.
CTA Performance, Survivorship Bias, and Dissolution Frequencies
57
TABLE 4.4 Survivorship Bias Analysis over Different PeriodsBias 1985–2003Bias 1985–1989Bias 1990–1994Bias 1995–1999Bias 2000–2003
0.55.40.55.50.67.30.56.20.44.4
per Monthper Yearper Monthper Yearper Monthper Yearper Monthper Yearper Monthper Year
Our database contains 1,899 CTAs (611 survived funds and1,288 dissolved funds as of December 2002).
Survivorship Bias over TimeFigure 4.1 reports the evolution of the survivorship bias calculated on athree-year rolling period starting January 1985 to December 1987 and ending January 2000 to December 2002. It allows us to analyze more preciselyhow the survivorship evolves over time.
1.000.900.800.700.600.500.400.300.200.100.0088 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 fundsas of December 2002). Numbers on the vertical axis are monthly percentages.
58
PERFORMANCE
The figure indicates that the monthly bias ending January 1985increases from around 0.7 percent at the beginning of the year to 0.85 percent after summer before reaching the bottom of 0.9 percent at the beginning of 1989. Afterward, it increases until January 1993 (0.9 percent) andthen decreases to a mean around 0.55 percent for the periods ending betweenJanuary 1994 and January 2000. Because the three-year periods end January 2000, the monthly survivorship bias decreases almost constantlyto 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 slowincrease that follows) can be explained by the fact that the surviving fundsunderperformed the whole database in 1988 and 1989. The first underperformance was in December 1988 (1.87 percent for the surviving fundsagainst 2.94 percent for the whole database). Moreover, this was the firstmajor underperformance, which has been followed by others during thenegative 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 sharpincrease in survivorship bias over the period ending November and December 1992 can be explained mainly by high overperformance in June, July,and August 1992 with an average of 3 percent monthly outperformance. Tosummarize, this figure identifies epochs during which surviving funds outperformed the whole database, and during which the difference betweensurviving funds and dissolved funds was less important.We also analyze the survivorship bias calculated over the positiveand negative months5 for the whole database. Interestingly, Table 4.5 indicates that the mean survivorship bias is the same over the three periodsstudied at 0.48 percent. The standard deviation and the median of thesurvivorship are also almost equal. The only significant difference is inthe minimum three-year rolling period, which is much higher for the negative months at 0.13 percent versus 0.06 percent for the whole periodand the positive months. The maximum is also almost equal between 0.87percent and 0.90 percent.
METHODOLOGYThe aim of this study is to determine if some CTAs consistently and persistently outperform their peers. To achieve this objective, we construct aCTA Global Index that contains all the funds present in our database and5We 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 reachpositive returns.
59
CTA Performance, Survivorship Bias, and Dissolution Frequencies
TABLE 4.5 Descriptive Statistics of the 3-Year Rolling-Period Survivorship Bias
Whole periodPositive monthsNegative months
Mean
Std. Dev.
Median
Min
Max
0.480.480.48
0.180.180.18
0.510.510.52
0.060.060.13
0.900.900.87
Std. dev. = standard deviation; Min = minimum; and Max = maximum of the 3-yearrolling-period survivorship bias calculated over the whole period studied (January1985–December 2002).
one index per CTA strategy. To test if some funds significantly outperformthe indices, we use the following regression.Rpt = aP + bp1RIt + ept
(4.1)
p = 1 to 1,899 and t = 1 to 216where RPt = return of CTA p at period tRIt = return of the index considered at period tWe run this analysis for each fund compared to the whole CTA database index but also for each fund compared to its strategy index. Once weobtain results, we want to determine if momentum is present in CTAreturns. Active CTA selection strategies could increase the expected returnon a portfolio if CTA performance is really predictable. We define thehypothesis that a CTA with an above-average return in this period also willhave an above-average return in the next period as the hypothesis of persistence in performance. Sirri and Tufano (1998) and Zheng (1999) stressedthe importance of persistence analysis in mutual funds. They documentlarge inflows of money into last year’s best performers and withdrawalsfrom last year’s losers. Capocci and Hübner (2004) have stressed this forhedge funds. They find that newly invested money in these best-performingmutual funds is a predictor of future fund performance.We apply the methodology of Carhart (1997) to our simple model. Allfunds are ranked based on their previous year’s return. Every January weplace all funds into 10 equally weighted portfolios, ranked from highest tolowest past returns. Portfolios 1 (High) and 10 (Low) are then furthersubdivided on the same measure. The portfolios are held until the followingJanuary and then rebalanced. This yields a time series of monthly returns oneach decile portfolio from January 1985 to December 2002. Funds that disappear during the course of the year are included in the equal-weighted average until they disappear, then portfolio weights are readjusted appropriately.
