2.55* / −1.47 / 1.19
1.39%a
−0.26%c
0.86%a
2.02* / −1.17 / 0.69
0.02%b
0.34%b
1.59%a
−0.25 / −1.71 / −1.39
a
Above average
bBelow average but positivecBelow average and negative*Significant at 5% level
ing that the Edhec CTA Index payoff resembles a long position on a putoption on currency risk factors and a long position on a call option on theGSCI. We can thus conclude that the performance of the Edhec CTA Indexis clearly affected by the evolution of the risk factors selected.A word of caution is in order. Even if CTA managers generally continueto invest in the same markets and follow the same investment strategies,they may engage in various factor timing strategies to take advantage ofmacroeconomic trends. In other words, they tend to increase or decreasetheir exposure to specific markets according to their expectations, whichmay in turn lead to a change in factor exposures. To illustrate this phenomenon we ran regressions using two-year rolling windows starting fromSeptember 1999 through August 2001, each time with one nonoverlappingobservation. We thus obtained betas from September 2001 through September 2003. Results are presented in Figure 2.3. It is interesting to note thatthe exposure to the Lehman Global U.S. Treasury Index, although evolvingthrough time, remains high (around 1.00) during the whole period. This isin contrast with the beta with respect to the S&P 500 index, which remainsrelatively low (around 0) with a steady down trend until April 2003. Theexposure to the GSCI is symmetrical to that of the S&P 500, showing anup trend from January 2003 though September 2003. In the same vein, overthe period of analysis CTA managers progressively increased their bet on therise of the USD against the yen while taking opposing bets on the USD versus
29
Benchmarking the Performance of CTAs
1 .50
1.00
Lehman Global U.S. Treasury
0.50USD to Yen
Sep-03
Mar-03
Sep-02
Mar-02
Sep-01
GSCI0.00
S&P 500–0.50USD to Major Currency
–-1.00
FIGURE 2.3
Edhec CTA Index Factor Exposure Evolution, September 1999 toSeptember 2003Source: Edhec Risk.
major currencies. Investors must obviously be aware of such time-varyingeffects when considering investment in CTAs.Three conclusions may be drawn from this analysis.1. The five risk factors selected can explain a significant part of the EdhecCTA Index variance.2. The exposure of the Edhec CTA Index to these risk factors appears tobe nonlinear.3. Risk factor exposures evolve through time, suggesting that multifactormodels such as the one we use may not be suited for performance measurement purposes.As largely documented in the literature, it would be interesting to integrateconditional factor models (Gregoriou 2003b; Gupta, Cerrahoglu, andDaglioglu 2003; Kat and Miffre 2002; Kazemi and Schneeweis 2003)and/or models including nonlinear risk factors (see Agarwal and Naïk2004; Fung and Hsieh 1997a, 2002b, 2003; Schneeweis, Spurgin, andGeorgiev 2001) to better benchmark CTA performance.
30
PERFORMANCE
CONCLUSIONLike hedge funds, CTAs are destined to play an important role in the diversification strategy of institutional investors. As evidenced in this chapter,they may be considered both risk reducers and return enhancers, due totheir specific exposure to a variety of risk factors (e.g., stock markets, interest rates, commodity markets, foreign exchange markets, etc.). This chapter has presented an original method for constructing a representative andpure CTA index that addresses some of the crucial issues investors are facing in the allocation process. It also has analyzed CTA return characteristics and the extent to which investors would be better off integrating CTAsin their global allocation. Further research should now focus on identifyinga conditional model with potentially nonlinear risk factors to replicate theEdhec CTA Global Index and measure CTA performance.
CHAPTER
3
Performance of ManagedFutures: Persistence and theSource of ReturnsB. Wade Brorsen and John P. Townsend
anaged futures investments are shown to exhibit a small amount of performance persistence. Thus, there do appear to be some differences inthe skills of commodity trading advisors. The funds with the highest returnsused long-term trading systems, charged higher fees, and had fewer dollarsunder management.Returns were negatively correlated with the most recent past returns,but the sum of all correlations was positive. Consistent with work in behavioral finance, when deciding whether to invest or withdraw funds, investorsput the most weight on the most recent returns. The results suggest that thesource of futures fund returns is exploiting inefficiencies.
