it. Therefore, the data clearly show that the returns to technical analysis have decreased.

3. Economic theory Any change in the way futures prices fluctuate could change the returns to technical analysis. If a structural change in price fluctuations has occurred, technical trading systems developed prior to the change may be obsolete, or changes may indicate that the need for technical trading to move the market to equilibrium has decreased. While some economists have placed technical analysis in the same category as astrology, there are sound theoretical explanations for the profitability of trend-following systems. Disequilibrium models such as those developed by Beja and Goldman (1980) and Grossman and Stiglitz (1980) are based on the assumption that prices do not instantaneously fully react to an information shock. Fundamental traders start moving the price toward equilibrium, but are unable to fully move the market due to risk aversion, capital constraints, or position limits. The result is price trends that technical analysts can detect and trade. The trending periods would be reflected in positive autocorrelation. Thus, any reduction in the autocorrelation of futures prices will decrease the profitability of trend-following systems. Empirical research, however, has only been able to detect a small amount of autocorrelation beyond what would be expected in an uncorrelated series (Irwin & Uhrig, 1984). The theoretical arguments for trend-following systems are based on a delayed movement toward equilibrium after new information enters the marketplace. The increased speed of news dissemination and market transactions and the increased use of trend-following systems likely have decreased the duration of market trends.

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A structural change in futures markets could be caused by many developments. Fundamental changes in markets have the possibility of modifying the way and speed in which traders react. A decrease in the cost of information, increase in the speed of financial transactions, decrease in computing cost, and an increase in the relative use of technical analysis, all have the potential to change the way prices fluctuate by increasing the reaction to new information and driving the market to equilibrium faster. These developments will have decreased the cost of using technical analysis and therefore may have decreased its profitability. In addition to these developments directly related to the futures industry, there are many economy wide changes that may have affected futures prices. Freer trade, better economic predictions, and fewer major shocks to the economy all may have lowered price volatility and therefore lowered the need for technical speculators to move the markets to equilibrium. Previous research by Boyd and Brorsen (1992) found a strong positive correlation between market volatility and technical trading profits so such a decrease in volatility would be expected to decrease technical trading profits. The Internet and decreased computer prices may have allowed markets to react faster to new information. If new information becomes available overnight, the change in prices between the close and open would be large. If price movements occur overnight then funds will either miss trading opportunities or will have to trade in the overnight markets that have higher liquidity costs. It is expected that advancements in markets such as increased news and transaction speed have caused the variance and kurtosis of close-to-open gaps to increase; however, the expected increase in the variance of gaps may be offset by a decrease in overall market volatility. If these structural changes have occurred, then there has been a decrease in demand for technical trading, which would be indicated by price volatility and decreased market reaction time. Another possible explanation for the reduced technical trading profitability is that the large increase in managed futures has distorted prices. Lukac, Brorsen, and Irwin (1988) found that different simulated technical trading systems signaled trades on the same day a significant number of days, which may allow for price distortion. In a recent Commodity Futures Trading Commission Report (2002, p. 7), the market surveillance staff reported: Over many years of observing the activity of commodity funds, the Surveillance staff has observed that, although a large number of funds may hold positions in a market, most of them do not trade on any given day. When funds do trade, however, they tend to trade in the same directions. Since many funds use technical, trend-following, trading systems, it is not clear whether fund activity contributes to the magnitude or direction of the price change or whether they are reacting to the price change. Empirical research is inconsistent as to whether an increase in the size of managed futures increases price volatility (e.g., Brorsen & Irwin, 1987; Holt & Irwin, 2000; Irwin & Brorsen, 1987). Increased technical trading should speed price adjustments (i.e., reduce inefficiency), but it would also increase the variance and kurtosis of price movements (Brorsen, Oellermann, & Farris, 1989). If the increase in managed futures has either distorted prices or increased efficiency of markets, the result would be increased price volatility, increased price kurtosis, and decreased autocorrelations.

