or negative. However, it is interesting to note that theDiscretionary Sub Index in Table 19.2 has a negative correlation with theS&P 500 but a high positive correlation with the MSCI Global.Most historical returns of the various CTA strategies (with the exception of Stock Index Sub) are higher than the benchmark group. Correspondingly, the standard deviations are mostly higher than the benchmarkgroup (but comparable with equity indices with an absolute difference inthe order of less than 7 percent).All CTA strategies have skewness greater than 1 (with the exception ofthe Stock Index Sub Index strategy, which has negative skewness). Further,all CTA strategies have positive excess kurtosis (between 0.77 and 18.61).
2We split the sample into deciles to study the relationships of the subsamples using the
Pearson correlation coefficient. It is well known that the correlation is much higher forhedge funds among themselves and with equity benchmarks during crisis than in normaltimes. It is also known that the better-performing hedge funds have higher correlationswith equity indices. We acknowledge that there are other methods, such as Copula-basedmethods, that will give a more complete picture of the associations among several assets.
342
279279279159279
Universe EWS&P 500MSCI GlobalLehman GlobalLehman US Agg
279279279159279
Sample Size
1−0.03−0.050.230.06
Universe Index
Universe IndexS&P 500MSCI GlobalLehman GlobalLehman US Agg
Correlation
Universe IndexS&P 500MSCI GlobalLehman GlobalLehman US Agg
Sample Size
1.42%0.85%0.72%0.63%0.11%
Mean
10.840.100.23
S&P 500
1.19%0.85%0.72%0.63%0.11%
Mean4.91%4.60%4.37%1.57%1.78%
DD by MARa1.19−0.59−0.510.190.60
Skewness
10.73
5.19%4.52%4.31%1.44%1.78%
Std. Dev.
5.38%4.60%4.37%1.57%1.78%
DD by MAR
Universe Index EW
10.200.20
1.62−0.59−0.510.190.60
Skewness
1
MSCI GlobalLehman Global Lehman US Agg
4.76%4.52%4.31%1.44%1.78%
Std. Dev.
Universe Index
4.812.161.11−0.095.23
Kurtosis
3.442.161.11−0.095.23
Kurtosis
0.850.500.421.27−0.03
Sharpe
0.750.500.421.27−0.03
Sharpe
Summary Statistics and Risk-Adjusted Measures for CTA Indices, S&P 500, MSCI Global, Lehman Global,and Lehman U.S. Aggregate (Various Sample Periods)
TABLE 19.2
3.112.011.784.990.73
Sortino
2.812.011.784.990.73
Sortino
343
Currency SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Correlation
Currency SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Universe EWS&P 500MSCI GlobalGlobalLehman US Agg
Correlation
Mean
Sample Size
10.030.030.090.10
Currency Sub
10.73
3.55%4.37%4.34%1.44%1.08%
Std. Dev.3.64%4.41%4.33%1.57%1.08%
DD by MAR
Currency Subindex
10.200.20
1.53−0.44−0.390.19−0.27
Skewness
1
4.720.450.25−0.090.05
Kurtosis
10.860.100.1810.200.14
10.73
1
S&P 500 MSCI Global Lehman Global Lehman US Agg
0.81%0.65%0.27%0.63%0.09%
10.840.100.23
159159159159159
Universe Index EW (continued)S&P 500 MSCI Global Lehman Global Lehman US Agg
1−0.11−0.130.200.10
Universe EW
TABLE 19.2 (continued)
0.640.350.041.27−0.13
Sharpe
2.581.550.494.990.93
Sortino
344
Discretionary SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Diversified SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Correlation
Diversified SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Mean
Sample Size1.44%0.75%0.48%0.63%0.06%
10.840.100.14
195195195159195
4.06%4.61%4.45%1.44%1.18%
Std. Dev.4.17%4.68%4.48%1.57%1.18%
DD by MAR
Diversified Sub Index
1.28−0.83−0.530.19−0.24
Skewness4.452.761.18−0.090.03
Kurtosis
10.73
3.23%4.61%4.45%1.44%1.18%
Std. Dev.
