3.38)
1.85
0.44
Deutschemark
184.5(1.64)
0.0088(1.09)
0.0121*(7.94)
0.0019(1.01)
−0.0019(−1.57)
4.06* 0.45
Eurodollar
35.7(1.60)
0.0010*(3.69)
0.0004*(11.61)
−0.0002*(−3.88)
−0.0001(−0.24)
0.38
0.69
Gold
74.7(0.71)
0.0234*(3.60)
0.0154*(7.97)
−0.0010(−0.77)
−0.0003(−0.29)
2.07
0.63
Livehogs
290.0(1.04)
0.3929*(3.55)
0.2272*(5.74)
0.0081(0.29)
−0.0306*(−3.05)
1.10
0.30
Naturalgas
120.6(0.42)
0.1115*(2.76)
0.1399*(8.94)
0.0256*(2.51)
0.0036(0.26)
0.52
0.47
S&P500
−657.7*(−3.61)
0.0268*(3.34)
0.0099*(10.19)
−0.0008(−0.45)
0.0035*(3.79)
1.03
0.53
Soybeans
−121.2(−0.44)
0.0140(0.71)
0.0423*(9.94)
−0.0132(−1.61)
−0.0003(−0.09)
1.05
0.57
Treasurybonds
83.8(0.78)
0.0126*(4.75)
0.0018*(12.96)
−0.0006(−0.39)
−0.0006(−1.93)
2.16
0.69
FuturesMarket
F-StatisticforDailyAdj.EffectsR2
MMA = managed money accounts, which are defined as large hedge funds and CTAs.The figures in parentheses are t-statistics. The F-statistic tests the null hypothesisthat parameters for the day-of-the-week dummy variables jointly equal zero.*Statistically significant at the 5 percent level.
164
RISK AND MANAGED FUTURES INVESTING
effects are observed only for the deutsche mark futures market. The averageadjusted R2 across all 13 markets is 0.52, indicating a reasonable fit of themodels, particularly in light of the relatively small sample size. The estimatedcoefficient for MMA trading volume is significantly positive at the 5 percentlevel in nine markets, with the remaining four markets having insignificantcoefficients (coffee, cotton, deutsche mark, and soybeans). All of the estimated coefficients for the rest of market volume are significant and positiveat the 5 percent level. Therefore, as expected, a positive relationship is exhibited between trading volume and price variability, regardless of the tradertype (MMA or all other). Four of the estimated coefficients for MMA openinterest are significantly negative (coffee, corn, crude oil, and eurodollar),while one is significantly positive (natural gas). For the rest of market openinterest, coefficients are negative and significant in five markets (coffee, copper, corn, crude oil, and hogs) and significantly positive in one market (S&P500). As mentioned previously, the mixed results for open interest are notsurprising due to the relatively short time period studied.Previous studies (e.g., Chang, Pinegar, and Schachter 1997) estimatevolatility effects of different trader types by comparing the relative size ofthe parameter estimates associated with the traders. For example, estimatesof b2 and b4 from regression equation 8.1 could be compared to determinethe volatility effects of MMAs and all other traders. However, this comparison can be misleading if the means of the respective independent variables are not of similar magnitudes. A better approach is to comparevolatility elasticities evaluated at the means of the independent variables.Estimates for the volatility elasticity of volume and open interest arereported in Table 8.6. The volatility elasticity of MMA volume ranges from−0.02 to 0.14, with a cross-sectional average of 0.09. This implies, on average, that a 1 percent increase in MMA trading volume leads to about a onetenth of 1 percent increase in futures price volatility. The volatility elasticityof all other volume ranges from 0.54 to 1.19, with an overall average of0.86. This estimate means that a 1 percent increase in all other market volume (besides MMA volume) leads to slightly less than a 1 percent increasein futures price volatility. Therefore, on a percentage basis, increases inMMA trading volume lead to much smaller increases in volatility than doincreases in all other market volume. Finally, it is interesting to note thatopen interest elasticities for MMAs average −0.10, indicating that MMAtrading contributes positively to market depth and liquidity.
