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THE EFFECTS OF DAILY PRICE LIMITS
ON COTTON FUTURES AND OPTIONS TRADING
Joan Evans and James M. Mahoney

Federal Reserve Bank of New York
Research Paper No. 9627

August 1996

This paper is being circulated for purposes of discussion and comment only.
The contents should be regarded as preliminary and not for citation or quotation without
permission of the author. The views expressed are those of the author and do not necessarily
reflect those of the Federal Reserve Bank of New York or the Federal Reserve System.
Single copies are available on request to:

Public Information Department
Federal Reserve Bank of New York
New York, NY 10045

The Effects of Daily Price Limits
on Cotton Futures and Options Trading

Joan Evans
and

James M. Mahoney"

Current version: August 15, 1996

Abstrac t
The New York Cotton Exchange (NYCE) imposes price limits on the trading of
cotton futures, whereby the price at which cotton futures trade during a day is
restricted to a band centered around the previous day's close. However, the
NYCE has no such restrictions on the trading of options on cotton futures. These
exchange rules allow for essentially a controlled experiment to study the market
participants' responses to the price limits on futures. We show that, as a higher
fraction of the trading day is constrained by the price limit, futures volume
significantly decreases, options volume significantly increases, but the average
aggregate volume of cotton trade remains unchanged. The empirical analysis
indicates that market participants react rationally to the price limit in the futures
market by transferring their trading activity to a market without price limits.

• Federal Reserve Bank of New York, Capttal Markets Function, Research and Market Analysis
Group. The
opinions expressed in this paper are those of the authors and do not necessarily represent
those of the Federal
Reserve Bank of New York or the Federal Reserve System. The authors would like to acknowle
dge the valuable
research assistance of Elizabeth Reynolds and Erika Nanke. All comments are welcomed
and appreciated.

The Effects of Daily Price Limits
on Cotton Futures and Options Trading

INTRODUCTION

Trading limits refer to exchange-mandated restrictions on trading during times of market
stress. They normally go into effect during times of extreme price volatility, unusually
high
trading volume, or massive one-sided order flow. Such mechanisms, including price
limits,
trading halts, circuit breakers, and position limits, have been in existence in many commod
ity
and financial markets for years.' Various arguments have been advanced concerning
their
effectiveness, and although the subject has received a great deal of scrutiny following
the stock
market crash of 1987, no consensus has emerged regarding their ultimate usefulness.
Many of
the theoretical arguments both for and against trading limits remain controversial, and
much of
the empirical evidence is inconclusive.
Opponents of trading limits argue that unfettered trading in the asset markets is more
efficient than regulated trading. Some of the more frequently cited disadvantages of trading
limits
are that they prohibit potentially mutually beneficial trades that would occur voluntarily,
that they
impose costs by preventing market participants from liquidating existing positions or establish
ing
new hedging positions, and that they create intermarket distortions by disrupting spot
and
futures price co-movements (CFTC Report, 1988; Chance, 1994). In addition, it has been
argued that the imposition of trading limits often impedes the price discovery process
by
upsetting the normal flow of information (Lee, Ready and Seguin, 1994), and by creating
what
many market participants call the "magnet effect'' (Hieronymus, 1971; Cantor, 1989; Fama,

1

Although different authors use terms in different ways, this paper uses the following terminolo
gy to
catagorize trading limits: price limits create a band within which the price of an asset can
trade; t~ading halts prohibit
trading of an asset during a time period in which it normally trades; circuit breakers proh1M
the _simultaneous trading
of an asset and a derivative security (such as futures or options) on the asset; and pos1t1on
limits control the net
amount of an asset that any one market participant can hold.

2
1989). This "magnet effect'' potentially leads. to in,crE111.sed trading volume and price variability as
large institutions, which would otherwise have the flexibility to choose the time periods and/or
market environments in which to trade, feel compelled to suboptimally advance the execution of
trades (Subrahmanyam, 1994).
Proponents of trading limits base their support on the notion that there Is a "public _good" ,
in maintaining an orderly market, and that individual traders do not take this externality into
account when trading. For example, trading limits can discourage unreasonable prices that
result from "excessive speculation" (Khoury and Jones, 1983), since they provide a cooling-off
, period that gives traders time to absorb new information (Ma, Rao and Sears, 1989). It is
believed that trading limits can serve as a partial substitute for margin requirements (Brennan,
1986),2 may lessen credit risks or a loss of confidence in the marketplace, and may curtail
detrimental trading strategies by formalizing the economic reality that markets have a limited
capacity to absorb enormous one-sided volume (Brady Commission, 1988). 3
This paper takes a unique approach in addressing the effectiveness of price limits.

4

Using data on cotton futures and options on futures at the New York Cotton Exchange (NYCE)
during 1995, we study the market's response to the imposition of the price limits with respect to
shifts and/or changes in trading volume and strategies. The cotton futures and options market

2

Brennan (1986) shows that price limits may serve as a partial substitute for margin requirements in
ensuring contract pertormance, and that it may be optimal to run some risk of a trading interruption in order to reduce
margin requirements (unless there is costless arbitrage between the cash and futures markets).
3 The Brady Commission (1988) suggests that circuit breakers protect both the markets and investors by
·,, potentially reducing the likelihood that flawed trading strategies (described as huge transactions in one direction
within a short time period) would be pursued to the point of disrupting the markets or threatening the financial
system.
4

It is important to distinguish between price limits (typically imposed on regulated futures exchanges) and
trading halts (typically imposed on stock exchanges) since, under price limits, trading can continue at or between the
upper and lower limits, while trading halts stop trading, regardless of price, for some period of time (Kodres and
O'Brien, 1994).

3
·provides an interesting opportunity to address QM~stions relating to price limits, since it is a
market where futures trading is subject to.limits while options on futures trading is not. 5 We
examine whether or not there is an obvious substitution effect by testing ii the volume in related
contracts (various options contracts and futures of different tenors) that are not in limit increases
when one or more futures contracts go into limit. We also examine the volume of various types
of options strategies (synthetic futures, deep-in-the-money options, or option spreads) that could
conceivably increase as a result of price limits.
The results of our analysis suggest that, on average, the total "price risk traded" on the
' NYCE remains essentially the same on days when one or more futures contracts are in limit
compared to days when the limits are not binding.• The composition of trading does change,
however, as there appears to be a seamless transition of trading from futures contracts to
options-based trading strategies.
The paper proceeds as follows. Section I provides background information for the cotton
market, including the spot market, the futures market, the options market, and the "spreads"
market. Section II describes the data that are used in the empirical ~nalysis. Section Ill tests for
competitiveness and efficiency in the cotton futures and options markets by examining the
concentration of trading and testing for arbitrage opportunities. In Section IV, we present
univariate regressions of trading volume and the fraction of the day that the futures are in limit.
In Section V, we present multiple regressions of trading volume and other possible explanatory
variables. Finally, Section VI provides a summary and conclusions as well as a discussion of

5

It is not uncommon to have price limits on the futures contracts and not the options contracts, a situation
found in many agricultural, metal and energy futures markets in the U.S. Most financial futures exchanges, however,
impose limits on both futures and options contracts.
6
As we define in more detail later, the total "price risk traded" is the sum of futures volume plus the sum of
options volume on a given day, where the options volume is delta-weighted to arrive at a futures contract equivalent.

4
other policy considerations.

I. BACKGROUND

The spot or cash commodity market refers to the marketplace in which the trading or
physical transfer of a commodity takes place. Producers and end-users who participate in the ..
cash market for commodities normally have genuine business interests in the commodities,
while those with speculative interests usually limit their trading to the derivatives markets. The
cash markets for commodities are often dispersed geographically and deals are usually
transacted in non-uniform (custom-tailored) lots.

A. Spot Market for Cotton in the United States

The spot market for cotton in the United States is generally quoted as a spread (often
referred to as "the basis") above or below the nearby futures contract price.7 Spot market prices
are recorded and made publicly available by the United States Department of Agriculture
(USDA) at the end of each day.• The USDA strives to report meaningful information; however,
the spot market for U.S. cotton operates without any formal guidelines on location, time or size
of trading unit and only informal requirements for reporting transactions (Anderson, Shafer and

7

. The basis is normally calculated by subtracting the cash price from the futures price (the cash market ..
normally trades at a discount to the futures due to the cost of carry) at a particular time and location. The basis
changes regularly due to changes in transportation costs, storage and handling, interest rates, grade of cotton and
various market forces such as supply and demand. The futures price of an asset can be related to its spot price by
an expression of the form:
F = se•<T-~

where F = the futures price, S= the spot price, T= expiration date of the option, I= the current time, and a is a
measure of the basis. The value of a can be either positive (implying futures prices are above spot) or negative
(implying futures prices are below spot).
8 The U.S. Cotton Futures Act of 1916 established the USDA system for determining and reporting spot
cotton quotations. Price information is collected by market news reporters who regularly visit or call trade members
within each designated spot market, analyze trade data and report average prices for the various qualities traded.

5
Haberer, 1996). The reported spotpricesxepresentan average price for various qualities at
multiple levels of production, i.e., they may include producer sales, inter-merchant trading, sales
to mills and cooperative pooling.• As such, cotton market participants are forced to rely heavily
on the quotations provided by the futures market and typically only look upon the USDA spot
quotations as providing general price levels fora given day; Although spotand forward markets.
exist in other parts of the world, there is little or no interaction with the over-the-counter (OTC)
market in the United States. 10
In summary, unlike for other commodities (e.g., metals or energy complex), reliable spot
price data for cotton are not always readily available. When the cotton futures market goes into
limit, liquidity in the cash market dries up, 11 and other derivative markets must take the place of
the futures market for price discovery since there are no foreign markets open to divert the
activity. A more thorough description of the spot market for cotton'in the United States can be
found in Anderson, Shafer and Haberer (1996).

B.