60
PERFORMANCE
Finally, in the last part of the study we want to determine empirically ifsome strategies are consistently better than others. To achieve this objectivewe use the next regression.12
RDt = α P + ∑ βP1RIt + ε Pt
(4.2)
i =1
P = 1 to 10 and t = 1 to 216where RDt = return of decile P at period tRIt = return of the 12 indexes (CTA Global Index, technicallycurrency, technically diversified, technically financial/metals,technically others, stock index, options, systematic, arbitrage,discretionary, fundamental, no category) at period tWe regress each decile against the CTA Global Index and each strategyindex. Doing so, we determine if some deciles are exposed to some strategies, which indicates that that strategy is particularly present in the corresponding decile.
PERFORMANCE ANALYSISHere we apply the model just discussed to our database to determine ifsome strategies significantly outperform the CTA Global Index over different time periods. In the next section we investigate whether momentumexists in CTA performance.Table 4.6 indicates some interesting results. First, we see that results aredifferent across strategies, indicating that the classification in substrategiesseems to be relevant. Second, the first column of the table reports the alphaof the different strategies once the performance of the CTA database considered as a whole is taken into account through the CTA Global Index.This is the performance not explained by the global CTA index. Seven outof the 11 strategies are significantly positive at the 5 or 1 percent significance level (technically financial/metals, technically currency, technicallyother, discretionary, stock index, arbitrage, and option strategies); two arenot significantly different from zero (fundamental and no category); andtwo are significantly negative (technically diversified and systematic). Theseresults indicate that all but two strategies produce returns significantly different from zero, which means that the individual strategies produce returnssignificantly different from their aggregation.66The CTA Global Index is composed of all the individual funds classified in the var-
ious strategies. It is the same funds classified differently.
61
CTA Performance, Survivorship Bias, and Dissolution Frequencies
TABLE 4.6 Relative Performance Analysis of Strategy Indices
Technically diversifiedTechnically financial and metalsTechnically currencyTechnically otherFundamentalDiscretionarySystematicStockArbitrageOptionNo category
Alpha
CTA Index
R2
−0.28***0.65**0.92***2.56***0.521.23***−0.58***1.86***1.01***2.03***0.16
1.14***0.64***0.38***0.33**0.56*0.39***1.30***−0.070.12*0.530.83***
0.920.380.180.040.080.290.950.000.020.030.74
This table reports the results of the regression from the strategy subindices to thewhole database for the January 1985 to December 2002 period except for technically others (August 1985 to May 1995 and October 1998 to April 2001) and foroption strategies (September 1990–December 2002).t-stat are heteroskedasticity consistent.***Significant at the 1 percent level.**Significant at the 5 percent level.*Significant at the 10 percent level.Numbers in the table are monthly percentages.
