CHAPTER 4 CTA Performance, Survivorship Bias, and Dissolution Frequencies Daniel Capocci U sing a database containing 1,892 funds (including 1,350 dissolved funds), we investigate CTA performance and performance persistence to deter- mine if some CTAs consistently and significantly outperform their peers over various time periods. To test the persistence hypothesis, we use a methodol- ogy based on Carhart’s (1997) decile classification. We examine performance across deciles and across CTA strategies to determine if some deciles are more exposed to certain strategies over time. We also analyze survivorship bias and its evolution over time. We conclude the study by analyzing the dis- solution frequencies across deciles and their evolution over time. INTRODUCTION AND LITERATURE REVIEW Unlike hedge funds, which appeared in the first academic journal in 1997, commodity trading advisors (CTAs) have been studied for a longer time. Many studies were published in the late 1980s and in the early 1990s (see, e.g., Elton, Gruber, and Rentzler 1987, 1989, 1990; Edwards and Ma 1988). More recently, Billingsley and Chance (1996) and Edwards and Park (1996) showed that CTA funds can add diversification to stocks and bonds in a mean-variance framework. According to Schneeweis, Savanayana, and McCarthy (1991) and Schneeweis (1996), the benefits of CTAs are similar to those of hedge funds, in that they improve and can offer a superior risk- adjusted return trade-off to stock and bond indices while acting as diversi- fiers in investment portfolios. Fung and Hsieh (1997b) showed that a constructed CTA style factor persistently has a positive return when the Standard & Poor’s (S&P) has a 49 c04_gregoriou.qxd 7/27/04 11:05 AM Page 49 negative return. According to Schneeweis, Spurgin, and Georgiev (2001), CTAs are known to short stock markets regularly. Fung and Hsieh (2001a) analyzed CTAs and concluded that their impact on portfolios is similar to that of a lookback call and a lookback put. 1 Gregoriou and Rouah (2003a) examined whether CTA percent changes in net asset values (NAVs) follow random walks. They found all classifications (except the diversified subindex) to behave as random walks. The effectiveness of CTAs in enhanc- ing risk-return characteristics of portfolios could be compromised when pure random walk behavior is identified. Kat (2002) found that allocating to managed futures allows investors to achieve a very substantial degree of overall risk reduction at limited costs. Managed futures appear to be more effective diversifiers than hedge funds. Regarding performance, Edwards and Caglayan (2001) concluded that during bear markets, CTAs provide greater downside protection than hedge funds and have higher returns along with an inverse correlation with stocks returns in bear markets. Schneeweis and Georgiev (2002) concluded that careful inclusion of CTA managers into investment portfolios can enhance their return characteristics, especially during severe bear markets. Schneeweis, Spurgin, and McCarthy (1996) observed that performance persistence was virtually inexistent between 1987 and 1995. There is little information on the long-term diligence of these funds (Edwards and Ma 1998; Irwin, Kruke- meyer, and Zulauf 1992; Kazemi 1996). Schwager (1996) reviews the litera- ture on CTA performance persistence and conducts his own analysis. He found little evidence that the top-performing funds can be predicted. According to Worthington (2001), between 1990 and 1998 the correlation of managed futures to the S&P 500 during its best 30 months was 0.33 and −0.25 during its worst 30 