the same inefficiency through their own testing. Also, the way the CTA trades may be imitated if the CTA tells others about his or her system. CTAs are clearlyconcerned about this potential problem; most keep their system secret andhave employees sign no-compete agreements.The dollars under management have a negative coefficient. The coefficient implies that for each $1 million under management, returns are0.00104 percentage points lower. This could be due to increased liquiditycosts from larger trade sizes. Returns would go to zero when a CTA had $1billion under management.Following Goetzmann, Ingersoll, and Ross’s (1997) arguments forhedge funds, managed futures exist because of inefficiencies in the marketand because the CTA either faces capital constraints or is risk averse. By thevery action of trading, the CTA is acting to remove these inefficiencies.Goetzmann, Ingersoll, and Ross (1997) argue that incentive fees exist partlyto keep a manager from accepting too much investment. Dollars undermanagement is a crude measure of excessive investment. Funds that trademore markets or more systems or trade less intensively presumably couldhandle more investment without decreasing returns.
Regression of the Absolute Value of Residualson CTA CharacteristicsWe also estimated a model similar to the one in Table 3.8 to explain the differences in the level of risk of the CTA returns (see Table 3.9). The mostimportant factor determining the level of risk of CTAs is the percentage
44
PERFORMANCE
TABLE 3.9 Regressions of Absolute Value of Residuals versus CTA CharacteristicsVariable
Coefficient
t-value
Long termMedium termCommissionAdministrative feeIncentive feeDiscretionNon-U.S.OptionsInterbankMarginTime in existenceFirst yearDollars under management
0.0270.0830.117*−0.1620.097*0.003−0.013*−0.011−0.0080.092*−0.029*−0.260*−0.001
0.060.243.52−1.372.290.67−2.39−1.30−1.027.21−10.45−5.34−0.78
F-test for commodities tradedF-test for timeF-test for homoskedasticity
1.137.74*11.96*
Note: The absolute value of residuals is a measure of riskiness.*significant at the 5 percent level.
devoted to margins. While diversified funds were the least risky, the difference was not statistically significant. More recent CTAs have lower riskhave lowered their risk over time.Commissions have a positive coefficient, but this may mean only thatCTAs who trade larger positions generate more commissions. Incentive feesseem to encourage risk taking. Since the incentive fee is an implicit option(Richter and Brorsen 2000), the CTA should earn higher incentive fees byadopting a more risky strategy. CTAs with more funds in non-U.S. marketstend to have lower risk. Presumably the non-U.S. markets provide someadditional diversification.
REGRESSIONS OF RETURNSAGAINST LAGGED RETURNSTo determine the weights to put on various lags, monthly returns wereregressed against average returns over each of the last three years and thestandard deviation of returns over the last three years combined. The modelwas estimated assuming cross-sectional heteroskedasticity and fixed effects
45
Performance of Managed Futures
TABLE 3.10 Regressions of Monthly Managed Futures Returnsagainst Lagged Returns and Lagged Standard DeviationRegressorAverage returns 1–12months agoAverage returns 13–24months agoAverage returns 25–26months agoStandard deviationlast 3 yearsF-test of time fixed effects
CTAs
Public
Private
−0.049*(−1.97)0.130*(5.93)0.069*(3.53)0.056*(4.16)35.38*
−0.059(−2.45)0.160*(7.02)0.074*(3.74)−0.024(−1.95)83.60*
−0.009(−0.33)0.142*(5.46)0.027(1.33)−0.027(−1.86)28.29*
*
significant at the 5 percent level.
for time. Ordinary least squares and random effects for time yielded similarresults. Random or fixed effects for CTAs are not included because a MonteCarlo study showed that such methods yielded tests with incorrect size.As shown in Table 3.10 there are cycles in CTA and fund returns. CTAstend to do well relative to other CTAs every other year. The sum of the threecoefficients is positive, which confirms the previous results regarding asmall amount of performance persistence. The negative coefficient onreturns during the first lagged year supports Schwager’s arguments thatCTA/fund returns are negatively correlated in the short run.More risk, as measured by historical standard deviation, leads to higherreturns for CTAs. Since CTAs are profitable, CTAs with higher leverageshould make higher returns and have more risk. In contrast, both publicand private fund returns are negatively related to risk. Thus, risk may differ for reasons other than leverage.