Futures Market for Cotton in the United States

The futures market serves as the primary source of price discovery for the U.S. cotton
market on an intraday basis. Unlike in many other markets, equilibrium price data flow from the
centralized futures market to the decentralized cash markets. Cotton futures are traded

9

Cooperative pools have been in existence in the U.S. cotton market since the late 1920's. Cooperative
pools are farmer-owned cotton marketing cooperatives that are established to sell the members' crops through a
centralized system. They are generally run by professional sales staffs who study and monitor cotton market trends
·, and try to maximize selling opportunities for Its members throughout the year.
10

The U.S. Farm Bill does not allow for imports of cotton unless the average U.S. price for cotton is above
the average world price for ten consecutive weeks.
11 · This

assertion is supported by anecdotal evidence from market participants. The only exception noted
was that the cash market activity did not always slow down uniformly, i.e., activity diminished more markedly during
limit-down days than during limit-up days.

6
exclusively on the New York Cotton Exchange (N¥C~). where futures prices are established
through a system of open outcry. 12 The futures market creates a common denominator by
providing a marketplace for a homogeneous product which serves the needs (to either hedge or
speculate) of a diverse group of market participants. There are various grade, staple and
micronaire specifications limiting the range of cotton that is tenderable on the NYCE; however,.,
roughly two-thirds of the annual U.S. cotton crop normally qualifies for delivery. 13
Cotton futures are traded in units of 50,000 pounds (approximately 100 bales) and prices
are quoted in cents and hundredths of a cent per pound. The per-contract minimum price
·fluctuation is 1/100 of.a cent·(one "point'') per pound below 95 cents per pound, and 5/100 of a
cent (5 points) per pound at prices of 95 cents per pound or higher. Therefore, a point is worth
five dollars per contract. Technically, the eligible trading months include the current month plus
one or more of the next twenty-three succeeding months. However, trading is normally limited to
the March, May, July, October, and December contract months, which are known as the active
trading months.
An interesting phenomenon occurs in the cotton futures market on volatile days. The
NYCE imposes trading restrictions on the underlying futures contracts when they reach
arbitrarily defined price limits but allows all options on futures as well as futures spreads (defined
below) to continue trading unconstrained by price limits. During the time period under which this
"analysis took place, all futures prices (with the exception of the spot month which· had no limit ii) ..

12

There are currently no other competing cotton futures exchanges in the world. Cotton yam futures trade
on the Nagoya Textile Exchange and the Osaka Textile Exchange in Japan; however, they are not viable hedging
instruments due to the basis risk (explained in more detail in footnote 7) and different trading hours. This is in
contrast to other commodity markets such as gold, oil or soybeans, where trading can shift to another geographic
location such as the United Kingdom when a U.S. futures exchange imposes price limits (Cantor, 1989).
13 The grade refers to the quality of the cotton, the staple to the length of the cotton leaf, and the micro.naire
to the thickness of its fiber.

7
Jls last 17 trading days) were subject to,a.2.cent.Jimit move above or below the previous day's
settlement price. This limit expanded to 3 cents when any contract month settled at 95 cents or
above or when three or more contract months closed in limit, and stayed at 3 cents for all
contracts for the next three sessions. 14

C.

Options on Futures
Options on cotton futures are traded on the New York Cotton Exchange. Each contract

represents an option on one NYCE futures contract. Strike prices are listed in one cent
increments and pricesiare,quoted in cents and hundredths of a cent. Options are not subject to
daily price limits. The eligible trading months include March, May, July, October, and December.
The nearest ten of the eligible months listed above are available for trading at any one time.

D.

Spreads
Spreads are pairs of futures or options trades that are transacted by one trader

simultaneously. A futures spread consists of the purchase of a futures contract with delivery one
month and the sale of a futures contract with delivery in a different month, a strategy often
referred to as a "calendar spread." Much of the risk in each position is essentially offset by the
other, resulting in a position that reflects the price differential between the two delivery months.
These spreads are not directly affected by directional movements in.the market: .,An options - ~,

spread can take many forms, depending on the options strategy bein•g pursued, e.g., a synthetic
futures, a straddle or a strangle. The trading prices of futures spreads and options spreads
(defined as the price differential) are not subject to any form of price limits on the NYCE.
14 Effective January 15, 1996, the limits were expanded to 3 cents. They expand to 4 cents ii any contract
month settles at or above $1.10 per pound until no contract month settles at or above $1.10 (Cotton Price LimitsRule 1.03).

8
.. _ II. DATA ON THE COTTON FUTURES AND OPTIONS MARKET
A.

Primary data sources
Two primary data sources were utilized in this analysis. The NYCE kindly provided us

with the Time and Sales and Broker Reconciliation reports which contain detailed trade data.
This dataset covers the period September 1-29, 1995, for a total of 20 business days.
September 1995 was selected since it was fairly representative of a typical month (in terms of
volatility and trading volume) in the cotton futures market during the 1994-95 crop cycle. 15 We
also used DAI/McGraw-Hill for opening and closing prices and volume data for the 1991-1995
period.
The Time and Sales report, which includes the opening prices and each price change
that occurred during each day, was used as our primary source of futures trading data. Table I
provides an example of the data contained in the Time and Sales report, which includes the
trade date, contract expiration, futures price and time of trade. The futures price is quoted as the
price per pound of cotton and in units of "points" (1/100 of a cent), so that a price of 8900, for
example, represents 89 cents per pound of cotton. The Time and Sales report does not include
the quantity traded. Volume data for futures trading was obtained from DAI which has daily
summary figures organized by expiration date.
The Broker Reconciliation report, which includes every individual option trade and spread
trade on futures and optlons·for each trading day, was used as our primary source of ,options · ,,

15 Futures trading during the 1994-95 crop cycle was very unusual by historical standards in terms of
volatility and number of trading sessions where price limits were in effect. Strong export demand in the United
States during the latter half of 1994 and most of 1995, due to poor crops in other cotton producing nations, created a
"classic" liquidity squeeze in the cotton market. A boll worm infestation in China drastically reduced China's cotton
production, heavy rains caused severe crop damage in India and Pakistan, and a drought in New South Wales and
Queensland hurt Australian production.

9
and spread data.

16

Table II provides an.exampJ.e.QJthe data in the Broker Reconciliation report

'Which is organized by trade date, contract expiration, strike price, an indication whether it was a
call or a put (for options trades), options price or futures price (for futures spreads), volume
traded and time of trade.

Figure 1 presents closing futures prices obtained from DAI covering the period from the:
beginning of 1991 through year-end 1995. It includes only the most actively traded contracts
which are identified by contract expiration date. Figure 1 is intended to provide a graphical
representation of the volatility of cotton futures prices over time. It is of interest to note the
· spikes that often occur when trading shifts from the July to the October contract. The cotton
crop cycle or marketing season runs from August 1 to July 31. If the supply and demand for
cotton remains relatively stable from one season to the next, the absolute change in price levels
from the July contract (old crop) to the October contract (new crop) can be fairly small.
· However, when there is an imbalance one year, the jump can be dramatic, as in the spike.
downward in 1995. 17

B.

Derived data series
An additional data series (synthetic futures prices) was derived using the data in the

Broker Reconciliation report. We derived a synthetic futures price series to examine the

· · relationship between cotton futures prices and cotton options on .futures. prices using .the put-call

16

The NYCE was careful in maintaining the confidential aspects of the data by not revealing the identity of
the transacting broker.
17 The forward curve for cotton is normally positively sloped i.e., the further out months are more expensive
than the nearby contract due to carrying charges associated with storing cotton. The forward curve was Inverted for
most of 1995 due to the crop shortages, but reverted with the October contract. October is often referred to as the
"swing" month since it is the first opportunity to trade the "new crop."

10
,, .parity relationship.for European options on futur.8$.~.8 Spread trades identified as synthetic
futures (the simultaneous trading of a long call option and short put option with the same strike
price and expiration) were used to derive a synthetic futures price. It can be shown via an
arbitrage argument 1• that the following relationship holds:
C + K

e-r(T-~ =

p

+

F

e-r(T-~

(1)

where: C = price of the call
P = price of the put
K = strike price
F = tutu res price
r = risk-free rate of return 20
t = time to expiration.
During non-limit periods C, P, K, F,

r, and tare all observable, so this formula can be used to

gauge the efficiency of the market (which is done in Section IV.B below). During non-limit
sessions, the price of the futures, F, is not observable, so that the put-call parity equation can be
used to derive the synthetic futures price from the observed data by solving equation (1) for the
synthetic futures price, F':

(2)

Figure 2 displays the synthetic futures prices (denoted by a circle) and the actual futures

prices (denoted by a square) for the December 1995 futures contract for each day in September

18

Options on cotton futures on the NYCE are American,style options. In theory, American-style options should be worth slightly more than a European option (assuming the risk-free rate of interest is positive and there is
' the chance that it will be optimal to exercise an American-style option early). However, there are currently no
commonly used analytic formulas for valuing American-style options on futures and the derivation for European-style
options is generally considered an adequate approximation.
·
19

The put-call parity relationship is determined by arbitrage and is not based on any specific model of
asset pricing dynamics such as log-normally distributed futures prices. We describe the arbitrage relationship in
more detail in Section IV.B.
20

The risk-free rate is defined as the continuously compounded short rate of interest, which we implement
as the 3-month Libor rate. The same rate was used for all contracts since the Libor yield curve was relatively flat for
the period within the study.