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4. Futures price data Daily futures prices from seventeen commodities are used to test hypotheses regarding a structural change in daily price movements. A diverse set of commodities is used representing four sectors: agricultural, financial, foreign exchange rates, and precious metals. The data were collected from the bridge/CRB commodity database. The tests of structural change separate the data into two distinct time periods. Time period one begins on January 1, 1975 or the first date on which data is available, and ends on December 31, 1990. Time period two begins on January 1, 1991 and ends on December 31, 2001. The split date coincides with the drop in technical trading returns that occurred after 1990 as shown in Fig. 1. In order to analyze the contracts typically traded by managed futures funds, a continuous series of prices is constructed utilizing one contract until thirty trading days prior to the expiration of a contract, then the price series uses the next subsequent contract month. The changes in variables are calculated before splicing the data so that no outliers are created when contracts are rolled over. For example, assume the rollover is to occur from the May contract to the July contract on March 19. On March 18, the change is calculated as the difference in the May contract prices on March 18 and March 17. On March 19, the change is calculated as the July contract price on March 19 minus the July contract price on March 18. Three market related variables are analyzed: daily returns, close-to-open price changes, and daily trading gaps. Percent daily returns are defined as rt = 100 × (ln st − ln st−1 )

(1)

where rt is the daily return for day t, and st is the futures settlement price for day t. Close-to-open price changes are the change between the settlement price of a futures contract and the opening price on the following day. Therefore, ct = ln ot − ln st−1

(2)

where ct is the logarithmic close-to-open change, ot is the opening price on day t, and st −1 is the previous day’s settlement price. The final statistic, breakaway trading gaps, is    ln ht − ln lt−1 , if ht ≤ lt−1 gt = ln lt − ln ht−1 , if lt ≥ ht−1 (3)   ‘missing’, otherwise where gt is the trading gap, ht is the highest price attained on day t, and lt is the lowest price attained on day t. A breakaway gap occurs whenever today’s price range does not include yesterday’s close.

5. Statistics tested 5.1. Daily return statistics More statistics are calculated for the daily returns than for other variables. Both short- and long-term statistics are generated. There are three distributional statistics that are calculated for daily returns: sample variance, relative skewness, and relative kurtosis.

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The p-day logarithmic return is calculated by summing daily returns. Long-run returns are calculated for lengths of 5 (weekly), 10 (biweekly), and 20 (approximately monthly) days. The long-run returns are overlapping in order to allow for greater power of bootstrap statistical tests (Harri & Brorsen, 2002). The variance ratio tests of Lo and MacKinlay (1988) also use overlapping data. The variance of weekly, biweekly, and monthly returns is calculated and analyzed for changes in long-run volatility. The multi-day returns also allow comparing short- and long-run effects. In order to compare daily returns to returns of longer time horizons, ratios of daily variance to 5-, 10-, and 20-day variances are calculated. Variance ratios have been used in market efficiency tests (Lo & MacKinlay, 1988; Poterba & Summers, 1988). With independent and identically distributed normal random variables, the variance of p-day returns is p times that of daily returns. Positive autocorrelation would cause variance ratios to be less than 1/p, as would leptokurtosis. 5.2. Daily breakaway gap and close-to-open change statistics The same statistics are calculated for both gaps and close-to-open changes. Four sample statistics are calculated for each variable: mean, variance, relative skewness, and relative kurtosis. Bootstrap tests are used to determine if any of the first four moments of gaps or close-to-open changes have significantly changed. 5.3. Autocorrelation statistics Structural change in autocorrelation of daily returns is also tested. Four statistics are calculated: the sum of the first 5 and first 10 autoregressive coefficients, and the sum of the first 5 and first 10 squared autoregressive coefficients. The sum of the squared coefficients is linearly related to the Box–Pierce and Ljung–Box Q.3 A p-lag autoregressive coefficient ρp is defined as ρp =

cov(rt , rt−p ) var(rt )

(4)

where cov(rt , rt−p ) is the covariance of rt and rt −p , and var(rt ) is the variance of daily returns. If E(rt ) = 0 then Eq. (4) is algebraically equivalent to N 

ρp =

(rt × rt−p )

t=p+1

(N − 1)(var(rt ))

(5)

where N is the sample size. 3 Under the null hypothesis of no autocorrelation for the Ljung–Box and Box–Pierce tests, the Q statistics are asymptotically pivotal (Box & Pierce, 1970; Ljung & Box, 1978). An asymptotically pivotal statistic is one whose distribution does not depend on any unknown parameters. For example, if a statistic converges in distribution to a chi-squared distribution, then the statistic is asymptotically pivotal. Horowitz argues that the bootstrap procedure has greater power with asymptotically pivotal statistics. In practice, however, the asymptotic pivotalness property has proven unimportant (Maausoumi, 2001), and therefore no attempt is made here to ensure that test statistics are asymptotically pivotal.

