:200009:2002
+10.0%+19.0%+29.5%−22.6%
48571830
Panel B: Financial CrisesExtreme Event
Start
Finish
Magnitude
# Obs
Russian CrisisAsian CrisisTerrorist Crisis
10:199708:199809:2001
11:199709:199810:2001
−13.0%−14.7%−18.2%
222
For both panels, start and finish dates are identified as the end-of-month tradingdays surrounding the subperiod under study. In Panel A, annualized returns arecomputed using closing values of the S&P 500 index. In Panel B, the magnitude ofthe crisis is computed by taking the minimum and maximum values of the S&P 500index during the event month.
1We do not include the Barclay Agricultural Traders Index in this study as the finan-
cial variables used for the return-generating model would not explain a significantproportion of the return variance.
108
PERFORMANCE
The bull market that lasted from the early 1990s until the end of the dotcom bubble in March 2000 is broken down into three subperiods. We referto the final 18 months prior to the market crash as “Strong Bull”; duringthis time the annualized return on the Standard & Poor’s (S&P) 500 was29.5 percent. We call the period from January 1990 to December 1993“Weak Bull” and the period from January 1994 to September 1998 “Moderate Bull.” Not only do the annualized returns nearly double from 10 percent to 19 percent over these two subperiods, the return distributions areconsiderably different over the two periods. The fourth and final subperiod that we investigate is the “Bear Market” that lasted from March 2000to September 2002, during which time the annualized return on the S&P500 was −22.6 percent.Three significant market crises occur during our sample period, each ofwhich caused a significant short-term drop in the market. Predictably, thesethree crises are the Russian default, the Asian currency crisis, and September 11 terrorist attacks. Interestingly, the magnitude and duration of thesethree shocks on the S&P 500 is very similar. Each event triggered a drop inthe S&P 500 of about 15 percent, and the time required for the index toreturn to its preevent level was generally two to three months. The threecrises occur in two different subperiods: “Moderate Bull” and “Bear.”Table 6.2 presents the descriptive statistics for the excess returns onthe CTA indices for the entire period as well as for the four subperiods.Although each individual CTA index has certain intrinsic characteristics,certain general properties appear to be common to all the CTAs in our sample. More specifically, the Jarque-Bera tests over the entire sample periodillustrate that all the CTA indices, with the sole exception of the diversifiedindex, exhibit nonnormality in their excess returns. Another common traitis the very poor results during the “Strong Bull” period: all the CTA indicesdisplay negative excess returns for this period of very high returns in thestock markets. As a matter of fact, this is unanimously the worst subperiodin terms of performance for all the CTA indices. These results are in accordance with previous findings by Edwards and Caglayan (2001) and Liang(2003), who identified the poor performance of CTAs in bull markets. Afurther examination of the mean excess returns over the four subperiodsreveals that for all the CTA indices, the highest excess returns are achievedin “Weak Bull,” which includes the recession of the early 1990s, and“Bear,” which followed the collapse of the dot-com bubble. This wouldseem to concur with the notion that CTAs possess valuable return characteristics during down markets.The descriptive statistics for the excess returns of the CTA indices seemto indicate that there exist similar return dynamics across the different typesof CTAs. The two subindices that exhibit marginally different return pat-
109
9.719.715.952.246.3114.1714.177.112.667.06
−0.05−0.080.04−0.810.36
−0.04−0.210.31−1.090.48
0.050.120.15−1.040.22
0.240.310.28−0.420.41
0.420.820.37−0.560.56
0.300.630.18−0.710.53
CTAIndex
SystematicTraders Index
Financial andMetal TradersIndex
6.726.725.881.515.89
Max
Median
Descriptive Statistics of Excess Returns
Mean
TABLE 6.2
3.464.473.002.013.132.232.042.441.352.50
−4.64−3.84−4.64−3.16−4.36
2.673.152.561.702.53
Std. Dev.