11
.11995.. One observation per half hour ,of trading ,wa.s selected beginning at 10:30 a.m. and
ending at 2:30 p.m., resulting in a maximum of nine observations-per day. (Observations may be
missing, if the futures were not trading or a synthetic futures trade did not take place during the
half hour.) The horizontal lines for each trading day denote the allowable trading range for that
day·· within a four cent or six-cent range centered at the previous day's close. 21 The vertical
shaded areas show the times that the contract was "in limit'.' -- either trading was at the limlt price
or no trading took place due to the price limit.
Figure 2 reveals several interesting features in the data series. First, there is a very
close· match between the price of the actual futures trades and the price of the synthetic futures
trades during non-limit (unshaded) times. We examine this relationship in more detail in Section
IV.B. Second, there can be extreme differences between the price limits and the synthetic
futures price during limit periods (such as September 12 and September 13). Third, there are
sometimes days with up limit periods followed by days with down limit periods (such as
September 18-19). Fourth, news events specific to cotton are very often responsible for the
large jumps in prices from one day to the next. For example, on September 11, the USDA's
monthly report on U.S. cotton production forecast a huge 7 percent or 1.5. million bale decline
(the largest one-month change since they began such reports in 1960) in production from the
previous month. The release of this news resulted in an 8 cent increase in the October futures
contract between the closing futures· price on September 11 · and the syrithetic futures price on.,,,.
September 12. Finally, there are days where futures trades take place at the price limlt, even
though the synthetic futures price is significantly outside the price limit range. Some market
participants have a self-imposed mandate that restricts them from.trading options and therefore

21

Futures were subject to a 2 cent limit (4 cent range) around the previous day's close from September 1September 14, a·3 cent limit (6 cent range) from September 15- September 27, and a 2 cent limit (4 cent range) for
September 28 and 29.
·

12
.1hey.are confined to trading in the lutures.mar.ket.,~ven if doing so implies trading at a
disadvantageous price relative to the synthetic futures.

Ill. COMPETITION AND EFFICIENCY IN THE COTTON FUTURES AND OPTIONS
MARKETS

This section explore the competition and efficiency in the cotton futures and options
markets. Section IV.A examines the level of market concentration in the options spreads
market, both during limit periods and non-limit periods. Section IV.B explores the efficiency in
the futures and options markets by examining the arbitrage relationship between the futures
contract and the synthetic futures trade when the futures are not in limit.

A.

Broker concentration

An important component of a market's competitiveness is the extent of concentration,
among market participants. In general, a more highly concentrated market leads to less
competitive pricing for the end user of the good or service. This section documents the extent.of
market concentration in the market for option spreads on cotton futures. 22
Two measures of market concentration are used. First, we use the Herfindahl·
Hirschman index (HHI), defined as:

(3)

where, for our purposes, s; is the market share of the

t• broker and N is the total number of

22 As mentioned previously, options spreads incorporate various portfolio strategies including synthetic
futures, straddles, strangles, etc. As shown later in the paper (Figure 6), options spreads comprise 40 to 60 percent
of all options trades. Data limitations do not allow us to study the market concentration in the futures and outright
options market.

13
· , brokers. The HHI llies·,between zero-and one.. Jo,~perfectly competitive industry, the HHI would
approach zero, w~ile in a monopolistic industry, the HHI would attain the maximum value of.1.0.
Second,

Wf calculate the four-firm (CR4) and eight-firm (CAB) concentration ratios,

which are defined ~s the percentage of total Industry sales originated by the four or eight leading
firms, respectively In the case of the cotton options spreads market, it is the percentage of the,
total volume of op~ion spreads trades transacted by the largest four or eight brokers.

Table Ill p sents the results of the market concentration analysis. We divide the data
series into two pa s, the first in which the futures market was in limit the entire day (September
· 12, 13, and 21), a d the second in which there were.no limit moves (September 8, 22, and 25).
The number of Ira sacting brokers increases from an average of 50 on non-limit days to an
average of 93 on limit days, as volume increases from an average of 4482 contracts to 13402
contracts. The H I values range from approximately 0.05 to 0.12 on limit days to 0.07 to 0.17
on non-limit days. These ranges appear to fall in the average range of competitiveness for .
various represent live industries in the United States (Scherer and Ross, 1990, p.77).
Table Ill al o presents the CR4 and CAB ratios for the six days we selected. For
·example, the CR4 ratios range in value from .372 to .458 on limit days to .458 to .588 on nonlimit days. Like th HHI values noted above, the CR4 and CAB ratios fall within the average
range of competiti eness (Scherer and Ross, 1990, p.77). We also compared these results to
data reported In th •1995 Central Bank Survey of Derivatives Market Activity. ,,The results
. suggest the comp titiveness of the cotton futures market is similar to that of the over-the-counter
market for foreign xchange and interest rate derivative contracts booked in the U.S., and more
competitive than t e OTC market for equity derivatives booked in the U.S.
I'

Overall, these results suggest that the market for cotton options spreads is fairly
competitive and likely becomes more competitive on limit days versus non-limit days, as the

14
.number of brokers and volume increase, ,arid,th1M.oncentration indices decline.

B.

The arbitrage relationship between futures and synthetic futures
A main tenet of economic theory is known as the law of one price, which states that

identical commodities should have identical prices. If the prices of two Identical commodities
were to differ, this arbitrage opportunity would allow a trader to buy the commodity at the
cheaper price and sell the commodity at the more expensive price, thus netting a riskless profit.
The existence of arbitrage is not consistent with an efficient financial market equilibrium. In
~, equilibrium, identical commodities sell at identical prices, and there are no arbitrage
opportunities. In this section, we test whether the market for cotton futures and options allows
for a certain type of arbitrage opportunity.
More specifically, we empirically test whether the market for cotton futures and options
exhibits this type of arbitrage opportunity during non-limit periods by comparing the actual
futures prices, denoted F,, with the synthetic futures prices, denoted f',. A synthetic futures trade
provides the same cash flow as a genuine futures contract, and therefore, via the arbitrage
argument given above, should have exactly the same price as the futures contract. The
synthetic futures price for each trade is derived from the options,price using formula (2) from
Section Ill. The corresponding actual futures price is estimated as the average futures prices of
all the futures that were reported during the same minute as the synthetic f1:1tures was ,reported.,
We drop from the sample of matched synthetic futures and actual futures all observations where
the actual futures price was at the limit price for the day, in order to eliminate prices that were not
indicative of the equilibrium price of the futures contract. 23 Over the 20 trading days in

23 Recall that, when the futures are in limit, the futures spreads continue to trade unconstrained by the
price limit. The exchange records each leg of the spread separately, but the only economically important number is
the differential between the prices. The exchange never records the futures price on either leg of the spread outside

15
...September 1995, there are 235 observatior:is1hat.rneet the criteria for simultaneous actual
futures and synthetic futures.
The no-arbitrage condition between the actual futures and the synthetic futures implies
that the futures price should equal the synthetic futures price for all times t for which both an
actual futures and a corresponding synthetic futures trade:
F;

=

F1•

However, this equation will not hold with strict equality for two reasons. First, the times of the
actual futures trade and synthetic futures trade will not exactly coincide (a situation referred to as
•'·

"nonsynchronous trading") because there is a random delay (from one to five minutes) from the
time the trade is executed to the time it is reported. In addition, the equality will not hold
precisely because both the futures and the options have bid-ask spreads that are not explicitly
taken into account here. The bid-ask spreads add a measure of imprecision to the equation.
Therefore, in order to allow for these imperfections, we regress the actual futures prices on.the
synthetic futures prices for all contract expirations:
F;

=

130

+

131 F1

+

e:,

This regression should yield a coefficient of zero for 130 and a coefficient of one for 13, if the
market were efficient. The error term e1 is meant to capture the effect of nonsynchronous
trading and the bid-ask spreads, and is assumed to have zero mean and constant variance. 24
· · ·The condition of no arbitrage also implies that the changes in the actual futures prices .·,
should equal the change in the synthetic future prices:

the boundary of the price limits, even if the equilibrium price of one of the contracts would have been outside the limit
if the limit did not exist. Therefore, the spread trades that are recorded at the limit price must be eliminated from the
data set for the arbitrage test, because these prices at the limit do not represent the price at which each leg
individually can be transacted.
24

All of the regressions in this paper were re-done using White's (1980) heteroskedastic (nonconstant
variance) adjusted standard errors, and all of the results were robust to this adjustment.

16
t1F;

=

!1Ft

This condition, again, will not hold with exact equality, due to the problems of nonsynchronous
data and bid-ask spread. Therefore, we regress the changes in actual futures prices and
synthetic futures prices for the most active expiration month,

t1F;

=

130

+

131 11Ft

+

et

which should also yield a coefficient of zero for 130 and a coefficient of one for 131 • Therefore, for
both regressions, the null hypothesis that the market exhibits no arbitrage opportunity implies
that 130 = 0 and 131 = 1, which we test empirically.
. Figure 3 presents graphically the relationship between the actual futures prices and the

synthetic futures prices for our data set of 235 observations. The regression results (with
standard error in parentheses)

F;

=

-30.02
(27.76)

R2

=

+

1.0033 Ft
(0.0032)

o.9979

RMSE = 22.12

indicate that, consistent with the absence of arbitrage, the 130 estimate of -30.02 is not statistically
significantly different from zero and the 131 estimate of 1.0033 is not statistically significantly
different from one. Additionally, the high

R2 of 0.9979 shows the tightness of fit of the

regression.
·11 market participants were using synthetic futures contracts to ..replicate or hedge actual.~
futures contracts, they would be more interested in the relationship of the changes in these
prices more than in the relationship of the levels. Figure 4 presents the relationship between
the changes in the synthetic futures price and the changes in the actual futures price for 207
changes in price for the December 1995 contract. These regression results (with standard
errors in parentheses)

17

t,.F/

=

-0.128
(1.883)

R2

=

+

1.0099 8F1
(0.024)

o.8957

RMSE

=

27.08

also indicate that the ~o estimate of -0.128 is not statistically significantly different from zero and
the ~, coefficient of 1.0099 is not statistically significantly different from one. Additionally, the

R2

of 0.8957 shows a strong positive relationship between changes in the synthetic futures price
and changes in the actual futures price.
In summary, Figures 3 and 4 and the corresponding regression results support the noarbitrage conjecture for the-cotton futures market during times of no price limits. With the
exception of some sample variation, most likely due to nonsynchronous trading and bid-ask
spreads, the theoretically predicted relationships between actual futures and synthetic futures
appear to hold. This strong relationship between the prices for futures contracts and the
synthetic futures options strategy provides evidence of an efficient market between cotton
futures and options when the futures are not in limit.