The positive alphas range from a monthly percentage difference of 0.65percent for technically financial/metals to 2.03 percent for option strategies;the negative alphas are −0.28 percent for technically diversified funds and−0.58 percent for systematic funds.Third, most betas are significantly positive at the 1 percent significancelevel. For four strategies (fundamental, stock index, arbitrage, and option)the beta is either significant at the 10 percent level or not significant. Thesestrategies all contain 52 funds or less, which means that they represent onlya small part of the index. This fact partly explains their limited exposure tothe CTA Global Index.Finally, the R2 column reports very different numbers. The R2 rangesfrom 0.00 for stock funds to 0.95 for systematic funds. As we could haveexpected, the highest R2 are obtained when the alphas are the lower andparticularly low when the beta is not significant.Table 4.7 reports the same results over different subperiods. We dividethe analysis in three six-year periods (January 1985 to December 1990, Jan-
62
CTA Index1.20***0.58***0.24**0.25*0.530.36***1.30***−0.280.15**NA0.90***
Alpha
−0.52**1.55**1.73***3.82***1.462.53***−1.25***3.66***2.49***NA0.50*
Tech divers.Tech fin/metTech currencyTech otherFundamentalDiscretionarySystematicStock
Jan 1997–Dec 2002
CTA Index0.92***0.58***0.49***−0.290.470.24***1.37***0.20
Alpha
−0.090.100.49***2.64*−0.350.62***−0.26***1.21***
Panel 1 (cont.): Subperiod analysis
Tech divers.Tech fin/metTech currencyTech otherFundamentalDiscretionarySystematicStockArbitrageOptionNo category
Jan 1985–Dec 1990
Panel 1: Subperiod analysis
0.850.440.330.010.030.130.980.03
R2
0.940.300.080.030.080.260.960.030.10NA0.78
R2−0.080.44**0.301.180.690.93***−0.50***0.54*0.54***1.290.04
Alpha
Tech divers.Tech fin/metTech currencyTech otherFundamentalDiscretionarySystematicStock
Jan 1998–Mar 2000
−0.46**0.56**0.86**NA0.720.81**−0.37***2.67***
Alpha
Panel 2: Bull market analysis
Tech divers.Tech fin/metTech currencyTech otherFundamentalDiscretionarySystematicStockArbitrageOptionNo category
Jan 1991–Dec 1996
TABLE 4.7 Subperiod Performance Analysis of the Various CTA Strategies
1.11***0.46***0.37**NA0.070.37**1.4***−0.20
CTA Index
1.04***0.74***0.85***0.600.52**0.29***1.48***0.44**0.080.790.62***
CTA Index
0.890.430.17NA0.000.150.980.02
R2
0.890.620.480.070.070.220.970.170.010.040.78
R2
63
0.080.150.223.43*−1.81*0.56***−0.21***0.421.33**1.59**0.28
Alpha
R20.870.400.390.040.110.110.980.050.240.020.45
0.84***0.49***0.51***−0.500.93*0.17**1.35***0.24−0.90**0.260.54***Tech divers.Tech fin/metTech currencyTech otherFundamentalDiscretionarySystematicStockArbitrageOptionNo category
Jan 1993–Dec 2002
Panel 3: 10-year analysis
ArbitrageOptionNo category
Jan 1998–Mar 2002
CTA Index1.00***0.71***0.58***−0.230.340.32***1.36***0.21*−0.43**0.180.48***
−0.100.140.36***1.72*0.620.70***−0.33***0.99***0.72***2.20***0.33***
−0.86***−0.640.23
CTA Index
Alpha
0.513.73***0.36**
Alpha
0.850.510.330.010.020.200.970.030.090.000.49
R2
0.270.050.19
R2
t-stat are heteroskedasticity consistent.Tech. divers. = technical diversified; tech. fin/met = technical financial/metals; tech. cur = technical currency; tech. other = othertechnical; stock = stock index.***Significant at the 1 percent level.**Significant at the 5 percent level.*Significant at the 10 percent level.Numbers in the table are monthly percentages.
Tech divers.Tech fin/metTech currencyTech otherFundamentalDiscretionarySystematicStockArbitrageOptionNo category
April 2000–Dec 2002
CTA Index
0.200.010.39
−0.75***0.250.44***
0.73*2.58***0.34***
ArbitrageOptionNo category
Panel 2 (cont.): Bear market analysis
R2
CTA Index
Alpha
Jan 1997–Dec 2002
TABLE 4.7 (continued)
64
PERFORMANCE
uary 1991 to December 1996, January 1997 to December 2002) in Panel 1before isolating bull and bear market periods in the last subperiod in Panel2. These periods are January 1998 to March 2000 for the bull market andApril 2000 to December 2002 for the bear market. This last analysis is particularly interesting because we can determine how the strategies performcompared to their peers during a bull and a bear market. For informationpurposes we also include a 10-year analysis in Panel 3.Results reported in Panel 1 indicate that few alphas change sign over thesubperiods, and no alpha that was significantly positive or negative for thewhole period becomes significantly negative or positive over the subperiods.The first line indicates that technically diversified funds underperformthe CTA Global Index over each subperiod, but this underperformance issignificant only over the first and last subperiods. Panel 2 indicates that thisstrategy underperforms during the bull market and that it slightly outperforms (but not significantly) during the bear market. Over a 10-year period,this strategy slightly underperformed. The adjusted R2 is high over each ofthe subperiods analyzed.Panel 1 indicates that technically financial/metals, technically currency,technically other, stock funds, arbitrage, option, and no category funds outperform over some subperiods and are in line with the CTA Global Indexover other. Discretionary and systematic funds always outperform