3.54%4.68%4.48%1.57%1.18%
DD by MAR
Discretionary Sub Index
10.200.05
3.28−0.83−0.530.19−0.24
Skewness
1
18.612.761.18−0.090.03
Kurtosis
S&P 500 MSCI Global Lehman Global Lehman US Agg
0.97%0.75%0.48%0.63%0.06%
Mean
1−0.02−0.030.230.18
Diversified Sub
195195195159195
Sample Size
TABLE 19.2 (continued)
1.480.410.211.27−0.21
Sharpe
0.690.410.211.27−0.21
Sharpe
5.101.711.044.990.54
Sortino
2.681.711.044.990.54
Sortino
345
Stock Index SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Correlation
Stock Index SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Mean
Sample Size
1.00−0.11−0.11−0.04−0.04
Stock Index Sub
1.000.73
3.00%4.63%4.25%1.41%1.09%
Std. Dev.3.02%4.68%4.47%1.50%1.09%
DD by MAR
Stock Index Sub Index
1.000.200.05
Kurtosis1.090.190.350.210.18
Skewness−0.44−0.55−0.560.30−0.21
1.00
1.000.94−0.010.041.000.02−0.04
1.000.68
1.00
S&P 500 MSCI Global Lehman Global Lehman US Agg
0.31%0.65%0.29%0.52%0.05%
1.00−0.130.080.22
111111111111111
Discretionary Sub Index (continued)S&P 500 MSCI Global Lehman Global Lehman US Agg
1.00−0.170.840.100.14
Discretionary Sub
(continued)
Discretionary SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Correlation
TABLE 19.2
0.170.320.060.99−0.27
Sharpe
1.071.430.554.220.44
Sortino
346
135135135135135
Trend FollowerS&P 500MSCI GlobalLehman GlobalLehman US Agg
Systematic SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Mean
Sample Size1.27%0.84%0.74%0.63%0.11%
1.000.900.000.06
243243243159243
3.16%4.27%4.06%1.39%1.07%
Std. Dev.3.22%4.31%4.07%1.49%1.07%
DD by MAR
Systematic Subindex
0.37−0.56−0.560.19−0.26
Skewness0.77−0.650.430.080.10
Kurtosis
1.000.71
6.41%4.48%4.31%1.44%1.33%
Std. Dev.
6.54%4.56%4.37%1.57%1.33%
DD by MAR
Trend Follower
1.000.080.01
1.05−0.74−0.510.19−0.16
Skewness
1.00
2.422.591.31−0.090.42
Kurtosis
S&P 500 MSCI Global Lehman Global Lehman US Agg
0.63%0.62%0.33%0.55%0.06%
Mean
1.00−0.11−0.060.310.31
Correlation Systematic Sub
Systematic SubS&P 500MSCI GlobalLehman GlobalLehman US Agg
Sample Size
TABLE 19.2 (continued)
0.550.500.441.25−0.07
Sharpe
0.510.340.111.08−0.23
Sharpe
2.092.041.854.910.89
Sortino
2.211.510.744.490.59
Sortino
347
Futures FundS&P 500MSCI GlobalLehman GlobalLehman US Agg
Correlation
Futures FundS&P 500MSCI GlobalLehman GlobalLehman US Agg
Trend FollowerS&P 500MSCI GlobalLehman GlobalLehman US Agg
Correlation
Mean
Sample Size
1.00−0.01−0.01−0.180.06
Futures Fund
1.000.73
4.43%4.52%4.31%1.44%1.78%
Std. Dev.4.54%4.60%4.37%1.57%1.78%
DD by MAR
Futures Fund Index
1.000.200.16
0.78−0.59−0.510.190.60
Skewness
1.00
2.392.161.11−0.095.23
Kurtosis
1.000.840.100.231.000.200.20
1.000.73
1.00
S&P 500 MSCI Global Lehman Global Lehman US Agg
0.93%0.85%0.72%0.63%0.11%
1.000.830.100.21
279279279159279
Trend Follower (continued)S&P 500 MSCI Global Lehman Global Lehman US Agg
1.00−0.04−0.070.240.17
Trend Follower
TABLE 19.2 (continued)
0.630.500.421.27−0.03
Sharpe
2.472.011.784.990.73
Sortino
3484.73%4.52%4.31%1.44%1.78%
Std. Dev.4.82%4.60%4.37%1.57%1.78%
DD by MAR1.10−0.59−0.510.190.60
Skewness2.932.161.11−0.095.23
Kurtosis
1.00−0.01−0.030.240.071.000.840.100.231.000.200.201.000.73
1.00
Futures Fund EW S&P 500 MSCI Global Lehman Global Lehman US Agg
0.93%0.85%0.72%0.63%0.11%
Mean
Futures Fund EW
0.540.500.421.27−0.03
Sharpe
2.142.011.784.990.73
Sortino
(in our case, the MAR is taken as 0 percent).
a DD by MAR measures the volatility of monthly returns below the minimal acceptable return (MAR) as established by the investor
FuturesFund EWS&P 500MSCI GlobalLehman GlobalLehman US Agg
Correlation
279279279159279
Sample Size
(continued)
Futures Fund EWS&P 500MSCI GlobalLehman GlobalLehman US Agg
TABLE 19.2
CTA Strategies for Returns-Enhancing Diversification
349
The Sharpe and Sortino ratios in most cases were higher for the fullsample period, suggesting that the return per unit risk is almost alwayshigher than the benchmark group.In Table 19.3, we take a closer look at the correlation coefficients atdifferent deciles. The ranking of the deciles is in accordance to the performance ofS&P 500 or MSCI Global. In other words, what we are attempting to do is to seehow correlated the strategies are with S&P at different times, the up markets (bullish period) and the down markets (bearish period) and the timesin between. We also have computed the numbers for the up period as wellas the down period.