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6. Procedures Formal tests of structural change are performed using bootstrap procedures. Due to the serial dependence of returns and gaps, both parametric tests and standard bootstrap procedures developed by Efron (1979) are not appropriate since they assume independence. The unique nature of the data and statistics requires the type of bootstrap procedure being used to be carefully selected. Two different bootstrap procedures are used to approximate the sampling distributions of the statistics. Nonautocorrelation statistics must be analyzed with a bootstrap that both accounts for serial dependency and also preserves the stationarity of the time series. The bootstrap procedure used for serial correlation statistics must maintain the long-term dependency in the data. Therefore, the data must be resampled in a way that preserves the dependency in the original time series. 6.1. Bootstrap method for daily returns, close-to-open changes and gaps For all statistics other than autocorrelation statistics, the stationary bootstrap (Politis & Romano, 1994) is used to construct confidence intervals for the statistics during the first time period. This type of bootstrap is applicable to weakly dependent stationary time series and has been used in financial studies such as Sullivan, Timmerman, and White (1999), and White (2000). The formation of the pseudo time series involves many steps. Let N1 be the sample size of the first time period and N2 be the sample size of the second time period. First the length of the block, l, is determined. This random length4 varies according to a geometric (0.10) variable. Next the starting observation, s, is chosen by randomly selecting a number according to a discrete uniform distribution. The starting block is generated by x1∗ = [xs , xs+1 , . . . , xs+l−1 ]. This process is repeated by selecting a new l and s to generate x2∗ . This process is continued and the vector X∗ is generated by concatenating the x∗i vectors until the pseudo series is greater in length than N1 . The generated series is then truncated such that the number of observations in X∗ equals N1 , the number of elements in the first time period. This process is repeated to form another pseudo-series Y ∗ , which is a 1 × N2 vector generated from stochastic length blocks of data from the first time period. Once the pseudo time-series sample is generated, the statistics of interest are calculated with X∗ and Y ∗ . For a test of a change in the mean, the difference in the mean of the elements of X∗ and Y ∗ is found: N1 N2 1  1  ˆ Θ1 = Xi − Yi (6) N1 N2 i=1

i=1

Following Good (2002), a test in the change of the variance is performed by calculating the ratio of the variance of X∗ to the variance of Y ∗  1 ¯ 2 1/(N1 − 1) N i=1 (Xi − X) ˆ2 = (7) Θ  2 ¯ 2 1/(N2 − 1) N i=1 (Yi − Y ) 4

Other choices of random lengths were considered and the results varied little. Even results with a standard bootstrap were not much different.

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Eq. (7) is used for daily, 5-, 10-, and 20-day returns. Tests of a change in relative skewness and relative kurtosis use the difference in the sample relative skewness and relative kurtosis in X∗ and Y ∗ . In contrast Dufour and Farhat (2001) use the absolute value of the change in skewness and relative kurtosis. The statistics used are thus: N1 N2 ¯ 3 ¯ 3 N1 N2 i=1 (Xi −X) i=1 (Yi − Y ) ˆ Θ3 = − (8) (N1 − 1)(N1 −2) (N2 − 1)(N2 − 2) sx3 sy3 and  N1 2 ¯ 4 (Xi − X) (N + 1) − 1) N 3(N 1 1 1 i=1 ˆ4= Θ − (N1 − 1)(N1 − 2)(N1 − 3) (N1 − 2)(N1 − 3) sx4   N1 ¯ 4 N2 (N2 + 1) 3(N1 − 1)2 i=1 (Yi − Y ) − − (N2 − 1)(N2 − 2)(N2 − 3) (N2 − 2)(N2 − 3) sy4 