theirpeers. Fundamental funds never significantly add to the performance of theCTA Global Index.Panel 2 is interesting because it indicates when specific strategies perform better than their peers. Technically financial/metals and technicallycurrency, stock funds, and the no-category funds perform better than theirpeers during bull markets, while arbitrage funds perform better during bearmarkets. Technically diversified funds significantly underperform in bullmarkets without deviating significantly from their peers in bear markets.Discretionary, systematic, and option funds always perform better thantheir peers whereas systematic funds always perform worse. Finally, fundamental funds perform in line with the CTA Global Index.Let us now compare the subperiods one by one instead of analyzinghow a strategy performed over each subperiod. In Panel 1, we see that fewalphas are significant over the January 1991 to December 1996 period. Thisindicates that most of the strategies are in line with the CTA Global Index.We see this pattern also in Panel 2, where most strategies out- or underperform significantly during the bull market while few do so during the bearmarket. Finally, over the 10-year period, many strategies significantly outperform the CTA Global Index. Astonishingly, technically diversified andtechnically financial/metals that respectively significantly under- and out-
CTA Performance, Survivorship Bias, and Dissolution Frequencies
65
perform during the whole January 1985 to December 2002 period do notsignificantly deviate from the index over the last 10 years.7Regarding the exposure to the index, some strategies (technically diversified, technically financial/metals, technically currency, discretionary, systematic) are always significantly exposed whereas others (technically otherand arbitrage funds) are exposed over some subperiods without alwaysbeing exposed. Fundamental, stock, and options funds are never or almostnever exposed to the index.The adjusted R2 does not change heavily over the subperiods analyzed.The biggest variations in this coefficient occur for technically financial/metalsfrom 0.30 for the January 1985 to December 1990 period to 0.62 for theJanuary 1991 to December 1996 period, for technically currency fundsfrom 0.08 over the January 1985 to December 1990 period to 0.48 for theJanuary 1991 to December 1996 period and for the no-category funds from0.78 for the January 1991 to December 1996 period to 0.39 over theDecember 1997 to December 2002 period.
Individual Fund ResultsIn this subsection we determine if the results obtained for the whole database are confirmed for individual funds. We will not report the resultsobtained for all the funds, but we will summarize. The first step in this analysis is to apply a filter on the database. To be included in the database, eachfund must have at least 24 months of data. We delete 385 funds to reach atotal of 1,508 funds. Then we apply the model to each individual fundregressed over the CTA Global Index. Results are summarized in Table 4.8.The table indicates that 13.7 percent of the funds significantly outperform the index at the 1 percent significance level over the period studied.Another 8.0 percent of the funds outperform at the 5 percent level. However,11.7 percent of the funds significantly underperform at the 1 percentsignificance level, and 5.7 percent do so at the 5 percent significance level.The right side of Table 4.8 indicates that 49.9 percent of the funds arepositively significantly exposed to the CTA Global Index at the 1 percentsignificance level. Another 10.3 percent of the funds are significantly positively exposed to the index at the 5 percent significance level. Few fundsare significantly negatively exposed to the CTA Global Index. 1.0 percent
7Logically, however, they respectively under- and outperformed during the first subperiod reported in Panel 1.
66
PERFORMANCE
TABLE 4.8 Summary of the Individual Results of the Performance Analysis,January 1985 to December 2002Positive CTA GlobalIndex Exposition
Positive AlphasSignificance levelNumber of fundsPercentage
1%20713.7%
5%1208.0%
10%885.8%
1%17611.7%
5%865.7%
5%15610.3%
10%885.8%
Negative CTA GlobalIndex Exposition
Negative AlphasSignificance levelNumber of fundsPercentage
1%75349.9%
10%845.6%
1%151.0%
5%241.6%
10%201.3%
t-stat are heteroskedasticity consistent.Numbers in the table are monthly percentages.
are exposed at the 1 percent significance level and 1.6 percent are exposedat the 5 percent significance level.These results are interesting because they indicate that, as a whole, 21.7percent of the funds significantly outperform the CTA Global Index while15.4 percent significantly underperform. Outperformance is one thing; persistence is another. It will be interesting to determine if this outperformanceis persistent and predictable or not. It is not surprising that most funds aresignificantly exposed to the index. However, there are some funds thatare significantly negatively exposed to the index.Table 4.9 reports descriptive statistics on the estimated coefficients. Theaverage 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
AlphaCTA Global IndexR2
Mean
Std. Dev.