M
INTRODUCTIONThere is little evidence from past research that the top performing managedfutures funds can be predicted (Schwager 1996). Past literature has primarily used variations of the methods of Elton, Gruber, and Rentzler (EGR).Yet EGR’s methods have little power to reject the null hypothesis of no predictability (Grossman 1987). Using methods with sufficient power to rejecta false null hypothesis, this research seeks to determine whether performance persists for managed futures advisors. The data used are from publicfunds, private funds, and commodity trading advisors (CTAs). Regressionanalysis is used to determine whether all funds have the same mean returns.This is done after adjusting for changes in overall returns and differences inleverage. Monte Carlo methods are used to determine the power of EGR’s
31
32
PERFORMANCE
TABLE 3.1 Descriptive Statistics for the Public, Private, and Combined CTA DataSets and Continuous Time ReturnsStatisticObservations# FundsPercentage returnsMeanSDMinimumMaximumSkewnessKurtosis
Public Funds
Private Funds
CombinedCTAs
32,420577
23,723435
57,0181,071
0.317.68−232.69229.73−2.08133.91
0.629.22−224.81188.93−0.4940.70
1.2810.53−135.48239.791.1424.34
methods. Then an out-of-sample test similar to that of EGR is used overlonger time periods to achieve greater power. Because some performancepersistence is found, we explain the sources of this performance persistenceusing regressions of (1) returns against CTA characteristics, (2) return riskagainst CTA characteristics, (3) returns against lagged returns, and (4)changes in investment against lagged returns.
DATALaPorte Asset Allocation provided the data, much of which originated fromManaged Accounts Reports. The CTA data include information on CTAsno longer trading as well as CTAs who are still trading. The data includemonthly returns from 1978 to 1994. Missing values were deleted by deleting observations where returns and net asset value were zero. This shouldhelp prevent deleting observations where returns were truly zero. Thereturn data were converted to log changes,1 so they can be interpreted aspercentage changes in continuous time.The mean returns presented in Table 3.1 show CTA returns are higherthan those of public or private returns. This result is consistent with those
it = ln (1 + dit /100) × 100, where, dit is the discrete timereturn. The adjustment factor of 100 is used since the data are measured aspercentages.
1The formula used was r
33
Performance of Managed Futures
in previous literature. The conventional wisdom as to why CTAs havehigher returns is that they incur lower costs. However, CTA returns may behigher because of selectivity or reporting biases. Selectivity bias is not amajor concern here, because the comparison is among CTAs, not betweenCTAs and some other investment. Faff and Hallahan (2001) argue that survivorship bias is more likely to cause performance reversals than performance persistence. The data used show considerable kurtosis (see Table 3.1).However, this kurtosis may be caused by heteroskedasticity (returns ofsome funds are more variable than others).
REGRESSION TEST OF PERFORMANCE PERSISTENCETo measure performance persistence, a model of the stochastic process thatgenerates returns is required. The process considered is:rit = αi + βi rt + εit ,ε it ~ N(0, σ i2 )
i = 1, K , n and t = 1, K , T
(3.1)
where rit = return of fund (or CTA) i in month trt = average fund returns in month tslope parameter bi = differences in leverage.The model allows each fund to have a different variance, which is consistent with past research. We also considered models that assumed that bi iszero, with either fixed effects (dummy variables) for time or random effectsinstead. These changes to the model did not result in changes in the conclusions about performance persistence.Only funds/CTAs with at least three observations are included. Themodel is estimated using feasible generalized least squares. The null hypothesis considered is that all funds have the same mean returns, provided thatadjustments have been made for changes in overall returns and differencesin leverage. This is equivalent to testing the null hypothesis H0: ai = a wherea is an unknown constant.Analysis of variance (ANOVA) results in Table 3.2 consistently showthat some funds and pools have different mean returns than others. Thisfinding does contrast with previous research, but is not really surprisinggiven that funds and pools have different costs. Funds and pools have different trading systems, and commodities traded vary widely. The test usedin this study measures long-term performance persistence; in contrast, EGRmeasures short-term performance persistence.
