RDP 8804: Pricing Behaviour in Australian Financial Futures Markets Tables

Malcolm Edey and Graham Elliott

June 1988

TABLE 1. ANNUAL TRADING VOLUMES OF MAIN SFE CONTRACTS
(thousands of contracts traded)
  Wool Bills Bonds SPI Options Other Total
1960–1978 (av.) 75         2 77
1979 75 2       189 266
1980 173 17       421 611
1981 67 28       359 454
1982 31 146       233 410
1983 22 161   180   127 490
1984 9 173 2 237   96 517
1985 7 594 242 282 22 76 1,223
1986 2 1,075 1,432 466 242 64 3,281
1987 1 2,095 2,064 625 568 16 5,369

Notes
(i) The options column includes only options on the major contracts (bills, bonds and SPI).
(ii) “Other” consists mainly of commodity futures (cattle, gold, silver) and currency futures, together with options on these (after 1985).

Source: Sydney Futures Exchange, and Rutledge (1983).
TABLE 2. AUTOCORRELATION FUNCTIONS FOR FIRST DIFFERENCED PRICE SERIES
Variable Sample
(short or long)		 Lag Length
  1 2 3 4 5 6 7 8
SPI spot S .09 −.01 .00 .11 −.15 −.14 −.07 −.03
  L .20* .19 .09 −.05 −.05 .03 .06 −.11
SPI futures S −.04 −.04 −.01 .14 −.14 −.17 −.08 .07
  L .12 .14 .12 −.08 −.06 −.07 .04 −.05
Bills spot S .08 −.10 .07 .20* .05 −.11 .00 .05
  L .06 −.09 .07 .16* .02 −.10 −.03 .05
Bills futures S .04 −.14 .13 .18* −.01 −.23* −.16* −.02
  L .05 −.12 .11 .10 −.04 −.24* −.15 .01
Bonds spot S .07 −.10 .12 .16* .04 −.12 −.05 .09
  L −.02 −.09 .05 .12 .06 −.11 −.06 .02
Bonds futures S .12 −.05 .12 .14 −.01 −.14 −.09 .05
  L .16* −.05 .04 .11 −.03 −.16* −.09 .05

Note: 5% critical value is 0.155.
Asterisk denotes significance at 5% level.
TABLE 3. PARTIAL AUTOCORRELATION FUNCTIONS FOR FIRST DIFFERENCED PRICE SERIES
Variable Sample
(short or long)		 Lag Length
  1 2 3 4 5 6 7 8
SPI spot S .09 −.02 .00 .11 −.18 −.11 −.05 −.04
  L .20* .16 .03 −.11 −.04 .01 .10 −.14
SPI futures S −.04 −.05 −.01 .14 −.13 −.17 −.10 .03
  L .12 .12 .09 −.13 −.07 −.05 .09 −.05
Bills spot S .08 −.11 .08 .18* .03 −.08 −.01 −.01
  L .06 −.10 .08 .15 .01 −.08 −.04 .01
Bills futures S .04 −.14 .15 .15 .02 −.22* −.20 −.10
  L .05 −.12 .13 .07 −.03 −.23* −.16 −.04
Bonds spot S .07 −.10 .14 .14 .05 −.11 −.07 .04
  L −.02 −.09 .05 .11 .08 −.11 −.07 −.02
Bonds futures S .12 −.07 .14 .11 −.02 −.14 −.10 .04
  L .16* −.07 .11 .07 −.05 −.15 −.07 .06

Note: 5% critical value is 0.155.
Asterisk denotes significance at 5% level.
TABLE 4: JARQUE-BERA TESTS FOR NORMALITY
  Skewness
(√b1)		 Kurtosis
(b2)		 Joint LM
 