months. According to Georgiev (2001), one of the drawbacks of CTAs is that during bull markets, their performance is gener- ally inferior to those of hedge funds. Brorsen and Townsend (2002) show that a minimal amount of per- formance persistence is found in CTAs, and there could exist some advan- tages in selecting CTAs based on past performance when a long time series of data is available and accurate methods are used. This chapter aims to detect performance persistence of CTAs. We want to determine if some CTAs consistently outperform their peers over time. In 50 PERFORMANCE 1 A lookback call is a normal call option, but the strike depends on the minimum stock price reached during the life of the option. A lookback put is a normal put option, but the strike depends on the maximum stock price reached during the life of the option. c04_gregoriou.qxd 7/27/04 11:05 AM Page 50 the next section, we describe the database, reporting the descriptive statis- tics of the funds and analyzing the correlation between the various strate- gies reported. The following section focuses on survivorship bias. We analyze the presence of this bias over the whole period studied but also over different time periods, including a bull and a bear market period. Further, we report the methodology used to analyze CTA performance and per- formance persistence before reporting the results of the performance analy- sis in the next section. The next section reports the results of the persistence analysis and analyzes the exposure of the deciles constructed on previous year’s performance to the individual strategies. Then we report the complete analysis of monthly and yearly dissolution frequencies. DATABASE In this section, we present our database and analyze the descriptive statistics of the data before reporting the correlation between the various strategies. Descriptive Statistics There are several CTA data providers. The providers most commonly used in academic studies are Managed Account Repots, TASS Management, and the Barclay Trading Group, Ltd. The latter represents one of the most (if not the most) comprehensive managed future databases. For our analysis we use the Barclay Trading Group database, which contains 1,892 individual funds (including 1,350 dissolved funds) over the January 1985 to December 2002 period. The Barclay Trading Group clas- sifies these funds in 7 categories that are subdivided in 17 strategies plus the no-strategy category. We grouped some strategies because they contain too few funds to give interesting results. As shown in Table 4.1, we obtained a total of 11 strategies. Note that we combined only those strategies that are in the same category. To perform our performance analysis, we will use the whole database and the classifications reported in Table 4.1. This will allow us to determine whether results differ across strategies and whether funds in particular strategies significantly outperform others. Previous studies often focused on fewer funds. For example, Schneeweis, Spurgin, and McCarthy (1996) studied 56 CTA funds from 1985 to 1991. Irwin, Zulauf, and Ward (1994) used a database containing 363 CTAs from 1979 to 1989. Other studies were larger. For example, Edwards and Park (1996) found 596 CTAs from 1983 to 1992 by supplementing the MAR/LaPorte CTA database with private sources. Diz (1996) and Fung and Hsieh (1997b) had 925 and 901 managed future programs from 1975 to CTA Performance, Survivorship Bias, and Dissolution Frequencies 51 c04_gregoriou.qxd 7/27/04 11:05 AM Page 51 1995, and from 1986 to 1996 respectively. They were both based on the Barclay Trading Group database. Funds in the Barclay Trading Group database can be classified into more than one strategy. This can lead to a bias when we compare different strategies since they can contain the same funds. In order to deal with this issue, we report each fund in one strategy only. 2 Before entering the body of the study, we analyze the composition of the database. Table 4.2 reports the descriptive statistics of the database. Funds are classified according to strategy. The last line reports the statistics for the whole database. 