Results
Lagged returns have significant negative
coefficients at five-minute intervals and
become mostly positive or insignificant
at the longer intervals.
Contemporaneous order imbalances are
positive and highly significant.
December 3, 2001
Richard Roll, UCLA
Results for Lagged OIB
OIB#t-1 is positive at five minutes, though
insignificant.
By ten minutes, it becomes negative and
significant. OIB$t-1 remains positive.
Pattern persists out to sixty minutes
but OIB$t-1 is insignificant.
Coefficients decline as trading interval
lengthens
Note that the contemporaneous OIB coefficients do
not decline much.
December 3, 2001
Richard Roll, UCLA
Table 4.A. Returns on lagged returns and OIB
Large Stocks, 1996
Explanatory
Variable
Midpoint
Returnt-1
OIB#t
OIB#t-1
OIB$t
OIB$t-1
R2
Return Interval (minutes)
Five
Ten
Fifteen
Thirty
Dependent Variable is the Midpoint Returnt, Large Stocks, 1996
-0.038 -0.066 -0.050 -0.095 -0.025 -0.083 0.037 -0.028
(-5.42) (-7.40) (-5.55) (-15.8) (-2.44) (-9.89) (3.33) (-2.27)
(-3.55) (-6.52) (-3.29) (-6.44) (-1.31) (-4.51) (1.52) (-0.95)
8.78
8.94
8.54
7.53
(7.10)
(6.83)
(6.81)
(6.28)
(37.5)
(30.1)
(25.1)
(16.9)
3.51
-0.943
-1.40
-1.79
(1.38)
(-3.58)
(-5.24)
(-5.51)
(0.30)
(-3.89)
(-4.93)
(-4.21)
4.60
4.96
4.99
4.91
(20.1)
(11.6)
(11.2)
(10.7)
(46.3)
(38.1)
(32.7)
(24.9)
0.829
0.481
0.349
0.092
(5.45)
(4.44)
(3.35)
(0.97)
(6.48)
(2.67)
(1.52)
(-0.11)
15.8
19.7
19.1
24.8
19.7
26.8
19.0
30.3
December 3, 2001
Richard Roll, UCLA
Sixty
0.090
(5.99)
(2.26)
6.77
(6.10)
(10.8)
-2.23
(-6.05)
(-3.71)
18.6
-0.009
(-0.80)
(-0.12)
4.95
(10.7)
(17.0)
0.007
(0.05)
(-0.31)
32.8
Traces of two types of investors
Smaller traders, (weighted equally in OIB#)
more likely to be “naïve”??
Their order imbalances offset by arbitrageurs
and/or specialists.
This takes at least ten minutes.
Relative sizes of coefficients for OIB#t and
OIB#t-1 give approximate proportion of naïve
trades that are offset.
At ten minutes, the initial price impact is offset by
about eleven percent (-0.943/8.94) while at 15, 30,
and 60 minutes it is offset by roughly 16%, 24%,
and 33%, respectively.
December 3, 2001
Richard Roll, UCLA
Astute traders
Lagged OIB$ significantly positive for five,
ten, and fifteen minutes (large stocks, 1996).
Insignificant at thirty minutes.
Traders respond to larger orders by jumping
on the bandwagon.
Rapid response; notice relative sizes of
contemporaneous and lagged coefficients for
OIB$.
Five minutes: lagged coefficient is about 18
percent as large
Percentage drops to 10%, 7%, 2%, and 0.1% as
interval lengthens from 10 to 60 minutes.
December 3, 2001
Richard Roll, UCLA
Better arbitrage in 1998?
OIB#t-1 declines as return interval lengthens
but it is negative even at five minutes, (1998,
large stocks)
Suggests that arbitrageurs were intervening more
quickly with countervailing trades in 1998.
OIB$t-1 shows no bandwagon effect in 1998
negative after five minutes but much smaller (in
absolute value) than OIB#t-1
At sixty minutes, about 36% of OIB# is
reversed (-2.87/7.89) while only about 10% of
OIB$ is reversed (-.455/4.43).
Larger orders contain more accurate information?
December 3, 2001
Richard Roll, UCLA
Table 4.B. Returns on lagged returns and OIB
Large Stocks, 1998
Explanatory
Variable
Midpoint
Returnt-1
OIB#t
OIB#t-1
OIB$t
OIB$t-1
R2
Return Interval (minutes)
Five
Ten
Fifteen
Thirty
Dependent Variable is the Midpoint Returnt, Large Stocks, 1998
-0.018 -0.044
0.00
-0.043 0.007 -0.045 0.055 -0.023
(-2.53) (-5.28) (0.01) (-5.75) (0.52) (-4.00) (4.79) (-2.55)
(-1.68) (-4.36) (0.11) (-3.11) (0.52) (-2.68) (2.37) (-0.32)
11.0
10.36
10.01
9.05
(10.5)
(9.87)
(9.62)
(9.85)
(50.9)
(37.0)
(30.8)
(21.4)
-0.864
-1.47
-1.75
-2.12
(-5.30)
(-7.01)
(-7.70)
(-9.26)
(-4.71)
(-5.75)
(-5.90)
(-5.57)
4.56
4.65
4.69
4.59
(16.9)
(17.4)
(17.2)
(17.8)
(48.8)
(37.8)
(32.9)
(24.7)
0.023
-0.167
-0.221
-0.423
(0.44)
(-2.59)
(-3.15)
(-4.97)
(0.12)
(-1.22)
(-1.46)
(-2.10)
21.7
19.9
22.9
22.9
23.8
25.5
24.0
28.5
December 3, 2001
Richard Roll, UCLA
Sixty
0.106
(8.83)
(2.61)
7.89
(8.93)
(13.2)
-2.87
(-10.2)
(-4.77)
22.4
-0.014
(-1.06)
(-0.39)
4.43
(17.4)
(17.0)
-0.455
(-4.30)
(-1.73)
30.8
Mid-Cap Stocks
Similar in many respects to large stocks.