ANALYSIS OF THE FINDINGSOur results show that all the CTA Indices and subindices generally havenegative correlation coefficients for the first decile with the S&P 500 Index.This means that these CTA strategies have negative association with theS&P 500 during the worst periods of the down markets. During the periods that the S&P 500 was doing extremely badly, the CTA strategies weredoing much better. In other words, these CTA strategies enhanced portfolioreturns during the worst periods of the down market (when the S&P wasexperiencing negative returns). Thus, inclusion of CTA strategies in equityportfolios would not only reduce portfolio volatility (as good diversifiers)but would also enhance the portfolio returns when times are “bad.”The results are almost similar with MSCI Global. However, 3 out of 10strategies exhibited positive correlation coefficients. The highest correlationcoefficient was only 0.2, indicating that these 3 strategies were still verygood diversifiers.Our results are consistent with previous findings that returns from CTAstrategies are less correlated with equity market indices during down markets than hedge fund strategies. One possible explanation is that CTAs,unlike hedge funds, are exposed to lower liquidity risk in down markets andtherefore do not suffer any severe “liquidity” squeeze.Table 19.4 presents the deciles analysis and points to the usefulness of theFutures Fund Index Strategy as a returns enhancing diversifier. For the firstdecile of both the S&P 500 and MSCI Global indices, the returns of theFutures Fund Index were both positive. This means that portfolio returnswould be enhanced in the “bad” period if a Futures Fund Index was included.We examine the relative advantage of including different percentages ofthe CTA Futures Index in an equity portfolio (using the MSCI Global) inTable 19.5. The results suggest that several combinations will provide positive absolute returns. For example, a combination of 60/40 of CTA FuturesIndex/MSCI Global had the highest return, of 10.22 percent. However, thiscombination did not provide the least number of negative returns. If one
350
1st Decile2nd Decile3rd Decile4th Decile5th Decile6th Decile7th Decile8th Decile9th Decile10th DecileDown HalfUp HalfOverall
TABLE 19.3
UniverseIndexEW
−0.21−0.250.23−0.32−0.15−0.230.070.02−0.140.04−0.260.11−0.11
UniverseIndex
−0.21−0.120.22−0.34−0.22−0.23−0.20−0.27−0.08−0.02−0.140.10−0.03
−0.05−0.04−0.010.35−0.520.07−0.020.200.140.600.260.080.03
−0.030.110.25−0.31−0.54−0.17−0.19−0.20−0.180.40−0.190.12−0.020.27−0.01−0.340.03−0.150.20−0.310.250.18−0.48−0.510.06−0.17
−0.30−0.27−0.57−0.35−0.35−0.36−0.330.35−0.240.33−0.110.02−0.11
−0.500.390.160.02−0.480.290.330.410.21−0.19−0.18−0.07−0.11
−0.170.100.18−0.06−0.41−0.24−0.21−0.32−0.410.08−0.150.12−0.04
Currency Diversified Discretionary Stock Index SystematicTrendSubindex SubindexSubindexSubindex Subindex Follower
Correlation with S&P
Sample Correlation Coefficients for CTA Indices with S&P and MSCI Global
−0.15−0.140.02−0.31−0.21−0.26−0.13−0.21−0.140.02−0.100.130.01
FuturesFundIndex
−0.15−0.140.18−0.37−0.29−0.25−0.25−0.26−0.140.00−0.120.12−0.01