Explaining the Volume and Volatility RelationshipThe results presented in the previous section provide strong evidence of apositive relationship between MMA trading volume and futures price
165
The Effect of Large Hedge Fund and CTA Trading on Futures Market Volatility
TABLE 8.6
Estimates of the Volatility Elasticity of Volume and Open Interestfor 13 Futures Markets, April 4, 1994–October 6, 1994.FuturesMarket
MMA NetVolume
Rest ofNearbyVolume
MMA NetOpen Interest
Rest ofNearbyOpen Interest
CoffeeCopperCornCottonCrude oilDeutsche markEurodollarGoldLive hogsNatural gasS&P 500SoybeansTreasury bonds
−0.020.080.080.030.080.040.130.120.100.080.110.030.14
1.330.760.630.601.191.050.980.820.540.691.221.191.11
−0.43−0.02−0.220.06−0.260.07−0.59−0.040.070.15−0.07−0.12−0.01
−1.17−0.40−0.55−0.02−0.49−0.31−0.06−0.04−0.110.031.00−0.02−0.33
MMA = managed money accounts, which are defined as large hedge funds and CTAs.
volatility. However, on its own, this result is not sufficient to conclude thatMMA trading is beneficial or harmful to economic welfare. A positive relationship between MMA trading volume and market volatility is consistentwith either a private information hypothesis (e.g., Clark 1973), where theinformation-driven trading of MMAs tends to move prices closer toequilibrium values, or a noise trader hypothesis (e.g., De Long, Schleifer,Summers, and Waldman 1990), where MMA trading is based on “noise” suchas trend-chasing or market sentiment and tends to move prices further fromequilibrium values. Weiner (2002, p. 395) states the issue in succinct terms:. . . the concern over whether these funds have a positive or negativeeffect on market functioning comes down to whether the funds can becharacterized as “smart money”—undertaking extensive analysis onpossible changes in future industry, macroeconomic, political, and soforth conditions and their likely consequences for prices—or “dumbmoney”—noise traders chasing trends or herding sheep, buying andselling because others are doing so.Following French and Roll (1986), three tests are used in this study in anattempt to distinguish between these two hypotheses.
166
RISK AND MANAGED FUTURES INVESTING
Variance Ratio Tests Under market efficiency, price changes follow a random walk. Therefore, return variance for a long holding period is equalto the sum of the daily return variances. However, under the noise traderhypothesis, the cumulated daily return variances are expected to be greaterthan the long holding period variance. This assumes that, over a longerholding period, the market corrects errors associated with noise trading.The daily variances include the effects of noise trading, while the longerholding period variance presumably does not. Therefore, the presence ofnoise trading can be identified through an analysis of return variance ratiosover different holding periods.Variance ratios are computed following the methodology of Campbell,Lo, and MacKinlay (1997). The q-day variance ratio isVRq =
σ q2
σ 12 ⋅ q
(8.3)
where s 2q = q-day holding period return variances 21 = daily holding period return variance.Note that overlapping q-period returns are used to estimate s 2q and one-dayreturns are used to estimate s 21 . The use of overlapping returns increasesthe efficiency of the variance ratio estimator.7 For a given commodity, thestandardized test statistic to test the null hypothesis that the variance ratioequals 1 is
ψq =
 2(2q − 1)(q − 1) nq (VRq − 1)3q
−1 / 2
(8.4)
where nq + 1 = number of original daily price observations.Campbell, Lo, and MacKinlay (1997) show that yq approximately followsa standard normal distribution in large samples. Variance ratios and associated test statistics are computed for six different holding periods: for q =2, 3, 5, 10, 15, and 20 days.
7The formulas for the variance estimators are found on pp. 52–53 in Campbell, Lo,and MacKinlay (1997). One technical issue is how to handle the computation offutures returns when nearby futures price series roll from the “old” nearby contractto the “new” nearby contract. To resolve this issue, returns for the first active dayof the “new” nearby contract are computed using the previous day’s price for the“new” contract, rather than the previous day’s price from the “old” contract.