52 PERFORMANCE TABLE 4.1 Grouping of Barclay Trading Group Strategies Grouped CTA Barclay Trading Strategies Group Strategy Technical Diversified Technical Diversified Technical Financial/Metals Technical Financial/Metals Technical Currency Technical Currency Other Technical Technical Interest Rate Technical Energy Technical Agricultural Fundamental Fundamental Diversified Fundamental Interest Rate Fundamental Financial/Metals Fundamental Energy Fundamental Currency Fundamental Agricultural Discretionary Discretionary Systematic Systematic Stock Index Stock Index Arbitrage Arbitrage Option Strategies Option Strategies No Category No Category Note: The left-hand side of the table reports the strategy classifica- tion used throughout the study; the right-hand side contains the original classification of the Barclay Trading Group. 2 Any fund that is reported in two strategies is classified into the one that contains the most funds. c04_gregoriou.qxd 7/27/04 11:05 AM Page 52 TABLE 4.2 Descriptive Statistics CTA January 1985–December 2002 Strategies (216 months) No. of % of Living Dead Mean t(mean) Std. Sharpe Funds the Total Funds Funds Return = 0 Dev. Median Min Max Skewness Kurtosis Ratio Technical Diversified 264 14% 44 220 1.72 5.38 4.70 0.83 −6.9 31.6 3.02 14.68 0.28 Technical Financial/ Metals 86 5% 11 75 1.78 6.33 4.12 0.95 −5.2 29.8 2.95 14.11 0.33 Technical Currency 58 3% 18 40 1.58 6.49 3.58 1.07 −14.5 15.6 0.64 3.73 0.33 Other technical 8 0% 0 8 3.18 5.35 7.25 1.92 −18.7 47.5 2.00 9.58 0.38 Total technical 416 22% 73 343 1.75 6.33 4.06 0.72 −5.2 25.3 2.92 13.27 0.33 Fundamental 19 1% 2 17 1.83 3.55 7.60 1.17 −20.4 57.4 2.48 16.14 0.19 Discretionary 299 16% 67 232 2.03 9.93 3.01 1.31 −3.9 18.8 2.42 9.24 0.54 Systematic 897 47% 350 547 1.70 4.73 5.27 0.83 −8.3 26.4 1.86 6.35 0.24 Stock Index 52 3% 16 36 1.89 4.39 6.33 1.14 −18.4 38.4 2.05 10.46 0.23 Arbitrage 27 1% 2 25 1.25 5.76 3.19 1.07 −14.8 12.0 −0.36 4.28 0.26 Option strategy 9 0% 0 9 2.62 4.66 8.24 2.57 −23.3 36.5 0.53 2.51 0.27 No Category 180 9% 28 152 1.62 6.20 3.84 0.95 −4.9 28.5 3.14 15.07 0.31 Total 1,899 100% 611 1,288 1.75 6.51 3.95 0.98 −5.2 21.9 2.37 9.06 0.34 t(mean) = 0 reports the t-statistic for the hypothesis that the mean monthly returns equal zero. Std. Dev. = standard deviation; Min = minimum; Max = maximum. The Sharpe ratio is calculated with a 5 percent risk-free rate. Note: The other technical strategy funds exist only for the August 1985–May 1995 period and for the October 1998–April 2001 period. Option strategy funds exist since September 1990. 