(9)

where sx and sy are the sample standard deviations of X∗ and Y ∗ , respectively. The process is repeated until 1000 new pseudo-series have been generated and the ˆ m (m = 1, 2, 3, 4) statistics calculated for each of the 1000 samples. The actual change Θ ˆ m , is then calculated. Θ ˆ m is the value of Eqs. (6)–(9) when the actual data in the statistic, Θ from time period one is the vector X and the actual data from time period two is the vector ˆ m = 0) is rejected if Θ ˆ m is less than the α/2 Y . The null hypothesis of no change (i.e., Θ ˆ ˆ percentile of Θm or greater than the 1 − α/2 percentiles of Θm . The levels of α selected for this study are 0.05 and 0.10. 6.2. Bootstrap methods for daily autocorrelations Any bootstrap autocorrelation test must maintain the dependence between observations. The block bootstrap methods maintain dependence asymptotically as the size of the block increases to infinity (Horowitz, 1999). However, in finite samples, block bootstrap methods alone produce autocovariance estimates that are biased toward zero. In order to fully maintain the dependence, a vector bootstrap procedure is used. Let N2 be the sample size of the second sub-period, and let p = {5, 10} be the length of autoregressive lags tested. Then form C to be a (N1 − p) × (p + 1) matrix comprised of row vectors ct where the jth element of ct is the return for day t − j + 1 from the first subperiod, such that ct = [rt , rt−1 , . . . , rt−j+1 , . . . , rt−p ] for all t > p. Bootstrap confidence intervals are formed by resampling blocks of row vectors (with replacement) from the matrix C to form a N1 × p + 1 matrix C∗ and a N2 × p + 1 matrix D∗ . The number of vectors in a block is a geometric (0.10) random variable. Therefore, C∗ and D∗ are similar to the pseudo-time series generated by the stationary bootstrap used for returns and gaps. Eq. (5) can then be rewritten as T −p (τi,1 × τi,k ) ρp,τ = i=1 for τ = {c, d} (10) var(τi,1 ) where var(τ i,1 ) is the variance of the first column vector of T ∗ , (T = {C, D}).

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The statistics of interest are the differences in the autocorrelation coefficients from C∗ and D∗ adjusted by the degrees of freedom. These statistics are then calculated from the simulated ρp ’s (10) by the equation

p p   w w ˆ 5 = N1 ρi,c − N2 ρ Θ , for w = {1, 2}, and p = {5, 10} (11) i=1

i=1

i,d

where p is the lag and w is the power to which the autoregressive coefficient is raised. ˆ 5. This process is repeated 1000 times to form an empirical bootstrap distribution of the Θ Let D be a (N2 − p) × (p + 1) matrix formed in the same manner as C, but using data ˆ 5 is the difference in the autocorrelations from the first from the second time period. Then Θ time period and the second time period (i.e., using the matrices C and D in Eqs. (10) and ˆ 5 = 0) is rejected if Θ ˆ 5 is less than the α/2 (11)). The null hypothesis of no change (i.e., Θ ˆ ˆ percentile of Θ5 or greater than the 1 − α/2 percentiles of Θ5 . In order to save space in this paper and prevent reporting several pages of insignificant statistics, only those statistics that have changed in one-third or more of the commodities or have substantial theoretical explanations are presented.

7. Results The volatility of futures prices5 has decreased. Table 3 shows that the variance of 1- and 20-day6 returns has decreased in 8 of the 17 commodities. Furthermore, Table 4 shows the frequency of gaps has decreased in 16 commodities and the variance of gaps has decreased in 9 commodities. The variance of close-to-open changes has decreased in 14 commodities as shown in Table 5. A reduction in volatility translates into less trading opportunities for technical funds (Boyd & Brorsen, 1992); thereby, reducing profit prospects. Technical trading systems profit by moving a market to equilibrium. If price equilibriums move little, there are few opportunities for technical systems to profitably trade. Therefore, the decreased volatility in short and long-run returns is consistent with the hypothesis that a structural change in futures markets caused a decrease in technical trading returns. Although the variance of several of the variables decreased, the kurtosis of daily returns (Table 6), breakaway gaps (Table 7), and close-to-open changes (Table 5) all increased in several commodities. The increased kurtosis suggests that when new information is released during nontrading hours, the market reacts quickly to this information and has already moved toward equilibrium by the open. The quicker jump to an equilibrium price may cause technical systems to not be able to execute a trade until prices have already moved toward equilibrium. The price autocorrelations show some significant changes. Tables 8 and 9 show the four autocorrelation measures. In 6 of the 17 commodities, at least one of the sums of 5

