RESEARCH OUTPUT AND FINDINGS
4.4 PERFORMANCE 1.1 Mean Equation
4.4.1.2 Decomposed Mean Equation
Important ARMA models (Schwert, 1989; Jiang and Chiang, 2000; and Chatrath et al., 1999) have helped to get expected and unexpected components of market volatility, trading activity and returns. In line with Schwert (1989), this study makes use of an ARMA model to decompose the mean equation variables into expected and unexpected components. Variables decomposed are net positions of hedgers and speculators, sentiment index and information variables. An extension of Equation 4.10.1 gives the decomposed mean equation as follows:
t
R =ϕ0 + ϕ Exp1 SI +t
ϕ
2UnexpSI +tϕ
3ExpNP
t +ϕ
4UnexpNP
t+
ϕ
5HPt-1 +ϕ
6ExpTbillyieldt+ϕ
7 UnexpTbillyieldt+ ϕ8ExpBAA-AAAt+ϕ9 UnexpBAA-AAAt
+ ϕ10ExpDivyieldt+ϕ11 UnexpDivyieldt+ ξt (4.10.2)
Similar to Thomakosi and Wang (2003) and Daigler and Chen (1999), autocorrelations (AC) and partial autocorrelations (PAC) are used in selecting an ARIMA specification85. The Akaike information criteria (AIC) provides a guide for the
appropriate lag order selection86. In line with Tam and Reinsel (1998), if autocorrelations appear to have a seasonal pattern87, SMA (Seasonal Moving Average) and SAR (Seasonal Autoregressive) are included in the ARMA model structure. Diagnostic tests using correlograms and Breusch-Godrey LM test88 help to assess the structure of the ARMA model (Sadorsky, 2003; Yang et al., 2001). Results for optimal lag selection (including seasonal variables), Q statistics and Breusch-Godrey LM test support an optimized model structure of the mean equation, without autocorrelation in variables. Ljung-Box Q test statistics and Breusch-Godfrey LM tests are again used, together with ARCH LM test, to check if the residuals from the mean equation are uncorrelated with
85 See Appendix 6.5.7 for more details.
86 R-squared values are also initially looked at, but, as expected, give too low values to be considered for
inferencing.
87 See Appendix 6.5.8 for estimating ARMA models (differencing and ARMA terms (including seasonal)) 88 See Appendix 6.5.10 for Breusch-Godfrey LM test.
133 past residuals89 (McKenzie and Holt, 2002). Results for these residuals tests support the series have white noise properties and can be found in Appendix 6.11 (Table 4.10.6). Full results of the decomposed mean equation are provided below in Table 4.10.3 and Table 4.10.490. Results are reported at 10% significance level.
Intercept NPt SIt HPt-1 Tbillyieldt BAA-AAA Divyieldt t
Exp Unexp. Exp Unexp. Exp Unexp. Exp Unexp. Exp Unexp.
Panel A : Hedger Minerals GC -9.68 -0.02 -0.02 0.19 -0.03 -5.90 4.24 1.46 0.90 0.50 -11.46 0.52 -5.36 -1.98 5.06 -3.95 1.88 SI -13.43 -0.11 -0.02 0.28 -0.05 -9.54 5.13 0.99 1.54 1.76 4.46 -1.51 -5.87 -2.23 6.52 -2.14 -3.97 3.89 HG -8.60 0.11 -0.01 0.21 0.14 3.88 27.37 -2.65 0.90 -0.13 -2.02 -18.71 -2.16 2.22 3.79 1.72 -3.83 PL 1.05 0.11 -0.04 0.15 0.16 -0.80 -4.18 3.22 -0.85 0.08 -18.55 1.00 2.52 8.00 CL -17.27 0.03 -0.02 0.35 0.00 33.02 16.84 -0.33 -1.37 -1.48 -104.97 13.18 -4.77 4.49 3.38 -2.50 2.30 HO -29.06 -0.30 0.11 0.55 0.07 -9.19 -23.91 -0.67 -0.07 -0.81 -37.45 6.21 -6.33 -2.71 4.65 /pto
This table shows the results for the decomposed mean equation for large hedgers. Rt is the futures return in
month t, in percent. NPt represents the net positions of large hedgers in month t. A net position is defined
as the long position less the short position of a trader type, in units of 1,000 contracts. SIt denotes the
Consensus index in month t. HPt-1 is the lagged own hedging pressure variable. Tbillyieldt, BAA-AAAt,
Divyieldt are the three information variables included in the model. All variables are differenced until they