The Effect of Large Hedge Fund and CTA Trading on Futures Market Volatility
167
An important statistical issue arises when interpreting the varianceratio test results. Specifically, what constitutes evidence against the nullhypothesis? If variance ratios across holding periods are independent, thenrejection of the null hypothesis of unity for one holding period is sufficientto reject the joint null hypothesis that variance ratios equal unity across allholding periods. Because of overlapping holding periods, it is unlikely thatthe independence assumption is valid. As a result, individual hypothesistests likely have a higher probability of Type I error than the specified significance level.To assess the joint significance of variance ratios correctly across holding periods, a joint test statistic is needed. The Bonferroni inequality provides a simple means for testing the joint null hypothesis that test statisticsare not different from unity. The inequality provides an upper bound forrejection of the joint null hypothesis when the test statistics are correlated.Intuitively, the Bonferroni test simple scales up the p-value of the most significant test statistic to account for the dependency. Miller (1966) providesa full explanation of the Bonferroni inequality and resulting joint testingprocedure.To implement the Bonferroni joint test for a given commodity, wedefine the maximum standardized test statistic as
{ }
ψ max = max ψ qq
(8.5)
where yq = standardized test statistic for the q-day holding period.The joint null hypothesis is rejected at the significance level a if y max isgreater than the critical value defined by1 − φ(ψ) =
α /c2
(8.6)
where f(.) = standard normal cumulative distribution functionc = number of restrictions testedBecause variance ratios are estimated for six holding periods, a jointhypothesis test for a given futures market imposes six restrictions. As aresult, the critical value for the Bonferroni joint test at the 5 percent levelis 2.63.
168
RISK AND MANAGED FUTURES INVESTING
Table 8.7 presents variance ratios and standardized test statistics foreach of the 13 markets. In only 2 variance ratios out of 78 is the nullhypothesis of unity rejected. The two significant ratios suggest the possibility of a short-run noise trading component in the gold market. The significant negative test statistics for the two-day and three-day holding periodsindicate that two- and three-day holding period return variances are lessthan two and three times the estimated daily variance. This fact implies thedaily return variances are larger due to the noise component. However, thisnoise component is traded away in the long run, as shown by the insignificant test statistics for the longer holding periods. The gold market also isthe only market out of 13 where the Bonferroni joint test statistic is significant. This rejection rate (0.077) is only slightly greater than would beexpected based on random chance and a 5 percent significance level. Overall, the variance ratio tests for this sample period do not support the noisetrader hypothesis, but instead support the private information hypothesisfor MMA trading.Because the sample period considered in the previous tests is somewhatlimited, a reasonable question is whether the results are sensitive to different time periods and longer sample periods. The first alternative sampleperiod considered is the previous six-month period from October 1, 1993,through March 31, 1994. As shown in Table 8.8, only 6 of 78 varianceratios are significantly different from unity for this sample period. The Bonferroni joint test statistic is significant only for the eurodollar futures market, which again is only slightly greater than what would be expected basedon random chance. The second alternative sample period considered is substantially longer and includes the previous six-and-one-quarter-year periodfrom January 