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臺大管理論叢
第
26
卷第
3
期
167
the two nearest expiration futures contracts),
DEP
t
(market depth)
ILLQ
t
(the Amihud (2002)
illiquidity proxy), and
Amivest
t
(the Amivest liquidity ratio). The primary independent variables of
concern include
OI
t
(open interest,),
EOI
t
, (expected open interest) and
UOI
t
(unexpected open
interest).
OI
t
is the open interest of the two nearest expiration futures contracts.
EOI
t
, and
UOI
t
are partitioned from
OI
t
using
ARIMA
model.
TTM
t
is the time-to-maturity (in days) of the futures
contracts with the largest volume.
D
j
(
j
= 3, 4, 5, 6) are four daily dummies for the day-of-the-
week effect. Both
ILLQ
t
and
Amivest
t
are multiplied by 1,000. Each H
0
is tested using the
F-statistics. The superscript a, b, and c indicate significance at the 1%, 5% and 10% confidence
levels, respectively.
Model (2) regresses the liquidity proxies against decomposed open interest. We find that
the unexpected open interest (
UOI
) increases with volume (
VOL
), depth (
DEP
), and
decreases with market impact (
ILLQ
). Note that the coefficient of
UOI
is positively
significant at the 5% confidence levels for regression using depth (
DEP
) as a liquidity proxy.
This relationship supports the view of Bessembinder and Seguin (1993) that
UOI
is a close
proxy for the current willingness of futures traders to risk capital by providing depths.
Moreover, the expected open interest positively associated with volume, depth, and Amivest
liquidity ratio, and negatively correlated with the Amihud illiquidity measures. The result is
consistent with the findings of Martell and Wolf (1987) and Moser (1994) that the cross-
sectional aggregated open interest share similar information contents of trading volume and
market depth.
In both Model (1) and (2), the
TTM
, time to maturity, is positively related to volume and
depth. The day-of-the-week dummies, on the other hand, are rarely significant. Regression
adjusted-
R
2
enhanced after adding the control variables, namely volume (for dependent
variable not volume) and/or depth (for dependent variable not depth). In sum, results are
consistent with testable implications (1) and (2), and hence support the Hypothesis 1, that
open interest reflects the participation of traders.
4.3 Test Results of Open Interest Reflecting Hedging Demand
Table 4 reports regression estimates for testable implications (3) of Hypothesis 2. We
are interested in whether open interest changes with spot volatility, thus reflects demand for
hedging. In Model (3), the coefficients of spot volatility are significantly positive at the 1%
level, regardless which volatility proxy (
Parkinson
,
GK
, or
RS
) is used. It suggests that
greater spot market volatility tends to induce increases in expected component of open
interest. While the expected open interest positively move with index volatility, the
unexpected open interest, on the other hand, does not correspond to spot volatility. In the