Coffee and wheat consistently change different than the other commodities. This is likely due to the breakup of the International Coffee Organization in 1989 (Indahsari, 1990) and the decrease in wheat subsidies by the federal government (United States Department of Agriculture, 2002). 6 Five- and 10-day variance ratio results are similar to 20-day ratios and therefore are not reported.

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Table 3 Variance of daily and 20-day returns for futures prices Commodity

Coffee Cocoa Corn Crude oil Deutsche Marks Eurodollars Feeder cattle Gold Heating oil Japanese Yen Live cattle Pork bellies Soybeans Standard and Poor’s 500 Sugar Treasury bonds Wheat

Variance of daily returns

Variance of 20-day returns

1975a –1990

1991–2001

1975a –1990

1991–2001

3.38 3.57 1.41 3.83 0.44 0.02 1.14 2.15 2.99 0.43 1.33 4.52 2.25 2.02 7.42 0.71 1.28

7.10++ 3.16∗∗ 1.52 3.60 0.48 <0.01∗∗ 0.53∗∗ 0.60∗∗ 3.14 0.58++ 0.60∗∗ 5.08+ 1.48∗∗ 1.09 3.29∗∗ 0.37∗∗ 1.52

99.9 77.5 35.5 105.4 10.2 0.5 27.0 45.5 84.6 11.1 28.2 116.3 51.0 25.8 160.2 16.9 26.2

162.4++ 60.9∗∗ 36.9 67.2 10.6 0.1∗∗ 11.1∗∗ 12.8∗∗ 67.0 12.6 11.0∗∗ 114.5 29.4∗∗ 17.9 66.2∗∗ 7.3∗∗ 40.9++

Notes. Hypothesis tests were performed using the two sample stationary bootstrap with 1000 repetitions. Statistically significant increases are denoted by ‘+’ at 0.10 level and ‘++’ at 0.05 level. Statistically significant decreases are denoted by ‘∗’ at 0.10 level and ‘∗∗’ at 0.05 level. a 1975 or the first date in the time series.

Table 4 Frequency and mean of breakaway gaps in futures prices Commodity

Coffee Cocoa Corn Crude oil Deutsche Marks Eurodollars Feeder cattle Gold Heating oil Japanese Yen Live cattle Pork bellies Soybeans Standard and Poor’s 500 Sugar Treasury bonds Wheat

Frequency of breakaway gaps

Variance of breakaway gaps

1975a –1990

1975a –1990

1991–2001

1.73 1.14 0.74 1.65 0.18 0.01 0.36 1.05 1.49 0.15 0.45 2.02 1.02 0.28 2.14 0.38 0.28

3.12++ 0.41∗∗ 0.42 1.43 0.21 <0.01∗∗ 0.15∗∗ 0.19∗∗ 0.81∗∗ 0.10∗∗ 0.11∗∗ 2.06 0.84 0.34 0.56∗∗ 0.14∗∗ 0.40

0.19 0.20 0.16 0.22 0.26 0.17 0.15 0.18 0.26 0.39 0.13 0.15 0.14 0.07 0.19 0.17 0.16

1991–2001 ∗∗

0.09 0.12∗∗ 0.10∗∗ 0.06∗∗ 0.15∗∗ 0.03∗∗ 0.09∗∗ 0.07∗∗ 0.08∗∗ 0.09∗∗ 0.06∗∗ 0.11∗∗ 0.07∗∗ 0.03∗∗ 0.09∗∗ 0.07∗∗ 0.15

Notes. Hypothesis tests were performed using the two sample stationary bootstrap with 1000 repetitions. Statistically significant increases are denoted by ‘+’ at 0.10 level and ‘++’ at 0.05 level. Statistically significant decreases are denoted by ‘∗’ at 0.10 level and ‘∗∗’ at 0.05 level. a 1975 or the first date in the time series.