4, 1988, through March 31, 1994. As shown in Table 8.9,only 17 out of 78 variance ratios are significantly different from unity.However, the Bonferroni joint test statistic is significant for 4 of the 13 markets (cotton, crude oil, Eurodollar, and S&P 500), more than would beexpected based on random chance.The last finding indicates that variance ratio test results may be sensitive to the use of a relatively small sample size. Nonetheless, the varianceratio results for alternative sample periods do not provide convincing evidence that the conclusion reached on the basis of the original sample periodis invalid. That is, variance ratio tests do not indicate substantial deviationsfrom market efficiency that would be associated with noise trading on thepart of MMAs. Instead, the results are more consistent with the hypothesisthat MMAs base their trading on valuable private information.Positive Feedback Trading Tests Buying after price increases and sellingafter price declines characterizes positive feedback trading. The existence of
169
The Effect of Large Hedge Fund and CTA Trading on Futures Market Volatility
TABLE 8.7 Variance Ratio Test Results for 13 Futures Markets, April 4,1994–October 6, 1994Holding Period Lengths
2 Day
3 Day
5 Day
10 Day
15 Day
BonferroniJoint Test20 Day Statistic
Coffee
1.08(0.86)
1.12(0.95)
1.19(1.00)
1.25(0.84)
1.49(1.32)
1.53(1.21)
1.21
Copper
0.920.91(−0.86) (−0.69)
0.92(−0.42)
0.96(−0.15)
0.97(−0.07)
1.00(0.00)
0.86
Corn
0.97(−0.30)
1.07(0.56)
0.96(−0.19)
0.78(−0.72)
0.98(−0.06)
1.00(0.01)
0.72
Cotton
1.08(0.91)
1.06(0.45)
1.10(0.52)
0.99(−0.03)
0.98(−0.06)
0.86(−0.32)
0.91
Crude oil
1.09(1.00)
1.09(0.68)
1.02(0.11)
1.26(0.89)
1.35(0.93)
1.58(1.33)
1.33
Deutschemark
1.02(0.17)
1.04(0.30)
1.09(0.49)
1.01(0.04)
0.78(−0.60)
0.73(−0.61)
0.61
Eurodollar
1.12(1.39)
1.19(1.43)
1.16(0.81)
0.78(−0.75)
0.74(−0.69)
0.71(−0.67)
1.43
Gold
0.72*0.71*(−3.25) (−2.16)
0.70(−1.58)
0.75(−0.86)
0.65(−0.94)
0.61(−0.90)
3.25*
Live hogs
1.030.35)
0.97(−0.21)
0.90(−0.54)
0.84(−0.54)
0.74(−0.69)
0.51(−1.11)
1.11
Natural gas
0.97(−0.29)
1.06(0.44)
1.24(1.24)
1.24(0.81)
1.18(0.49)
1.19(0.43)
1.24
Soybeans
1.03(0.31)
1.09(0.69)
0.96(−0.23)
0.82(−0.59)
0.99(−0.02)
0.98(−0.03)
0.69
S&P 500
0.840.93(−1.86) (−0.52)
0.86(−0.71)
0.74(−0.87)
0.75(−0.66)
0.73(−0.61)
1.86
Treasurybonds
0.880.86(−1.35) (−1.06)
0.77(−1.18)
0.52(−1.63)
0.49(−1.37)
0.48(−1.19)
1.63
FuturesMarket
The figures in parentheses are Z–statistics.*Statistically significant at the 5 percent level.
170
RISK AND MANAGED FUTURES INVESTING
TABLE 8.8 Variance Ratio Test Results for 13 Futures Markets, October 1,1993–March 31, 1994Holding Period Lengths
3 Day
5 Day
10 Day
15 Day
BonferroniJoint Test20 Day Statistic
Coffee
0.78*0.74(−2.46) (−1.95)
0.62(−1.94)
0.46(−1.79)
0.44(−1.49)
0.39(−1.39)
2.46
Copper
0.950.98(−0.57) (−0.14)
1.01(−0.05)
1.00(−0.01)
1.02(−0.04)
0.95(−0.12)
0.57
Corn
1.03(0.39)
0.97(−0.25)
0.92(−0.41)
1.05(0.16)
1.31(0.83)
1.74(1.68)
1.68
Cotton
1.07(0.76)
1.09(0.67)
1.14(0.71)
1.45(1.49)
1.65(1.72)
1.94*(2.13)
2.13
Crude oil
0.99(−0.11)
1.03(0.20)
1.03(0.17)
1.11(0.36)
1.21(0.56)
1.39(0.88
0.88
Deutschemark
0.97(−0.38)
1.03(0.20)
1.03(0.14)
0.87(−0.43)
0.93(−0.18)
0.95(−0.12)
0.43
Eurodollar
1.22*(2.51)
1.25(1.91)
1.43*(2.21)
1.85*(2.83)
2.41*(3.74)
3.02*(4.58)
4.58*
Gold
0.980.95(−0.22) (−0.35)
0.88(−0.60)
0.74(−0.87)
0.73(−0.72)
0.70(−0.68)
0.87
Livehogs
1.08(0.86)
1.10(0.76)
1.08(0.42)
1.11(0.38)
1.19(0.51)
1.47(1.07)
1.07
Naturalgas
1.04(0.40)
1.12(0.90)
1.13(0.67)
1.28(0.92)
1.38(1.01)
1.67(1.51)
1.51
Soybeans
1.06(0.66)
1.00(0.02)
0.95(−0.27)
1.03(0.11)
1.02(0.05)
1.03(0.08)
0.66
S&P 500
0.930.96(−0.82) (−0.28)
1.02(0.11)
0.87(−0.43)
0.76(−0.63)
0.71(−0.65)
0.82
Treasurybonds
1.04(0.47)
1.10(0.50)
1.09(0.30)
1.24(0.64)
1.44(0.99)
0.99
FuturesMarket
2 Day
1.02(0.15)
The figures in parentheses are Z-statistics.*Statistically significant at the 5 percent level.