UNIVARIATE ANALYSIS OF TRADING VOLUME

In this section, we explore how the futures price limits in the cotton market affect the
overall volume in cotton trading at the NYCE. In principle, the market volume traded could
decline significantly as price transparency is reduced by the price .limit; trading could .switch fro.ro
· one futures contract to futures-based trading strategies; or trading could switch from the futures
contracts to a variety of options-based strategies, including high-delta options (defined below),
synthetic futures, other spread trades, or individual options. First, we document how futures
trading decreases as price limits become binding on the futures contracts. Second, we explore
the response to these limits in terms of substitution from contracts in limit to those not in limit.

18
Thir.d, we develop a measure of aggre.gate trad,iQg.across futures and options to determine
whether the aggregate volume of cotton traded is influenced by the imposition of trading limits.

A. The effect of price limits on futures volume
Figure 5 presents the number of futures contracts traded (represented by bars and using

the left scale) and the fraction of the day in limit (represented by the line and using the right
scale), for the December 1995 contract for each trading day in September 1995. The fraction of
day in limit is defined as the ratio of the number of minutes in a trading session that the futures
' · ' •., traded at its 'limit ,to the ,total fl Umber of minutes in a trading session (250 minutes for cotton
futures). The bar representing the number of futures contracts traded is divided into contracts
that were traded as calendar spread trades and those that were not. The total number of
contracts traded is significantly negatively correlated with the fraction of day in limit. The
· univariate regression of the fraction of day in limit on the number of futures contracts traded
yields the results (standard errors are in parentheses):
Number of futures contracts1 = 7671 - 5113 Fraction of day in limit1

(758) (1591)

R2

=

o.329

RMSE

=

2656

The negative and significant coefficient on the Fraction of day in limit variable implies that a
·, ·

·significant decline in futures contracts traded occurs as the fraction of the day in limit increases,,
The regression suggests that, on average, 7671 contracts should trade on a day when the
futures is not in limit at all (Fraction of day in limit= 0) and 2558 contracts should trade on a day
when the futures is in limit ail day (Fraction of day in limit= 1).
One possible reaction by market participants to a futures contract hitting its limit price is
to use a futures-based trading strategy. For example, one way for a trader to gain exposure to

19
the December futures contract-thatJs.jn limit is tQ..R,Urchase a March futures contract that is not in
limit and to simultaneously short the December-March spread contract. 25 A univariate
regression of the number of overall futures spread contracts traded on the fraction of the day
that the most active contract (December 1995 expiration) was in limit yields the following results
(with standard errors in parentheses):
Number of futures spread contracts, = 1537 + 329 Fraction of day in fimit

1

(762) (457)

R2

=

0.023

RMSE = 732

This regression result suggests that there is not significant substitution from futures in limit to
other futures-based strategies, as the coefficient on the independent variable Fraction of day in
limit is not significantly different from zero. This result is not entirely surprising, since when one

futures contract goes into limit, other contracts tend to follow, thus rendering this strategy
infeasible.
Further analysis indicates that even when the most actively traded contract is in limit all
day while others are not, there is only a mild futures-to-futures substitution. For example, on
September 13, the December 1995 through October 1996 futures contracts were in limit all day
while the December 1996 contract was not in limit at any time during the day. The December
1995 contract traded only 540 contracts, down from an average of alm'Ost 7000 during non-limit•
days, while the December 1996 contract traded only 673, up from an average of 120 contracts
on days when the earlier contracts were not in limit. A drop of 6500 December 1995 contracts
coincided with an increase of only 550 December 1996 contracts. So, even during the

25

limits.

As mentioned previously, futures spreads, like options and options spreads, are not subject to price

20
· infrequent periods where one futures <:ontractis in.Jimit and others are not there is not
'

-

substantial futures-to-futures substitution of trading.

B.

The effect of price limits on options volume
Figure 6 presents the number of options contracts traded (bars and left scale) and the

fraction of the day In limit (lines and right scale), for the December 1995 contract for each trading
day in September 1995. The bar representing the number of options contracts traded is divided
into three parts: synthetic futures contracts, other spread trades, and outright options contracts.
· · The total number of contracts that traded is significantly positively correlated with the fraction of
day in limit. The univariate regression of the fraction of day in limit on the number of options
contracts traded yields the results (standard errors are in parentheses):
Number of options contracts,

=

4784 + 9272 Fraction of day in limit,
(913) (1917)

R2

=

o.541

RMSE

=

3162

Therefore, a significant increase in options contracts traded occurs as the fraction of the day in
limit increases. The regression suggests that, on average, 4784 contracts should trade on a day
when the futures is not in limit at all (Fraction of day in limit= 0) and 14,056 contracts should
· trade on a day when the futures is in limit all day (Fraction of day in limit= ·1 ).
Interestingly, each of the three categories of options-based strategies (synthetic futures,
other spread trades such as call spreads and straddles, and individual options) is significantly
positively correlated with the fraction of day in limit. We now explore some of the advantages
and disadvantages of various options-based strategies as substitutes for futures when limits are
in effect.

21
Trading could switch from futures to (.ligh-.d.elta options. High-delta options have price
sensitivities to changes in futures prices that closely resemble the futures itself. A single highdelta option has the advantage over combinations of low-delta options in that, like the futures
itself, high-delta options are not significantly affected by volatility (i.e., high-delta options have
low "vega risk"). The major difference between a high-delta option and a futures contract is that,
while the futures requires no upfront premium, the high-delta option generally requires a
significant upfront premium. Tables IV and V present evidence that there is not a significant
substitution between futures and high-delta options. Table IV displays the distribution of the
1

'"" ·

ratio of underlying futures price to the call options' strike prices (the "moneyness ratio'!) on three
days that the futures was not in limit at all (September 8, 22 and 25) and three days when the
futures was in limit all day (September 12, 13 and 21 ). This moneyness ratio is the major
determinant of an option's delta. 26 Table V displays similar information for put options. While
the average moneyness ratios indicate that the average delta of a traded option increases as
more of the day is in limit, careful consideration of the distribution of the moneyness ratio

"

indicates that, in fact, a lower percentage of high-delta options trade on limit days. The increase
in average moneyness is the result of decreased trading in out-of-the-money options and an
increased trading in at-the-money options. Market participants are not trading more high-delta
options in substituting options for futures.
Rather than using high-delta options, traders are using synthetic futures and other • , .,,
options spread trades to replicate the futures that are in limit. The two legs of a synthetic futures

26

This ratio is monotonically related to the option's delta. Given the times to expiration and interest rate
environment In the market for cotton in September 1995, for calls, a ratio of 0.9 corresponds to a delta of
approximately .25, a ratio of 0.95 corresponds to a delta of approximately .40, a ratio of 1.0 corresponds to a delta
· of approximately .5, a ratio of 1.05 corresponds to a delta of approximately .65, and a ratio of 1.1 corresponds to a
delta of approximately .75. For puts, this scale is inverted, with a ratio of 0.9 corresponding to a delta of
approximately -.75, etc.

22
contract each has a delta of approximately 0.5, explaining the increase in the use of options with
such deltas. The synthetic futures strategy is quite similar to the outright futures contract in that
it is not exposed to volatility changes, and has the advantage over high-delta options in that it
requires little or no up 0 front premiums. In addition to spread trades, limit days are accompanied
by significant Increases in individual options, which Is another method of gaining exposure
similar to that of a futures contract. For example, two long options contracts with a delta of 0.5
have the same price exposure as the futures contract (but have additional volatility exposure). It
may be the case that some of the individual options trading is recorded as individual options but
•in actuality may be,a synthetic futures (or other options-based strategy) that has been "legged
into," i.e., each leg of the exposure (the call leg and the put leg) is done with separate brokers, in
which case the trade would not get recorded as a spread trade, but rather as two individual
options trades.

C.

The effect of price limits on total cotton risk traded

The evidence from the graphed data and supporting univariate regressions clearly
indicates that futures volume decreases and options volume Increases as the futures price limit
is binding for a larger fraction of the day, with a variety of options-based strategies replacing the
in-limit futures contract. How complete is the substitution of trading from futures to options? In
order to address this question, a measure of the total price risk of cotton that is traded in.a day,is
needed. A reasonable way of aggregating the risk of futures and options that trade on the
exchange is to sum the futures volume and the options volume, where the options are weighted
by the absolute value of its own delta: 27

27

The delta of an option is the change in price that the option will experience if the underlying futures
contract increases by one. A futures contract (as well as a synthetic futures contract) has a delta of one. The delta
of an options contract will be between zero and one. When the strike price of the options contract is near the futures

23
Total cotton price risk traded1

=

NFutures

L
1•1

N0pr1ons

V;utures +

L

V6ptlons

1
X IDelta 1

i.:c1

where V~u1u,es represents the volume of futures contracts traded in trade i, V 01'P1ions
.
represents the
volume of options contract traded in trade i, NFurures is the total number of transactions involving
futures contracts,

N0p11ons

Is the total number of transactions involving options contracts, and

Delta1 is the delta of the option in trade i.

