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Market Liquidity and Trader Welfare in Multiple Dealer
Markets
Evidence from Dual Trading Restrictions
Peter R. Locke
Commodity Futures Trading Commission
2033 K Street, N.W.
Washington, DC 20581
202-418-5287
Fax: 202-418-5527
E-mail: PLOCKE@CFTC.GOV
Asani Sarkar
Federal Reserve Bank of New York
Research Department
33 Liberty Street
New York, NY 10045
212-720-8943
Fax: 212-720-1773
E-mail: ASANI.SARKAR@NY.FRB.ORG
Lifan Wu
California State University, Los Angeles
Department of Finance and Law
5151 State University Drive
Los Angeles, CA 90032
213-343-2870
Fax. 213-343-6461
This version: July, 1998
Sarkar and Wu are grateful to the Office for Futures and Options Research of the University of
Illinois at Urbana-Champaign for financial support, and to the Commodity Futures Trading
Commission and the Chicago Mercantile Exchange for the provision of data. We also thank the
referee, the editor, Paul H. Malatesta, and seminar participants at the Federal Reserve Banks of
Atlanta and New York for comments. The views stated here are those of the authors and do not
necessarily reflect the views of the Federal Reserve Bank of New York, the Federal Reserve
System or the Commodity Futures Trading Commission or their respective staffs. All errors and
omissions are our responsibility alone.
Market Liquidity and Trader Welfare in Multiple Dealer Markets
ABSTRACT
Peter R. Locke
Asani Sarkar
Lifan Wu
JEL Classification number: G12, G13, G18
In the context of dual trading restrictions, we examine whether aggregate liquidity measures are
appropriate indicators of trader welfare in multiple dealer markets. Consistent with our theoretical
results, we show empirically that dual trading restrictions did not affect market liquidity significantly,
but dual traders of above-average skills may have quit brokerage and switched to trading exclusively
for their own accounts following restrictions. Further, customers of these dual-traders had lower
trading costs in the period before restrictions relative to the trading costs of all customers after
restrictions.
Market Liquidity and Trader Welfare in Multiple Dealer Markets
I. Introduction and Background
The market microstructure literature has, at least since Demsetz (1968), focused primarily on the
bid-ask spread as a measure of transactions costs and market efficiency. It has long been recognized,
however, that the quoted bid-ask spread is inadequate for measuring market liquidity. According to
Stoll (1985) and Grossman and Miller (1988), for example, the bid-ask spread measures liquidity
precisely only when the market maker simultaneously crosses a trade at the bid and the ask.
Hasbrouck (1993) discusses the shortcomings of traditional measures of transactions costs (such as
the bid-ask spread) and proposes new, improved measures of liquidity.
In spite of criticisms, the bid-ask spread continues to be widely used for comparative market
analysis and regulatory studies, as Hasbrouck (1993) points out. For example, an important
regulatory issue of recent times is dual trading, a practice whereby floor traders on a futures exchange
execute trades for their proprietary accounts and customers on the same day.1 The extensive
literature evaluating the market liquidity impact of restrictions on dual trading focuses mainly on the
bid-ask spread. The empirical evidence, however, remains confusing. Depending on the market
studied, the correlation between dual trading and the bid-ask spread may be negative, positive or
zero.2
In this paper, we provide---in the context of dual trading regulation---additional theoretical and
empirical evidence that aggregate liquidity measures (such as the average bid-ask spread) may be
misleading indicators of traders' welfare in multiple dealer markets. In particular, we argue that, if
dealers are heterogeneous with respect to trading skills, then the average bid-ask spread measures
customers' cost of trading with a dealer of average skill. Therefore, a regulation may have little effect
1
on the average bid-ask spread, but still hurt highly skilled dealers and their customers.
Our theoretical model analyzes the consequences of "dealer heterogeneity”. In the model, based
on Spiegel and Subrahmanyam (1992), hedgers and informed customers execute their orders through
futures floor traders (dual traders and pure brokers). Risk-neutral informed customers trade based
on signals about the asset value. Risk-averse hedgers trade to protect the values of their endowments
of the risky asset. We assume that floor traders are of different skill levels and, further, that a more
skilled floor trader attracts more hedgers to trade. Also in the spirit of Grossman (1989), the average
skill of dual traders is assumed to be higher than that of pure brokers.
One result of the model is that customers' welfare and dual traders' personal trading revenues are
increasing in the skill level, implying that a restriction on dual trading is welfare-reducing for
customers of dual traders with above-average skill levels. Yet, provided the difference in average
skill levels between dual traders and pure brokers is not too large, market depth (the inverse of the
price impact from a trade) is relatively unaffected. These results are consistent with Fishman and
Longstaff (1992), who, in the context of front running, argue that "customers' preferences regarding
a market's trading rules cannot always be measured by the resulting bid-ask spread."
Our empirical analysis uses futures markets data to examine two episodes of dual trading
restrictions: the Chicago Mercantile Exchange's (CME) top-step rule, which has effectively restricted
dual trading in the S&P index futures since June 1987; and CME rule 552, which has restricted dual
trading in high volume contracts since May 1990. To study the effects of rule 552, we examine the
Japanese Yen futures contract.3 Our results show that neither market depth nor the average realized
bid-ask spread changed significantly following each of these restrictions.
Next, we investigate whether dual traders were heterogenous with respect to their skill levels and
2
whether the restrictions had a differential impact on different dual traders. We find that dual traders
were heterogenous with respect to their pre-restriction trading patterns. For example, the group of
dual traders who chose to become pure brokers following restrictions was primarily engaged in
trading for customers prior to restrictions.
Most importantly, we find that those dual traders who, following restrictions, became locals (i.e.,
traded exclusively for their own accounts), had significantly higher average personal trading volume
and personal trading revenues prior to restrictions, as compared to those dual traders who continued
to broker for customers following restrictions. Further, these differences occur on days when dual
traders traded exclusively for their own account, and thus cannot be attributed to their customers’
information. Since our theoretical model implies a correlation between dual traders' skill levels and
their personal trading quantity and revenues, these results are consistent with the idea that highly
skilled dual traders traded exclusively for their own accounts in the post-restriction period. In
addition, customers of these skilled dual traders had lower trading costs before restrictions, relative
to all customers after restrictions. Thus, dual trading restrictions may harm customers by reducing
the quality of brokers who do customer business, as conjectured by Grossman (1989).
For regulatory policy, our analysis identifies areas of concern, although the overall economic
impact of dual trading restrictions remains difficult to quantify. The effect of restrictions on average
liquidity in these markets appears to be neutral, with potentially negative effects for some customers
and traders. Broad-based measures of liquidity (such as the bid-ask spread), used in previous studies,
are unable to capture the distributional effects of regulation---a subject of increasing interest by
legislators. Our research, of course, makes no attempt to evaluate concerns about the frequency or
severity of trading abuses underlying most dual trading restrictions.4
3
Regarding dealer heterogeneity, Cohen, Maier, Schwartz and Whitcomb (1986) comment on the
complexity of the price formation process due to the "dynamic interaction of a large and diverse
group" of trading agents. Kleidon and Willig (1995) discuss how diversity among Nasdaq market
makers may make it difficult for market makers to collude. Cao, Choe and Hatheway (1997) and
Corwin (1996) document significant heterogeneity among New York Stock Exchange (NYSE)
specialist firms. Leuthold, Garcia and Lu (1994) find that some large traders in the frozen pork
bellies futures market have significant price forecasting abilities. Board, Vila and Sutcliffe (1997)
note substantial differences in quoting and trading behavior of market makers on the London Stock
Exchange. To our knowledge, however, this paper is the first to analyze the link between dealer
heterogeneity, market liquidity and the consequent implications for regulatory policy.
Our results are related to those of Bacidore (1997) and Ahn, Cao, and Choe (1996, 1997) who
find that decimalization reduces quoted spreads but has no effect on trading volume. On the Nasdaq
markets, apparently inferior execution (as measured by the bid-ask spread) by Nasdaq dealers has not
deterred new firms from listing there or existing firms from continuing to remain on the exchange,
as pointed out by Christie and Schultz (1994) and Lee (1993). In contrast, we find restrictions affect
skilled dual traders but not realized spreads or market depth. The results of all these papers are,
however, consistent with the idea that aggregate liquidity is only one dimension of market quality.
The theoretical literature refers to heterogenous trading motives of dual traders. Grossman (1989)
asserts that dual traders are superior at order execution and market making. Also, dual traders
provide flexibility by reacting quickly to changing market conditions, and, by competing with both
pure brokers and market makers (at least in the short run), they enhance market liquidity. Fishman
and Longstaff (1992), on the other hand, model dual traders as mimicking the trading decisions of
4
informationally-motivated traders and reducing their trading profits. Roell (1990) and Sarkar (1995)
show that dual traders may also hurt uninformed traders and, as a consequence, liquidity may
decrease.5
As mentioned earlier, the empirical evidence on the effect of dual trading on liquidity is mixed and
confusing. The Commodity Futures Trading Commission (CFTC) (1989) concludes that, while dual
traders appear to supply liquidity with their personal trades, their personal trading is no more
important than that of locals. Chang and Locke (1996) find that, in the high volume markets they
examine, a restriction on dual trading has a positive effect on liquidity. But Smith and Whaley (1994)
and Walsh and Dinehart (1991) offer evidence that dual trading may enhance liquidity.
The rest of the paper is organized as follows. Section II provides a theoretical analysis of dual
trading and market liquidity when futures floor traders have different skill levels. In section III, we
empirically estimate the effect of dual trading restrictions on the bid-ask spread. Section IV
documents the occupational choice of dual traders following restrictions and estimates trading
patterns and relative trading skills of dual traders prior to restrictions. In section V, we estimate
trading costs of customers of different dual trader groups, both before and after restrictions. Section
VI concludes.