34
PERFORMANCE
TABLE 3.2 Weighted ANOVA Table: Returns Regression for Public Funds,Private Funds, and Combined CTA DataStatisticSum of squared errorsInd. meansGroup meanCorrected totalR2Mean aVariance of aF-statisticsα’sβ’s
Public Funds
Private Funds
CombinedCTAs
1,75128,33562,2210.480.278
1,94810,88236,3750.350.297
2,33322,75182,4080.311.099
1.160
2.277
2.240
2.9447.44
4.3224.10
2.1220.61
Only about 2 to 4 percent of the variation in monthly returns acrossfunds can be explained by differences in individual means. Because the predictable portion is small, precise methods are needed to find it. Without thecorrection for heteroskedasticity, the null hypothesis would not have beenrejected with the public pool data. Even though the predictability is low, itis economically significant. The standard deviations in Table 3.2 are large,implying that 2 to 4 percent of the standard deviation is about 50% of themean. Thus, even though there is considerable noise, there is still potentialto use past returns to predict future returns.As shown in Table 3.3, the null hypothesis that each fund has the samevariance was rejected. This is consistent with previous research that showssome funds or CTAs have more variable returns than others. The rescaledresiduals have no skewness, and the kurtosis is greatly reduced. The
TABLE 3.3 F-Statistics for the Test of Homoskedasticity Assumptionand Jarque-Bera Test of Normality of Rescaled ResidualsStatisticHomoskedasticitySkewnessRelative kurtosis
Public Funds
Private Funds
CombinedCTAs
1.41−0.173.84
4.32−0.023.05
5.150.352.72
Performance of Managed Futures
35
rescaled residuals have a t-distribution so some kurtosis should remaineven if the data were generated from a normal distribution. This demonstrates that most of the nonnormality shown in Table 3.1 is due toheteroskedasticity.
MONTE CARLO STUDYIn their method, EGR ranked funds by their mean return or modifiedSharpe ratio in a first period, and then determined whether the funds thatranked high in the first period also ranked high in the second period. Weuse Monte Carlo simulation to determine the power and size of hypothesistests with EGR’s method when data follow the stochastic process given inequation 3.1. Data were generated by specifying values of α, β, and σ. Thesimulation used 1,000 replications and 120 simulated funds. The meanreturn over all funds, r̄t, is derived from the values of α and β as:
Σα iΣε it+nnrt =Σβ i1−nwhere all sums are from i = 1 to n.A constant value of α simulates no performance persistence. For thedata sets generated with persistence present, α was generated randomlybased on the mean and variance of β’s in each of the three data sets. To simulate funds with the same leverage, the β’s were set to a value of 0.5. Thesimulation of funds with differing leverage (which provided heteroskedasticity) used β’s with values set to 0.5, 1.0, 1.5, and 2.0.To match EGR’s assumption of homoskedasticity, data sets were generated with the standard deviation set at 2. Heteroskedasticity was created byletting the values of σ be 5, 10, 15, and 20, with one-fourth of the observations using each value. This allowed us to compare the Spearman correlationcoefficient calculated for data sets with and without homoskedasticity.The funds were ranked in ascending order of returns for period one(first 12 months) and period two (last 12 months). From each 24-monthperiod of generated returns, Spearman correlation coefficients were calculated for a fund’s rank in both periods. For the distribution of Spearmancorrelation coefficients to be suitably approximated by a normal, at least 10observations are needed. Because 120 pairs are used here, the normalapproximation is used.Mean returns also were calculated for each fund in period one andperiod two, and then ranked. The funds were divided into groups consist-
36
PERFORMANCE
ing of the top-third mean returns, middle-third mean returns, and bottomthird mean returns. Two additional subgroups were analyzed, the top threehighest mean returns funds and the bottom three funds with the lowestmean returns. The means across all funds in the top-third group andbottom-third group also were calculated.To determine if EGR’s test has correct size, it is used with data whereperformance persistence does not exist (see Table 3.4). If the size is correct,the fail-to-reject probability should be 0.95. When heteroskedasticity ispresent (data generation methods 2 and 3), the probability of not rejectingis less than 0.95. The heteroskedasticity may be more extreme in actualdata, so the problem with real data may be even worse than the excess TypeI error found here.Next, we determine the power of EGR’s test by applying it to datawhere performance persistence really exists (see Table 3.5). The closer thefail-to-reject probability is to zero, the higher is the power. The Spearmancorrelation coefficients show some ability to detect persistence when large
TABLE 3.4 EGR Performance Persistence Results from Monte Carlo GeneratedData Sets: No Persistence Present by Restricting a = 1Data Generation MethodGenerated Data SubgroupsMean returnstop 1/3middle 1/3bottom 1/3top 3bottom 3p-valuesreject-positive zreject-negative zfail to rejecttest of 2 meansreject-positivereject-negativefail to reject
1a
2b
3c
1.251.251.251.251.26
1.251.251.221.151.19
0.700.720.680.610.68
0.0210.0280.951
0.0410.0370.922
0.0410.0390.920
0.0260.0280.946
0.0320.0200.948
0.0320.0260.942
aData generated using a = 1, b = .5; s = 2.