The Effect of Large Hedge Fund and CTA Trading on Futures Market Volatility
171
TABLE 8.9
Variance Ratio Test Results for 13 Futures Markets, January 4,1988–March 31, 1994Holding Period Lengths
3 Day
5 Day
10 Day
15 Day
BonferroniJoint Test20 Day Statistic
Coffee
0.970.96(−1.35) (−1.07)
0.99(−0.23)
0.97(−0.34)
0.98(−0.15)
1.01(0.10)
1.35
Copper
1.03(1.22)
1.02(0.50)
1.00(0.01)
1.02(0.27)
1.00(0.03)
0.98(−0.15)
1.22
Corn
1.020.97(−0.66) (−0.87)
0.91(−1.71)
0.86(−1.66)
0.88(−1.13)
0.89(−0.87)
1.71
Cotton
1.10*(3.86)
1.11*(3.06)
1.12*(2.19)
1.18*(2.07)
1.27*(2.50)
1.34*(2.70)
3.86*
Crude oil
1.02(0.97)
1.01(0.39)
0.91(−1.62)
0.76*(−2.78)
0.77*(−2.12)
0.81(−1.53)
2.78*
Deutschemark
1.03(1.22)
1.01(0.29)
0.98(−0.41)
0.96(−0.44)
1.00(0.00)
1.03(0.22)
1.22
Eurodollar
1.07*(2.96)
1.06(1.64)
1.04(0.64)
1.10(1.22)
1.13(1.21)
1.20(1.58)
2.96*
Gold
0.970.95(−1.18) (−1.43)
0.91(−1.63)
0.90(−1.13)
0.92(−0.78)
0.91(−0.70)
1.63
Live hogs
1.03(1.10)
0.99(−0.14)
0.97(−0.51)
0.98(−0.26)
0.95(−0.43)
0.94(−0.49)
1.10
Natural gas
1.02(0.76)
0.99(−0.19)
1.01(0.11)
1.11(1.02)
1.24(1.82)
1.37*(2.39)
2.39
Soybeans
1.06*(2.20)
1.04(1.16)
1.04(0.64)
1.01(0.06)
1.00(−0.01)
0.98(−0.14)
2.20
S&P 500
0.90*0.94*(−2.21) (−2.58)
0.84*(−2.90)
0.72*(−3.24)
0.70*(−2.81)
0.70*(−2.38)
3.24*
Treasurybonds
1.02(0.92)
0.99(−0.16)
0.93(−0.88)
0.92(−0.76)
0.93(−53)
1.10
FuturesMarket
2 Day
1.04(1.10)
The figures in parentheses are Z-statistics.*Statistically significant at the 5 percent level.
172
RISK AND MANAGED FUTURES INVESTING
this type of trading may lead to decreases in market efficiency by creatingexcessive volatility. For instance, when new bullish fundamental information is received, and price increases to its new fundamental value throughrational trading, positive feedback traders continue to buy, driving pricepast its rational value. Following Kodres (1994) and Irwin and Yoshimaru(1999), positive feedback trading is identified for a given market by estimating this regression model:5
NETMMATVt = α1 + ∑ β i ∆pt − i + ε ti =1
(8.7)
where NETMMATVt = net trading volume of MMAs (number of long contracts minus number of short contracts) on day t∆pt − i = continuously compounded futures return on dayt−iet = standard normal error term.Based on Irwin and Yoshimaru’s results, five lagged price returns areincluded in the model for all markets. Note that NETMMATVt takes onpositive values when MMAs are net buyers of contracts, negative valueswhen MMAs are net sellers, and zero when no volume is recorded. Slopecoefficients in equation 8.7 can be thought of as the sensitivities of MMA“demand” to past price movements. Positive slope coefficients are evidenceof positive feedback trading by MMAs, whereas negative coefficients areevidence of negative feedback trading. The net feedback effect is given bythe sum of slope coefficients for each regression. The significance of feedback trading is determined by testing whether the sum of the estimatedslope coefficients (for lagged price returns) is greater than zero.Table 8.10 provides estimation results for equation 8.7. The sum ofslope coefficient estimates is positive in nine markets, close to zero in onemarket, and negative in three markets. Of the nine positive sums, t-statistics indicate six are significantly different from zero. Thus, statistically significant evidence of positive feedback trading among MMAs is found inabout half of the markets studied. The average adjusted R2 across all 13markets is 0.09, ranging from a high of 0.35 (cotton) to a low of −0.02 (coffee). Overall, this provides some evidence of positive feedback trading onthe part of MMAs. However, because positive feedback terms explain only9 percent of the variation in MMA trading volume, it can be concluded thatMMA trading decisions are influenced only in small part by past pricechanges. It is interesting to note the similarity of these results to Irwin andYoshimaru’s (1