DOES INVESTING IN LOSERS MAKE SENSE?The regressions versus lagged returns in Table 3.10 offer some support forportfolio rebalancing and for Schwager’s (1996) argument that investingwith a manager after recent losses is a good idea. The theory behind theargument is that CTAs profit by exploiting inefficiencies and that returnsare reduced when more money is devoted to a trading system. This idea issupported here by the results in Table 3.11. Further, the idea is consistentwith arguments put forward by Goetzmann, Ingersoll, and Ross (1997).
46
PERFORMANCE
TABLE 3.11 Regression of Monthly Returns and New Moneyagainst Various Functions of Lagged ReturnsVariable1 month ago returns1 month ago gains2 months ago returns2 months ago gains3 months ago returns3 months ago gainsAverage returns 4–12 monthsAverage returns 13–24 monthsAverage returns 25–36 months36-month standard deviationF-test for time fixed effects
Monthly Returns
New Moneya
0.001(0.04)0.026(1.24)−0.083*(−5.95)0.064*(3.14)−0.058*(4.16)−0.093*(4.55)−0.010(−0.48)0.134*(6.12)0.080(4.06)0.003(0.22)33.33*
0.155*(5.94)−0.107(−2.83)0.148*(5.72)−0.082(−2.12)0.087*(3.60)0.001(0.03)0.550*(13.04)0.198*(4.61)0.055(1.32)−1.3 E−4(−0.01)2.09
aNew money represents additions or withdrawals. More money was withdrawn
than added so the mean was negative (−0.83 percent per month).*significant at the 5 percent level.
We also tested whether money flows out as Schwager (1996) suggested.The new money in dollars under management (monthly percentage changein dollars minus percent returns) was regressed against lagged returns andlagged standard deviations. The term “new money” may be a misnomer,because money tends to be withdrawn rather than added. The lags for themost recent three months were separated, and a dummy variable was addedfor positive returns.The results in Table 3.11 show that investment and disinvestment are afunction of lagged returns. Only returns in the most recent two years weresignificantly related. The disinvestment due to negative returns is greaterthan the investment that occurs with positive returns for the most recenttwo months. This is an indication of some asymmetry. There is no asymmetry for lags greater than three months.
Performance of Managed Futures
47
The flow of dollars does not match the changes in expected returns.People put most weight on the recent past and tend to over react to shortrun losses. The movement of money out of funds may explain at least partof the short-run negative autocorrelations in returns. Thus, the results dooffer some support for Schwager’s (1996) hypothesis that money flows out.
PRACTICAL IMPLICATIONSSome funds and CTAs have higher returns than others. Given the importance of the subject, we will try to address how to select the best funds.Recall, however, that the performance persistence is small and that in someyears any method used will do worse than the average across all funds.Because performance persistence is small relative to the noise in thedata, it is important to use a lot of data. Unfortunately, the four-year andthree-year selection periods used in this study may be too small. A regression approach would allow using all the data when some funds have twoyears of data and others eight. But data previous to when the CTA hadmade a major change in the trading system or a fund had switched advisorsshould not be used.Because of the low predictability of performance, it would be difficultto select the single best fund or CTA. Therefore, it might be better to investin a portfolio of CTAs. Picking CTAs based on returns in the most recentyear may even be worse than a strategy of randomly picking a CTA.
CONCLUSIONThis research finds a small amount of performance persistence in managedfutures. Performance persistence could exist due to differences in either costor in manager skill. Our results favor skill as the explanation, becausereturns were positively correlated with cost. A regression model was estimated including the average fund return as a regressor. The regressionmodel indicated some statistically significant performance persistence. Theperformance persistence is small relative to the variation in the data (only 2to 4 percent of the total variation), but large relative to the mean.The regression method was expected to be the method with the highestpower. Monte Carlo simulations showed that the methods used in pastresearch often could not reject false null hypotheses and would reject truenull hypotheses too often.Out-of-sample tests confirmed the regression results. There is some performance persistence, but it is small relative to the noise in the data. Areturn/risk measure showed more persistence than either of the return
48
PERFORMANCE
measures. Although past data can be used to rank funds, precise methodsand long time periods are needed to provide accurate rankings.CTAs using short-term trading systems had lower returns than CTAswith longer trading horizons. CTAs with higher historical returns are nowcharging higher fees. CTA returns decreased over time and more recentfunds have lower returns. At least part of this trend is likely survivorshipbias. As dollars under management increased, CTA returns decreased. Thefinding of fund returns decreasing over time (and as dollars investedincrease) suggests that funds exist to exploit inefficiencies.The dynamics of returns showed small negative correlations for returnsin the short run, especially for losses. The net effect over three years is positive, which is consistent with a small amount of performance persistence.The withdrawal of dollars from CTAs shows that investors weight the mostrecent returns more than would be justified by changes in expected returns.Although several different methods of analysis were used, the resultspaint a consistent picture. To adequately select CTAs or funds based on pastreturns, several years of data are needed.