II. The Futures Trading Model
There is a single futures contract with random value v, where v is distributed normally with mean
0 and variance Ev. Futures customers include n informed traders, each of whom receives a signal
about the true asset value and submits market orders. For an informed trader i, i=1,..,n, the signal
is si = v + ei , where ei is drawn from a normal distribution with mean 0 and variance Ge . There are
also many risk-averse uninformed traders ("hedgers"). As in Spiegel and Subrahmanyam (1992), each
5
hedger j has random endowment wj units of the futures contract. The endowment wj is normally
distributed with mean 0 and variance Ew, and is independent of v. Hedgers have negative exponential
utility functions with risk-aversion parameter R. As in Kyle (1985), the asset is priced by a market
maker who makes zero expected profits conditional on the net order flow realized.
Customers submit orders to floor brokers for execution. There are potentially many floor traders
in the futures pit, with varying skill levels. For our analysis, it is not important what precise skill a
floor trader is endowed with (although, in the next section, we provide an example of a skill). We
do require that such skills exist, that they differ across traders, and, most important, that a higher
skilled floor trader attracts more hedgers to trade the futures contract.
Assumption 1. Higher skilled floor traders attract more hedgers to trade with them.
Why don't higher skilled floor traders attract more informed traders? It can be shown (proof
available upon request) that dual traders’ expected profits are decreasing in the number of informed
traders n when n is large enough. The reason is that an increase in the number of informed traders
decreases the value to dual traders of mimicking informed trades.
In our analysis, we do not distinguish between individual floor traders, but rather between two
broad categories: dual traders and pure brokers. Pure brokers accept customer orders for execution.
Dual traders may, in addition to brokerage, trade for their own accounts. We assume that the average
skill level of dual traders is equal to or higher than that of pure brokers.6 Thus, from assumption one,
more hedgers trade with dual traders than with pure brokers on average.
Assumption 2. The average skill level of dual traders is at least as high as that of pure brokers.
In the following section, we discuss these two assumptions in detail. We provide an example of
a specific skill, and illustrate the relationship between skill levels and the number of customers
6
(assumption one) and between skill levels of dual traders and pure brokers (assumption two).
A. Heterogeneously Skilled Futures Floor Traders: A Discussion
We discuss our assumptions with the help of an example of a skill---the ability to search for the
“true” price P of the asset (i.e., the liquidation value of the asset). At any time, several prices (bids
and offers) are advertised in the pit. Assume that floor traders observe these prices with error. The
error may occur because, for example, a trader is uncertain as to whether a particular price represents
a trade at a bid or an offer. A more skilled trader distinguishes between bid and ask prices with
greater accuracy to obtain a better estimate of the true price P.
To illustrate, suppose the pit is fragmented into several isolated sub-markets i, i=1,...,L each with
its own, distinct sub-market price pi. Suppose floor trader j observes a signal sij= pi+uij, where uij is
floor trader j’s error in observing pi. Let uij be normally distributed with mean zero and variance Ej.
Similarly, floor trader k observes sik=pi+uik, where uik is distributed normally with mean zero and
variance Ek. If Ej<Ek, we say floor trader j is more skilled than floor trader k.
Sub-market prices pi, i=1,...,L are noisy indicators of the true price P. Thus, by searching submarkets i=1,...,n, n#L, floor trader j receives signals s1j,..,snj to form an estimate of the true price
E(P*s1j,..,snj)=ajSj, where Sj=3i sij, aj = cov(P, sij)/ var(Sj). The forecast error of floor trader j is *PE(P*s1j,..,snj)*. Suppose floor traders j and k search the same number of sub-markets m. If floor
trader j is more skilled than floor trader k (Ej<Ek), she has a lower forecast error. This attracts more
hedgers to trade with floor trader j, increasing her commission income, which, in turn, provides her
the resources to “search” more sub-markets subsequently (assuming search is costly). Over time,
floor trader j establishes a larger customer base and a reputation for superior skills.
7
To illustrate assumption two, suppose floor traders incur a cost w>0 when searching for prices.
Floor trader j’s objective is to select n, the number of sub-markets to search, that minimizes her
search cost function (for example, a candidate search cost function may be [(forecast error)2 + wn2]).
A pure broker searches till her expected marginal commission income equals her marginal search
costs. A dual trader, in addition to commission income, also earns trading revenues and so, on
average, a dual trader searches more prices, and is more likely to become skilled.7
B. The Dual Trading Model
Let "i be an index of hedger participation with floor trader i. Formally, floor trader i attracts "ih
hedgers to participate in trading, where h$1 and "$1.
From assumption one, if floor trader i is more
i
skilled than floor trader j, then "i>"j. Since there is a correspondence between skill levels and the
hedger participation indices, we henceforth refer to "i as the skill level of floor trader i.
Let "b represent the average skill level of pure brokers and let "d represent the average skill level
of dual traders. From assumption two, "d $"b. We normalize so that pure brokers as a group have
an average skill level "b=1 and dual traders as a group have an average skill level "d$1. From now
on, we write "$1 (without the subscript) to refer to the average skill level of dual traders only. Our
results are qualitatively unchanged if we allow "b to vary, so long as we interpret "="d/"b$1 as the
dual trader’s relative skill level. A formal proof of this assertion is available upon request.
In the empirical analysis, we will be concerned with dual traders and pure brokers as groups,
rather than as individuals. Thus, when solving the model, we assume there is a single dual trader
(group) with skill level "$1, and "h hedgers and n informed traders as customers. Similarly, we
assume a single pure broker (group) with skill level one and h hedgers and n informed traders as
8
customers. " and h are common knowledge. Initially, we consider only equilibria where hedgers and
informed customers choose either the dual trader or the pure broker. In section E, we analyze the
case where the dual trader and the pure broker coexist.
In this section, we compute the equilibrium when hedgers and informed customers choose the dual
trader. Informed trader i, i=1,..,n chooses xi,d to maximize conditional expected profits E[(vpd)xi,d*si], where the price is pd = 8d yd , the net order flow is yd = xd +ud + z, the aggregate informed
trade is xd =Gixi,d, ud is aggregate hedgers’ order flow and z is the dual trader’s order flow. Hedger
j, j = 1,..,"h submits market order uj,d. uj,d is chosen to maximize, conditional on endowment w,
j
hedger j's certainty equivalent profits Gj,d = E(Hj,d *w)
where Hj,d is hedger j's
j - (R/2)var(H
j,d *w),
j
profits. Hedgers' total order flow is ud = Ej uj,d . We assume that hedger j follows a linear trading
strategy uj,d = Ddw.j *Dd* denotes the absolute hedging intensity with the dual trader.
The dual trader chooses her personal trading quantity z after observing the n-vector of
informed trades {x1,d,..,xn,d} and the "h vector of hedger trades {u1,d,.., u"h,d}. Thus, the dual trader
chooses z to maximize conditional expected profits E[(v-pd)z*{x1,d ,..,xn,d, u1,d,.., u"h,d}]. Finally, she
submits the net order flow yd to the market maker for execution. Given that the market maker makes
zero profits, the price is pd = E(v*yd).
Define t=Gv/Gs, where t is the unconditional precision of an information signal. Note that
0#t#1. Further, define Q = 1+t(n-1), where (Q-1)si represents informed trader i's conjecture
(conditional on si) of the remaining (n-1) informed traders' signals. For example, if t=1 (perfect
information), informed signals are perfectly correlated, Q=n, and informed trader i conjectures that
other informed traders know (n-1)si--i.e., the informed trader believes other informed traders have
the same information as she. Lemma 1 describes the solution to the trading model when hedgers and
9
informed customers choose the dual trader.
Lemma 1: Suppose informed customers and hedgers choose the dual trader. An equilibrium exists
if n > 1, t>0 and N1>N2/p", where N1 and N2 are defined in (5) and (6) below. Informed customer
i trades xi,d =Ads,i the dual trader trades z =Bxd - (0.5)ud, hedger j trades uj,d = Ddw,j j = 1,...,"h, where
Dd<0, the market price is pd = 8dyd and:
(1)
Ad '
-F
&8dDd '
N
-2
Dd '
(4)
r
"
nEv
1
Q&1
B '
(2)
(3)
"thEw
(Q&1)
(&Dd)
2Q
-F
ntEv
2
1%Q
"hEw
& N1
N3
N1 &
, where
"
(5)
N1 ' REv(2&t)
(6)
N2 ' 2
(7)
N3 '
F
ntEv
hEw
ntREv
h(1%Q)
As in Spiegel and Subrahmanyam (1992), for 8d>0, Dd<0 in equilibrium. Since N1>N3$N3/"
from definition, we need N1>N2/p", which requires that the number of informed traders n is small
10
while ", R, h, Ew and Ee are all large. Intuitively, the amount of noise and risk-aversion must be large
relative to information for the market maker to price the asset.
From (2), n > 1 implies B>0: the dual trader piggybacks on the informed order. From (1),
piggybacking reduces informed trades (relative to the no-dual-trading benchmark) by the factor (Q1)/Q. Also, from the equilibrium z, the dual trader offsets half of hedgers’ order flow.