Figure 7 presents the futures-equivalent number of contracts traded (bars and left scale)
and the fraction of day in limit (line and right scale) for the December 1995 contract for each
· trading day In September Hl95. The -regression of the Total cotton price risk traded on the
Fraction of day in 1/mit indicates that these two variables are not significantly correlated

(standard errors are in parentheses):
Total cotton price risk traded1 = 9372 - 731 Fraction of day in limit1

(922) (1936)

R2

=

-0.047

RMSE = 3194

This result is evidence that the existence of price limits does not significantly limit the total cotton
price risk traded. There appears to be a seamless transition in volume from the contracts that
are in limit to the options market, to the extent that the total volume traded on limit days is not
significantly different from the total volume traded on a day that was not in limit at all.

D. Section summary
Price limits could potentially lead to several market responses suggested earlier.
price, its delta is approximately one-half. By summing the futures and the delta-weighted options, we arrive at the
equivalent number of futures that are represented by the total volume of trading. -We do not distinguish between a
negative and positive delta, because the sign of the delta depends on whether one is the buyer or the seller of the .
· 'Option, For example, a call option has a positive delta for the buyer, but a negative delta for the seller, Therefore, in
measuring total cotton price risk traded, we sum futures traded and the options traded, where the options are
weighted by the absolute values of their deltas

24
Empirically, we find that futures volume drops sigrailicantly while options volume increases
significantly, when price limits are in effect. The increase in options trading does not coincide
with trading in high-delta options, but rather does coincide with an Increase in synthetic futures
trading, other options spread trading and with individual options trading. There does not appear
to be a significant impact of the price limit on the total cotton price risk traded, but rather only a
substitution from the futures market to the options market. The efficiency of the options market
as represented by the close fit between actual futures and synthetic futures documented earlier
may help explain the willingness of market participants to transfer their volume over to the
options marketwhen the-futures go into limit.
We now turn from this univariate analysis to a multivariate analysis to determine the
importance of other variables on the volume of futures and options traded during limit and nonlimit periods.

V. MULTIVARIATE ANALYSIS OF TRADING VOLUME

This section explores more fully the effect of price limits on futures volume, options
·volume and total volume traded by using three explanatory variables in the multiple regressions
to help explain the patterns of the volume of contracts traded In the futures market, in the options
market and in the aggregate.
First, the fraction of day in limit,.as mentioned earlier, is the fraction of the trading day •,.,.
(out of the 250 minute daily trading session) that the futures price trades at the limit or does not
trade because the equilibrium price (measured by the synthetic futures price) is outside the limit.
Second, volatility is a measure of the price variability during the trading day. In most
financial markets, a positive relationship has been documented between volume and volatility.
More volatile days are associated with important news events, and the news, as well as the

25
· resulting movement in prices, tends to.give.market.participants reasons to trade to change their
exposures. The daily volatility estimate (derived by Garman and Klass, 1980), approximates
daily volatility on date t as a function of the closing price on date t-1 and the opening price,
maximum price and minimum price on date t. 2• For our purposes, we substituted the synthetic
futures price for the actual futures price for the fraction of the day that the futures was in limit to
determine each of the Inputs into the price volatility.
Third, the distance from the price limit to the equilibrium price in the absence of the price
limit (as measured by the average synthetic futures price) is used as another explanatory
· "' variable. If options have higher transactions costs than futures, then a trader may be more
willing to trade the futures at the limit price than to trade the synthetic futures at a slightly more
advantageous price, if the price advantage is less than the differential in transactions costs. In
addition, cotton traders may be less willing to trade on days where the futures price has moved
significantly outside the price limit boundaries when compared to days where the futures price
barely breaches the price limits, due to the increased lack of transparency on the days with
larger price moves.29 This measure is implemented by measuring the average difference

28

The formula that Garman and Klass (1980) derive is as follows. Let C, represent the closing price on
date t, o, represent the opening price on date t, H, represent the maximum (high) price on date t, L, represent
the
minimum (low) price on date t, u,= H,- o, d,= L, - O,, and c, = c, - Or Then the estimate of volatility on date
tis:

02 "'0.12 (0 r

C 1)2

-

t-

f

+

~-•

0.88 _u_
(1-~

where
i'J'' • 0.511(u1-d1) 2

-

0.019[cJu,•dJ-2u,dJ - 0.383c1'

and f is the fraction of the day that the contract trades (0.1736 in the case of cotton futures). We chose
to use this
formula over calculating the volatility estimate from the intraday data because such an estimate from lntraday
data
· ·will be function of the size of the bid-ask spread, which is not likely to remain constant between limit days
and nonlimit days. The Garman-Klass (1980) estimate is much more robust to differences in bid-ask spread.
29 For example, compare the small breach of the price limits on
September 7 and the large breach of the
price limit on September 12 in Figure 2. Traders may be more willing to rely on the prices from the.syn~h~t
ic futures
market on September 7 than September 12 due to the difference in the size of the breach of the pnce hm,ts.

26
· between the synthetic futures price .and the priGe.Jimit, .for those observations that were outside
the price limits. Therefore, on days in which price limits were not triggered, this value would be
zero, and on days that were in limit all of the time, this value would be the (absolute value of the)
difference between the average synthetic futures price and the price limit that had been
violated. 30
Tables VI, VII and VIII report the results of six specifications of the ordinary least

squares (OLS) regression of the form:
Volume traded1

=

130

+
+

131 fraction of day in limit1 + 132 volatility1
133 distance outside limit1 .

where Volume traded; is measured by three different dependent variables on date t Futures
contracts traded,, Options contracts traded,, and Total volume traded,. The first three

specifications in each table represent each of the independent variables by itself (univariate
regressions). The other three specifications represent combinations of the independent
variables (multiple regressions).

Futures volume: The univariate regressions for futures volume (Models 1, 2 and 3 in Table VI)
show that the fraction of day in limit and the distance from the limit price to the synthetic price
are significantly negatively related to futures volume. A larger fraction of the day in limit leads to
fewer futures contract traded, and a larger distance from the limit price to the synthetic price
leads to fewer futures contracts traded. The multiple regressions (Models 4, 5, and 6 in Table VI)
30 An additional independent variable, the number of days since the futures last traded unconstrained by
the price limits, is introduced to gauge potential "pent-up" demand. Pent-up demand to trade cotton futures may be

driven by traders who can only use the futures market due to institutional restrictions. In Figure 3, for example, the
December 1995 futures contract was in limit for two straight days •· from the close on September 11 to the open on
September 14. The inclusion of this variable tests whether there is unexpectedly high demand for futures when the
futures market opens after being in limit for a period of time. The coefficients on this variable were never
significantly different from zero (at the 10% level) and the inclusion of this variable in the regressions never changed
the sign or .the significance levels of the coefficients of the other independent variables.

27
·. suppol't the significance of all of the independent~ariables simultaneously. The volatility enters
the regression as significant when the other independent variables are taken into consideration.

Options volume: The univariate regressions for options volume (Models 1, 2 and 3 in Table VII)
show that the fraction of day in limit, the volatility and the distance from the limit price to the
synthetic price are significantly positively related to options volume. A larger fraction of the day
in limit leads to more options contract trading, a larger distance from the limit price to the
synthetic price leads to more options contracts traded, and a larger volatility leads to more
options contracts trading. The multiple regressions (Models 4, 5 and 6 in Table VII) support the
significance of the fraction of day in limit, but show that the volatility and the distance from the
limit price to the synthetic futures price do not have an independent effect on the volume of
options traded, after the fraction of day in limit is taken into account.

Overall volume: The univariate and multiple regressions for total volume of cotton traded
(Models 1-6 In Table VIII), defined again as the sum of the futures volume plus the delta. weighted options volume, show none of the explanatory variables individually, and no
combination of these variables, are able to explain a significant portion of the variability of the
total volume of cotton traded. The only variable that comes into the regressions as significantly
different from zero is the distance from the limit to the synthetic futures price in Model 6, which ,.
, ·

contains all of the explanatory variables; it is significant at the 10% level, but the entire
regression is not significant at the 10% level. The price limits and the characteristics of the price
limits that are impounded in these explanatory variables are uncorrelated with the total amount.
of cotton price risk that was traded during the month of September 1995.
The lack of explanatory power of any of the variables included in the regression raises

28
two.questions that•are difficult to.address,.directly••..Eirst, what is the true impact of price limits on
the trading of cotton risk, if an equivalent exposure is easily attained and an equivalent level of
trading transfers from the futures market to the alternative market? The fact that none of the
explanatory variables enter the Overall Volume regression as significant suggests that the
impact on trading volume Is most likely only cosmetic, shifting trading from one venue •· the ...,
futures pit •· to another venue •· the options pit, If the objective of the price limits is to limit
trading during volatile periods, which is the focus of most of the theoretical arguments in support
of trading limits, the objective is not being fulfilled.
· Second, shouldn't we·be able to explain some of the variation in volume? For example,
as mentioned previously, trading volume for many traded assets is positively correlated with
volatility; why not for cotton? Two further tests were performed to estimate the impact of futures
volatility on futures volume in the absence of the futures price limits. First, the futures price limits
are lifted in the last 17 days of trading for each of the futures contracts, (One effect of lifting the
price limits is to allow the settlement price to converge to the spot price as the expiration of the .
contract approaches.) Attempts to estimate the relationship between volume and volatility on
futures during these periods were unsuccessful, because as the expiration date of the futures
contracts approach, the volume quickly diminishes to near zero, The low volume is presumably
dominated by hedgers unwinding their positions so as not to deliver the actual cotton at
expiration, and arbitrageurs ensuring the futures and spot price remained aligned, Therefore,
we consider the results from a statistical study of the volume-volatility relationship during the last
17 days of futures trading to be unrepresentative of the broader relationship between volume
and volatility. Second, we attempted to estimate the relationship between volume and volatility
solely on days in which the futures did not go into limit at all. For the calendar year 1995, we ran
the regression

29
Futures contracts traded1 = 130 + 131 Volatility1

on each contract using daily data, eliminating the last 17 trading days of a contract (for reasons
given above) and days In which the futures experienced any limit period. The relationship was
not significant for any of the contract expirations studied (from May 1995 to May 1996).
However, this evidence of an absence of a volume-volatility relationship is,not strong .evidence, ,
· because the exclusion of large values in the explanatory variable (in this case, volatility on days
that experienced any limit periods), in general will decrease the likelihood of discovering a
significant relationship, even if such a relationship exists. It remains unclear why the relationship
""1letween·voiume and volatility, that is so clearly documented for other assets, does not appear in
the market for cotton futures.