53 c04_gregoriou.qxd 7/27/04 11:05 AM Page 53 Table 4.2 indicates that the systematic strategy is the most represented strategy (with 897 funds) followed by total technical funds (416 funds) and discretionary funds (299 funds). Other technical funds, option strategy funds, and fundamental funds count only 8, 9, and 19 funds respectively. The database contains 611 dissolved funds as a whole, 350 of which follow the systematic strategy. Note that all the other technical funds and option strategy funds are dissolved over the period studied. The median returns indicate the same patterns. Regarding the statistics, the highest mean monthly return is achieved by the other technical funds (with 3.18 percent per month) followed by the option strategy funds and discretionary funds (with 2.62 percent and 2.03 percent per month). Many strategies offer a monthly return of between 1.6 percent and 1.9 percent per month. The lowest returns are those of the arbitrage funds (with 1.25 percent) followed by the technical currency funds (with a monthly return of 1.58 percent). All the monthly returns are significantly different from zero over the period studied. The fundamental funds and the other technical funds are the more volatile funds with a standard deviation of 7.60 and 7.25 percent. Because there are few funds applying these strategies, there is no diversification effect, which can explain why the returns of these strategies are so volatile. The strategies that offer the most stable returns are the discretionary funds (with a standard deviation of 3.01 percent) and the arbitrage funds (with a standard deviation of 3.19 percent). As one could expect, the strategies that are the most volatile also have the lowest minimum return and the highest maximum return. The monthly minimum returns can reach −20.4 percent for the fundamental strategy whereas the maximum of this strategy is 57.4 percent. The returns are usually positively skewed (the only exception is the arbitrage strategy) and their distributions tend to have fat tails, as evidenced by the large values for kurtosis. When risk and returns are considered together through the Sharpe ratio, 3 the discretionary funds emerge with the highest Sharpe ratio (0.54) followed by other technical funds (with 0.38). Fundamental funds offer a Sharpe ratio of only 0.19. Correlation Analysis Table 4.3 reports the correlation coefficients between the various strategies for the January 1985 to December 2002 period. It indicates that the CTA 54 PERFORMANCE 3 The Sharpe ratio is the ratio of the excess return over the standard deviation. We use a risk-free rate of 5 percent for this calculation. c04_gregoriou.qxd 7/27/04 11:05 AM Page 54 55 TABLE 4.3 Correlation between the CTA Strategies, January 1985 to December 2002 Allcta Arb Discret Funda Option Stock System Teccur Tecdiv Tecfin Tecoth Nocat AllCTA 1.00 −0.18 0.41 0.25 0.12 0.26 0.98 0.68 0.93 0.73 0.14 0.81 Arb −0.18 1.00 0.20 −0.02 0.08 0.05 −0.21 −0.18 −0.13 −0.05 0.24 −0.01 Discret 0.41 0.20 1.00 0.14 0.13 0.18 0.27 0.16 0.42 0.27 0.00 0.32 Funda 0.25 −0.02 0.14 1.00 0.01 0.08 0.22 0.17 0.22 0.20 −0.02 0.12 Option 0.12 0.08 0.13 0.01 1.00 0.62 0.12 −0.01 0.03 0.11 0.02 0.12 Stock 0.26 0.05 0.18 0.08 0.62 1.00 0.25 0.09 0.14 0.13 0.01 0.29 System 0.98 −0.21 0.27 0.22 0.12 0.25 1.00 0.70 0.89 0.71 0.18 0.79 Teccur 0.68 −0.18 0.16 0.17 −0.01 0.09 0.70 1.00 0.56 0.56 0.12 0.56 Tecdiv 0.93 −0.13 0.42 0.22 0.03 0.14 0.89 0.56 1.00 0.66 0.05 0.73 Tecfin 0.73 −0.05 0.27 0.20 0.11 0.13 0.71 0.56 0.66 1.00 0.10 0.50 Tecoth 0.14 0.24 0.00 −0.02 0.02 0.01 0.18 0.12 0.05 0.10 1.00 0.9 Nocat 0.81 −0.01 0.32 0.12 0.12 0.29 0.79 0.56 0.73 0.50 0.09 1.00 AllCTA = CTA Global Index; Arb = arbitrage; Discret = discretionary; Funda = fundamental; Stock = stock index; System = systematic funds; Teccur = technical currency; Tecdiv = technical diversified; Tecfin = technical financial/metals; Tecoth = other technical; Nocat = no category. c04_gregoriou.qxd 7/27/04 11:05 AM Page 55 56 PERFORMANCE global index is almost exactly correlated with the systematic funds. This can be partly explained by the fact that this strategy contains