C. The Solution When a Pure Broker is Chosen
Now, we compute the equilibrium assuming that hedgers and informed customers choose the
pure broker. Informed trader i, i=1,..,n chooses xi,b to maximize conditional expected profits E[(vpb)xi,b*s],
i where the price is pb = 8byb, the net order flow is yb = xb+ub, the aggregate informed trade
is xb =Gixi,b, and ub is aggregate hedgers’ order flow. Hedger j, j = 1,..,h submits market order uj,b to
the pure broker. uj,b is chosen to maximize (conditional on endowment) the certainty equivalent
profits of hedger j, j = 1,..,h, defined as Gj,b = E(Hj,b*w)
j - (R/2)var(Hj,b *w),
j where Hj,b is hedger j's
profits with the pure broker. Denote hedgers' total trading volume with the pure broker as ub = Ejuj,b.
We assume hedger j follows a linear trading strategy uj,b = Dbw.j *Db* denotes the absolute hedging
intensity with the pure broker. The pure broker submits the net order flow yb to the market maker
for execution. Thus, the price is pb = E(v*yb). Lemma 2 describes the solution when hedgers and
informed customers choose the pure broker.
Lemma 2: Suppose hedgers and informed customers choose the pure broker. An equilibrium exists
if t > 0 and N1 > N2, where N,i i = 1,2,3 are defined in (5)-(7). Informed customer i trades xi,b = Absi,
hedger j trades uj,b = Dbw,j j= 1,...,h, where Db < 0, the price is pb = 8byb, and:
11
F
Ab ' (&Db)
(8)
&8bDb '
(9)
Db '
(10)
thEw
nEv
-F
1
1%Q
ntEv
hEw
N2 & N1
N1 & N3
D. Floor Trader Heterogeneity, Customers' Welfare and Market Depth
In this section, we relate trader heterogeneity to customers' welfare and market depth. Our
first result shows that higher skill levels are “good” for customers and the market. Higher levels of
" affect the hedging intensity in two opposite ways. An increase in the skill level reduces the price
impact of hedger trades and enables the uninformed traders to hedge more. But it reduces the
incentive to hedge by increasing the residual endowment risk (i.e., the uncertainty arising from not
knowing the endowments of other hedgers) which, in turn, increases the variance of the price,
conditional on the hedger’s own endowment. Formally, the residual endowment variance is given by
("h-1)REw(8dDd)2/4. In contrast, the total endowment risk "hREw (8d Dd )2 /4 is independent of the
number of hedgers because the increase in variance due to an increase in the number of hedgers "h
is exactly offset by a reduction in the price impact (8dDd)2.
An increase in " increases the hedging intensity if the marginal decrease in the price impact
is greater than the marginal increase in the residual endowment risk. This is likely to occur if the price
impact (N2) is initially relatively high and the relative endowment risk (N3) is initially relatively low.
More precisely, Proposition 1 requires that (N2)2>N1N3, which is likely if R, Ew and Ev are not too
12
large relative to the number of informed traders n and the information precision t.8 This ensures that
the hedging intensity, informed profits, and market depth increase with the skill level. A slightly
stronger version of the same condition ensures that hedgers’ utility is also increasing in the skill level.
Proposition 1. Let N2 - (N1 N3 )½ = k. If k>0, then the hedging intensity, informed profits and the
market depth are increasing in the skill level ". If, in addition, k is large (as defined in the appendix),
then hedgers' utility is also increasing in ".
Proposition 1 implies that policy makers should consider the effects of futures regulation on
the average skill level of floor traders. Since skill levels are difficult to infer, the common method is
to evaluate rules by estimating changes in the market bid-ask spread or depth. From (3) and (9), the
difference in market depth between the dual trader and pure broker is:
(11)
1
1
&
' (1%Q)
8d
8b
hEw
"*Dd*
ntEv
2
& *Db*
In the next proposition, we compare market depth with and without dual trading.
Proposition 2. Suppose (N2)2 > N1N3. There exists "Ú (defined in the appendix), 1<"Ú<4, such that
if " is greater (less) than "Ú, market depth increases (decreases) with a ban on dual trading. If "="Ú,
then market depth is unaffected by a ban on dual trading.
There are two effects of dual trading on market depth. Market depth is halved with the dual
trader because she offsets half of hedgers' order flow. But higher hedger participation with the dual
trader also increases depth by a factor p". Hence, provided the hedging intensity is increasing in ",
depth increases with dual trading when " exceeds four. When "=1, the hedging intensities are the
same with the dual trader and the pure broker, and depth decreases with dual trading, reflecting the
dual trader's reduction of the hedgers' net order flow. When " is between one and four, market depth
13
may remain unchanged when dual trading is banned.
Proposition 2 rationalizes the conflicting empirical results found in studies of dual trading.
A ban on dual trading may lead to an increase or decrease in market depth, depending on the relative
skill levels of the dual trading population. In particular, if dual traders are highly skilled relative to
pure brokers, market depth decreases when dual trading is banned. However, if the difference in skill
levels between dual traders and pure brokers is not that great, a ban on dual trading may have no
discernible effect on depth. Consistent with this idea, Chang and Locke (1996) find that a ban on dual
trading did not affect liquidity, and argue that dual traders were marginal providers of liquidity prior
to the ban.
Corollary one determines the magnitude of the critical skill level "Ú in a given market.
Corollary 1. "Ú is negatively related to the price impact of hedgers' trades.
In our model, hedgers' price impact with dual trading is given by 8d*Dd*, or equivalently, by
the variable N2. The following examples show the relationship between "Ú and N2.
Example 1 (market where hedgers' price impact is high). Let N2 = N1 - 0, where 0>0 and arbitrarily
small. Since, in equilibrium, N2 < N1 , (N1 - 0) is the highest allowable value of the price impact.
Further, since N1>N3, (N2)2 > N1 N3 is satisfied. We show in the appendix that "Ú = 1 + 20, where
0>0 and arbitrarily small. Thus, in markets where hedgers' price impact is high, even moderately
skilled dual traders have a positive effect on liquidity.
Example 2 (market where hedgers' price impact is low). Let (N2)2 - N1N3 = 0 and N3=*, where 0>0,
* >0 and both 0 and * are arbitrarily small. Thus, the price impact is at its lowest allowable limit, yet
(N2)2 > N1N3. We show in the appendix that "Ú = 4 - 80, where 0>0 and arbitrarily small. Thus, in
markets where hedgers' price impact is low, dual traders must be highly skilled to have a positive
14
impact on liquidity.
Proposition 3. If (N2)2 > N1 N3 , then dual trader's expected trading volume and revenues are
increasing in ".
Thus, restrictions are likely to hurt dual traders of above average skills more, since their
opportunity cost of not dual trading is also higher than average. As a result, customers of skilled dual
traders are worse off from the restrictions (by proposition one). If many highly skilled dual traders
quit trading the affected contract, the average skill level of the remaining dual traders goes down, and
depth decreases. However, if there are few high-skilled dual traders, market depth may not decrease
discernibly, yet some customers are adversely affected.
We can formalize the idea “market depth does not decrease discernibly” as follows.9 Suppose
" is close to, but not equal to, "i. If a ban on dual trading leads to a large change in market depth,
then the effect is “discernible”. We can show (proof available upon request) that, for reasonable
values of the asset volatility Ev, the market depth function is not very elastic with respect to ", when
" is close to "i. Specifically, let M be the difference in market depths (i.e., the right-hand-side of
(11)), and suppose we perturb any one of the parameters Ni, i=1,2,3, by an arbitrarily small amount
,. Let M, be the resulting change in M. Then, for reasonable values of Ev, M,/M < 1.
Corollary 2. If (N2)2 > N1N3, then a ban on dual trading hurts dual traders of above average skills and
their customers. However, there may be little effect on market depth.
E. Coexistence of Pure Brokers and Dual Traders
In this section, we extend the dual trading model by allowing pure brokers and dual traders
to coexist prior to the dual trading ban. For the sake of brevity, proofs are not reported, but are
15
available from the authors upon request.
There are two brokers in the market, a dual trader and a pure broker. Assume that n1
informed traders execute orders through the dual trader, and n2 informed traders execute orders
through the pure broker, with n1+n2=n. For simplicity, we assume uninformed traders are noise
traders, as in Kyle (1985). A proportion "d of noise trades u go though the dual trader, while a
proportion "b of noise trades u go through pure brokers, with "d$"b.10
Informed trader i, i=1,..,n1 submits xi,d to the dual trader, whereas informed trader j, j=1,..,n2
submits xj,b to the pure broker. The dual trader observes the orders of n1 informed traders and noise
trades of size "du, and trades z(x1,"du), where x1 =Gixi,d. The price is p = 8y, the net order flow is y
= x1+x2 +z +"du+"bu, x2 = Gjxj,b is the aggregate informed trade with the pure broker, and the size of
noise trades with the pure broker is "bu. Informed trader i, i=1,..,n1, maximizes conditional expected
profits E[(v-p)xi,d*s],
i given the dual trader’s optimal trading rule z(x1,"du) and the trades of informed
traders executing through the pure broker. Similarly, informed trader j, j=1,..,n2 maximizes profits
E[(v-p)xj,b*sj], given the trades of the other agents.
The basic difference in solution method with the previous models is that, given z(x1,"du), the
trading intensities Ad and Ab of informed traders executing through the dual trader and the pure
broker, respectively, must be solved simultaneously. When n1=0, the model collapses to the pure
broker solution in lemma two. When n2=0, the model collapses to the dual trader solution in lemma
one.
For n1>0 and n2 >0, we can show existence of equilibrium, but comparative static exercises
are difficult due to the complexity of the expressions. However, numerical examples suggest that the
qualitative results obtained earlier do not change. For example, suppose t=0.1,"b=1, n1=10 and n2=1.