Median
Min
Max
0.14%0.89%0.18
1.841.070.21
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 consistent.Numbers in the table are monthly percentages.
CTA Performance, Survivorship Bias, and Dissolution Frequencies
67
ation of 1.84 percent. The average beta (in our case the beta is measuredrelative to our CTA Global Index) is 0.89. This means that the average CTAis not completely exposed to the market. This number can be compared tothe beta of a portfolio with an equity index like the S&P 500. The only difference is the reference index.The average R2 is 0.18 percent with a standard deviation of 0.21 percent. These figures may seem to be low, but R2 is always lower for individualfunds than it is for indexes. The minimum and maximum are respectively−0.04 and 0.87 indicating that the index explains almost 90 percent of thefund’s performance.
PERSISTENCE IN PERFORMANCENow we want to determine if there is persistence in CTA performance. Toachieve this objective, we rank the funds in deciles D1 through D10 eachyear based on previous performance. Decile 1 contains the worst-performingfunds, while decile 10 contains the best-performing funds. We also divide thetwo extreme deciles (D1 and D10) into three subdeciles.
Global ResultsTable 4.10 reports the descriptive statistics of each decile. It shows someinteresting features. The mean returns are more or less stable between decileD1 and D7. The only exception is D6, which is slightly higher. Then, between D8 and D10, the increase is more pronounced. The last three decilesoffer a higher performance. The median returns show the same pattern withlower figures. The standard deviation indicates that top-performing decilefunds have returns that are much more variable. This effect is more important in the subdeciles, where the monthly standard deviation can reach almost 20 percent. There is no significant difference around the minima exceptfor subdeciles where the minima are lower (particularly from top-decile funds).The maximum increases with the performance of the funds. The monthlymaximum returns can reach 140 percent for top-performing funds.The kurtosis is large and the skewness is positive for all deciles. Moreover, they both increase with the performance. This means that goodperforming funds have positively skewed performance distribution withfat tails. This is in accordance with the minimum and maximum results.Finally, the Sharpe ratios calculated with a 5 percent risk-free rate are smallin magnitude. The highest ratios are those of poorly performing funds. This isexplained by the fact that the standard deviation is higher among the wellperforming funds.
68
PERFORMANCE
TABLE 4.10 Decile Descriptive Statistics Based on Previous Year’s Performance
D1D2D3D4D5D6D7D8D9D10D1aD1bD1cD10aD10bD10c
MeanReturn
Std.Dev.
Median
Min
Max
1.241.021.071.101.051.351.211.671.872.671.301.331.963.171.901.31
4.713.343.003.223.223.794.084.565.666.185.495.095.9919.9914.777.72
0.390.510.510.610.560.820.591.100.851.681.080.761.180.850.870.77
−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
30.3820.6715.2119.8624.4219.9127.5535.0046.7545.3858.4628.8350.10140.91100.9534.74
Skewness Kurtosis1.691.741.661.972.591.862.372.813.973.565.701.823.582.451.930.56
7.076.394.797.8414.656.1112.1415.7225.3420.2857.776.8324.2013.6910.163.04
SharpeRatio0.170.250.270.250.260.220.200.180.140.130.150.160.140.040.060.11
Std. Dev. = standard deviation; Min = minimum; Max = maximum. The Sharperatio is calculated with a 5 percent risk-free rate.Numbers in the table are monthly percentages.
Table 4.11 contains the results of the persistence analysis. The alphaindicates that all deciles but decile 10 underperform relatively to the index.Underperformance is significant only for D2, D4, D5, D6, D7, and D9.These results indicate that when the performance of the index is taken intoaccount, most funds do not add value (they destroy value) over the January1985 to December 2002 period. Interestingly, D10 (containing previousyear’s best-performing fund) has a positive but not significant alpha. Alldeciles are positively exposed to the CTA Global Index, although D1, D6,D8, and D9 are the only ones that are significantly exposed. The adjustedR2 obtained is quite high for each decile. However, for subdeciles (especiallythose for D1), the R2 is relatively low.8
8We have analyzed the data to understand this point, and we have concluded thatmany funds in the worst-performing decile are dissolved each year. This means thatthese subdeciles do not contain a lot of funds, which leads to less stable returns compared to whole deciles.