are stationary. NPt, SIt, Tbillyieldt, BAA-AAAt, and Divyieldt are decomposed using ARMA model
specifications. Autocorrelations (AC) and partial autocorrelations (PAC) are used in selecting an ARIMA specification. The Akaike information criteria (AIC) is used to select the appropriate lag order. SMA (Seasonal Moving Average) and SAR (Seasonal Autoregressive) variables are included in the ARMA model if autocorrelations appear to have a seasonal pattern. Diagnostic tests using correlograms and Breusch- Godrey LM test are used to assess the structure of the ARMA model. Ljung-Box Q test statistics are again used to check if the residuals from the model are nearly white noise, i.e, no serial correlation left in the residuals. The numbers in italics are t-statistics relevant to the hypothesis that the relevant parameter is zero at 10% significance level. Estimated mean equation is
t
R =ϕ +0 ϕ Exp1 SIt+ϕ2UnexpSIt+ϕ3ExpNPt +ϕ4 UnexpNPt +ϕ 5 HPt-1+ 6
ϕ ExpTbill yield t+ϕ7 UnexpTbill yield t + ϕ8ExpBAA - AAA t+ϕ9 UnexpBAA -AAA t +
10
ϕ ExpDivyield t+ϕ11 UnexpDivyield t+
89 See Appendix 6.5.9 for Ljung-Box Q statistics specification, Appendix 6.5.12 for ARCH LM test. 90 Since, standard inference procedures do not apply to regressions that contain an integrated dependent
variable or integrated regressors (like in ARMA), stationary testing is also performed on the mean equations, and residuals were found stationary.
Table 4.10.3
134 Financials SP -9.39 -0.07 -0.02 0.24 0.02 -27.43 2.24 2.10 -0.97 -0.08 64.81 2.21 -4.06 -2.11 5.84 -3.28 2.56 ED -0.65 0.00 0.00 0.01 0.00 -0.26 -3.06 -0.18 0.05 0.01 -1.48 0.08 -3.43 3.46 -2.92 -2.02 US -3.54 0.00 -0.01 0.08 0.07 -0.93 -12.25 -0.46 -0.40 -0.17 -6.51 2.31 -2.46 2.53 3.97 Currencies BP -11.23 0.00 0.06 0.24 0.05 -1.07 -1.29 -1.68 0.16 -0.19 -14.51 5.87 -5.05 3.62 5.07 4.28 3.13 SF -5.58 -0.03 -0.06 0.14 0.05 -1.57 -3.81 -1.89 0.83 -0.10 -3.77 4.65 -2.52 -4.07 2.90 2.46 -2.37 CD -1.49 -0.02 -0.01 0.03 0.03 -0.07 2.78 -0.09 0.67 -0.14 -1.71 -1.30 -2.26 -2.45 2.07 4.69 -0.20 JY -7.50 -0.05 0.00 0.20 -0.02 -1.11 -4.91 3.51 0.93 0.32 10.86 -0.45 -4.37 -2.86 5.51 3.41 Agriculturals W -9.21 -0.58 0.01 0.08 -0.04 -7.33 -18.30 0.68 0.43 0.05 33.27 -0.69 -3.45 -6.38 -2.31 KW -4.44 2.85 0.12 0.11 -0.01 8.97 -21.86 -0.57 0.87 0.41 40.94 5.29 -1.74 5.00 2.18 MW -7.43 -2.09 0.50 0.14 0.00 -8.75 -12.24 -2.81 1.36 0.48 22.84 2.14 -2.77 -5.06 1.75 2.68 C -5.01 -0.09 0.00 0.08 0.16 -21.35 -14.05 -1.24 -1.14 -0.46 -22.90 -0.25 -1.73 -5.05 5.57 -4.93 -1.50 S 6.34 -0.19 -0.03 -0.15 -0.01 -13.84 0.85 -1.29 -2.02 -0.07 13.14 0.53 2.18 -7.89 -2.79 -5.05 BO -21.14 -0.10 0.00 0.45 -0.04 -7.92 -9.34 -1.10 -1.85 0.69 1.48 1.67 -10.09 -3.78 9.45 -1.74 -4.44 1.74 SM -10.32 -0.38 0.07 0.18 -0.03 -21.50 0.95 -0.97 1.28 0.32 -0.71 3.86 -4.79 -9.43 2.00 3.75 -1.71 -7.35 PB -24.31 2.04 1.99 0.63 0.22 1.77 -11.14 0.28 10.47 0.13 -44.02 4.67 -3.44 3.65 3.07 2.09 LH -11.86 -0.99 -0.25 0.25 -0.14 -4.74 -44.85 6.17 6.24 1.28 -27.08 7.85 -1.74 -5.04 -2.43 -1.85 2.24 1.94 LC -13.74 -0.10 -0.01 0.28 0.02 -10.23 -0.44 -1.30 0.94 -0.03 -6.26 4.99 -4.78 4.91 -2.84 1.80 FC -13.50 1.28 -0.25 0.28 -0.03 -2.20 4.31 0.67 -1.85 -0.18 9.73 -1.58 -6.98 1.93 6.69 -1.68 -1.97 SB -4.96 -0.13 0.03 0.08 0.02 -6.66 -5.77 1.97 1.70 1.55 58.68 9.39 -3.13 2.13 CC -8.52 -0.37 0.21 0.15 0.01 -24.73 -21.43 -4.54 3.82 0.17 -7.77 12.56 -1.65 -3.39 2.28 -3.14 -1.79 1.66 KC -33.64 -0.17 0.03 0.86 0.05 -14.48 14.51 -0.73 3.77 0.81 60.19 -10.59 -4.86 6.10 -2.32 CT -9.67 -0.58 0.04 0.22 -0.04 -19.07 1.85 -1.37 -1.35 0.29 43.11 10.08 -2.08 -6.68 2.27 -5.21 1.87 LB -65.83 -1.29 0.41 1.54 0.01 -0.28 -7.79 -4.81 -9.67 -1.05 23.29 1.74 -6.60 6.52 -1.70