16
Then, in the extended model, the (inverse of) market depth 8 = 1.06/Eu/[("d+2)/Ev]. Now,
suppose there is a ban on dual trading, and the ten informed traders executing through the dual trader
all switch to the pure broker. Then n1=0, n2=11 and (the inverse of) market depth is 8b, where 8b is
given by (9), after substituting Eu=(-Db)hEw to adjust for the fact that uninformed traders are noise
traders, instead of hedgers. It can be shown that, if "d=1.02, (1/8) = (1/8b )---i.e., market depth
remains unchanged when dual trading is banned.
We have established the possibility that, as a consequence of regulation, an unchanged level
of average liquidity may coexist with a decrease in some traders' welfare. The remainder of this paper
analyzes empirically whether such a scenario holds for two specific episodes of dual trading
restrictions.
III. An Empirical Analysis of Market Liquidity and Dual Trading Regulation
In this section, we consider the impact of dual trading restrictions on market liquidity. In
section IV we analyze dual trader heterogeneity. Our null hypothesis is:
Hypothesis 1. Dual trading restrictions have no effect on market liquidity.
After describing our data, we look at some preliminary statistics to infer whether markets
were sufficiently active for customers to benefit from higher skill levels (section B); and to infer the
skill level of dual traders relative to that of pure brokers (section C). Finally, in section D, we directly
estimate the change in liquidity after restrictions.
A. Data and Sample Descriptions
The Computerized Trade Reconstruction (CTR) data is used for two futures contracts which
17
trade on the CME, the S&P 500 index and the Japanese Yen. The data consist of detailed records
for every transaction on the floor of the exchange. For each transaction, the record contains the trade
type, the broker's identification number, the number of contracts traded, the buy-sell indicator and
the price. The record also indicates four different customer types for a floor trader’s transaction.11
For identifying dual trading, only two types--trades executed for the trader's own account and for
outside customers--are relevant, and only these transactions are included in the sample.
To categorize floor traders, we calculate a trading ratio for each floor trader for each day she
is active. Specifically, define d as the proportion that personal trading volume is of a floor trader's
total trading volume on a day. For each floor trader, a trading day is a local day if d>0.98, a broker
day if d<0.02 and a dual day if d lies on the closed interval [0.02, 0.98].12 A floor trader with at least
one dual day in the sample is defined as a dual trader. A floor trader with only local (broker) days
in the sample is defined as a local (pure broker).
We use a three-month window to examine the effect of the CME's rules. The sample period
covers May 1 through July 31, 1987 for the S&P 500 index futures contract with the top-step rule
effective from June 22. For the Yen, the sample period covers April 1 through June 28, 1991, with
the rule banning dual trading effective from May 20. The pre and post-rule samples are defined
according to the event date on which the rule was imposed. For both contracts, there are 35 days in
the pre-rule sample and 29 days in the post-rule sample.13 Floor traders are categorized as dual
traders, pure brokers or locals in each of the two samples separately.
B. Trading Activity in Futures Markets
For higher skill levels to benefit customers and market liquidity, proposition one requires that
18
the market is "sufficiently" active. Among other things, this means that h, the number of hedgers, is
large (see footnote 8). We proxy h by the average number of daily trades for customers and the
average daily customer trading volume.
Table 1 shows summary statistics on the typical daily trading of a floor trader before and after
restrictions. We combine the local days, broker days, and dual trading days of all traders. For the
S&P 500 futures, activity on dual trading days is lower after the top step rule. Activity on other types
of trader days actually increased, however, so that average daily customer trades and trading volume
show little change overall. For the Yen futures, however, activity falls on both dual and non-dual
trading days, so that average daily customer trades and trading volume are lower after restrictions.
In absolute terms, the level of activity is high compared to other futures contracts both before
and after restrictions. For example, the daily means of customer trades and trading volumes are
higher than the numbers reported by Locke and Sarkar (1996) for the Treasury Bills, Soybean Oil and
Live Hog futures in 1990-91. Further, dual trading was banned in the Yen futures from 1991 because
the CME deemed it was a high-volume contract. The relatively high volume levels of the S&P 500
futures is common knowledge. Thus, markets in our sample appear to have been sufficiently active
for higher skill levels of dual traders to benefit customers.
C. The Relative Importance of Dual Trading
As an indication of ", the skill level of dual traders relative to that of pure brokers, we study
the relative importance of dual trading to the market. The justification comes from lemma A2 of the
appendix, which shows that hedgers' trading volume is increasing in ". The relevant statistics are
shown in table 1.
19
(12)
St ' a0 % a1Vt % a2VOLt % a3Mt % a4Dt % e t
Statistics for the S&P 500 are presented in the upper half of table 1. Prior to the top-step
rule, dual trading days accounted for only about 23% of all trader days, but 45% of all trades, 47%
of total trading volume and 72% of all customer volume. Following the top-step rule, only 8% of
trader days, 12% of trades and less than 12% of trading volume occurred on dual trading days. The
numbers for the S&P 500 futures suggest that, relative to that of pure brokers, the average skill level
of dual traders may have been high before restrictions, but possibly decreased following restrictions.
The lower half of table 1 shows statistics for the Japanese Yen. Relative to the S&P 500, dual
trading days were a smaller part of total market activity even prior to the ban. Dual trading days
accounted for 15% of trader days, 23% of trades and 25% of trading volume. Following restrictions,
dual trading days accounted for 6% or less of total trader days, number of trades or trading volume.
These numbers suggest that average skill levels of dual traders in the Yen futures were, perhaps, no
higher than that of pure brokers prior to restrictions.
D. The Effect of Dual Trading Restrictions on Market Liquidity
We proxy liquidity by two measures: the average realized bid-ask spread and the market
depth. The average bid-ask spread is computed as the volume weighted average buy price minus the
volume weighted average sale price for all customers (i.e., it is the negative of customer trading
profits). We calculate the spread for each day for each floor trader and then aggregate across all
customer trades. Separate calculations are made both before and after the dual trading restrictions.
To estimate the effect of the restriction on liquidity, the following regression is estimated:
where, for day t , St is the realized spread in dollars, Vt is customer trading volume,
20
VOLt
is
the standard deviation of buy prices for customer trades, Mt is the number of floor traders trading
for their own account, and Dt ' 1 in the pre-rule periods and 0 otherwise. This analysis parallels
Smith and Whaley (1994) and Chang and Locke (1996).
Our results are presented in table 2. For neither contract is the coefficient a4 significantly
different from zero, indicating that the realized bid-ask spread was unaffected by restrictions, a result
consistent with Chang and Locke (1996). The Durbin-Watson statistic D=2.3 for the S&P 500 and
D=1.81 for the Yen. Since the upper critical value of D is 1.73 for both contracts, the null hypothesis
of zero autocorrelation cannot be rejected at the five per cent level of significance.
We rerun (12) using the price impact of a trade (the inverse of market depth) as the dependent
variable. The price impact is defined as in Kyle (1985)---i.e., the change in the price divided by the
change in the net order flow. Empirically, the price impact is calculated as follows. For each trading
bracket, we divide the price change (the difference between the prices of the first and last trades in
the bracket) by the net customer trading volume in the bracket to obtain the price impact for that
bracket. We then average across trading brackets in a day to get the daily price impact. The results,
reported in table 3, are consistent with those in table 2. For neither contract is the coefficient a4
significantly different from zero, indicating that the market depth was unaffected by restrictions.
IV. Trader Heterogeneity and Dual Trading Restrictions.
In the above analysis, we failed to find evidence that dual trading restrictions affect liquidity.
However, there was some indirect evidence suggesting that dual traders in the S&P 500 possessed
relatively high skills prior to restrictions. Further, after the top step rule, dual traders appear to have
21
only average skill levels. In this section, we examine more rigorously whether the restrictions had
a greater impact on dual traders of above-average skills.
Our procedure for establishing heterogeneity of dual traders is as follows. First, we record
the occupational choice of dual traders following restrictions (e.g., whether a dual trader became a
pure broker following restrictions). Next, the dual trader sample in the pre-restriction period is split
into subsamples based on the observed occupational choice of these dual traders following
restrictions. Finally, we test for systematic differences in dual traders' personal trading volume and
revenues (both correlated with skill levels, by proposition three) across different groups of dual
traders for the pre-restriction period. To control for information-based dual trading, the comparisons
are made only for days in which dual traders traded exclusively for their own accounts.
A. Occupational Choice of Dual Traders Following Restrictions
In this section we follow dual traders in the respective markets, from their behavior in the prerestriction period to their choice of occupation in the post-restriction period. A dual trader has four
possible reactions to the restrictions. First, they could continue to dual trade according to the CME's
rules--i.e., if they are not on the top step of the S&P 500, or if they switch from local to broker once
a day in the Yen pit. Second, they could become locals. Third, they could become exclusive brokers.
Fourth, they may exit the particular contract which is subject to the restriction.
Panel A of table 4 reports this transition matrix for all floor traders around the time
restrictions were implemented. Of floor traders switching occupations but not quitting, the primary
migration involves dual traders and brokers becoming locals. The percentage of floor traders who
continue in their original occupations following restrictions are: for the S&P 500, 25% of pure
22
brokers, 67% of locals and 61% of dual traders; for the Yen, 36% of pure brokers, 62% of locals and
58% of dual traders, respectively. Panel B shows that, for both contracts, the transition matrix for
dual traders changes very little when we consider active floor traders (defined as those who traded
on at least 2 days during the pre-rule sample period). We obtain similar results when we define active
dual traders as those trading for at least three or four days.