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Table 5 Mean and variance of close-to-open changes in futures prices Commodity

Coffee Cocoa Corn Crude oil Deutsche Marks Eurodollars Feeder cattle Gold Heating oil Japanese Yen Live cattle Pork bellies Soybeans Standard and Poor’s 500 0.66 Sugar Treasury bonds Wheat

Variance of close-to-open changes

Kurtosis of close-to-open changes

1975a –1990

1975a –1990

1991–2001

8.64 2.58 13.44 11.12 5.83 89.94 7.90 9.36 6.83 3.44 4.01 3.80 9.16 42.18 6.61 12.65 25.96

67.33++ 2.74 17.85 25.41++ 7.26 32.56 12.29 86.64++ 32.02++ 8.21++ 7.96++ 6.42++ 30.39++

1.35 1.37 0.45 1.82 0.23 <0.01 0.31 1.03 1.57 0.26 0.36 1.17 0.66 0.11∗ 2.35 0.37 0.29

1991–2001 1.93++ 0.73∗∗ 0.28∗∗ 0.68∗∗ 0.14∗∗ <0.01∗∗ 0.11∗∗ 0.15∗∗ 0.86∗∗ 0.09∗∗ 0.09∗∗ 1.28 0.32∗∗ 410.12 0.61∗∗ 0.06∗∗ 0.43+

7.25 16.10 12.98

Notes. Hypothesis tests were performed using the two sample stationary bootstrap with 1000 repetitions. Statistically significant increases are denoted by ‘+’ at 0.10 level and ‘++’ at 0.05 level. Statistically significant decreases are denoted by ‘∗’ at 0.10 level and ‘∗∗’ at 0.05 level. a 1975 or the first date in the time series.

Table 6 Skewness and kurtosis of daily returns for futures prices Commodity

Skewness of daily returns 1975a –1990

Coffee Cocoa Corn Crude oil Deutsche Marks Eurodollars Feeder cattle Gold Heating oil Japanese Yen Live cattle Pork bellies Soybeans Standard and Poor’s 500 Sugar Treasury bonds Wheat

−0.28 0.05 −0.01 −0.14 0.20 0.62 −0.08 −0.10 −0.06 0.32 −0.10 −0.01 −0.11 −5.52 −0.04 0.21 0.32

Kurtosis of daily returns

1991–2001 ++

0.47 0.37++ −0.02 −2.14∗∗ 0.01 0.33 −0.07 0.63++ 0.10 0.84++ −0.02 0.01 −0.05 −0.28 −0.05 −0.36 0.15

1975a –1990 4.05 0.64 1.90 4.85 2.44 10.19 0.46 4.00 2.44 3.13 0.26 −0.59 0.96 158.43 1.85 5.80 5.94

1991–2001 8.08++ 2.27++ 1.86 36.11++ 1.90 6.55 1.04++ 18.11++ 3.37 8.62++ 0.75++ 0.02++ 2.99++ 5.11 2.46 2.06∗∗ 1.32∗∗

Notes. Hypothesis tests were performed using the two sample stationary bootstrap with 1000 repetitions. Statistically significant increases are denoted by ‘+’ at 0.10 level and ‘++’ at 0.05 level. Statistically significant decreases are denoted by ‘∗’ at 0.10 level and ‘∗∗’ at 0.05 level. a 1975 or the first date in the time series.