the greatest num- ber of funds. Forty-four coefficients out of sixty-six (66 percent of the co- efficients) are under 0.5, indicating that most of the strategies are not correlated. The lowest coefficient is the one between arbitrage and system- atic funds at −0.21. There are nine negative coefficients in total represent- ing 14 percent of the coefficients. SURVIVORSHIP BIAS Performance figures are subject to various biases. One of the most impor- tant is the survivorship bias that appears when only surviving funds are taken into account in a performance analysis study. The common practice among suppliers of CTA databases is to provide data on investable funds that are currently in operation. When only living funds 4 are considered, the data suffer from survivorship bias because dissolved funds tend to have worse performance than surviving funds. Survivorship bias has already been studied. Fung and Hsieh (1997b) precisely analyzed this bias and estimated it at 3.4 percent per year. They also concluded that survivorship bias had little impact on the investment styles of CTA funds. Returns of both surviving and dissolved CTA funds have low correlation to the standard asset classes. Survivorship Bias over Various Time Periods Here we analyze the presence of survivorship bias in CTAs returns over var- ious long-term time periods. We first study the whole period covered before dividing it into subperiods. Table 4.4 reports the survivorship bias obtained from our database. Survivorship bias is calculated as the performance difference between sur- viving funds and all funds. All returns are monthly and net of all fees. The first part of the table indicates a survivorship bias of 5.4 percent per year for the entire period. This figure is higher than the one obtained in previous studies. Table 4.4 shows the bias was higher during the 1990 to 1994 period (7.3 percent) and during the 1995 to 1999 period (6.2 percent) but lower during the 2000 to 2003 period (4.4 percent). 4 By “living funds” we mean funds still in operation at the moment of the analysis. c04_gregoriou.qxd 7/27/04 11:05 AM Page 56 CTA Performance, Survivorship Bias, and Dissolution Frequencies 57 Survivorship Bias over Time Figure 4.1 reports the evolution of the survivorship bias calculated on a three-year rolling period starting January 1985 to December 1987 and end- ing January 2000 to December 2002. It allows us to analyze more precisely how the survivorship evolves over time. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 88 88 89 89 90 90 91 91 92 92 93 93 94 94 95 95 96 96 97 97 98 98 99 99 00 00 01 01 02 02 FIGURE 4.1 Evolution of the Survivorship Bias (3-year Rolling Period) Our database contains 1,899 CTAs (611 survived funds and 1,288 dissolved funds as of December 2002). Numbers on the vertical axis are monthly percentages. TABLE 4.4 Survivorship Bias Analysis over Different Periods Bias 1985–2003 0.5 per Month 5.4 per Year Bias 1985–1989 0.5 per Month 5.5 per Year Bias 1990–1994 0.6 per Month 7.3 per Year Bias 1995–1999 0.5 per Month 6.2 per Year Bias 2000–2003 0.4 per Month 4.4 per Year Our database contains 1,899 CTAs (611 survived funds and 1,288 dissolved funds as of December 2002). c04_gregoriou.qxd 7/27/04 11:05 AM Page 57 58 PERFORMANCE 5 We take a month as a positive month if the whole database has a positive per- formance. We consider a month as negative if the whole database does not reach positive returns. The figure indicates that the monthly bias ending January 1985 increases from around 0.7 percent at the beginning of the year to 0.85 per- cent after summer before reaching the bottom