Are floor traders’ occupational choice due to dual trading restrictions, or for reasons
unrelated to regulation? For an answer, note that the restrictions should have little effect on the
occupational choice of locals and pure brokers. In panel A, instances of pure brokers and locals
switching occupations are extremely few, although many discontinue trading. When we consider
relatively active floor traders, however, higher proportions of locals and pure brokers remain in their
original occupations than do dual traders. When we consider the population of floor traders who
switched occupations, but did not quit trading, this difference in behavior of dual traders and others
is even more striking. Thus, the evidence suggests that the restrictions played a key role in dual
traders’ occupational choice.
Our examination of the relevant CFTC data also indicates that dual traders who quit their
home pit following restrictions did not migrate to a different pit in the exchange. This is consistent
with Chang, Locke and Mann (1994), who examine exchange-wide trading in the currency and
Eurodollar markets affected by Rule 552, and Kuserk and Locke (1993), who present evidence of
the lack of migration of traders across various commodities within a day.
B. Dual Traders' Relative Trading Pattern Before Restrictions
Table 5 shows summary statistics for dual traders who changed occupations following
23
restrictions. Dual-locals (dual-brokers) were dual traders in the pre-restriction period who switched
to executing exclusively personal (customer) trades in the post-restriction period. Dual-quitters are
those dual traders in the pre-restriction period who failed to trade in the affected contract in the postrestriction period.
For both contracts, dual-brokers were predominantly involved in trading for their customers
on all their days in the pre-rule period. For example, in the S&P 500, dual-brokers had only 24 local
days out of 261 trader days. On their dual trading days, they traded only 116.25 contracts on average
for their own accounts, but 588.68 contracts for customers. Similarly, for both contracts, dual-locals
were almost entirely involved in trading for their own accounts on both their dual and non-dual days
prior to the top-step rule.
The trading of dual-quitters show no consistent pattern. In the S&P 500, they were primarily
locals when they were not dual trading, but mostly traded for customers on their dual days. In the
Yen pit, dual-quitters traded mainly for customers on both their dual and nondual trading days.
Table 6 shows the trading pattern for dual-duals (i.e., those floor traders who were dual
traders both before and after restrictions). In contrast to the other dual trader groups, dual-duals
have substantial trading activity on both local and broker days, although they tend to trade relatively
more for customers than for their own accounts. This is particularly true for the pre-restriction period.
These results establish the heterogeneity of dual traders with respect to their trading patterns.
Proposition three predicts that skill levels are correlated with dual traders' personal trading
volume. We take the personal trading volume of dual-duals in the pre-restriction period as our
benchmark, and compare it with the personal trading volumes of the remaining three dual trader
groups for the pre-restriction period. Since higher personal trading by dual traders could be
24
motivated by both private information and skill levels, we perform the comparison for the local days
of dual traders only---days when they are less likely to know the customer order flow.
Hypothesis 2. During the pre-restriction period, the distribution of personal trading quantities of
all four dual trader groups on their local days are the same.
Table 7 reports personal trading quantities of different groups of dual traders on their locals
days prior to restrictions. The Wilcoxon Z statistic is used to test the null hypothesis that the
distribution of personal trading quantities for dual-duals is the same as the remaining dual trader
groups (i.e., dual-brokers, dual-locals and dual-quitters). For both contracts, dual-locals had the
highest mean and median daily personal trading volumes on their local trading days. The Wilcoxon
Z statistic indicates that the distribution of personal trading quantities for dual-locals was significantly
different than that of dual-duals for both contracts. Further, dual-brokers had the lowest mean and
median quantities among the four groups in all but one case, although the distribution of their
quantities was not significantly different from that of dual-duals.
Since skills and personal trading quantities are correlated, we conclude that dual traders who
continued to provide brokerage for customers following restrictions (i.e., dual-duals and dualbrokers) had lower trading skills than dual traders who quit brokerage following restrictions (i.e.,
dual-locals). We defer judgement on the dual-quitters, who had significantly lower quantities than
dual-duals in the S&P 500 pit.
C. Dual Traders' Personal Trading Revenues Before Restrictions
Proposition three further suggests that trading skills are correlated with dual traders’ personal
trading revenues. We use the dual-duals as the benchmark group and compare the distribution of
25
their per contract revenues during the pre-restriction period with those of the other three dual trader
groups (i.e., dual-brokers, dual-locals, and dual-quitters). As before, the comparisons are made only
for local days of dual traders prior to dual trading restrictions.
Hypothesis 3. During the pre-restriction period, the distribution of personal trading revenues per
contract of all four dual trader groups on their local days are the same.
Aggregate trading revenues for each dual trader are computed on a daily basis. For each
trader, and for each day, the value of purchases is subtracted from the value of sales, with imbalances
valued at the daily settlement price (marked-to-market). Daily revenues are then divided by the
number of round-trip transactions for each floor trader, to obtain daily revenues per contract.
Table 8 reports personal trading revenues per contract of different groups of dual traders on
their local days prior to dual trading restrictions. For the S&P 500, dual-locals had the highest mean
and median revenues per contract; their median revenues per contract were higher than that of dualduals by a cash equivalent value of $32.50 per contract. Both dual-duals and dual-brokers had lower
per contract mean and median revenues compared to the other two groups. The Wilcoxon Z statistic
indicates that the distribution of personal trading revenues per contract for dual-locals was
significantly different than that of dual-duals.
For the Yen, dual-locals had higher median revenues per contract than all other groups except
dual-brokers. However, differences in the distribution of revenues between different groups of dual
traders were not significant. The results here support our earlier result on trading quantities. Dual
traders who quit brokerage to trade for themselves had higher trading skills compared to those dual
traders who continued to broker customer trades following the restrictions. The evidence is strong
for the S&P 500 and weak for the Yen futures.
26
For the S&P 500, dual-quitters had higher mean and median revenues than dual-duals, and
the Wilcoxon test shows that the distribution of their revenues is significantly different from that of
dual-duals. Recall that dual-quitters in the S&P 500 had lower mean and median quantities than
dual-duals. Thus, evidence on the skill level of dual-quitters in the S&P 500 is inconclusive.
We combine the dual-duals and the dual-brokers into one group and repeat the analyses of
tables 7 and 8. This has three benefits. The number of observations for the combined group is 537
for the S&P 500 and 91 for the Yen, whereas the number of observations for dual-brokers is very
small (24 for the S&P 500 and 2 for the Yen). Also, we remove a potential error from misclassifying
some dual-brokers as dual-duals.14 Finally, we have a sharper comparison between the trading skills
of dual traders who continued to broker and those who did not. The results (not reported but
available upon request) are not qualitatively different from those of tables 7 and 8.
Finally, we repeat the analysis of table 8 using aggregate personal trading revenues. The
results do not change, except that dual-quitters no longer have significantly different daily revenues
from the combined group. This is not surprising, since dual-quitters had lower mean and median
quantities and higher mean and median revenues per contract compared to dual-duals.
V. Dual Trading Restrictions and Customer Trading Costs Revisited
In this section, we directly test our conjecture that some customers may have been hurt by
dual trading restrictions, even though customers as a group were not. In particular, customers of dual
traders who quit brokerage may have higher trading costs after restrictions, especially in the S&P 500
futures. Thus, we combine dual-locals and dual-quitters into one group, called non-brokers.15 We
compute customer trading costs of the three dual trader groups---dual-duals, dual-brokers, and non-
27
brokers---on their broker days before restrictions. We compare the distribution of these trading costs
to the distribution of customer trading costs on the broker days of all brokers (i.e., dual traders and
pure brokers) after restrictions. As before, customer trading costs for a group are the volume
weighted average buy price minus the volume weighted average sale price for all customers in that
group.
Table 9 reports the results. In the S&P 500 futures, customers of all dual trader groups had
higher mean and median trading costs on their broker days after restrictions, although the difference
in the distribution of trading costs is significant only for customers of non-brokers (at a 7 per cent
level of significance), and marginally significant for customers of dual-brokers (at a 10.42 per cent
level of significance). This result supports Grossman’s (1989) contention that, by speculating with
their own capital, dual traders have a better “feel” for the market and, consequently, are able to get
better “fills” for customers. The distribution of trading costs for customers of dual-duals do not
change after restrictions, supporting our contention that these dual traders are of average skills.
Customer trading costs of all groups remain unchanged in the Yen futures, consistent with earlier
results suggesting that the skill differential between dual traders and pure brokers is not large in the
Yen futures.
VI. Conclusion
In the context of dual trading restrictions, we examine whether aggregate liquidity measures
are appropriate indicators of trader welfare in markets with multiple, heterogeneously skilled dealers.
Our theoretical results show that dual trading restrictions, while hurting skilled dual traders and their
customers, may have little impact on market depth if average skill levels of dual traders and pure
28
brokers are not too different. We find empirical evidence consistent with the above scenario.
Although the average cost of liquidity in our sample did not change significantly after dual trading
restrictions, dual traders of above-average trading skills switched to trading exclusively for their own
accounts after restrictions. Further, their customers had lower trading costs before restrictions
relative to customers in the post-restriction period.
Our results suggest that, in multiple dealer markets, broad based liquidity measures may be
insufficient to capture the total welfare effects of microstructure regulation. Traditional liquidity
measures may need to be supplemented by welfare indicators for specific groups of dealers and their
customers (e.g., professional and retail customers).
29
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31
Footnotes
1. In 1992, the U.S. Congress passed the Futures Trading Practice Act, which, among other things, compelled the
Commodity Futures Trading Commission (CFTC) to pass regulations to prohibit dual trading on high volume contracts. The
regulations allow affected exchanges to petition for relief based on 1) an acceptable audit trail (i.e., ability to track a floor
traders' activities), or 2) a threat to the hedging utility and price discovery function of futures markets, should the practice
of dual trading be prohibited.