135 Intercept NPt SIt HPt-1 Tbillyieldt BAA-AAAt Divyieldt
Exp Unexp. Exp Unexp. Exp Unexp. Exp Unexp. Exp Unexp.
Panel B : Speculator Minerals GC -11.05 0.00 0.00 0.22 -0.01 -5.19 2.57 1.12 0.50 0.45 -11.29 1.03 -3.72 3.86 -4.51 1.67 SI -12.36 0.00 0.04 0.32 -0.05 -7.70 5.88 1.32 1.42 1.83 -0.89 -1.27 -5.35 7.58 -1.87 -2.88 4.05 HG -6.47 -0.08 0.13 0.15 0.13 3.29 22.11 -3.33 1.59 -0.23 1.03 -18.39 -1.95 2.04 4.04 -3.91 PL -4.79 -0.02 -0.19 0.12 0.16 -3.08 -6.81 3.53 -1.09 0.12 -13.26 2.41 -1.83 -2.33 1.98 9.18 -2.27 CL -17.11 0.10 -0.25 0.33 0.02 28.49 16.71 0.96 -2.30 -1.37 -115.01 11.35 -4.49 -2.68 3.85 2.77 -2.91 1.96 HO -33.19 0.04 0.04 0.73 0.05 -0.93 -17.04 0.65 -0.79 -0.79 -32.03 4.67 -6.16 5.54 Financials SP -9.25 0.04 -0.06 0.25 0.03 -13.66 3.42 1.50 -0.33 -0.21 62.00 1.14 -3.95 6.11 -1.99 2.27 ED -0.68 0.00 0.00 0.01 0.00 -0.02 -3.05 -0.17 0.03 0.01 -1.52 0.10 -4.61 4.39 -2.84 -1.92 US -3.54 -0.01 0.01 0.08 0.07 -0.47 -11.91 -0.38 -0.54 -0.13 -6.76 1.68 -2.49 2.67 4.36 /pto This table shows the results for the decomposed mean equation for large speculators. Rt is the futures
return in month t, in percent. NPt represents the net positions of large speculators in month t. A net
position is defined as the long position less the short position of a trader type, in units of 1,000 contracts. SIt denotes the Consensus index in month t. HPt-1 is the lagged own hedging pressure variable. Tbillyieldt,
BAA-AAAt, Divyieldt are the three information variables included in the model. All variables are
differenced until they are stationary. NPt, SIt, Tbillyieldt, BAA-AAAt, and Divyieldtare decomposed using
ARMA model specifications. Autocorrelations (AC) and partial autocorrelations (PAC) are used in selecting an ARIMA specification. The Akaike information criteria (AIC) is used to select the appropriate lag order. SMA (Seasonal Moving Average) and SAR (Seasonal Autoregressive) variables are included in the ARMA model if autocorrelations appear to have a seasonal pattern. Diagnostic tests using correlograms and Breusch- Godrey LM test are used to assess the structure of the ARMA model. Ljung- Box Q test statistics are again used to check if the residuals from the model are nearly white noise, i.e, no serial correlation left in the residuals. The numbers in italics are t-statistics relevant to the hypothesis that the relevant parameter is zero at 10% significance level. Estimated mean equation is
t
R =ϕ0+ϕ1ExpSIt+ϕ2UnexpSIt+ϕ3ExpNPt +ϕ4UnexpNPt +ϕ5 HPt-1+ 6
ϕ ExpTbill yield t +ϕ7UnexpTbill yield t + ϕ8ExpBAA -AAA t+ϕ9 UnexpBAA -AAA t +
10
ϕ ExpDivyield t+ϕ11 UnexpDivyield t+ ξt
Table 4.10.4
136 Currencies BP -6.83 -0.05 0.01 0.15 0.05 -0.41 -1.77 -2.50 -0.35 -0.24 -7.05 6.12 -4.06 4.06 4.30 -1.94 3.02 SF -6.10 -0.07 -0.03 0.14 0.06 -1.49 -7.79 -2.40 0.14 0.30 -8.01 6.09 -3.35 3.23 4.19 -2.29 -1.91 2.11 CD -1.80 0.01 -0.01 0.04 0.03 -0.06 3.82 -0.05 0.70 -0.11 -1.42 -1.79 -2.35 2.31 6.01 -1.84 JY -10.34 0.06 0.05 0.26 0.00 -0.21 -13.25 3.94 1.29 0.48 12.59 1.04 -8.13 1.74 2.67 8.71 3.54 Agriculturals W -5.97 0.69 -0.16 0.12 -0.01 2.11 -24.50 -0.45 -0.79 0.15 49.33 -1.31 -2.26 2.47 -1.98 2.32 1.77 KW -3.72 -1.22 -0.05 0.09 -0.02 -1.01 -22.25 -1.55 -0.15 0.19 53.74 2.71 -2.41 1.96 MW -4.33 1.38 0.85 0.10 -0.01 0.90 -6.36 -1.96 1.59 0.38 35.06 1.52 1.81 C -10.49 0.00 0.02 0.19 0.26 -9.11 -19.64 -1.90 -1.56 -0.44 -22.84 -0.28 -3.63 3.34 9.33 -2.47 S 1.24 0.05 0.20 -0.03 -0.02 1.56 3.48 0.42 -3.45 0.39 29.70 1.07 5.29 BO -24.40 -0.43 -0.03 0.54 0.01 -4.80 -8.58 -1.47 -1.37 0.73 6.24 1.84 -11.30 11.85 -2.48 1.75 SM -8.64 0.05 0.19 0.20 -0.02 -5.20 -1.42 0.18 -2.35 0.37 -0.03 2.59 -3.71 2.77 4.06 PB -28.24 -0.83 -1.39 0.71 0.20 -0.42 -9.48 0.85 8.38 0.17 -40.02 2.19 -3.50 3.62 2.81 1.63 LH -21.40 -0.43 0.61 0.51 -0.09 6.63 -37.71 9.04 6.27 1.48 -38.22 9.77 -3.31 2.80 3.24 1.65 2.81 1.79 LC -15.03 0.02 0.00 0.31 0.02 -7.37 -1.31 -1.37 0.93 -0.01 -8.08 4.73 -5.83 6.07 -3.07 1.69 FC -12.61 0.34 0.61 0.26 -0.02 -1.18 -0.78 0.73 -1.50 -0.16 13.52 -2.18 -6.97 3.03 6.84 SB -10.79 -0.07 0.06 0.24 -0.01 3.11 -10.15 2.13 0.61 1.71 61.22 9.56 -3.29 3.97 2.52 CC -18.95 0.61 -0.17 0.43 0.02 -14.42 -29.00 -3.20 2.46 0.03 -11.67 17.52 -4.49 2.57 4.28 2.45 KC -27.28 0.79 0.27 0.68 0.03 -19.14 22.53 0.19 4.01 0.95 63.86 -12.39 -3.61 1.82 4.29 -3.06 CT -13.84 0.27 -0.12 0.32 -0.02 -7.98 -15.07 -3.14 -4.10 -0.33 42.60 11.37 -3.70 3.57 4.32 -2.24 1.67 LB -68.64 2.48 4.48 1.61 0.01 -0.05 -1.90 -4.43 -9.71 -1.02 14.61 0.57 -7.32 2.51 7.36 -1.86
137 Findings from Table 4.10.3 show that in 17 markets, expected components of net positions of hedgers are significantly related to the actual futures returns at 10% significance level. Importantly, 15 of these 17 markets are from the agricultural group, and exhibit a significant negative sign. Expected components of net positions are positive and significant only in feeder cattle and wheat (Kansas). The presence of significant negative signs on expected net positions is consistent with earlier findings in Table 4.6 where net positions of hedgers exhibit a negative relationship towards returns. Unexpected components of net positions for hedgers are significant only in six cases, where gold and Swiss francs exhibit a negative sign. The difference in significance between expected and unexpected components for net positions of hedgers suggest that hedgers are informed players by adjusting their net positions more often at the start of the trading month rather than in a noisy way all throughout the month91. This result can be compared with Table 4.10.4, where the unexpected component of net positions of speculators is significant in 10 futures markets92 at 10% significance level. Six out of these 10 markets exhibit a significant positive sign, supporting the finding in Table 4.6 that speculators’ net positions and returns are positively related. This tends to be also the case for the expected component of net positions of speculators, where in five out of six markets a positive significant sign is displayed. The mere positive significance of the expected component for net positions for speculators suggests that these players are less informed than hedgers. This is further supported by more significance (both negative and positive) of unexpected net positions for speculators compared to hedgers, suggesting speculators are traders who change their net positions more often than hedgers all throughout the month to get higher returns. These findings also support Canoles et al. (1998) that both hedgers and speculators are financially sophisticated, well-educated, well-capitalized, and that hedgers are better informed in setting better expected net positions to determine actual returns. The poor significance of expected net positions, and the greater significance of unexpected net positions of speculators in determining
91 This is in contrast to uninformed noisy traders or small traders who tend to lose in futures markets. 92 Note again that some of the net positions of speculators are differenced series. See Appendix 4.10 for
138 returns, support Murrell (1979) and Hyde (1978) that speculators can be in the market for recreational utilities and not only higher returns or profits.