CHAPTER
4
CTA Performance,Survivorship Bias,and Dissolution FrequenciesDaniel Capocci
sing a database containing 1,892 funds (including 1,350 dissolved funds),we investigate CTA performance and performance persistence to determine if some CTAs consistently and significantly outperform their peers overvarious time periods. To test the persistence hypothesis, we use a methodology based on Carhart’s (1997) decile classification. We examine performanceacross deciles and across CTA strategies to determine if some deciles aremore exposed to certain strategies over time. We also analyze survivorshipbias and its evolution over time. We conclude the study by analyzing the dissolution frequencies across deciles and their evolution over time.
U
INTRODUCTION AND LITERATURE REVIEWUnlike 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 Ma1988). More recently, Billingsley and Chance (1996) and Edwards and Park(1996) showed that CTA funds can add diversification to stocks and bondsin a mean-variance framework. According to Schneeweis, Savanayana, andMcCarthy (1991) and Schneeweis (1996), the benefits of CTAs are similarto those of hedge funds, in that they improve and can offer a superior riskadjusted return trade-off to stock and bond indices while acting as diversifiers in investment portfolios.Fung and Hsieh (1997b) showed that a constructed CTA style factorpersistently has a positive return when the Standard & Poor’s (S&P) has a
49
50
PERFORMANCE
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 tothat of a lookback call and a lookback put.1 Gregoriou and Rouah (2003a)examined whether CTA percent changes in net asset values (NAVs) followrandom walks. They found all classifications (except the diversifiedsubindex) to behave as random walks. The effectiveness of CTAs in enhancing risk-return characteristics of portfolios could be compromised whenpure random walk behavior is identified. Kat (2002) found that allocatingto managed futures allows investors to achieve a very substantial degree ofoverall risk reduction at limited costs. Managed futures appear to be moreeffective diversifiers than hedge funds.Regarding performance, Edwards and Caglayan (2001) concluded thatduring bear markets, CTAs provide greater downside protection than hedgefunds and have higher returns along with an inverse correlation with stocksreturns in bear markets. Schneeweis and Georgiev (2002) concluded thatcareful inclusion of CTA managers into investment portfolios can enhancetheir return characteristics, especially during severe bear markets. Schneeweis,Spurgin, and McCarthy (1996) observed that performance persistence wasvirtually inexistent between 1987 and 1995. There is little information onthe long-term diligence of these funds (Edwards and Ma 1998; Irwin, Krukemeyer, and Zulauf 1992; Kazemi 1996). Schwager (1996) reviews the literature on CTA performance persistence and conducts his own analysis. Hefound little evidence that the top-performing funds can be predicted.According to Worthington (2001), between 1990 and 1998 the correlationof 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 thedrawbacks of CTAs is that during bull markets, their performance is generally inferior to those of hedge funds.Brorsen and Townsend (2002) show that a minimal amount of performance persistence is found in CTAs, and there could exist some advantages in selecting CTAs based on past performance when a long time seriesof data is available and accurate methods are used.This chapter aims to detect performance persistence of CTAs. We wantto determine if some CTAs consistently outperform their peers over time. In
1A lookback call is a normal call option, but the strike depends on the minimumstock price reached during the life of the option. A lookback put is a normal putoption, but the strike depends on the maximum stock price reached during the lifeof the option.
CTA Performance, Survivorship Bias, and Dissolution Frequencies
51
the next section, we describe the database, reporting the descriptive statistics of the funds and analyzing the correlation between the various strategies reported. The following section focuses on survivorship bias. Weanalyze the presence of this bias over the whole period studied but also overdifferent time periods, including a bull and a bear market period. Further,we report the methodology used to analyze CTA performance and performance persistence before reporting the results of the performance analysis in the next section. The next section reports the results of the persistenceanalysis and analyzes the exposure of the deciles constructed on previousyear’s performance to the individual strategies. Then we report the completeanalysis of monthly and yearly dissolution frequencies.
DATABASEIn this section, we present our database and analyze the descriptive statisticsof the data before reporting the correlation between the various strategies.