FuturesFundEW
351
1st Decile2nd Decile3rd Decile4th Decile5th Decile6th Decile7th Decile8th Decile9th Decile10th DecileDown HalfUp HalfOverall
TABLE 19.3
UniverseIndexEW
−0.540.20−0.170.02−0.300.13−0.040.300.300.15−0.230.12−0.13
UniverseIndex
−0.230.11−0.08−0.01−0.340.20−0.090.310.390.25−0.180.10−0.05
(continued)
0.140.45−0.39−0.01−0.10−0.040.010.13−0.040.320.040.020.03
−0.09−0.05−0.290.31−0.020.18−0.020.300.150.28−0.14−0.01−0.03
−0.670.40−0.430.20−0.280.030.20−0.06−0.100.37−0.260.100.84
−0.51−0.28−0.54−0.330.310.000.240.44−0.37−0.06−0.060.02−0.110.20−0.070.100.200.40−0.19−0.07−0.36−0.19−0.44−0.30−0.26−0.06
−0.280.060.150.17−0.310.15−0.250.25−0.050.08−0.230.07−0.07
Currency Diversified Discretionary Stock Index Systematic TrendSubindex SubindexSubindexSubindexSubindex Follower
Correlation with MSCI Global
−0.130.100.000.13−0.340.21−0.010.310.380.26−0.200.13−0.01
FuturesFundIndex
0.15−0.440.600.10−0.210.38−0.050.51−0.37−0.54−0.180.12−0.03
FuturesFundEW
352
MeanStd. Dev.DD byMAR
FundIndexvs.S&P 500
4.26%
2.08%3.69%
28
Skewness−1.44Kurtosis3.53Sharpe2.00Sortino6.35Correlation
Sample Size
Futures
FuturesFundIndex28
FuturesFundIndex
−2.709.00−5.22−7.22−0.15
8.63%−0.831.57−0.59−1.60
3.60%−0.63−0.67−15.76−9.69−0.14
3.44%
−3.32%0.64%
28
S&P500
10–20%
−7.74% −0.43%3.53% 3.58%
28
S&P500
0–10%
28
S&P500
0.963.700.180.89
5.49%
0.12−0.99−15.82−10.440.02
1.92%
0.54% −1.84%5.46% 0.39%
28
FuturesFundIndex
20–30%
28
S&P500
1.070.701.474.97
4.84%
0.17−0.86−7.13−9.95−0.31
0.69%
1.90% −0.59%4.43% 0.34%
28
FuturesFundIndex
30–40%
0.58−0.170.472.08
3.15%
0.57%3.09%
27
FuturesFundIndex
−0.49−0.906.3011.11−0.21
0.70%
0.63%0.29%
27
S&P500
40–50%
Summary Statistics, Correlation Coefficients, and Risk-Adjusted Measures for Futures Fund Index with S&Pand MSCI Global
TABLE 19.4
353
Sample Size
MeanStd. Dev.DD byMAR
Futures
FundIndexvs.S&P 5001.54%
3.79%0.00−1.3417.1012.54−0.26
1.48%0.30%
28
S&P500
0.13%3.78%
28
FuturesFundIndex
50–60%
Skewness0.03Kurtosis0.41Sharpe−0.06Sortino0.18Correlation
(continued)
TABLE 19.4
0.71−0.100.672.73
3.10%
0.72%3.01%
28
FuturesFundIndex
0.49−0.8824.2313.43−0.13
2.64%
2.57%0.41%
28
S&P500
60–70%
0.620.770.060.56
4.38%
0.29%4.37%
28
FuturesFundIndex
−0.05−1.2163.1814.55−0.21
3.87%
3.79%0.25%
28
S&P500
70–80%
1.714.181.013.58
5.89%
1.75%5.61%
28
FuturesFundIndex
−0.16−1.3041.4815.71−0.14
5.32%
5.20%0.57%
28
S&P500
80–90%
0.43−0.491.334.51
6.37%
2.29%5.93%
28
FuturesFundIndex
1.050.2624.2318.430.02
8.63%
8.27%1.88%
28
S&P500
90–100%
354
Sample Size
MeanStd. Dev.DD byMAR
Skewness−0.12Kurtosis−0.33Sharpe3.17Sortino8.69Correlation
Futures
FundIndexvs.MSCI
Global
−1.663.01−6.17−7.44−0.130.922.890.993.53
5.67%
8.25%
3.79%
281.67%5.41%
28
FuturesFundIndex
−0.54−0.95−15.24−9.660.10
3.49%
−3.36%0.67%
28
MSCIGlobal
10–20%
2.44% −7.57%2.86% 2.94%
28
MSCIGlobal
0–10%
FuturesFundIndex
(continued)
TABLE 19.4
−0.430.06−0.53−1.42
3.69%
−0.38%3.67%
28
FuturesFundIndex
−0.06−0.61−21.49−10.530.00
1.92%
−1.86%0.29%
28
MSCIGlobal
20–30%
1.033.100.060.52
4.78%
0.31%4.77%
28
FuturesFundIndex
−0.47−0.79−6.71−9.790.13
0.69%
−0.58%0.36%
28
MSCIGlobal
30–40%
−0.250.970.241.18
4.26%
0.50%4.23%
27