Pre-Crash Sample:
SPI 0.00 3.63 2.44
Bills 1.05 6.39* 97.60*
Bonds 0.08 4.15* 8.20*
Full Sample:
SPI −4.48* 38.34* 9,137.12*
Bills 0.83 5.62* 66.00*
Bonds −0.20 7.88* 164.55*
Notes:
  1. The measure of skewness (√b1) is defined by b1 = Inline Equation where mi is the ith central moment. The theoretical value of b1 is zero for the normal distribution. Positive skewness indicates a long right-hand tail.
  2. Kurtosis is measured by b2 = Inline Equation (= 3 for the normal). High kurtosis indicates that extreme values have a high probability of occurring, relative to the normal.
  3. LM is a joint test for skewness and kurtosis as specified by Bera and Jarque (1986).
The critical values for the measure of skewness (√b1) and kurtosis (b2) are given in White and MacDonald (1980). The LM test specified by Bera and Jarque (1986) is distributed as a chi-square with two degrees of freedom. Asterisk denotes significance at the 5% level.
TABLE 5: EFFICIENCY TESTS BASED ON LAGGED PRICES
(PRE-CRASH SAMPLE)
Market Constant Lagged Futures Lagged Spot
  1 2 3 4 5 1 2 3 4 5
SPI .84×10−2*
(.28×10−2)		 .10
(.23)		 −.01
(.25)		 .07
(.27)		 .44
(.27)		 .28
(.23)		 −.17
(.29)		 .02
(.30)		 −.12
(.31)		 −.35
(.31)		 −.34
(.26)
Bills .64×10−3
(.37×10−3)		 .08
(.08)		 .00
(.09)		 .12
(.09)		 .18*
(.08)		 .09
(.09)		 −.03
(.10)		 −.14
(.10)		 .15
(.10)		 −.10
(.10)		 −.08
(.10)
Bonds .97×10−4
(.17×10−3)		 −.05
(.17)		 −.02
(.20)		 −.15
(.21)		 −.21
(.19)		 −.24
(.17)		 .19
(.18)		 −.06
(.20)		 .36
(.21)		 .30
(.20)		 .22
(.16)
TABLE 6. EFFICIENCY TESTS BASED ON LAGGED PRICES
(FULL SAMPLE)
Market Constant Lagged Futures Lagged Spot
  1 2 3 4 5 1 2 3 4 5
SPI .31×10−2
(.39×10−2)		 −.08
(.24)		 −.09
(.36)		 −.12
(.40)		 .60
(.40)		 .47
(.35)		 .24
(.29)		 .27
(.45)		 .25
(.47)		 −.95*
(.47)		 −.49
(.40)
Bills .50×10−3
(.35×10−3)		 .12
(.08)		 .01
(.08)		 .07
(.08)		 .13
(.08)		 .03
(.08)		 −.02
(.10)		 −.15
(.10)		 .19
(.10)		 −.12
(.10)		 −.07
(.10)
Bonds .73×10−4
(.16×10−3)		 .09
(.14)		 .01
(.16)		 .01
(.17)		 −.16
(.16)		 −.22
(.14)		 .08
(.13)		 −.07
(.15)		 .15
(.16)		 .23
(.15)		 .16
(.12)

Notes: Dependent variable in each case is changed in future price. Estimated new contract dummies are not reported.
TABLE 7: EFFICIENCY TESTS BASED ON EXPECTED PREMIUMS
  Pre-Crash Sample   Full Sample  
Market Constant Expected Premium DW Constant Expected Premium DW
SPI .76×10−2
(.21×10−2)		 .07
(.15)		 2.14
 		 .26×10−2
(.39×10−2)		 .11
(.22)		 1.72
 
Bills .58×10−3
(.38×10−3)		 −.04
(.12)		 1.96
 		 .46×10−3
(.36×10−3)		 −.02
(.11)		 1.86
 
Bonds .65×10−4
(.18×10−3)		 −.08
(.18)		 1.91
 		 .78×10−4
(.17×10−3)		 −.03
(.13)		 1.78
 
TABLE 8: ARCH TESTS FOR CONDITIONAL HETEROSKEDASTICITY
  Lag Length Pre-Crash Sample Full Sample
SPI 1 1.13 0.30
Bills 1 17.74* 14.54*
Bonds 3 7.82* 8.09*

Note: The test statistic is a χ2 test for joint significance of the β coefficients in equation (6). An asterisk denotes significance at the 5% level.
TABLE 9: GRANGER CAUSALITY TESTS – VOLATILITY
  Pre-crash sample   Full sample
Volatility Volume Lagged
Volume		 Lagged
Futures
Volatility		 Volume Lagged
Volume		 Lagged
Futures
SPI −.20×10−6* (.95×10−7) .19×10−6* (.96×10−7) .03 (.06)   .11×10−6 (.39×10−6) .93×10−6 (.90×10−6) .09 (.06)
Bills .12×10−8 (.14×10−8) −.93×10−9 (.14×10−8) .13* (.06)   .15×10−8 (.12×10−8) −.88×10−9 (.19×10−8) .12* (.06)
Bonds .45×10−9 (.29×10−9) .21×10−9 (.25×10−9) .44* (.10)   .12×10−9 (.44×10−9) −.76×10−10 (.40×10−9) .33 (.18)

Notes: The dependent variable in each case is the squared change in spot price (st−st−1)2.
TABLE 10: GRANGER CAUSALITY TESTS IN LEVELS
  Pre-Crash Sample   Full Sample
Lag Length
Selected		 F1
 		 F2
 		 Lag Length
Selected		 F1
 		 F2
 
SPI 1 0.65 4.69*   2 1.01 2.41
Bills 2 0.24 3.26*   2 0.54 4.25*
Bonds 2 1.73 8.98*   2 1.28 14.60*
Notes: F1 tests for causality from spot to futures prices.
F2 tests causality in the reverse direction.