Descriptive StatisticsThere are several CTA data providers. The providers most commonly usedin academic studies are Managed Account Repots, TASS Management, andthe Barclay Trading Group, Ltd. The latter represents one of the most (ifnot the most) comprehensive managed future databases.For our analysis we use the Barclay Trading Group database, whichcontains 1,892 individual funds (including 1,350 dissolved funds) over theJanuary 1985 to December 2002 period. The Barclay Trading Group classifies these funds in 7 categories that are subdivided in 17 strategies plus theno-strategy category. We grouped some strategies because they contain toofew funds to give interesting results. As shown in Table 4.1, we obtained atotal of 11 strategies. Note that we combined only those strategies that arein the same category.To perform our performance analysis, we will use the whole databaseand the classifications reported in Table 4.1. This will allow us to determinewhether results differ across strategies and whether funds in particularstrategies 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 CTAsfrom 1979 to 1989. Other studies were larger. For example, Edwards andPark (1996) found 596 CTAs from 1983 to 1992 by supplementing theMAR/LaPorte CTA database with private sources. Diz (1996) and Fung andHsieh (1997b) had 925 and 901 managed future programs from 1975 to
52
PERFORMANCE
TABLE 4.1 Grouping of Barclay Trading Group StrategiesGrouped CTAStrategiesTechnical DiversifiedTechnical Financial/MetalsTechnical CurrencyOther Technical
Fundamental
DiscretionarySystematicStock IndexArbitrageOption StrategiesNo Category
Barclay TradingGroup StrategyTechnical DiversifiedTechnical Financial/MetalsTechnical CurrencyTechnical Interest RateTechnical EnergyTechnical AgriculturalFundamental DiversifiedFundamental Interest RateFundamentalFinancial/MetalsFundamental EnergyFundamental CurrencyFundamentalAgriculturalDiscretionarySystematicStock IndexArbitrageOption StrategiesNo Category
Note: The left-hand side of the table reports the strategy classification used throughout the study; the right-hand side contains theoriginal classification of the Barclay Trading Group.
1995, and from 1986 to 1996 respectively. They were both based on theBarclay Trading Group database.Funds in the Barclay Trading Group database can be classified intomore than one strategy. This can lead to a bias when we compare differentstrategies since they can contain the same funds. In order to deal with thisissue, we report each fund in one strategy only.2Before entering the body of the study, we analyze the composition ofthe database. Table 4.2 reports the descriptive statistics of the database.Funds are classified according to strategy. The last line reports the statisticsfor the whole database.2Any fund that is reported in two strategies is classified into the one that containsthe most funds.
53
14%
5%
3%0%22%1%16%47%3%1%0%9%100%
264
86
58841619299897522791801,899
18073267350162028611
11
44
40834317232547362591521,288
75
220
1.583.181.751.832.031.701.891.252.621.621.75
1.78
1.72
6.495.356.333.559.934.734.395.764.666.206.51
6.33
5.38
Dead Mean t(mean)Funds Return=0
3.587.254.067.603.015.276.333.198.243.843.95
4.12
4.70
Std.Dev.
1.071.920.721.171.310.831.141.072.570.950.98
0.95
0.83
Median
January 1985–December 2002(216 months)
2.95
3.02
15.6 0.6447.5 2.0025.3 2.9257.4 2.4818.8 2.4226.4 1.8638.4 2.0512.0 −0.3636.5 0.5328.5 3.1421.9 2.37
29.8
−5.2−14.5−18.7−5.2−20.4−3.9−8.3−18.4−14.8−23.3−4.9−5.2
31.6
−6.9
3.739.5813.2716.149.246.3510.464.282.5115.079.06
14.11
14.68
0.330.380.330.190.540.240.230.260.270.310.34
0.33
0.28
SharpeMin Max Skewness Kurtosis Ratio
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 2001period. Option strategy funds exist since September 1990.