VI. POLICY CONSIDERATIONS AND CONCLUSIONS

This paper highlights several points about the effects of exchange-mandated trading
limits on the level of market activity. We found, in the case of cotton futures, trading volume can
easily shift from one contract to another, and that the aggregate level of trading appears
unaffected by the price limits.
A broad implication of this result is that trading volume can potentially shift to another
domestic exchange, to a foreign exchange, or to the OTC market, if an exchange attempts to
unilaterally impose trading limits on its participants. This empirical finding strongly supports the,.
conclusion of the Brady Commission Report (1988) that, in order.for trading limits to be effective,
regulations need to be coordinated across markets. if the objective is to limit trading, then
coordination across market venues is critical.
While trading volume does readily shift from one market to another, an Interesting
question arises concerning the effect of price limits on the quality of price quotes and trading

30
· during limit periods versus•non-limit periods •. .f.o.i;.example, the trading limits could produce some .
forms of market inefficiencies, because the shift from futures contracts to options-based
strategies potentially shifts the price discovery mechanism and the transfer of risk function from
the futures market to the options market where there is less transparency. 31 This phenomenon
could serve as the focus of future research.
Another Important policy consideration is that not all market participants are Influenced in
the same way by the imposition of a price limit. As mentioned previously, some investors may
be constrained by individual Institutional rules that forbid them from trading options. These
investors ·have no'Choice ,butto trade the underlying futures contract when the limits are in effect
(at a price dictated by·the limit), even though they could potentially receive a more
advantageous price trading the equivalent synthetic futures.
In order to fully evaluate any trading limit, including price limits, one needs to address the
intended effect of the trading halt•· why the exchange imposes trading limits. The focus of this
paper, however, is strictly on the observable effects of price limits on trading volume. We
conclude that their effect on trading volume is, at most, minimal.

31

The price of the underlying (the futures contract) becomes an unobservable variable along with the
volatility of the underlying, which is always unobservable.

31

. References
Anderson, Carl G., C. Shafer, and M. Haberer, 1996, Producer price for cotton qualities vague,
1996 Beltwide Cotton Conference.
Brady Commission, 1988, Report of the Presidential Task Force on Market Mechanisms, (U.S.
Government Printing Office, Washington, D.C.).
Brennan, Michael J., 1986, A theory of price limits in futures markets, Journal.of Financial .
Economics 16, 213-233.
Cantor, Richard, 1989, Price limits and volatility in soybean meal futures markets, The Federal
Reserve Bank of New York Research Paper, No.8904.
Chance, Don M., 1994, Futures pricing and the cost of carry under price limits, The Journal of
Futures Markets 14, 813-836.
Commodity Futures Trading Commission (CFTC), 1988, Final report on Stock index futures and
cash market activity during October 1987 to the U.S. Commodity Futures Trading
Commission, in: Kamphuis, Kormendi and Watson, eds., Black Monday and the future of
the financial markets (Dow Jones-Irwin Inc., Homewood, Illinois), pp 341-360.
Fama, Eugene F., 1989, Perspectives on October 1987, In: Kamphuis, Kormendi and Watson,
eds., Black Monday and the future of the financial markets (Dow Jones-Irwin Inc.,
Homewood, Illinois), pp 71-81.
Hieronymus, Thomas A., 1971, Economics of Futures Trading for Commercial and Personal
Profit (Commodity Research Bureau, New York).
Khoury, Sarkis J., and G. Jones, 1983, Daily price limits on futures contracts: Nature, impact,
and justification, Review of Research in Futures Markets 3, 23-39.
Kodres, Laura E., and O'Brien, Daniel P., 1994, The existence of Pareto-superior price limits,
The American Economic Review 84, 919-932.
Lee, Charles M. C., M. Ready, and P. Seguin, 1994, Volume, volatility, and New York Stock
Exchange trading halts, Journal of Finance 49, 183-212.
Ma, Christopher K., R. Rao, and S. Sears, 1989, Volatility, price resolution, and the effectiveness
of price limits, Conference on Regulatory and Structural Reform of Stockand Futures
Markets.
Scherer, F.M., and David Ross, 1990, Industrial Market Structure and Economic Performance,
3rd Edition, (Houghton Mifflin Company, Boston) .
. . Subrahmanyam, Avanidhar, 1994, Circuit breakers and market volatility: A theoretical
perspective, Journal of Finance 49, 237-254.

32

Table I

Futures Data

a;

i~ffi'll!l,~ble prov)dee example. oUhe data that are provided In the Time and Safes file for the
,i!>;o~Y[~llpn$l'acts :~rovid'3q by,tf:le New York Qo!:lon ExchaQge.
·s:tt\)!Itl,,r,,:,;y,,-::~:"''.:Yl:::,-~;~t"r·::>-~, -•s'·•.---•:_,·?:-_·•-··•--~?if~:- ____
.:- . > -..--::

\,!brr';;k,;if ·;.
19950901
19950901
19950901
19950901
19950901

1995
1995
1995
1995
1995

10
10
10

10
10

1030
1030
1030
1039
1039

8445
8440
8430
8360
8350

Table II

_, it 1:

..

Options Data

.,
•· · 'fnls'tableprovides ·an example of the data that are provided In the Broker Reconcillationflle
.. ,.,
·•· •· ~'lfor•alfroption~£Ontracts and• futures spread trades1provided ·by the New York Cotton
..
t;' ,_' .·; .
.,
Exchange.
,.

fl"f~dePate

19950901
19950901
19950901
19950901
19950901

....

"\

Contract· Contract
..
Motith .·· Year

10
10
10
10
10

1995
1995
1995
1995
1995

Strike
.•

7000
7000
7300
7600
7600

Call/
Put
C
C

p
p
p

Premium

Volume

'.Flme

.

1510
1600
5
12
7

6
7
1
1
10

1121
1250
1030
1134
1212

Trade
N.umber

50019
50013
50001
50056
50007

33

T,_blelll

Oonc.entration•8atlo.s for eottoJ\1 e~o.~er,1
... ... •t.(r;:ci.-:Yr,1/ \ . • ·•·'~.ntJ
•~··
···t.i'adm~
.,.~•.··• .: \•?*:·•
. ·•
-~~:f'l!';t_,,~». -{: -,.;.;
?t·•/J,,!!JJ1:.-iJvi.''i ·-'
,:/,J;j:

:·.•.• >•Sei,,,L.s'.,•• .•; i .,

--~$

'

'.'."'.0f\. ,,J-::.'.

;;.•<·-·--'~:,_,,,. -\ • -.,

-;y,-_-,.. '"':10;.,,J:

;

,, · :·-

:--J\ · ·-·. :.;" ·,,,
-:f'.---,c.,;,,_.,·.<?14)\·-/·''-:;v_:-~->--·

,_

1/'-'IYef -·:
':-t-;; :: ;,, ;
.vi• .•:c.·
· -·.--·" :.,·;:.:.:.':··--,,::{'.•"-,···,

'i111!iistabl~·!ihowil different measuresrof broker concentration in the options
ma1'ketdn$eptember H19j5. J1rne clata are btoken into limit days
r1'el!>tem~~r12, l$,a.nd 2t) a.ndm0h'1lin'l1t daYs{Sept~mber 8, 22, •and 25;). the
!\f:il~nl,t~.@l#l?li~9hma:n index ·is d~fil'IEt<i . as ·the sam· of the sqaaredmatketslllar.
·
~ffl:i~;J;>rpl<ers, anti the 4~bt9kerancJ,8•broker oe>nqentration,ratios ar•,fllfe,
~"',
-~s;tf:ta .t :invlllve.th!:l+mPst,,active,4 a.Ad•8 brpkers,.J'Elspemi~y. .· .·
'~~ voh.nne of option$preatls is defined as the nunilier of options contracts that·
'.'t~detl ,thatwere designated as .$pread trades, and the total namber of
'transacting brokers is definedas thenamber of brokersthatwe.re involved in at
>1111a~t one optie>ns spread trade daring the day.
UmitOays

Non-Lll'lilt

Days

Sept 12

Sept 13

Sept 21

Septa

Sept 22

Sept25

0.0569

0.1189

0,0615

0.0891

0.0709

0.1683

~arokerfiatio

.372

.458

.441

.496

.458

.588

8-Broker Ratio

.607

.609

.610

.680

.669

,796

9296

12841

13683

2094

5876

5477

85

88

106

50

57

43

·Helflndahl•lllrschman
·Index'

}f.gtt1me of. Option

~pr,ads

;,iotal#of
ifr:l!n.sactlng Brokers

The Herfindahl index measures the amount of market concentration in an industry. The index
number lies between zero and one, where zero represents perfect competition.

34
•s

___

_

_ •"

Tal)lelV _-- _- _-_ _

r::

<:: -_ _ ' .1'"?

Di$tribution of Mbneyness Ratfos 1)·aded on .t..imit Day• anij Non-L.im\l

, CALL QPTiONS

wtiele

Distnbllft6n of m~·ratios _for three llrr11t days and t~~. ti()ll<-limit days;·
the rrt~e
themostrecentfutures price (or synthetic futures price for 6mit days)i,jl,ided by the.siriki
-

-

_r

- .\.