−7.91−7.91−7.09−5.03−5.73
−6.13−6.13−5.18−4.62−4.66
Min
0.480.800.390.030.18
0.600.670.23−0.220.17
0.380.460.30−0.410.28
Skewness
3.233.673.051.852.64
3.993.443.002.562.78
3.363.402.733.223.00
Kurtosis
6.88*5.96*1.470.990.33
17.04**4.010.480.290.20
4.98*1.991.040.550.40
J-B
11014.3714.376.992.766.29
−0.350.40−0.44−0.55−0.39
0.371.040.08−0.220.12
−7.99−7.99−4.07−1.82−2.413.305.222.291.392.09
1.441.711.331.301.42
3.614.073.512.433.40
−7.35−7.02−6.88−5.77−6.01−3.26−3.26−2.61−2.88−3.07
Std. Dev.
Min
1.410.790.920.711.44
1.071.710.68−0.480.23
0.350.410.38−0.230.18
Skewness
6.442.973.672.314.42
7.639.333.712.553.17
2.992.902.932.352.67
Kurtosis
138**4.96*9.09**1.8712.95**
181**103**5.56*0.840.31
3.461.371.360.470.29
J-B
Excess returns are calculated as the difference between the returns on the CTA indices and the return on the 3-month treasury billover the same period.** The values are significant at the 10 percent level.** The values are significant at the 5 percent level.
CurrencyTraders Index
DiscretionaryTraders Index
7.857.853.921.803.67
−0.05−0.03−0.48−0.030.06
−0.020.29−0.30−0.350.07
11.7111.719.763.187.97
0.060.170.07−0.540.53
0.460.730.46−0.520.64
Max
Median
Mean
(continued)
DiversifiedTraders Index
TABLE 6.2
The Performance of CTAs in Changing Market Conditions
111
terns are the Discretionary Traders Index and the Currency Traders Index.These two indices display the highest skewness and kurtosis; the former isthe only index to exhibit negative returns over the entire sample.Table 6.3 examines the correlation coefficients between the differentCTA indices as well as between the CTA indices and the first two returnmoments of the Russell 3000 (Russell squared). The results for the entiresample as well as the subsamples confirm our earlier findings. The correlation coefficient between the CTA index, the Financial and Metal TradersIndex, the Systematic Traders Index, and the Diversified Traders Index arepositive and close to 1 for all the different periods. The Currency TraderIndex and the Discretionary Index have the lowest correlation coefficientwith the other CTA indices. The coefficients are still positive between all theindices and for all the subperiods, but the correlation coefficient is muchsmaller. Over the entire period, all of the CTA indices have a small and negative correlation coefficient with the Russell 3000 index and a positive relation with the square of the Russell 3000 returns. These results are consistentduring the four subperiods with the exception of the Currency and Discretionary indices, which have a positive relation with the Russell 3000 in certain subperiods. These correlations remain nonetheless small in magnitude.
EXPLAINING CTA RETURNSHere we introduce three types of return-generating processes that may behelpful in understanding monthly CTA returns over the period. We first perform a classical multifactor analysis using risk premia similar to the Famaand French (1993) and Carhart (1997) models, with an additional factorrelated to stock dividend yields, in a similar spirit to Kunkel, Ehrhardt, andKuhlemeyer (1999). We then use a simple specification aimed at capturingthe exposure to skewness and kurtosis. Finally, we select several other factors that have been applied to performance studies of hedge funds and/orCTAs to identify the best linear asset-pricing model for each particular subperiod under study.