2. Studies of dual trading featuring the bid-ask spread include the Commodity Futures Trading Commission (1989), Walsh
and Dinehart (1991), Fishman and Longstaff (1992), Smith and Whaley (1994), and Chang and Locke (1996).
3. CME's top-step rule (Rule 541) states: A member, who has executed an S&P 500 futures contract order while on the
top step of the S&P 500 futures pit, shall not thereafter on the same day trade S&P 500 futures contracts for his account.
Rule 552 banned dual trading in all "mature liquid" contracts (i.e., contracts with "daily average volume of 10,000 contracts
or more...over the previous six months". As of December 1991, five commodities were affected by Rule 552: Pound
Sterling, Swiss Franc, Japanese Yen, Deutsche Mark, and Eurodollars. Our choice of the Yen was determined by data
availability. However, Chang and Locke (1996) show that the Yen is representative of the affected contracts.
While the two rules appear different, their effects on dual trading are similar. The top-step rule bans dual trading only
on the top-step of the pit, while Rule 552 bans dual trading in all active contracts. However, the pit geography dictates that
brokers stand on the top step of the pit to maintain sight contact with their clerks and the trading desk. Thus, the top-step
rule severely constrains brokers from dual trading., as table one in our paper illustrates.
4. There is little academic research on the potential abuses from dual trading. An exception is Park, Sarkar and Wu (1998),
who examine whether dual traders misallocate customer trades. An example of rising legislative interest in distributional
issues is a recent bill in the U.S. Senate that proposes a relaxation of CFTC oversight of markets restricted to "professional"
investors, defined as certain banks, companies and select individuals with assets of more than $10 million. See the Wall
Street Journal, February 10, 1997.
5. In Fishman and Longstaff (1992), the effect of dual trading on liquidity may or may not be negative. But, Sarkar (1995)
shows that, if order size is variable, then dual trading may reduce liquidity. In Roell (1990), market liquidity is lower because
32
of dual trading, although some uninformed traders are better off.
6. However, we leave open the possibility that an individual dual trader may be less skilled than an individual pure broker.
This could happen if a floor trader made a mistake when deciding, on the basis of her skill level, whether to become a dual
trader or a pure broker.
7. An implication of our assumptions is that, if dual trading is prohibited in a particular futures contract, some customers
may no longer trade that contract, at least temporarily. Instead, they may trade a related futures contract or a related security,
such as an options contract. Such behavior is optimal if investors allocate their wealth across different markets to achieve
a particular risk-return combination, and are sensitive to the relative skill levels of brokers in these different markets.
8. Our condition ensures that hedgers do not “over hedge” their endowments (i.e., it is not the case that *Di* > 1 for i=b,d).
As Spiegel and Subrahmanyam (1992) point out, “over hedging” occurs when the covariance between the price and the asset
value is large. Although an interesting theoretical possibility, “over hedging” may be quite rare in practice.
Since equilibrium requires that N1>N 2, our condition also implies N 2>N 3. In terms of the model’s exogenous
parameters, the inequality N2>N3 is likely to be satisfied for high values of h, and low values of R, Ew and Ev. Note that our
existence condition imposes no restriction on the relationship between N2 and N3.
9. We thank the referee for bringing this issue to our attention.
10. The behavior of noise traders can be modeled, although this would add considerably to the model’s complexity.
11. The four types are: trading for own account, trading for a clearing members' house account, trading for another member
present on the exchange floor, and trading for any other type of customer.
12. The 2% filter is used to allow for the possibility of error trading. As Chang, Locke and Mann (1994) state, "when a
broker makes a mistake in executing a customer order, the trade is placed into an error account as a trade for the broker's
personal account. The broker may then offset the error with a trade for the error account. A value of 2% for this error trading
seems reasonable from conversations with CFTC and exchange staff."
13. The difference in the size of the pre-rule and post-rule samples arises because the two regulatory events do not fall
exactly in the middle of our sample period.
14. In particular, trades maintained in traders’ error accounts appear identical to proprietary trading in the data set. This
33
error account trading, combined with customer trading, will appear to be dual trading in the post-restriction period.
15. Since the number of broker days for dual-locals and dual-quitters is small, we cannot obtain meaningful estimates of
customer trading costs for these groups separately.
34
APPENDIX
Proof of Lemma 1.
The profits of the j-th hedger is:
"h
Hj,d ' v(uj,d % wj) & 8duj,d(uj,d % Ddj wm% z % xd)
(A1)
m…j
The j-th hedger chooses uj,d to maximize certainty equivalent profits:
Gj,d = E(Hj,d*w)-(R/2)Var(H
j
j,d*w).
j
From the proof of proposition 3 in Sarkar (1995), Dd is given implicitly by (after replacing
h by "h):
(8d Dd)2
("h&1)Ew %
4
nt(Q%2)
(2&t)
Dd 8d % REv 1&
% REv
' 0
2
(1%Q)
(1%Q)
RDd
-)]
(
[
(A2)
Given her observations of {x1,d,..,xn,d; u1,d ,..,u"h,d }, the dual trader chooses her trade z to
maximize expected profits Ad = E[{(v-pd)z}*{x1,d ,.., xn,d ; u1,d,..,u"h,d}]. Let E(v*{x1,d ,.., xn,d}) = bxd.
From the first-order condition of the dual trader's maximization problem:
z '
(b&8d)x d
28d
&
ud
(A3)
2
Informed customer i chooses her trade xi,d to maximize expected profits:
AI = E[{(v -pd)xi,d}*si]
conditional on si, and the dual trader's optimal trading rule z(xd,ud). From Bayes’ rule, b = t/(AdQ)
and E(sj *s)i = tsi for j…i. Incorporating (A3) and substituting for b in AI and solving for xd, we get:
44
t(Q&1)
x ' A s, where A '
8dQ(1%Q)
d
d
d
(A4)
From (A3) and (A4):
yd '
u
t
n
s % d , where s'3i'1si.
(1%Q)8d
2
(A5)
(3) follows from solving 8d=cov(v,yd)/var(v,yd). From (3) and (A2), we get (5) , (6) and (7).
Proof of Lemma 2.
See the proof of lemma 3 in Sarkar (1995).
Proof of Proposition 1.
We first prove the following lemmas.
Lemma A1. d**Dd*/dp
p" is strictly increasing in /" if (N2)2 > N1N3.
Proof: Since *Dd* = /"[/"N1-N2]/["N1-N3],
d*Dd*/dp" = [/"N1-N2]/["N1-N3] + [/"N1 /("N1-N3)2][-N3 + 2 /"N2 - "N1].
The first term above is positive if the equilibrium conditions /"N1 > N2 and "N1> N3 are satisfied.
The roots of [-N3 + 2 /"N2 - "N1] = 0 are:
N
1
2
" ' 2 ±
N N & N2
N1 1 3
_____,f- -
_j
N1
_
(A6)
Evaluated at p"=N2/N1 < 1, d*Dd*/dp" = N2 > 0.
From (A6), d*Dd*/dp" = 0 has no real roots when (N2)2 > N1N3. Thus, d*Dd*/dp" can never change
sign and is always positive for " > 1.
45
Lemma A2. (i) *Dd* = *Db* if " =1. (ii) *Dd* > *Db* if ">1 and (N2)2 > N1N3.
Proof. Part (i) follows from definition. Part (ii) follows from part (i) and lemma A1.
Now we prove the proposition.
(i) Unconditional expected profits of the informed trader in the dual trading model are AdGv/[2(1+Q)]
and, from (1), Ad is increasing in ".
(ii) From (3), 8d is decreasing in " if *Dd* increases with ".
(iii) The utility of the j-th hedger in the dual trading model is (after dividing through by (w)j 2 and
adding a constant term to normalize):
Gj,d
(wj)
%
2
REv
'&
2
8d
2
&
(Dd)2
-( [( -)
%
R
nt(2%Q)
(D d)2 Ev 1 &
2
(1%Q)2
REv(2&t)*Dd*
% (8dDd)2("h & 1)
Ew
-~
4
(A7)
1%Q
Denote by S1 the sum of the second and last terms on the right-hand side (RHS) of (A7):
-)
RE
nt(2%q)
S1 ' &- v (Dd)2 1 &
2
(1%Q)2
(
2&t
% REv(&D d)1%Q
(A8)
Taking derivative of S1 with respect to %":
r rll-l-)
dS1
d "
'
d*Dd*
d "
REv D d 1 &
nt(2%Q)
(1%Q)
%
2
2&t
1%Q
(A9)
Given (N2)2 > N1N3, d*Dd*/dp" >0. The first term in parenthesis is negative, since Dd <0 and
46
the term in square brackets is positive. The second term in parenthesis is positive. We show below
that the sum of the two terms in parenthesis is positive.
First, we note that *Dd*<1. This follows because N1 > N2 in equilibrium which implies N2 >
N3, since (N2)2 > N1N3. In addition, ">1. Since *Dd* = ["N1 - /"N2 ]/["N1 - N3 ], these facts imply
*Dd*<1.
Second, the expression (2-t)/(1+Q) + 1 - [nt(2+Q)]/[(1+Q)2 ] sums to:
(2&t)(1%Q) % (1%Q)2 & nt(2%Q)
(1%Q)2
(A10)
Consider the numerator of (A10). Make the substitution nt = (1+Q) - 2t. The value of the
2
numerator is: (2-t)(1+Q) + (1+Q)2 - (1+Q)(2+Q) + (2-t)(2+Q) > (2-t)(1+Q) + (1+Q)
-
(1+Q)(2+Q) + (2+Q) = 4+2Q > 0. Thus, the positive term in the parenthesis dominates the
negative term, and dS1 /d /" >0.