of 0.9 percent at the begin- ning of 1989. Afterward, it increases until January 1993 (0.9 percent) and then decreases to a mean around 0.55 percent for the periods ending between January 1994 and January 2000. Because the three-year periods end Janu- ary 2000, the monthly survivorship bias decreases almost constantly to 0.12 percent in December 2002. We analyze these results to determine how such variations are possible. On one hand, the sharp decrease in the January 1989 results (and the slow increase that follows) can be explained by the fact that the surviving funds underperformed the whole database in 1988 and 1989. The first underper- formance was in December 1988 (1.87 percent for the surviving funds against 2.94 percent for the whole database). Moreover, this was the first major underperformance, which has been followed by others during the negative months in 1989 (e.g., −3.9 percent against −1.85 percent in March, −2.54 percent against −0.91 percent in April). On the other hand, the sharp increase in survivorship bias over the period ending November and Decem- ber 1992 can be explained mainly by high overperformance in June, July, and August 1992 with an average of 3 percent monthly outperformance. To summarize, this figure identifies epochs during which surviving funds out- performed the whole database, and during which the difference between surviving funds and dissolved funds was less important. We also analyze the survivorship bias calculated over the positive and negative months 5 for the whole database. Interestingly, Table 4.5 indi- cates that the mean survivorship bias is the same over the three periods studied at 0.48 percent. The standard deviation and the median of the survivorship are also almost equal. The only significant difference is in the minimum three-year rolling period, which is much higher for the nega- tive months at 0.13 percent versus 0.06 percent for the whole period and the positive months. The maximum is also almost equal between 0.87 percent and 0.90 percent. METHODOLOGY The aim of this study is to determine if some CTAs consistently and per- sistently outperform their peers. To achieve this objective, we construct a CTA Global Index that contains all the funds present in our database and c04_gregoriou.qxd 7/27/04 11:05 AM Page 58 [...]... −8.37 −5.70 4. 34 −6.97 −6.07 −7.11 −7. 14 −6.16 −7.93 −6.63 −12.86 −11.09 −12. 74 46 .29 −29.39 − 24. 47 Max 30.38 20.67 15.21 19.86 24. 42 19.91 27.55 35.00 46 .75 45 .38 58 .46 28.83 50.10 140 .91 100.95 34. 74 Skewness Kurtosis 1.69 1. 74 1.66 1.97 2.59 1.86 2.37 2.81 3.97 3.56 5.70 1.82 3.58 2 .45 1.93 0.56 7.07 6.39 4. 79 7. 84 14. 65 6.11 12. 14 15.72 25. 34 20.28 57.77 6.83 24. 20 13.69 10.16 3. 04 Sharpe Ratio... 1991–Dec 1996 TABLE 4. 7 Subperiod Performance Analysis of the Various CTA Strategies 1.11*** 0 .46 *** 0.37** NA 0.07 0.37** 1 .4* ** −0.20 CTA Index 1. 04* ** 0. 74* ** 0.85*** 0.60 0.52** 0.29*** 1 .48 *** 0 .44 ** 0.08 0.79 0.62*** CTA Index 0.89 0 .43 0.17 NA 0.00 0.15 0.98 0.02 R2 0.89 0.62 0 .48 0.07 0.07 0.22 0.97 0.17 0.01 0. 04 0.78 R2 63 R2 0.08 0.15 0.22 3 .43 * −1.81* 0.56*** −0.21*** 0 .42 1.33** 1.59** 0.28... −1.05** −0 .40 ** −0.21** −0.31** 0.00 −0.26*** −0.15 −0.21** 0.02 0.79** −0.02 2.17 −0.78 0 .41 −0.61** 0.29 0.91** 0.20 1.01*** 0.78 0.83*** 0. 84 0.98*** 0.86 0.91*** 0.89 1.05*** 0. 94 0.80*** 0.87 1.18*** 0.87 1.19*** 0. 84 1. 34* ** 0. 64 2.13* −0.02 0.02 −0. 04 0. 94* * 0.03 0. 64* ** 0.15 0. 64* ** 0.35 0 .43 *** 0.01 R2 adj D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D1a D1b D1c D10a D10b D10c Dec 2002 Apr 2000– −0 .45 −0.08... Index R2adj 1. 