bData generated using a = 1, b = .5; s = 5, 10, 15, 20.
cData generated using a = 1, b = .5, 1, 1.5, 1; s = 5, 10, 15, 20.
37
Performance of Managed Futures
TABLE 3.5 EGR Performance Persistence Results from Monte Carlo GeneratedData Sets: Persistence Present by Allowing a to VaryData Generation MethodGenerated Data SubgroupsMean returnstop 1/3middle 1/3bottom 1/3top 3bottom 3p-valuesreject-positive zreject-negative zfail to reject.000test of 2 meansreject-positivereject-negativefail to reject.000
1a
2b
3c
4d
3.211.870.804.93−1.60
2.772.091.413.471.14
2.571.851.153.260.86
1.481.301.141.681.06
1.0000.0000.000
0.8270.0000.173
0.8230.0000.177
0.1490.0030.848
1.000.0000.000
0.2680.0000.732
0.2580.0000.742
0.0430.0120.945
aData generated using a = N(1.099,4.99); b = .5, 1, 1.5, 2; s = 2.
bData generated using a = N(1.099,4.99); b = .5; s = 5, 10, 15, 20.
cData generated using a = N(1.099,4.99); b = .5, 1, 1.5, 2; s = 5, 10, 15, 20.dData generated using a = N(1.099,1); b = .5, 1, 1.5, 2; s = 5, 10, 15, 20.
differences are found in CTA data. But they show little ability to find persistence with the small differences in performance in the public fund dataused by EGR. The test of two means has even less ability to detect persistence. Thus, the results clearly can explain EGR’s findings of no performance persistence as being due to low power; Table 3.5 does show that EGR’smethod can find performance persistence that is strong enough.
HISTORICAL PERFORMANCE AS AN INDICATOROF LATER RETURNSResults based on methods similar to those of EGR are now provided. Theprevious Monte Carlo findings were based on a one-year selection periodand a one-year performance period. Given the low power of EGR’s method,we use longer periods here: a four-year selection period with a one-yearperformance period, and a three-year selection period with a three-year per-
38
PERFORMANCE
formance period. Equation (3.1) was estimated for the selection period andthe performance period. Because the returns are monthly, funds havingfewer than 60 or 72 monthly observations respectively were deleted toavoid having unequal numbers of observations.The first five-year period evaluated was 1980 to 1984. The next fiveyear period was 1981 to 1985. Three methods are used to rank the funds:the α’s (intercept), the mean return, and the ratio α/σ. For each parameterestimated from the regression, a Spearman rank-correlation coefficient wascalculated between the performance measure in the selection period andthe performance measure for the out-of-sample period. The null hypothesis is of no correlation between ranks, and the test statistic has a standardnormal distribution under the null. Because of losing observations withmissing values and use of the less efficient nonparametric method (ranking), this approach is expected to have less power than the direct regression test in (3.1).Table 3.6 presents a summary of the annual results. Because of theoverlap, the correlations from different time periods are not independent,so some care is needed in interpreting the results. All measures show somepositive correlation, which indicates performance persistence. Small correlations are consistent with the regression results. Although there is performance persistence, it is difficult to find because of all the other randomfactors influencing returns.The return/risk measure (α/σ) clearly shows the most performance persistence. This is consistent with McCarthy, Schneeweis, and Spurgin (1997),who found performance persistence in risk measures. The rankings basedon mean returns and those based on α’s are similar. Their correlations weresimilar in each year. Therefore, there does not appear to be as much gain asexpected in adjusting for the overall level of returns.The three-year selection period and three-year trading period showhigher correlations than the four-year selection and one-year trading periods except for the early years of public funds. There were few funds in theseearly years and so their correlations may not be estimated very accurately.Rankings in the three-year performance period are also less variable than inthe one-year performance period. The higher correlation with longer trading period suggests that performance persistence continues for a long time.This fact suggests that investors may want to be slow to change their allocations among managers.The next question is: Why do the results differ from past research? Actually, EGR found similar performance persistence, but dismissed it as beingsmall and statistically insignificant. Our larger sample leads to more powerful tests. McCarthy (1995) did find performance persistence, but his results