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Table 7 Variance and skewness of breakaway gaps in futures prices Commodity

Skewness of breakaway gaps 1975a –1990

Coffee Cocoa Corn Crude oil Deutsche Marks Eurodollars Feeder cattle Gold Heating oil Japanese Yen Live cattle Pork bellies Soybeans Standard and Poor’s 500 Sugar Treasury bonds Wheat

0.33 0.39 0.86 0.15 −0.07 1.73 −0.26 −0.09 −0.17 0.54 −0.30 0.09 0.15 −0.91 −0.65 1.41 −0.33

Kurtosis of breakaway gaps

1991–2001 ++

3.77 0.37 1.06 −3.94∗ −0.48 0.60 1.01++ −3.46∗∗ 4.38++ 0.73 1.05++ −0.16 −0.25 −1.98 1.09++ −1.19 2.15

1975a –1990

1991–2001

7.34 2.33 11.25 25.31 11.26 22.91 3.65 9.01 6.85 4.96 3.55 2.21 6.50 6.56 7.23 23.34 28.12

33.27++ 2.40 8.79 42.95 5.10 11.55 7.71++ 30.84++ 42.02++ 5.30 9.53++ 2.62 7.84 13.17 6.44 14.42 13.95

Notes. Hypothesis tests were performed using the two sample stationary bootstrap with 1000 repetitions. Statistically significant increases are denoted by ‘+’ at 0.10 level and ‘++’ at 0.05 level. Statistically significant decreases are denoted by ‘∗’ at 0.10 level and ‘∗∗’ at 0.05 level. a 1975 or the first date in the time series.

Table 8 Sums of first 5 and first 10 autoregressive coefficients times the number of observations for futures prices Commodity

Sum of first five autoregressive coefficients 1975a –1990

Coffee Cocoa Corn Crude oil Deutsche Marks Eurodollars Feeder cattle Gold Heating oil Japanese Yen Live cattle Pork bellies Soybeans Standard and Poor’s 500 Sugar Treasury bonds Wheat

463.4 14.2 76.3 199.7 54.9 167.2 459.2 −61.5 309.1 144.9 241.0 349.4 68.9 −436.4 −6.1 157.1 −187.5

Sum of first 10 autoregressive coefficients

1991–2001 ∗

−61.6 −57.3 20.1 −247.7 25.5 288.2 79.4∗∗ 204.0 −113.2 −61.5 −19.5 −9.2∗∗ −256.4 −344.8 76.6 −260.2∗∗ 174.3+

1975a –1990

1991–2001

780.1 53.5 395.5 526.6 286.5 375.2 284.8 −38.0 402.4 503.1 56.0 484.5 183.3 −599.0 102.9 252.6 101.2

88.3∗ −48.1 257.1 −291.4 47.9 644.5 −188.0 111.4 −91.8 53.6 −375.5∗ 257.4 −94.8 −438.5 −136.5 −229.3 397.0

Notes. Hypothesis tests were performed using the two sample stationary bootstrap with 1000 repetitions. Statistically significant increases are denoted by ‘+’ at 0.10 level and ‘++’ at 0.05 level. Statistically significant decreases are denoted by ‘∗’ at 0.10 level and ‘∗∗’ at 0.05 level. a 1975 or the first date in the time series.

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Table 9 Sums of first 5 and first 10 squared autoregressive coefficients times the number of observations for futures prices Commodity

Coffee Cocoa Corn Crude oil Deutsche Marks Eurodollars Feeder cattle Gold Heating oil Japanese Yen Live cattle Pork bellies Soybeans Standard and Poor’s 500 Sugar Treasury bonds Wheat

Sum of first five squared autoregressive coefficients

Sum of first 10 squared autoregressive coefficients

1975a –1990

1991–2001

1975a –1990

1991–2001

26.0 9.5 10.9 53.7 4.1 26.9 17.2 21.3 54.0 4.3 7.5 14.6 2.7 54.7 7.6 6.0 14.6

16.4 7.6 14.3 36.7 4.8 47.6 10.2 26.7 8.8 5.5 7.1 10.3 13.8 12.6 17.7 15.2 33.3

34.8 15.4 29.1 72.9 9.8 30.6 20.6 25.6 59.2 15.8 21.2 17.9 8.9 61.7 12.1 8.0 25.7

21.6 10.9 25.0 40.2 13.3 64.5 28.7 31.2 18.2 9.6 22.9 22.0 20.9 19.1 25.0 35.4+ 37.3