24 1.02 1.07 1.10 1.05 1.35 1.21 1.67 1.87 2.67 1.30 1.33 1.96 3.17 1.90 1.31 4. 71 3. 34 3.00 3.22 3.22 3.79 4. 08 4. 56 5.66 6.18 5 .49 5.09 5.99 19.99 14. 77 7.72 −0.33 −0.20** −0.09 −0.19** −0.25*** −0.18** −0 .47 *** −0.19* −0 .40 *** 0.20 1.82 −0.09 0.16 −0.39 −0.27 0.07 0.97*** 0.76*** 0.71*** 0.80*** 0.80*** 0. 94* ** 1. 04* ** 1.15*** 1 .40 *** 1.52*** 0.82*** 1.23*** 0.71*** 1. 04* ** 0.99*** 1.17***... that the standard deviation is higher among the wellperforming funds 68 PERFORMANCE TABLE 4. 10 Decile Descriptive Statistics Based on Previous Year’s Performance Mean Return D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D1a D1b D1c D10a D10b D10c 1. 24 1.02 1.07 1.10 1.05 1.35 1.21 1.67 1.87 2.67 1.30 1.33 1.96 3.17 1.90 1.31 Std Dev 4. 71 3. 34 3.00 3.22 3.22 3.79 4. 08 4. 56 5.66 6.18 5 .49 5.09 5.99 19.99 14. 77 7.72... to 47 percent in 19 94 for D1 and from 44 .6 percent in 1993 to 40 percent in 19 94 for D2) Since then, depending on the year and on the decile considered, the dissolution frequencies increase or decrease Rates are particularly high in 1999 for the best- and worst-performing funds, with dissolution frequencies of respectively 39.5 percent (against 30.3 percent in 1998 and 29.6 percent in 2000) and 69 .4. .. 1.22*** 1.07*** 2.27** 0.88** 0.32 1. 04* ** 0. 54* ** 0. 74* ** Index 0.55 0.61 0.87 0.91 0.95 0.91 0.92 0.91 0.85 0.75 0.18 0.00 -0.03 0.68 0 .44 0 .46 R2 adj BearMarket Period Alpha D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D1a D1b D1c D10a D10b D10c Dec 2002 Jan 1993– −0 .47 ** −0.28*** −0.13* −0.05 −0.12*** −0.10* −0.26*** −0.15*** −0.25*** 0.38** −0.21 0. 04 0. 74* * 2.57 0.67 0. 64 1.12*** 0.97*** 0.85*** 0.81*** 0.79***... dissolution frequencies lower than D10 75% 65% 55% 45 % 35% 25% 15% 5% D2 D4 D6 D8 D10 –5% 86 FIGURE 4. 3 88 90 92 94 96 98 00 02 Evolution of the Yearly Dissolution Frequencies across Deciles between 1986 and 2002 CTA Performance, Survivorship Bias, and Dissolution Frequencies 77 60% 50% 40 % 30% 20% 10% 0% −10% 86 87 88 89 90 91 92 93 94 95 96 97 98 99 00 01 02 FIGURE 4. 4 D10–D9 D1–D2 D1–D10 Spread between Dissolution... coefficients The average alpha is 0. 14 percent (median 0.107 percent) with a standard devi- TABLE 4. 9 Descriptive Statistics of the Individual Performance Estimation, January 1985 to December 2002 Mean Alpha CTA Global Index R2 0. 14% 0.89% 0.18 Std Dev Median Min Max 1. 84 1.07 0.21 0.11% 0.69% 0.09 −8.06% −6. 24% −0. 04 22.09% 5 .45 % 0.87 Min = minimum; Max = maximum Std Dev = standard deviation; t-stat are heteroskedasticity... 0.28 Alpha R2 0.87 0 .40 0.39 0. 04 0.11 0.11 0.98 0.05 0. 24 0.02 0 .45 0. 84* ** 0 .49 *** 0.51*** −0.50 0.93* 0.17** 1.35*** 0. 24 −0.90** 0.26 0. 54* ** Tech divers Tech fin/met Tech currency Tech other Fundamental Discretionary Systematic Stock Arbitrage Option No category Jan 1993–Dec 2002 Panel 3: 10-year analysis Arbitrage Option No category Jan 1998–Mar 2002 CTA Index −0.86*** −0. 64 0.23 CTA Index 1.00*** . 7.60 1.17 −20 .4 57 .4 2 .48 16. 14 0.19 Discretionary 299 16% 67 232 2.03 9.93 3.01 1.31 −3.9 18.8 2 .42 9. 24 0. 54 Systematic 897 47 % 350 547 1.70 4. 73 5.27 0.83 −8.3 26 .4 1.86 6.35 0. 24 Stock Index. Ratio Technical Diversified 2 64 14% 44 220 1.72 5.38 4. 70 0.83 −6.9 31.6 3.02 14. 68 0.28 Technical Financial/ Metals 86 5% 11 75 1.78 6.33 4. 12 0.95 −5.2 29.8 2.95 14. 11 0.33 Technical Currency 58 3% 18 40 1.58 6 .49 3.58. 0.17 D2 1.02 3. 34 0.51 −5.70 20.67 1. 74 6.39 0.25 D3 1.07 3.00 0.51 4. 34 15.21 1.66 4. 79 0.27 D4 1.10 3.22 0.61 −6.97 19.86 1.97 7. 84 0.25 D5 1.05 3.22 0.56 −6.07 24. 42 2.59 14. 65 0.26 D6 1.35