Multifactor ModelWe start with the four-factor model proposed by Carhart (1997), butexclude the factor mimicking the value premium, namely the “High minusLow” (HML) book-to-market value of equity, that yields significant resultsfor none of our regressions. This factor is replaced by an additional factorrelated to the risk premium associated with high-yield dividend-payingstocks. Although there is only limited and controversial evidence of theactual value added of this factor in the explanation of empirical returns,Kunkel et al. (1999) find that there is a significant empirical return compo-
112
10.990.90
10.970.900.980.640.78−0.260.33
CTA IndexSystematicFin/MetDiversifiedDiscretionaryCurrencyRussell2Russell
CTA IndexSystematicFin/Met
10.980.890.980.570.68−0.200.25
CTA IndexSystematicFin/MetDiversifiedDiscretionaryCurrencyRussell2Russell
CTAIndex
10.91
10.930.970.530.85−0.200.34
10.890.970.500.74−0.190.25
Systematic
10.650.79−0.260.32
Average Bull Market
10.870.520.81−0.200.40
1
10.560.63−0.230.28
Weak Bull Market
10.850.470.63−0.180.30
10.43−0.430.40
10.39−0.070.16
Diversified Discretionary
Entire Period
Fin. andMetal
TABLE 6.3 Correlations between Excess Returns on CTA Indices and Russell 3000
1−0.220.30
1−0.100.09
Currency
1−0.10
1−0.34
Russell
1
1
Russell
2
113
0.970.710.680.000.30
10.980.850.980.590.38−0.22−0.11
10.990.950.990.330.67−0.370.19
CTA IndexSystematicFin/MetDiversifiedDiscretionaryCurrencyRussell2Russell
CTA IndexSystematicFin/MetDiversifiedDiscretionaryCurrencyRussell2Russell
CTAIndex
DiversifiedDiscretionaryCurrencyRussell2Russell
TABLE 6.3 (continued)
10.950.990.260.64−0.350.19
10.830.980.470.36−0.24−0.13
0.960.660.680.000.33
Systematic
Diversified
Discretionary
10.700.53−0.070.37
0.920.290.61−0.410.18
0.780.410.380.010.18
10.300.60−0.360.24
Bear Market
10.520.26−0.26−0.15
Strong Bull Market
0.840.600.630.040.37
10.300.19−0.08
10.30−0.100.01
10.430.120.16
Average Bull Market (continued)
Fin. andMetal
1−0.18−0.02
1−0.10−0.10
10.09−0.02
Currency
1−0.59
10.66
1−0.51
Russell
1
1
1
Russell2
114
PERFORMANCE
nent associated with high-yield dividend-paying stocks, which is explainedin Martin and van Zijl (2003) by a tax differential argument. The equationfor the market model is:rt = a + b1Mktt + b2SMBt + b3UMDt + b4HDMZDt + et
(6.1)
where rt = CTA index return in excess of the 13-week T-Bill rate,Mktt = excess return on the portfolio obtained by averaging thereturns of the Fama and French (1993) size and book-tomarket portfoliosSMBt = the factor-mimicking portfolio for size (“Small Minus Big”)UMDt = the factor-mimicking portfolio for the momentum effect(“Up Minus Down”)HDMZDt = difference between equally weighted monthly returns ofthe top 30 percent quantile stocks ranked by dividendyields and of the zero-dividend yield stocks (“HighDividend Minus Low Dividend”).Factors are extracted from French’s web site (http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html). Table 6.4 summarizes theresults of this regression over the entire period and the four subperiods.For all but one subperiod (Weak Bull), the adjusted R-squared coefficients are extremely low and often negative. The only statistically significant linear relationship is observed for the Weak Bull subperiod, while themodel is unable to explain anything during the Strong Bull subperiod. Thesignificance of the regressions is especially poor for the Discretionary andCurrency strategies, whose different pattern of returns had already beenobserved through their correlation structure. During the period from 1990to 1993, it appears that only the coefficient of the dividend factor is significantly positive for all indices except the Discretionary Index.2These rather weak results confirm the inaccuracy of classical multifactor models for the assessment of required returns of commodity tradingadvisors. This is in contrast with pervasive evidence of the ability of theCarhart (1997) model to explain up to an average of 60 percent of the variance of hedge funds strategies (see Capocci, Corhay, and Hübner, 2003;Capocci and Hübner, 2004), providing further evidence of the completelydifferent return dynamics of these financial instruments.
2Of course, the replacement of this risk premium, the only one that seems to have
explanatory power, by the traditional HML factor would have yielded even loweradjusted R-squared.