From (3) and (6), we can write (-8dDd) = c/p", where c= N2/(1+Q) > 0.
Denote by S2 the sum of the first and third terms of (A7):
S2 '
cDd
&
"
_j
Rc 2
(D )2("h & 1)Ew
2" d
(A11)
Taking the derivative of S2 with respect to p":
47
dS2
c
dDd
Dd
-J-1
(_; L)J _;
'
d "
"
c
"
&
d "
"
dD
Rc
c
(D )2("h & 1)Ew & R Dd d ("h & 1)Ew & Rch(D d)2Ew
" d
" d "
_j
%
(
_j
(A12)
Next, define (Dd') = [N2 - p"N1 ]/["N1-N3 ]. Therefore, Dd /p" = Dd' and dDd/dp" = Dd/p"
+p" (dDd '/dp"). Substituting for dDd/dp" in (A12):
dS2
-
d "
'
'c
dD d
d "
_j
c
l
_j
"
(REwc)(&Dd) ("h
/
& 1)
L
%
dDd
d "
(A13)
[
_j
% hD d
In the following lemma, we derive sufficient conditions to ensure d(Dd')/dp" > 0, which is
a necessary condition for dS2/dp" > 0.
Lemma A3. Let N2 - (N1N3)½ = k >0. If k > [("
"N1 )½- %N3 ]2/2/
/", then d (Dd ' ) /d p" > 0.
Proof: d(Dd')/dp" evaluated at N2 - (N1N3)½ = k is:
'
dDd
N1
'
("N1 & N3)2
2 "k %
)_J]
_j
d "
N1N3 & N3 & "N1
(_f
(A14)
The RHS of (A14) is positive if k > [("N1 )½- %N3 ]2/2/".
If (A14) is satisfied, the only negative term in (A13) is -(c//")(REwc)h(Dd)2. Next, we show
this term is bounded from above in absolute value, as follows. To derive the upper bound on
(c//")(REwc)h(Dd)2, note that (Dd)2//" < 1 because /" $ 1 and, as shown earlier, (Dd)2 < 1. In the
next lemma, we compute an upper bound on c2(REw)h.
48
Lemma A4. hRE
Ewc2 < 4/
/(2E
Ev)//
/Ew.
Proof: (N2)2 > N1N3 implies:
2 > R
EvEw(2&t)
_f
_ ___,f
(A15)
(1%Q)
From the definition of c:
nt
REwhc 2 ' 4REv
(1%Q)2
4REv
<
<
(1%Q)
8 Ev
_j
(A16)
f
(1%Q)Ew(2&t)
<
_J
_j
4 2Ev
Ew
The first inequality follows because (1+Q) > nt, the second inequality follows from (A15), and
the final inequality follows from Q$1 and t#1. We note that as the ratio Ev/Ew becomes large, N2
becomes large, Dd becomes small and, consequently, the negative term
(c//")(cREw)h(Dd)2 cannot become arbitrarily large. Hence, at some value of k large enough, the
positive term d(Dd')/dp" will outweigh the negative term in (A13). To show that at least one such
value of k exists, choose N1=N2+,, and "=1+0, where , and 0 are positive and arbitrarily small. At
these values, k is positive and finite, but Dd is arbitrarily small, and so the negative term
(c//")(REwc)h(Dd)2 is arbitrarily small.
Hence, if lemma A3 is satisfied, both S1 and S2 are increasing monotonically with respect to
", and hedger j’s expected utility is higher with the dual trader. This completes the proof.
49
Proof of Proposition 2.
(i) Suppose p"=1. From lemma A2, *Db*= *Dd*. From (11), (1/8d) < (1/8b). If p"=2, then
(1/8d) > (1/8b) since, from lemma A2, *Dd*>*Db* when ">1.
(ii) (1/8d) = (1/8b) if and only if p"*Dd* - 2*Db*=0. Substituting for *Db* and *Dd* from (4)
and (10):
"*Dd* & 2*Db* '
_j
_j
( ")3N1(N1&N3) % ( ")2[N2(N1%N3) & 2(N1)2] % 2N3(N1&N2)
_j
(A17)
("N1 & N3)(N1 & N3)
The numerator on the RHS of (A17) is a cubic equation in p" . We show that there exists
at least one real root (p")Ú to this cubic equation, satisfying 1< (p")Ú<2. Let:
a = N1(N1 - N3) > 0
(A18)
(A20)
d = 2N3(N1-N2) > 0
(A19)
b = N2(N1 + N3) - 2(N1)2 < 0
Make the substitution p" = (1+2y)(-b/3a), and note that " and y are positively correlated.
Then the numerator on the RHS of (A17) can be rewritten as:
y3 - (0.75)y = (0.25)), where ) = (13.5)a2d/*b*3 - 1
(A21)
and where *b* denotes the absolute value of b. We use Cardano’s formula (Abramowitz and
Stegun, 1970, page 17) to solve for the roots of (A21). Define q = -(0.25) and r = -)/8. Further,
define:
50
s1 '
r % (q 2 % r 3)1/2 1/3
s2 '
r & (q 2 % r 3)1/2 1/3
(A22)
Denoting i as the complex number /(-1), the roots of (A21) can be written as:
z1 ' s1 % s2
r
r
i 3
(s & s2)
2 1
i 3
z3 ' &(0.5)(s1 % s2) &
(s & s2)
2 1
z2 ' &(0.5)(s1 % s2) %
(A23)
Next, we show that, given " $ 1, any real root (p")Ú of (A17) must satisfy 1 < (p")Ú <2.
To do so, we note that, given N2>(N1N3)1/2, and N1 > N2 > N3, the range of values for N2 0 (pN1pN3,
N1).
For the lower limit on (p")Ú, let N2 = N1 - 0, where 0>0 and arbitrarily small. As 060,
b6(-a) and d60. Therefore, ) 6 -1, (b/a)6 -1, r6 1/8, (q3+r2)60, s160.5 and s2 6 0.5. Thus, z1 61,
while z2=z3<0. Consequently, (p")Ú = (1+2y)(-b/3a)6 (1+2)/(3) = 1.
For the upper limit on (p")Ú, let N2 - pN1pN3 = 0 and, further, let N360, where 0>0, 0>0 and
both are arbitrarily small. As 060, a6(N1)2, b6(-2a), d60. Therefore, ) 6 -1, (b/a)6-2, r6 1/8,
(q3+r2)60, s160.5 and s26 0.5. Thus, z161, while z2=z3<0. Consequently, (p")Ú6 (1+2)2/(3) = 2.
Proof of Corollary 1.
Since p" is positively related to y (defined in the previous proof), we will show that y is
negatively related to N2, the price impact of hedger trades. In fact, it is sufficient to show that )
(defined in A21) is negatively related to N2.
51
Taking the derivative of ) with respect to N2:
27N3a 2b 2
*)
'
&b&3(N1 & N2)(N1 & N3)
*N2
'
b6
27N3a 2b 2
b6
(A24)
&N1(N1 % 3N3) % 2N2(N1 % N3)
Thus, *)/*N2 < 0 if:
N2 < N1(N1+3N3)/2(N1+N3).
Since (N1+3N3)/2(N1+N3) < 1, the condition requires that N2 is sufficiently less than N1.
Proofs of examples 1 and 2.
The proofs are contained in the proof of proposition 2.
Proof of Proposition 3.
(i) Define dual trader's expected trading volume as E(*z*), which is proportional to the standard
deviation of z. Since z = [xd/(Q-1)] - ud(0.5), after substituting for xd, the variance of z is:
var(z) = [(0.25)hG
Gw(1+Q)/Q]"
"(Dd)2, which is increasing in " if N2>(N1N3)1/2.
(ii) Dual trader's unconditional expected revenues are E[(v-pd)z]. In equilibrium:
-J (-
l
8xQ
8u
E[(v&p d)z] ' E v & d d & d d
Q&1
2
1
ntEwEv
2Q
(_f-)
_j
u
1
x & d
Q&1 d
2
' "h*D d*
[(
-
(A25)
The terms in parenthesis are independent of ". Thus, as long as *Dd* is increasing in ", dual
52
trader's revenues are increasing in ".
53
Table 1
Trading Activity Before and After Dual Trading Restrictions
Local days
Number of
Before
After
Broker days
Before
Dual trading days
After
Before
All
After
Before
After
S&P 500
Trader days
8,934
8,989
1,560
2,693
3,173
1,037
13,667
12,719
483,428
513,677
84,176
274,441
458,283
107,892
1,025,887
896,010
own account
483,428
513,677
-----
-----
135,684
41,254
619,157
554,886
customer
-----
-----
84,176
274,441
322,599
66,638
406,730
341,124
1,396,106
1,474,505
425,652
936,266
1,632,196
324,375
3,453,954
2,735,146
own account
1,396,106
1,474,505
-----
-----
538,050
122,927
1,934,184
1,597,431
customer
-----
-----
425,652
936,266
1,094,146
201,448
1,519,770
1,137,715
13,812
17,713
2,405
9,463
13,094
3,721
29,311
30,897
own account
13,812
17,713
-----
-----
3,877
1,423
17,690
19,134
customer
-----
-----
2,405
9,463
9,217
2,298
11,621
11,763
39,889
50,845
12,161
32,285
46,634
11,185
98,684
94,316
own account
39,889
50,845
-----
-----
15,373
4,239
55,262
55,084
customer
-----
-----
12,161
32,285
31,261
6,946
43,422
39,232
Trades
Volume
Daily trades:
Daily volume:
Japanese Yen
Trader days
2,241
1,435
971
910
563
135
3,775
2,480
128,910
64,407
65,298
49,215
59,399
7,261
253,607
120,883
own account
128,910
64,407
-----
-----
14,562
1,564
143,452
65,976
customer
----
-----
65,298
49,215
44,837
5,697
110,155
54,907
558,528
297,661
374,240
339,488
309,749
36,166
1,242,517
673,315
own account
558,528
297,661
-----
-----
47,385
5,819
605,637
303,473
customer
-----
-----
374,240
339,488
262,364
30,347
636,880
369,842
3,683
2,221
1,866
1,697
1,697
250
7,246
4,168
3,683
2,221
-----
-----
416
54
4,099
2,275
-----
-----
1,866
1,697
1,281
196
3,147
1,893
15,958
10,264
10,693
11,706
8,850
1,247
35,501
23,218
15,958
10,264
-----
-----
1,354
201
17,304
10,465
-----
-----
10,693
11,706
7,496
1,046
18,197
12,753
Trades
Volume
Daily trades:
own account
customer
Daily volume
own account
customer
Local (broker) days are days on which floor traders traded exclusively for their own (customers') accounts. Dual trading days are days when
floor traders traded both for their own accounts and for customers. There are 35 days before and 29 days after the dual trading restrictions.