39
Performance of Managed Futures
TABLE 3.6 Summary of Spearman Correlations between Selectionand Performance PeriodsData Set SelectionCriterionFour and oneaCTAmean returnsaa/sPublic fundsmean returnsaa/sPrivate fundsmean returnsaa/sThree and ThreebCTAmean returnsaa/sPublic fundsMean returnsaa/sPrivate fundsMean returnsaa/s
AverageCorrelation
YearsPositive (%)
Years Positive andSignificant (%)
0.1180.1140.168
8383100
252542
0.0840.0880.202
757583
333342
0.0680.0470.322
585892
17050
0.1880.1860.253
9191100
554564
−0.0150.0010.149
454555
363636
0.2120.2210.405
9191100
363664
aCorrelation
between a four-year selection period and a one-year performanceperiod. Averages are across the twelve one-year performance periods. The same statistic was used for the rankings in each period.bThree-year selection period and three-year trading period.
are questionable because his sample size was small. McCarthy, Schneeweis,and Spurgin’s (1997) sample size was likely too small to detect performancepersistence in the mean. Irwin, Krukmeyer, and Zulauf (1992) placed fundsinto quintiles. Their approach is difficult to interpret and may have led tolow power. Schwager (1996) found a similar correlation of 0.07 for mean
40
PERFORMANCE
returns. Schwager, however, found a negative correlation for his return/riskmeasure. He ranked funds based on return/risk when returns were positive,but ranked on returns only when returns were negative. This hybrid measure may have caused the negative correlation. Therefore, past literature isindeed consistent with a small amount of performance persistence. Performance persistence is found here because of the larger sample size and a slightimprovement in methods. As shown in Table 3.6, several years yielded negative correlations, and many positive correlations were statistically insignificant. Therefore, results over short time periods will be erratic.The performance persistence could be due to either differences in trading skills or differences in costs. There is no strong difference in performance persistence among CTAs, public funds, and private funds.
PERFORMANCE PERSISTENCEAND CTA CHARACTERISTICSBecause some performance persistence was found, we next try to explainwhy it exists. Monthly percentage returns were regressed against CTA characteristics. Only CTA data are used since little data on the characteristics ofpublic and private funds were available.
Data and Regression ModelTable 3.7 presents the means of the CTA characteristics. The variables listedwere included in the regression along with dummy variables. Dummy variables were defined for whether a long-term or medium-term trading systemwas used. The only variables allowed to change over time were dollarsunder management and time in existence.The data as provided by LaPorte Asset Allocation had missing valuesrecorded as zero. If commissions, administrative fees, and incentive feeswere all listed as zero, the observations for that CTA were deleted. Thiseliminated most but not all of the missing values. If commissions were zero,the mean of the remaining observations was imputed.A few times options or interbank percentages were entered only as ayes. In these cases, the mean of the other observations using options orinterbank was imputed. When no value was included for non-U.S., options,or interbank, these variables were given a value of zero. Margins often wereentered as a range. In these cases, the midpoint of the range was used. Whenonly a maximum was listed, the maximum was used.If the trading horizon was listed as both short and medium term, theobservation was classed as short term. If both medium and long term or all
41
Performance of Managed Futures
TABLE 3.7 Mean and Standard Deviation of CTA CharacteristicsVariableCommissionAdministrative feeIncentive feeDiscretionNon-U.S.OptionsInterbankMarginTime in existenceFirst yearDollars undermanagement ($million)
Units% of equity% of equity% of profits%%%%% of equity investedmonths
Mean
SD
5.72.519.927.717.05.313.921.855.087.9
4.71.54.537.926.315.729.310.945.44.9
34.8
131.6
Note: These statistics are calculated using the monthly data and were weighted bythe number of returns in the data set.