Notes. Hypothesis tests were performed using the two sample stationary bootstrap with 1000 repetitions. Statistically significant increases are denoted by ‘+’ at 0.10 level and ‘++’ at 0.05 level. Statistically significant decreases are denoted by ‘∗’ at 0.10 level and ‘∗∗’ at 0.05 level. a 1975 or the first date in the time series.

autocorrelation changed significantly. All but two of the significant changes are a decrease in autocorrelation. In addition the variance ratios in Table 10 show weak evidence of decreased autocorrelation. Under the assumption of independent and normally distributed changes, these ratios should be near 1/p. Eight of the commodities showed a significant increase in the ratios and almost all of the ratios moved closer to 1/p, which indicates less autocorrelation. A majority of the technical trading systems are trend following, and a decrease in the autocorrelation of daily returns would likely decrease the profitability of trend-following systems. While the change in price serial correlation is not pronounced, it is in a direction consistent with technical trading being less profitable. One weakness of the autocorrelation tests is that they could be influenced by the changes in variance or kurtosis. For example, the three livestock commodities that show statistical significance in Table 8 all have price limits. A reduced frequency in hitting price limits could have occurred due to the reduced variance. Less frequent hitting of price limits could cause the reduced autocorrelation. The three livestock commodities do indeed show decreased frequency of moves: pork bellies fell from 17 to 10%, feeder cattle from 5.5 to 2.2%, and live cattle from 5.2 to 1.4%. This provides further evidence that the primary change in markets was reduced variability. All but one of the funds in Table 10 that show an increased variance ratio also show increased leptokurtosis. The increased leptokurtosis may be partly responsible for the increased variance ratio. Alternatively, decreased autocorrelation would cause increased leptokurtosis.

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Table 10 Ratio of daily variance to 5-day and 20-day variance for futures prices Commodity

Coffee Cocoa Corn Crude oil Deutsche Marks Eurodollars Feeder cattle Gold Heating oil Japanese Yen Live cattle Pork bellies Soybeans Standard and Poor’s 500 Sugar Treasury bonds Wheat

Ratio of daily variance to 5-day variance

Ratio of daily variance to 20-day variance

1975a –1990

1991–2001

1975a –1990

1991–2001

0.17 0.18 0.18 0.16 0.19 0.17 0.17 0.19 0.16 0.19 0.18 0.17 0.19 0.25 0.20 0.18 0.20

0.19+

0.033 0.046 0.039 0.036 0.043 0.039 0.042 0.047 0.035 0.038 0.047 0.038 0.044 0.078 0.046 0.042 0.048

0.043++ 0.051 0.041 0.053++ 0.045 0.034 0.048 0.046 0.046+ 0.046+ 0.055++ 0.044 0.050 0.061 0.049 0.051+ 0.037∗∗

0.21++ 0.18 0.22++ 0.19 0.17 0.18 0.20 0.21++ 0.20 0.19 0.19++ 0.20 0.22 0.20 0.20 0.17∗∗

Notes. Hypothesis tests were performed using the two sample stationary bootstrap with 1000 repetitions. Statistically significant increases are denoted by ‘+’ at 0.10 level and ‘++’ at 0.05 level. Statistically significant decreases are denoted by ‘∗’ at 0.10 level and ‘∗∗’ at 0.05 level. a 1975 or the first date in the time series.

Although many market variables show evidence of change, there are still a few statistics7 that did not significantly change. The average size of close-to-open price changes and breakaway gaps did not consistently change. The skewness of returns, gaps, and close-to-open changes changed in only a few commodities.

8. Conclusions Technical trading returns have been lower after 1990 than they were before. Futures prices are examined for evidence of a structural change that could explain the reduced profitability. The results show evidence of a structural change in prices that may have reduced technical trading profitability. The two dominant changes are a decrease in price volatility and an increase in the kurtosis of price changes occurring while markets are closed. There is also a slight indication of reduced autocorrelation. These changes are consistent with the reduced profitability of technical trading being due to changes in the overall economy. The results are not consistent with increased technical trading having caused the structural change, because in that case price volatility should have increased. If economic conditions changed

7

Five-minute intraday prices of six commodities were also examined, but no clear pattern of change was found.

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so that prices became more volatile, then presumably returns to technical trading would increase.

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