Moreover, expected sentiment variables are positive and significant for both players in most markets. Unexpected sentiment variables are significant for hedgers in 13 markets and significant for speculators in 10 markets. In eight similar markets, unexpected sentiment is significantly positive for both hedgers and speculators93. Live hogs, soybean meal, soybean oil, feeder cattle and silver display a significant negative unexpected sentiment variable for hedgers, while only live hogs and silver have a significant negative unexpected sentiment variable for speculators. Overall, findings of sentiment over returns showing a positive relationship are consistent with the herding behaviour of speculators, and bullish trend in the 1990s. Also, consistent with Table 4.10.1 and 4.10.2, the lagged hedging pressure variable is significant and negative mostly in agricultural markets.
Results for information variables were mixed. Only live hogs (Eurodollars) exhibited a significant and negative expected T-bill yield coefficient for hedgers (speculators). Unexpected T-bill yield had a significant and positive effect for hedgers and speculators in Japanese yen and live hogs. Unexpected T-bill yield had a negative effect on hedgers’ return in Eurodollars and cocoa, and a negative effect on speculators’ return in Eurodollars, British pounds and Swiss francs. It can be observed that T-bill yield not only has more effect on financial and currency groups, but also that speculators’ returns are more affected by unexpected changes in T-bill yield. This supports the fact that speculators are more reliant on adjusting their returns all throughout the month based on changing variables like T-bill yield.
Expected corporate spread had a significant positive effect only on hedgers’ return in pork bellies and live hogs, and a significant negative effect only on both
93 Since the same sentiment data is used for both hedgers and speculators, the relationship between
sentiment and return should normally be the same when regressing the mean equation. Any difference is due to net positions being different, which eventually affect sentiment variables differently.
139 hedgers’ and speculators’ return in lumber. Unexpected corporate spread has had a positive effect on both players’ return in gold, silver, soybean oil and sugar. Interestingly too is that the expected dividend yield has had a negative effect on crude oil, and a positive effect on S&P500 futures for both players. This is consistent with crude oil and market dividend yield bearing a negative relationship, and that the market dividend yield has been increasing over the 1990–2000 period resulting in higher returns. Further, unexpected dividend yield has had a significant positive effect for hedgers in crude oil, British pounds, live cattle and cotton; and a significant positive effect for speculators in crude oil, British pounds, Swiss francs, live cattle, cocoa and cotton. Unexpected dividend yields were negative, however, for copper for hedgers; copper and Canadian dollars for speculators. Results not only support that dividend yield tends to affect crude oil, major financials and currencies more than agriculturals, but that speculators’ returns are more positively affected by unexpected dividend yield changes. Mainly to financials, minerals and currencies, findings of decomposed information variables suggest that unexpected T-bill yield appears to be more significant to returns for speculators, and unexpected corporate spread and dividend yield appears to be more positively significant to returns of speculators. These again support that speculators’ returns are based also on changing (unexpected) components of information variables all throughout the month, hence, their volatile trading habits.
4.4.2 Volatility