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Price Movements and Price Discovery in Futures and Cash Markets
Author(s): Kenneth D. Garbade and William L. Silber
Reviewed work(s):
Source:
The Review of Economics and Statistics,
Vol. 65, No. 2 (May, 1983), pp. 289-297
Published by: The MIT Press
Stable URL: /stable/1924495 .
Accessed: 09/03/2012 06:06
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PRICE MOVEMENTS
AND PRICE
DISCOVERY
IN
FUTURES
AND CASH
MARKETS
Kenneth D. Garbade
and William L.
Silber*
I.
Introduction
R
are two of
and price discovery
ISK transfer
the major contributions
of futures markets
to
the organization
of economic activity
(Working
(1962), Evans (1978,
p. 80), and Silber
(1981)).
Risk transfer refers to hedgers
using futures
con-
tracts to shift price
risk to others. Price
discovery
refers to the use
of futures prices for pricing
cash
market transactions
(Working (1948),
Wiese (1978,
p. 87), and Lake
(1978, p. 161)).
The significance
of both contributions
depends upon a
close rela-
tionship between the
prices of futures
contracts
and cash commodities.
This paper examines
the characteristics
of price
movements
in cash (or spot) markets
and futures
markets for storable
commodities. Section
II pre-
sents an analytical
model of simultaneous
price
dynamics
which suggests that, over short
intervals
of time, the correlation
of price changes
is a func-
tion of the elasticity
of arbitrage between
the
physical commodity
and its counterpart
futures
contract. Greater
elasticity fosters
more highly cor-
related price changes,
and thereby facilitates
the
risk transfer function.
The elasticity of supply
of
arbitrage services
is constrained by, among
other
things, storage
and transaction costs. Thus,
futures
contracts
will not, in general, provide perfect
risk
transfer facilities
over short time horizons.
The essence of the
price discovery
function of
futures markets hinges
on whether new informa-
tion is reflected
first in changed futures prices
or in
changed cash prices
(Hoffman (1932,
pp. 258-
259)). The model
in section
II
provides a frame-
work for analyzing
whether one market
is dom-
inant in terms of information
flows and price
discovery.
In section III we develop a model based
on section
II which is appropriate for estimating
the lead-lag relationship
between cash prices
and
futures prices.
Section IV presents empirical
estimates of the
parameters of the
model for seven different
stor-
able commodities: wheat, corn,
oats, frozen orange
juice concentrates, copper,
gold, and silver.
The
cost of arbitrage between
cash and futures differs
across these commodities.
For this reason we are
not surprised to find inter-commodity
differences
in the correlation of short-run
price changes and
in the substitutability of
futures contracts for cash
market positions. With
respect to the price
dis-
covery function of futures
markets, we find that
while futures markets dominate
cash markets, cash
prices do not merely
echo futures prices; there
are
reverse information flows
from cash markets
to
futures markets as well.
II.
A Model of Simultaneous
Price
Dynamics
This section sets forth
a model of concurrent
price changes in
a cash market and
a futures
market, and uses that
model to examine: (1)
the
effect of arbitrage on the
correlation of price
changes
in the two markets; and (2) the
notion of
price discovery.
We first present an equilibrium
price relationship
assuming an infinite elasticity
of
supply
of arbitrage services, and
then extend that
relationship to the case
of a finite elasticity
of
supply.
Prices with Infinitely Elastic
A.
Equilibrium
Arbitrage
Let
Ck
be the natural logarithm
of the cash
market price of a storable
commodity
in
period k,
and let
Fk
be the natural logarithm of the
contem-
poraneous price
on a futures contract for
that
commodity
for settlement after a time
interval
Tk.
(All prices
are expressed in natural logarithms.)
If
the following "perfect
market" assumptions hold:
(1) no taxes
or transaction costs; (2) no
limitations
on borrowing; (3) no costs (other
than financing)
to storing a long cash market position,
e.g.,
no
[
289
1
Received for publication
December
15, 1981. Revision
accepted for publication July
29, 1982.
* New York University.
This paper was supported
by NSF Grant No. SES-8103156
and by grants from J.
Aron & Co. and Bankers
Trust Co.
Deborah Black provided
excellent assistance,
and Mary Jaffier
typed the drafts with her
usual speed and accuracy.
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