=

"is defined•im the ratio of
of the option:

-

Moneyness Ratio R rutures price lstiie priel:I

i\?f

-"~'..:."'
~-

Fraction
ofdayln

Fl<0.90

0;9<><F1<0.95

0.95<R<t.0

1.0<R<1.05;l 1.05<R<1.1

R>1.1

lt.k0,25

0.25<1t.l<0.35

0.35<1Lll.<0,5

o.s<1At<o.as;; :o,65<1t.l<0.75

lt.1>0.75

I

0.1

0.0

19.5

11.0

11.1

37.1

1.9

0.0

2.9

14.5

22.1

53.8

2.5

2.1

5.0

38.6

13.3

41.1

0.7

1.2

1.3

25.3

21.3

29.0

0.0

5.5

Septa

None

0.92

60.9

27.2

4.8

6.9

Sept22

None

0.99

10.8

26.8

20.7

Sep_t 25

None

0.96

34.7

23.1

Sept 12

All

1.00

4.8

Sept 13

All

0.98

Sept 21

All

1.01

35

r _·: .-_.-;.:, ,r~<-'.:~r--_--:, -/_ :_:-_-,•_"' -.-. ,:,-·_. ·"'• ·. _·7·-:~te·v=: ,' "· _ ·- _-~"\ili\_ - .- .-">?··-··:<'
Ois-qttott cd Mdneyness Raftos Traded on ~imit o,,s
anfit Non~iffiit
PUT OPTION$
.
PistrlOOti~!l ofn\~neyliel!$ rafii>siorthree rirnit days and thtee ddn4imtt~. Wile~ tlie ril~~~·-•·rned as the tat/o of
.

.

,

,,

~

the tllpst recent futures price (or synthetic .futurE?S price for limit da~) div!tled byt~~ ~rike~s<lf ffi~ option:
•
.t
-A::
:·.
--- ..
-._,_ - :,,
- .- - _. - l·.-- --.
MoneyneSS Ratio. Ft:; Futures. priceistfikeprie::e..
.
.,,..
'
,.w

.'... ·

"

,,,

',

•i'. ' '""
~--

·

R:>1,1

R<0.9

Septa

None

1.04

25.1

12.7

29.8

30.0

2.3

0.0

Sept22

None

1.03

31.9

39.9

18.6

18.6

0.0

0.0

Se.et 25

None

1.06

65.2

13.8

13.9

2.0

5.1

0.0

Sept 12

All

1.04

12.9

21.6

54.0

11.6

0.0

0.0

Sept 13

All

1.03

27.3

12.4

20.9

39.3

0.0

0.0

Sept21

All

1.04

26.9

33.2

22.5

17.4

0.0

0.0

36

~ - F . . . -i!i•'II- . ·... '!{ .. · . . ·•· •·
.
,
:r,
Rtig~sfons of Fbtures Voturrte on Pos.sibtellPfanatery
.

.

.

'

•'

. ' .. :.<:_, ___ ,:· .----·

' '

·=>·":''}

".· .
oi~x~1icatiortSoflblJI'f<jJ1°'Wing
resu1ts.:--•-•.
the
~:;lfh,s ™>1e reports
"'•',
', •.,•
v_,)•·:.-"'·, ·,,
. . ., · futilres vo/ume tradedi = 130 + 131 fraction of day l~ limit1 + 132 vofi
\>· ·,,· :__ '._

·•

"

'.c,';

i.

t"__ .··. ---

.

.

·

'_-._

.1

.

,:_.·-<~?;{,,, ,_:_

',

,-_

·••

e outsk.fe~it,.
;+ ·.~: distanc
·/ ... ,.. _'..,.i .
'

"' +··--

Mdieis 1-3 are the uniVariate regres$fons with one ir'ldepencffl~variatileat a
M9(l~s 4-6 are the multiple regressioli~,with combinations RJ the independe1

Model

FUTURE$.

';,':'

Multl pl~~s ions

Univariate ijgres!illons
General effect
Intercept
Fraction of day in limit
Volatility
Distance. from (jmit tc:)
tic pr1~
average synthe
""',,,
c·---··---· '·

1

f>oSitive

+ 7671 •••

I 1'4~ative

-5113* **

2

+ 6810 •••

F•value for entire
regressfon
indicates significance at the 10% level
*
••
indicates significance at the 5% level
indicates significance at the 1% level
***

4

. 6

5
-"~

+ 7669 •••
-5125 ••

+ 7539 ***

+ 6634 ***

*

- 3183 *

- 3457

+ 303 **

1
-10

- 18.69 ***

I Negative

-2

+ 6800 ***

-125

Posi~ive

R

3

- 33 **

0.329

0.051

0.285

0.290

0.355

0.471

10.323 ***

2.014

8.558 •••

4.567 **

6.227 ***

6.643 ***

37

,__ -__ . :_:_

['-·

.

.:

·.

. .

""- ·-·=-/F;_._,_,.,_"----> :·---- . ." _,_--,- ... ?0r:--,----~- - "·'-'/?2s:r'-·- -~J!w_)CT<,, ,able VU . .,·. ..·.·.. ·..· . .,.,.. . .· ...• / c·. ~ .

-

. ·.

.

R~essie>ns of Options .votiijne on Pb(sibte ifcpra~ : . ·; bf•
·,:.

1

,

- 1:

,

'3

·

This table •reportslhe reso1tsof~x.~peemca~rls~~~c,~{f~

·2 Options· volume:h-;JdecJ1. = /!0 f /!1 fractkJn of ~Sf itJi,~. f '1}2 Vf9a'titfti .· k
'~
;
t R cJi. ta " ui{;Jtli!J .~ : .. ..
•;, :'
l: fl . ' .:='
':f'-_-, , : ,•·. \{ t-'3 _· lS ~_:f!;~::_.-_-·-::-,-::'f!l/#ltt '.-_)>::_t,}:_:_,:·;/ . --.:-/I/"i_\_

I

M~ 1-3 !!re the univariate regressii>nswith one intlepen~v~~a1J~fmlie
Modfils
4-6 are the multiple
regressions
with comtsinations·olihe indepm\dent
. _.-·---~·
_,
-~-- ...~les
\,_,

L

--~

-•"•

-

'

.

OPTIONS

1·Qenet1'1 effi!ct

1

"

Positive

+ 4784 •••

F=ractiO!' of day In tlinlt

Pd$itive

+ 9272 •••

Volatifi~•~ .

Non.e

1n,er~p1

.r.

~.::-~

Dlstar\¢9 from tilnit to,
a.vera.9.· . e"SJrithetic grf(:e.
,C,,•-°'

Model
.
.:C.. ..C..c._:_,,_:_::23_._~ -·-

_ . -~

Univariate· ri!lrressions

,,,,,'

.. 0 . . '

~

+ 6763 •••

l None

I
0.541

',
0.106

--

F-value tot entin!
regression
•
••

•••

indicates significance at the 10% level
indicates significance at the 5% level
indicates significance at the 1% level

23.385 •••

3.255 *

6

+ 4786 •••

+ 9325 •••

+9253*** I +9236***

+ 22.75 ••

Ji.

s

-4

(

R2

I

+ 6357 •••

*

;
A~-

:4

3

+ 6358 •••

-

~~•~ple.·iffl~sions

-

2

+225

''

f"
..

.

0.182
5.231 ••

+ 4841 •••

-18
0

+1

0.514

0.484

..

0.514
11.045 •••

11.043 •••

6.936 •••

38

. .· tahie viu ·.
. ..
..·•· ·
RegtflSions of Overall Volume on Pos$fbte tip.Ian~
.

:!Hes

.•. •This table repo~ the results 6f 'six specifk:a.tlons Of mitortoWing i~
Total volume traded, = 130 +, 131 fraction of day in ~ + ~ vatatidljf,i• •
;;,t0.~.•.·

.f,_ ..,-3
~. distance
oufsfde
."tf~-..,
iM.1t.·· .
···
.

··

.· ,1?,h,;

0

MoqE!ls h3 are the univariate regressfons with one i n d ~ varlalJle at a ' '
Models 4-6 are the multiple regressiohs With combinations of'the1~ent
so_''

.

'

''"

/

'

.'

'.

.

', ,'

"~

•

Model

AGGREGATE VOLUME

-·'i:"C;<·---"'' "' '

Muitrpl& ~i!ll:dons

Unfvariate regressions.
G~raleffect

J Foisitive

Intercept .

Fr~ction of day In lim~.... lN<ine
Volatility.

1
+ 9371***

llfult t1>

average synthetic
pti~
-,...
·-,_~

+ 9264 ***

None
. '
None

4

3
+9442···

- 731

n

+9380···
-686

- 21

~:<.'f:o.

Distance from

2

5
+ 9235 •••
+970

-4
-8

6
+ 8355 •••
+ 1236
+295

- 11

- 33

,•

R.2
F-value for entire
regreSiiOn
•
indicates significance at the 10% level
••
indicates significance at the 5% level
•••
indicates significance at the 1% level

-0.047

-0.052

0.013

-0.108

-0.036

0.05

0.143

0.053

1.240

0.068

0.667

1.373

*

· FIGURE 1

DAILY CLOSING PRICES FOR MOST ACTIVELY TRADED COTTON
. FUTURES CONTRACT
1991 -1995

100

80

60 -I
I

3/91

7/¥1
-

51p1

I

!

5/941

r2/9$
I

10/91

'

3/94

17/94

10/94 i
!12194

3/95

12/95

?/95
$/951

io/95

I

Figure 1 presents the daily closing prices (in cents per pound) for the most active cotton futures
contract from year-end 1990 ot year-end 1995. Contracts are separated by verticles lines and
are identified by expiration month/year.

FIGURE2

FUTURES & SYNTHETIC PRICES AT 30-MINUTE INTERVALS
December 1995 contract

I
I
I
I

0.95

fl
_r

l~vd

¢'

0.90

0.85

0.80 -

.

0.75

I
I
I
I
I
I
-I
I
I
I
I _I
1-1
I
I
I )-1
I_I_
I ·--~
I . I

!