three were listed, it was classed as medium term. Any observations withdollars under management equal zero were deleted.Attempts were made to form variables from the verbal descriptions ofthe trading system, such as whether the phrase “trend following” wasincluded. No significance was found. These variables are not included inthe reported model because many descriptions were incomplete. Thus, theinsignificance of the trading system could be due to the errors in the data.The remaining data still may contain errors. The most likely source of errorwould be treating a missing value as a zero. Also, the data are originallyfrom a survey, and the survey itself could have had some errors. The presence of random errors in the data would cause the coefficients to be biasedtoward zero. Thus, one needs to be especially careful to not interpret aninsignificant coefficient as being zero.The fees charged are approximately half of what Irwin and Brorsen(1985) reported for public funds in the early 1980s. Thus, the industryappears to have become more competitive over time. The largest reductionof fees is in the commissions charged.Cross-sectional heteroskedasticity was assumed. Random effects wereincluded for time and for CTA. The conclusions were unchanged whenfixed effects were used for time. Considering random effects for CTAs is
42
PERFORMANCE
important because many of the variables do not vary over time. Ignoringrandom effects could cause significance levels to be overstated.
Regression of Mean Returns on CTA CharacteristicsTable 3.8 presents the regressions of monthly percentage returns against CTAcharacteristics. Short-term horizon traders had lower returns than the longterm and medium-term traders. The coefficient of 0.30 for medium-termtraders means that monthly percentage returns are 0.30 higher for mediumterm traders than for short-term traders. For comparison, CTA monthlyreturns averaged 1.28 percent. All three fee variables had positive coefficients.Two of them (administrative and incentive fee) were statistically significant.The fee variables represent the most recent fees. This means that CTAs withlarger historical returns charge higher fees. It may also means that CTAswith superior ability are able to charge a higher price. A 20 percent incentivefee corresponds to monthly returns of 0.44 percentage points higher than aCTA with no incentive fee, so the coefficient estimates are large.TABLE 3.8 Regressions of Monthly Returns versus Explanatory VariablesVariable
Coefficient
t-value
InterceptLong termMedium termCommissionAdministrative feeIncentive feeDiscretionNon-U.S.OptionsInterbankMarginTime in existenceFirst yearDollars under management
13.900*0.210*0.300**0.0140.066**0.022*−0.0010.002−0.0040.0030.004−0.016**−0.145*−0.00104**
2.081.843.201.312.041.95−0.861.22−1.731.481.24−2.45−1.91−2.13
F-test for commodityF-test for timeF-test of homoskedasticity*significant at the 10 percent level**significant at the 5 percent level
0.519.05**8.71**
Performance of Managed Futures
43
None of the coefficients for discretion, non-U.S., options, interbank,and margin were statistically significant. The set of dummy variables forcommodities traded were also not statistically significant. However, thecoefficients for options and interbank cannot be considered small sincethese variables range from zero to 100. Thus, the coefficient of −0.004means that firms with all trading in options have monthly returns 0.4 percentage points lower than a CTA that did not trade options.Both the time in existence and the year trading began had negative coefficients. The negative sign is at least partly due to selectivity bias. SomeCTAs were added to the database after they began trading. CTAs with poorperformance may not have provided data. This could cause CTAs to havehigher returns in their first years of trading. A negative sign on the first-yearvariable suggests that the firms entering the database in more recent yearshave lower returns. Thus, selectivity bias may be less in more recent years.CTA returns also may genuinely erode over time. If CTAs do notchange their trading system over time, others may discover