115
The Performance of CTAs in Changing Market Conditions
TABLE 6.4
Regression Results Using Modified Fama-French FactorsEntirePeriod
WeakBull
ModerateBull
StrongBull
Bear
CTA Index
b1b2b3b4R2adj
−0.0610.0010.077*0.0640.047
−0.0310.3730.217*0.658**0.324
0.014−0.437**−0.119−0.1750.051
−0.0900.062−0.040−0.066—
−0.2230.0110.051−0.0820.044
Systematic
b1b2b3b4R2adj
−0.063−0.0030.102**0.0890.043
0.0580.5830.2221.020**0.286
0.014−0.517**−0.137−0.1880.057
−0.1100.062−0.020−0.060—
−0.2800.0190.060−0.115*0.046
Fin/Metal
b1b2b3b4R2adj
−0.0340.0090.0430.070*0.033
0.0350.1710.1010.433**0.308
0.031−0.469−0.077**−0.2240.087
0.0240.071−0.0040.013—
−0.270**0.0210.014−0.0870.065
Diversified
b1b2b3b4R2adj
−0.120−0.0020.098*0.0620.050
−0.0260.4400.2430.853**0.314
−0.045−0.599**−0.242−0.2360.057
−0.1470.086−0.012−0.076—
−0.331*0.0050.067−0.1430.059
Discretionary
b1b2b3b4R2adj
−0.038−0.014−0.031−0.024—
−0.153**0.0120.0560.1000.172
0.025−0.170**−0.160*−0.191**0.111
−0.0340.0150.0360.009—
−0.004−0.041−0.045−0.040—
Currency
b1b2b3b4R2adj
0.021−0.0210.0790.122**0.031
−0.0130.3920.3640.915**0.265
0.046−0.1760.151−0.0710.000
−0.0150.003−0.070−0.005—
−0.0610.0840.0060.020—
** The values are significant at the 10 percent level.** The values are significant at the 5 percent level.
116
PERFORMANCE
Multi-Moment ModelIt is natural to suspect that the positive skewness and high kurtosis of CTAreturns reported in Table 6.2 could render our index returns sensitive to amultimoment asset pricing specification. Such a framework also may capture a significant proportion of the optionlike dynamics of CTAs reportedby Fung and Hsieh (1997b) and Liang (2003), because the nonlinear payoff structure of option contracts generates fat-tailed, asymmetric optionreturn distributions.We choose to adopt a simple specification for the characterization of amultimoment return-generating model, in a similar vein to the study ofFang and Lai (1997), who report significant prices of risk for systematiccoskewness and cokurtosis of stock returns with the market portfolio. Theirfirst-pass cubic regression resembles:rt = α + β1rm, t + β 2rm2, t + β 3rm3, t + ε t
(6.2)
where rm,t = excess return on the market indexUnlike the prêt-à-porter specification proposed in equation 6.1, wherethe market factor chosen had to be neutral with respect to size considerations, the index chosen in equation 6.2 is the one whose influence on CTAreturns is likely to be highest. In accordance with previous studies, we usethe Russell 3000 index as a proxy for the market portfolio.Table 6.5 summarizes the results of regression equation 6.2 over theentire period as well as the four subperiods.The regressions still explain, on average, a very low proportion of theCTA returns variance. Yet four extremely interesting patterns can be noticed.1. The multimoment regression seems to provide a slightly better fit thanthe multifactor model presented in equation 6.1, with the exceptionof the “Weak Bull” period, where the multifactor dominates for all butthe Discretionary strategy.2. The most significant regression coefficient appears to be b2, which isthe loading on the squared market return. It is positive for the globalperiod as well as for the “Weak Bull” subperiod for most CTA indices.3. The patterns of the Discretionary and Currency indices exhibit majordifferences with respect to the rest of CTA indices, which behave in verysimilar ways. For these indices, closely related to the behavior of financial markets, the coefficient of the Russell 3000 index is negative for thewhole period, but only because it is significantly negative during the first