TechnicalDiversifiedTechnicalFinancial/MetalsTechnicalCurrencyOther technicalTotal technicalFundamentalDiscretionarySystematicStock IndexArbitrageOption strategyNo CategoryTotal
No. of% ofLivingFunds the Total Funds
CTAStrategies
TABLE 4.2 Descriptive Statistics
54
PERFORMANCE
Table 4.2 indicates that the systematic strategy is the most representedstrategy (with 897 funds) followed by total technical funds (416 funds) anddiscretionary funds (299 funds). Other technical funds, option strategyfunds, and fundamental funds count only 8, 9, and 19 funds respectively.The database contains 611 dissolved funds as a whole, 350 of which followthe systematic strategy. Note that all the other technical funds and optionstrategy funds are dissolved over the period studied. The median returnsindicate the same patterns.Regarding the statistics, the highest mean monthly return is achievedby the other technical funds (with 3.18 percent per month) followed bythe option strategy funds and discretionary funds (with 2.62 percent and2.03 percent per month). Many strategies offer a monthly return of between1.6 percent and 1.9 percent per month. The lowest returns are those of thearbitrage funds (with 1.25 percent) followed by the technical currencyfunds (with a monthly return of 1.58 percent). All the monthly returns aresignificantly different from zero over the period studied.The fundamental funds and the other technical funds are the morevolatile funds with a standard deviation of 7.60 and 7.25 percent. Becausethere are few funds applying these strategies, there is no diversificationeffect, 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 astandard deviation of 3.19 percent).As one could expect, the strategies that are the most volatile also havethe lowest minimum return and the highest maximum return. The monthlyminimum returns can reach −20.4 percent for the fundamental strategywhereas the maximum of this strategy is 57.4 percent. The returns areusually positively skewed (the only exception is the arbitrage strategy)and their distributions tend to have fat tails, as evidenced by the large valuesfor kurtosis.When risk and returns are considered together through the Sharperatio,3 the discretionary funds emerge with the highest Sharpe ratio (0.54)followed by other technical funds (with 0.38). Fundamental funds offer aSharpe ratio of only 0.19.
Correlation AnalysisTable 4.3 reports the correlation coefficients between the various strategiesfor the January 1985 to December 2002 period. It indicates that the CTA3The 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.
55
1.00−0.180.410.250.120.260.980.680.930.730.140.81
Discret
0.410.201.000.140.130.180.270.160.420.270.000.32
Arb
−0.181.000.20−0.020.080.05−0.21−0.18−0.13−0.050.24−0.010.25−0.020.141.000.010.080.220.170.220.20−0.020.12
Funda0.120.080.130.011.000.620.12−0.010.030.110.020.12
Option0.260.050.180.080.621.000.250.090.140.130.010.29
Stock0.98−0.210.270.220.120.251.000.700.890.710.180.79
System0.68−0.180.160.17−0.010.090.701.000.560.560.120.56
Teccur0.93−0.130.420.220.030.140.890.561.000.660.050.73
Tecdiv0.73−0.050.270.200.110.130.710.560.661.000.100.50
Tecfin
0.140.240.00−0.020.020.010.180.120.050.101.000.09
Tecoth
0.81−0.010.320.120.120.290.790.560.730.500.91.00
Nocat
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 = othertechnical; Nocat = no category.
AllCTAArbDiscretFundaOptionStockSystemTeccurTecdivTecfinTecothNocat
Allcta
TABLE 4.3 Correlation between the CTA Strategies, January 1985 to December 2002
56
PERFORMANCE
global index is almost exactly correlated with the systematic funds. This canbe partly explained by the fact that this strategy contains the greatest number of funds. Forty-four coefficients out of sixty-six (66 percent of the coefficients) are under 0.5, indicating that most of the strategies are notcorrelated. The lowest coefficient is the one between arbitrage and systematic funds at −0.21. There are nine negative coefficients in total representing 14 percent of the coefficients.
SURVIVORSHIP BIASPerformance figures are subject to various biases. One of the most important is the survivorship bias that appears when only surviving funds aretaken into account in a performance analysis study. The common practiceamong suppliers of CTA databases is to provide data on investable fundsthat are currently in operation. When only living funds4 are considered, thedata suffer from survivorship bias because dissolved funds tend to haveworse 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. Theyalso concluded that survivorship bias had little impact on the investmentstyles of CTA funds. Returns of both surviving and dissolved CTA fundshave low correlation to the standard asset classes.
Survivorship Bias over Various Time PeriodsHere we analyze the presence of survivorship bias in CTAs returns over various long-term time periods. We first study the whole period covered beforedividing it into subperiods.Table 4.4 reports the survivorship bias obtained from our database.Survivorship bias is calculated as the performance difference between surviving funds and all funds. All returns are monthly and net of all fees. Thefirst part of the table indicates a survivorship bias of 5.4 percent per yearfor the entire period. This figure is higher than the one obtained in previousstudies. Table 4.4 shows the bias was higher during the 1990 to 1994period (7.3 percent) and during the 1995 to 1999 period (6.2 percent) butlower during the 2000 to 2003 period (4.4 percent).
4By “living funds” we mean funds still in operation at the moment of the analysis