Coefficient of the contemporaneous OIB
always positive and larger than for
large-cap stocks.
⇒a given OIB has a larger impact on mid-
cap stocks.
⇒Inventory and asymmetric information
are more important for stocks that trade less
frequently
December 3, 2001
Richard Roll, UCLA
Table 4.C. Returns on lagged returns and OIB
Mid-Cap, 1996
Explanatory
Variable
Midpoint
Returnt-1
OIB#t
OIB#t-1
OIB$t
OIB$t-1
R2
Return Interval (minutes)
Five
Ten
Fifteen
Thirty
Dependent Variable is the Midpoint Returnt, Mid-Cap Stocks, 1996
-0.052 -0.009 -0.069 -0.058 -0.056 -0.045 -0.003 -0.028
(-2.28) (-0.30) (-5.17) (-3.62) (-3.48) (-3.01) (-0.22) (-1.84)
(-5.66) (-3.62) (-4.03) (-3.88) (-2.44) (-2.69) (-0.25) (-0.85)
19.8
24.2
23.6
22.02
(10.4)
(8.33)
(8.77)
(9.26)
(24.8)
(23.2)
(19.8)
(14.4)
6.42
1.59
1.52
-1.32
(5.57)
(1.69)
(1.88)
(-2.36)
(7.94)
(1.83)
(0.47)
(-0.78)
6.85
8.15
8.72
9.77
(10.2)
(10.5)
(10.91)
(10.79)
(20.2)
(17.8)
(15.92)
(12.67)
2.43
1.41
1.17
0.588
(5.45)
(2.77)
(4.79)
(2.15)
(6.86)
(3.21)
(2.01)
(0.82)
17.5
9.88
23.2
11.6
24.7
13.3
26.8
18.1
December 3, 2001
Richard Roll, UCLA
Sixty
0.024
(0.97)
(0.63)
20.2
(8.37)
(9.70)
-2.87
(-3.46)
(-1.66)
28.0
-0.042
(-1.66)
(-0.59)
10.4
(7.95)
(8.88)
0.716
(1.35)
(0.32)
21.0
Differences between the mid-cap
and large stock groups
Coefficient of lagged mid-cap return
significantly negative in some cases out to
thirty minutes.
Lagged OIB#t-1 not negative until thirty
(fifteen) minutes in 1996 (1998).
⇒ arbitrage takes a bit longer for mid-cap stocks.
OIB$t-1 coefficient declines as interval
lengthens but is negative only after thirty
minutes in 1998.
⇒Slower arbitrage activity in Mid-Cap group
December 3, 2001
Richard Roll, UCLA
Table 4.D. Returns on lagged returns and OIB
Mid-Cap, 1998
Explanatory
Variable
Midpoint
Returnt-1
OIB#t
OIB#t-1
OIB$t
OIB$t-1
R2
Return Interval (minutes)
Five
Ten
Fifteen
Thirty
Dependent Variable is the Midpoint Returnt, Mid-Cap Stocks, 1998
-0.033 0.001 -0.017 -0.012 -0.022 -0.034
0.009 -0.035
(-3.54) (0.09) (-1.63) (-1.30) (-2.33) (-4.81) (0.84) (-2.62)
(-3.63) (0.55) (-1.39) (-1.14) (-1.38) (-2.05) (0.52) (-1.22)
23.8
25.6
25.90
23.9
(12.6)
(11.7)
(10.7)
(10.3)
(46.2)
(37.7)
(32.3)
(22.9)
5.18
0.225
-1.82
-3.91
(5.14)
(0.37)
(-3.54)
(-9.65)
(7.40)
(-0.59)
(-2.49)
(-3.67)
6.28
7.08
7.61
8.01
(6.58)
(6.61)
(6.39)
(6.18)
(25.6)
(20.8)
(18.2)
(13.8)
1.51
0.690
0.135
-0.038
(4.93)
(3.38)
(1.17)
(-0.27)
(5.06)
(1.68)
(0.38)
(-0.05)
19.4
6.68
22.9
8.03
24.6
9.06
25.3
10.7
December 3, 2001
Richard Roll, UCLA
Sixty
0.061
(3.56)
(1.68)
21.67
(9.97)
(14.9)
-6.23
(-9.18)
(-3.95)
25.4
-0.017
(-0.93)
(-0.35)
8.42
(6.44)
(10.2)
-0.509
(-1.40)
(-0.66)
13.6
I’m done
Thanks for your kind attention
December 3, 2001
Richard Roll, UCLA
December 3, 2001
Richard Roll, UCLA