117
The Performance of CTAs in Changing Market Conditions
TABLE 6.5
Cubic Regression of CTA Indices on the Russell 3000 Index
CTA Index
Systematic
Fin/Metal
Diversified
Discretionary
Currency
EntirePeriod
WeakBull
ModerateBull
StrongBull
Bear
b1b2b3R2adj
−0.115*0.021**0.0010.064
−0.522**0.043**0.005**0.186
0.1480.022−0.00020.073
0.1890.081−0.017—
0.048−0.028−0.0040.111
b1b2b3R2adj
−0.1510.026**0.0000.053
−0.629**0.065**0.007**0.156
0.1940.027−0.0000.098
0.0510.122−0.015—
0.161−0.034−0.0060.118
b1b2b3R2adj
−0.0610.021*0.00030.082
−0.3170.035*0.004*0.231**
0.1750.0360.00020.162
0.1670.085−0.013—
0.005−0.031−0.0040.148
b1b2b3R2adj
−0.1360.026**0.00020.081
−0.584**0.054**0.0050.150
0.1770.028−0.0010.109
0.3300.131−0.0280.065
0.127−0.033−0.0060.121
b1b2b3R2adj
−0.0210.009*0.0003*0.011
−0.0930.022**−0.0010.290
0.0670.0160.00040.034
0.0530.039−0.006—
0.105−0.002−0.001—
b1b2b3R2adj
−0.193**0.026**0.002**0.029
−0.755**0.068**0.008*0.136
0.099−0.009−0.001—
−0.055−0.0150.002—
−0.176−0.000.001—
** The values are significant at the 10 percent level.** The values are significant at the 5 percent level.
subperiod. From 1994 onward, it becomes positive, although not significant. Thus, this is not evidence of a systematic contrarian strategy.Notice that the coefficient for the Russell 3000 is typically greater (inabsolute value) than the corresponding loading for the market returnin Table 6.4, indicating that this index is more suitable as an explanatory variable for CTA indices than a proxy that gives more weight tolarge capitalization companies.
118
PERFORMANCE
4. Neither the multifactor nor the multimoment specification has explanatory power for the most extreme movements, namely the “Strong Bull”and “Bear” market conditions.These facts lead us to conclude that additional factors are essential tocapture the dynamics of CTA returns and that a subperiod analysis isrequired since the returns seem to exhibit very little stationarity. Additionally, the Discretionary and Currency CTA indices need to be studied independently, as their return distributions are dissimilar to those of the otherCTA indices.
Tailor-Made SpecificationsThe starting point of the analysis is driven mostly by empirical considerations. The traditional approaches discussed previously explain a fraction ofthe variations in CTA returns, but these factors need to be accompanied,and occasionally replaced, by alternative return-generating processes. Itwould be incorrect to assume that the strategies of CTA managers remainstatic over time; the managers adapt to changes in the financial and commodity markets as well as to specific market conditions that managed derivative portfolios such as CTAs are capable of exploiting. As a result, wewould expect the pricing model to change with evolving market conditions.Three families of factors can be used for the construction of empiricallyvalid models. The first candidates are the ones we used in the previous subsections. Some of them, and especially the dividend factor for equation 6.1and the squared market return for equation 6.2, should not necessarily bethrown out of the empirical model. We thus define variables SMB, HML,and HDMZD as in equation 6.1 and variables RUS, RUS2, and RUS3 corresponding to the Russell 3000 index to the power of 1, 2, and 3 respectively.The second candidates are financial or commodity indices that havebeen used previously in the mutual or hedge funds performance measurement literature. Among the large set of potential candidates, we haveselected: the return on the Goldman Sachs Commodity Index (GSCI), previously used by Capocci and Hübner (2004); the return on Moody’s Commodity Index (MCOM); the U.S. Moody’s Baa Corporate Bond Yield toproxy for the default risk premium (DEF) as well as the monthly change onthis yield (∆DEF); the U.S. 10-year/6-month Interest Rate Swap Rate toproxy for the maturity risk premium (MAT) as well as its monthly change(∆MAT); and finally the monthly change in the U.S. dollar/Swiss francexchange rate to proxy for the currency risk premium (FX). These dataseries were extracted from the JCFQuant database.
The Performance of CTAs in Changing Market Conditions
119
Finally, we use the option strategy factor proposed by Agarwal andNaik (2002) and Liang (2003) to capture the optionality component ofCTA returns. We construct the series of returns on the one-month ATM callwritten on the Russell 3000 index (ATMC) for this purpose.For each subperiod, we select the set of variables that provides the highest information content for the regressions. We use the same sets of variables for the Systematic, Finance/Metals, Diversified, and Global CTAindices, implying that the results do not strictly respect the minimization ofthe Akaike Information criterion. Table 6.6 presents the differentiatedmodel results for these indices.The results are consistent across the different indices, both in terms ofsign and magnitude of the coefficients, but they vary considerably over thedifferent subperiods. The results over the entire period show a markedincrease in the adjusted R-squared when compared to the two previousmodel specifications. The explanatory power of the variables is, however,still relatively limited when we consider the entire period, with R-squaredranging from 12.2 percent for the CTA index up to only 19.4 percent forthe Financial and Metals index. The square of the