I
I
I
I
·1
I
I
I
I
I

I
I
I
I
I
I
I
I
I
I
I
I

p

. ,J'/

!

-~

1-1_1_
I
1-1
I
I
I
I
I.
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
9/27 9/28 9/29

Figure 2 presents the level of futures prices and synthetic future prices (in dollars per pound) for
the month of September 1995 for the December 1995 cotton futures contract. There are 9
observations per day, one per half hour from 10:30am to 2:30pm. The horizontal lines each day
represent the price limits, the 4-cent or 6-cent band of prices, centered around the previous day's
close, in which all transactions must take place. The solid squares represent the levels of the
futures prices, and the hollow circles represent the levels of the synthetic futures prices. The
· vertical shaded areas represent times when the futures were trading at the,limit or when the
futures were not trading at all and the synthetic futures prices were outside the price limits.

FIGURE3

ACTUAL FUTURES PRICES & SYNTHETIC FUTURES PRICES
September 1995 for contracts of all tenor
10,000 , - - - - - - - - - - - - - - - - - - - - - - - - ~

9,500 r

/-~

Q)

0

'C:

a.

9,000

~

1/)
Q)
~

:::,

'5

lL
0

""
..c

-5Q)

8,500

JI

~

(/)

8,000 -

,.

,,..

•

,,prf

••

,Ill

\

7,500 ~ - ~ - - ~ ' - - ~ - ~ ' - - ~ · - - - ' ~ - ~ - - ~ ' - - - ' - - - - - - - '
7,500
8,000
8,500
9,000
9,500
10,000

Actual Futures Price

Figure 3 presents the relationship between the actual futures price and the synthetic futures
prices (in points per pound) during the month of September 1995 for futures contracts of all
tenors. Each synthetic futures trade in September was matched with a futures contract of
the same tenor which was reported at the same minute. If more than one futures or
synthetic futures traded were reported at the same minute, the equally weighted average
futures or synthetic futures was used.

F/GURE4

CHANGES IN ACTUAL VERSUS SYNTHETIC. FUTURES PRICES
September 1995 for December 1995 contract

800 . - - - - - - - - - - - - - - - - - - - - - - - - - - ~

•
600

400

-

••
•

200

•
•
••

••

•

•

0

,I'
·200

••
• ••
•

-400 .___.,___
-400

_.__......__
-200

_ _ . _ _ ~ - - ~ - - ' - - - - ' - - . . . . . . __
0

200

400

_ _ . _ _ ~_
600

___,

800

Change in Actual Futures Price

Figure 4 presents the relationship between changes in futures prices and synthetic futures
prices (in points per pound), using the data used in Figure 3, but for the December 1995
contract only.

FIGURES

VOLUME OF FUTURES TRADES VERSUS FRACTION OF DAY IN LIMIT
20 , - - - - - - - - - - - - - - - - - - - - - - - - - , - - - ~ 1.2

15

Cl

w

•

SPREAD TRADES

B

NONSPREAD TRADES

•

Fraction of day In limit

:::;

Cl

<
a:
t--

~

t-~

0.8 1!;
u,

~

-g

"'u,

"

~
a: t--

10

0.6 IL
0

0

.c

z

t--

z
0
u

0
0.4

5

~

a:

IL

0.2

·o

o
1

5

6

7

8

11

12

13 14 15 18 19 20 21
DATE

22 25 26 27 28 29

Figure 5 presents the daily total volume of futures contracts for the month of September 1995
' (bars and left axis) as well as the fraction of day that the December 1995 contract was in limit.
• The total futures volume is broken into two catagories -- spread trades and non-spread trades.
The graph highlights the relationship that few futures trade on days that are in limit all day (such
September 12, 13 and 21) relative to days that are not in limit at all.

FJGURE6

VOLUME OF OPTIONS TRADES VERSUS FRACTION OF DAY IN LIMIT
25

1.2
P2 Synthetic futures
•

20 0
w
0

<
a:

Other spread trades

t::
:::;

IE Nonspread option lrades

El

::;

Fractiion or day In limit

0.8

.,"'

I-

-c

~
C)

gi

15

~

C:

0

0.6 u.
0

0

<
a: i=
Iz

z

z

10
o:4

0

C)

~

a:
u.

5
0.2
0

0
1

5

6

7

8

11 12 13 14 15 18 19 20 21 22 25 26 27 28 29

DATE
Figure 6 presents the· daily total volume of options contracts for the month of September 1995
(bars and left axis) as well as the fraction of day that the December 1995 contract was in limit.
The total options volume is broken into three catagories •· synthetic futures trades, other spread trades,
and non-spread options trades. The figure highlights the relationship that more options trade on
; days that are in limit all day (September 11, 12, and 21) than on other days.

FIGUR El

TOTAL RISK TRADED VERSUS FRACTION OF DAV IN LIMIT
30
1.2
•

'C

Ill Delta•adjusted options volume

Cl)

'C

A

~

tl

i
0

"

i:

i

:,
CT

Cl)

'

Fu1ures volume

Fraction of day In tlml!

I-

20
0.8

i::,"'
"'
0

0.6

i=

~
:J
~

~

IL

0

z

0

10

0.4

"'
I!!
:,
'!5

IL

j::

u<(
er
IL

0.2
0
1

5

6

7

8

11

12 13 14 15 18 19 20 21
Date

0
22 25 26 27 28 29

• Figure 7 presents the daily total risk traded (defined as the sum of the.futures and
the delta•
' weighted options volume) for all contracts traded in September 1995, as well as
the fraction of
the day in limit for the December 1995 futures contract. The total risk traded is broken
into ·
two catagories: the futures volume and the delta-weighted options volume. The
analysis i
indicates that the fraction of day in limit and the total risk traded. are not significantly
correlated.

FEDERAL RESERVE BANK OF NEW YORK
RESEARCH PAPERS

1996

·The following papers were written by economists at the Federal Reserve Bank·•of•New
York either alone or in collaboration with outside economists. Single copies of up to six papers
are available upon request from the Public Information Department, Federal Reserve Bank of
New York, 33 Liberty Street, New York, NY 10045-0001 (212) 720-6134.

9601. Bartolini, Leonardo, and Gordon M. Bodnar. "Are Exchange Rates Excessively Volatile? And
What Does 'Excessively Volatile' Mean, Anyway?" January 1996.
· 9602. Lopez, Jose A. "Exchange Rate Cointegration Across Central Bank Regime Shifts."
January 1996.
9603. Wenninger, John, and Daniel Orlow. "Consumer Payments Over Open Computer Networks."
March 1996.
9604. Groshen, Erica L. "American Employer Salary Surveys and Labor Economics Research:
Issues and Contributions." March 1996.
9605. Uctum, Merih. "European Integration and Asymmetry in the EMS." April 1996.
9606. de Kock, Gabriel S. P., and Tanya E. Ghaleb. "Has the Cost of Fighting Inflation Fallen?"
April 1996.
9607. de Kock, Gabriel S. P., and Tania Nadal-Vicens. "Capacity Utilization-Inflation Linkages:
A Cross-Country Analysis." April 1996.
• 9608. Cantor, Richard, and Frank Packer. "Determinants and Impacts of Sovereign Credit Ratings."
April 1996.
9609. Estrella, Arturo, and Frederic S. Mishkin. "Predicting U.S. Recessions: Financial Variables
as Leading Indicators." May 1996.
9610. Antzoulatos, Angelos A. "Capital Flows and Current Account Deficits in the 1990s: Why Did
Latin American and East Asian Countries Respond Differently?" May 1996.

9611. Locke, Peter R., Asani Sarkar, and Lifan Wu. "Did the Good Guys Lose? Heterogeneous
Traders and Regulatory Restrictions on Dual Trading." May 1996.
9612. Locke, Peter R., and Asani Sarkar. "Volatility and Liquidity in Futures Markets." May 1996.
9613. Gong, Frank F., and Eli M. Remolona. "Two Factors Along the Yield Curve." June.1996.
9614. Harris, Ethan S., and Clara Vega. "What Do Chain Store Sales Tell Us About Consumer
Spending?" June 1996.
9615. Uctum, Merih, and Michael Wickens. "Debt and Deficit Ceilings, and Sustainability of Fiscal
Policies: An Intertemporal Analysis." June 1996.
9616. Uctum, Merih, and Michael Aglietta. "Europe and the Maastricht Challenge." June 1996.
9617. Laster, David, Paul Bennett, and In Sun Geoum. "Rational Bias in Macroeconomic Forecasts."
July 1996.
9618. Mahoney, James M., Chamu Sundaramurthy, and Joseph T. Mahoney. "The Effects of
Corporate Antitakeover Provisions on Long-Term Investment: Empirical Evidence." July 1996.
9619. Gong, Frank F., and Eli M. Remolona. "A Three-Factor Econometric Model of the U.S.
Term Structure." July 1996.
9620. Nolle, Daniel E., and Rama Seth. "Do Banks Follow Their Customers Abroad?" July 1996.
9621. McCarthy, Jonathan, and Charles Steindel. "The Relative Importance of National and Regional
Factors in the New York Metropolitan Economy." July 1996.
9622. Peristiani, S., P. Bennett, G. Monsen, R. Peach, and J. Raiff. "Effects of Household
Creditworthiness on Mortage Refinancings." August 1996.
9623. Peristiani, Stavros. "Do Mergers Improve the X-Efficiency .and Scale Efficiency.. of U.S.
Banks? Evidence from the 1980s." August 1996.
9624. Ludvigson, Sydney. "Consumption and Credit: A Model of Time-Varying Liquidity
Constraints. " August 1996.
9625. Ludvigson, Sydney. "The Channel of Monetary Transmission to Demand: Evidence from the
Market for Automobile Credit." August 1996.

9626. Sobol, Dorothy M. "Central and Eastern Europe: Financial Markets and Private Capital
Flows." August 1996.