The sample periods are May 1 to July 31, 1987 for the S&P 500 and April 1 to June 28, 1991 for the Japanese Yen.
35
Table 2
Realized Bid-ask Spreads Before and After Dual Trading Restrictions
S&P 500 and Japanese Yen Futures
S&P 500 Futures
a0
a1
a2
a3
a4
20.21i
(3.44)
-0.0005i
(-2.007)
0.168i
(4.128)
-0.03
(-0.81)
4.74
(1.304)
N=64
F=11.083
Prob>F = 0.001
Japanese Yen Futures
-1.62
(-1.334)
-0.0001
(-0.332)
1129.3i
(2.47)
N=64
F=5.036
Prob>F = 0.0015
0.04
(1.25)
0.07
(0.079)
Changes in customer trading costs due to dual trading restrictions are estimated from the following regression:
S t ' a0 % a1V t % a2VOL t % a3M t % a4D t % e t
where, for day t , S t is the measure of customer trading costs (average buy price minus average sale price) in dollars, V t is customer
trading volume, VOL t is the standard deviation of buy prices for customer trades, M t is the number of floor traders trading for their own
account, and D t ' 1 in the pre-rule periods and 0 otherwise. T-statistics are shown in parentheses. Estimates significant at the 10 per
cent level are starred. N is the number of observations. The sample periods are May 1 to July 31, 1987 for the S&P 500 and April 1 to
June 28, 1991 for the Japanese Yen.
36
Table 3
Customer Price Impact Before and After Dual Trading Restrictions
S&P 500 and Japanese Yen Futures
S&P 500 Futures
a0
a1
a2
a3
a4
35.77
(1.65)
-0.00007
(0.015)
-44.08
(-0.829)
0.036
(0.28)
-6.87
(-1.511)
0.23i
(1.84)
1.61
(0.872)
N=64 F=1.05
Prob>F = 0.389
Japanese Yen Futures
0.362
(0.078)
N=64 F=4.157
-0.0004
(-0.277)
-3.515
(-0.23)
Prob>F = 0.0049
Changes in customer trading costs due to dual trading restrictions are estimated from the following regression:
PIM t ' a0 % a1V t % a2VOL t % a3M t % a4D t % e t
where, for day t , PIMt is a measure of the price impact of customer trades (daily average of the price change for customer trades divided
by the net customer trading volume in each trading bracket) in dollars, V t is customer trading volume, VOL t is the standard deviation of
buy prices for customer trades, M t is the number of floor traders trading for their own account, and D t ' 1 in the pre-rule periods and 0
otherwise. T-statistics are shown in parentheses. Estimates significant at the 10 per cent level are starred. N is the number of observations.
The sample periods are May 1 to July 31, 1987 for the S&P 500 and April 1 to June 28, 1991 for the Japanese Yen.
37
Table 4
Floor Trader Transition: S&P 500 and Japanese Yen Futures
Panel A: Post-restriction choice for all floor traders
Pre-restriction
choice
Pure broker
Local
Dual trader
Discontinued
Pre-restriction
total
S&P 500
Pure broker
52
8
5
140
205
Local
7
325
36
116
484
Dual trader
14
61
149
20
244
Post-restriction
total
73
394
190
276
933
Japanese Yen
Pure broker
38
0
1
67
106
Local
1
80
2
46
129
Dual trader
4
12
30
6
52
Post-restriction
total
43
92
33
119
287
Panel B: Post-restriction choice for active floor traders
Pre-restriction
choice
Pure broker
Local
Dual trader
Discontinued
Pre-restriction
total
S&P 500
Pure broker
31
1
4
9
45
Local
0
305
32
51
388
Dual trader
14
61
149
10
234
Post-restriction
total
45
367
185
70
667
Japanese Yen
Pure broker
23
0
1
10
34
Local
0
71
2
10
83
Dual trader
4
11
30
3
48
Post-restriction
total
27
82
33
23
165
Floor traders are classified in a 35 day period before dual trading restrictions according to whether they were pure brokers, locals or dual traders.
These same floor traders are separately classified in a 29 day period after dual trading restrictions according to the same criteria and whether they
continued to trade in the affected contract. In panel B, active floor traders are those who traded on at least two days in the pre-restriction period.
Some floor traders were dual traders before restrictions, but traded as pure brokers on some days and as locals on other days following the
restrictions. These floor traders are omitted from the samples. The sample periods are May 1 to July 31, 1987 for the S&P 500 and April 1 to June
28, 1991 for the Japanese Yen.
38
Table 5
Activity of Dual Traders who Changed Occupations or Quit
S&P 500 and Japanese Yen Futures
Dual-brokers
Trader Day
Type
Before
Local
Broker
Dual-locals
After
Dual
Broker
Before
Local
Broker
Dual
Dual-quitters
I
After
Local
I
Before
Local
Broker
Dual
S&P 500
Trader days
24
102
135
204
892
31
352
1,075
146
13
107
Transactions
127
6,318
18,798
18,108
57,347
567
36,062
59,433
5,805
234
9,582
Volume
345
32,344
95,166
72,260
165,705
1,786
151,524
166,580
17,685
1,701
23,963
Average daily
trades:
5.29
61.94
139.24
88.76
64.29
18.29
102.45
55.29
39.76
18
89.55
own account
5.29
-----
18.96
-----
64.29
-----
55.16
55.29
39.76
-----
35.93
customer
-----
61.94
120.29
88.76
-----
18.29
47.29
-----
-----
18
53.62
14.38
317.1
704.93
354.22
185.77
57.61
430.47
154.96
121.13
130.85
223.95
14.38
-----
116.25
-----
185.77
-----
233.69
154.96
121.13
-----
82.76
-----
317.1
588.68
354.22
-----
57.61
196.78
-----
-----
130.85
141.2
Average daily
volume:
own account
customer
Japanese Yen
Trader days
2
42
10
25
262
8
45
185
10
10
19
Transactions
31
6,550
760
2,196
17,070
31
3,163
8,278
110
515
1,112
Volume
59
69,635
7,303
28,661
73,002
254
10,734
32,873
200
2,936
6,014
15.5
155.95
76
87.84
65.15
3.88
70.29
44.75
11
51.5
58.53
own account
15.5
-----
8.6
-----
65.15
-----
62.76
44.75
11
-----
12.95
customer
-----
155.95
67.4
87.84
-----
3.88
7.53
-----
-----
51.5
45.58
29.5
1,657.98
730.3
1,146.44
278.63
31.75
238.53
177.69
20
293.6
316.53
own account
29.5
-----
35.5
-----
278.63
-----
224.49
177.69
20
-----
41.11
customer
-----
1,657.98
694.8
1,146.44
-----
31.75
14.04
-----
-----
293.6
275.42
Average daily
trades:
Average daily
volume:
Dual-brokers (dual-locals) are floor traders who were classified as dual traders before the restrictions but switched to trading only for their
customers' (own) accounts following the restrictions. Dual-quitters are floor traders who were classified as dual traders before the restrictions but
quit trading in the affected contract month afterwards. The sample periods are May 1 to July 31, 1987 for the S&P 500 and April 1 to June 28,
1991 for the Japanese Yen.
39
Table 6
Activity of Continuing Dual Traders
S&P 500 and Japanese Yen Futures
Dual-duals
Before
Trader Day Type
Local
Broker
After
Dual
Local
Broker
Dual
S&P 500
Trader days
513
465
2,530
865
1,531
947
Transactions
26,070
29,151
390,577
56,017
203,095
102,146
Trading volume
77,709
151,184
1,353,170
203,075
672,679
308,554
Average daily trades:
50.82
62.69
154.38
64.76
132.66
107.86
own account
50.82
-----
42.88
64.76
-----
40.13
customer
-----
62.69
111.5
-----
132.66
67.74
151.48
325.13
534.85
234.77
439.37
325.82
151.48
-----
168.77
234.77
-----
119.74
------
325.13
366.08
-----
439.37
206.08
Average daily volume:
own account
customer
Japanese Yen
Trader days
89
323
487
106
480
129
Transactions
4,799
38,072
54,250
4,288
34,482
6,940
Trading volume
12,626
165,120
285,437
12,602
209,831
33,579
Average daily trades:
53.92
117.87
111.4
40.45
71.84
53.8
own account
53.92
-----
23.38
40.45
-----
11.8
customer
-----
117.87
88.01
-----
71.84
42
141.87
511.21
586.11
118.89
437.15
260.3
141.87
-----
73.58
118.89
-----
43.84
-----
511.21
512.53
-----
437.15
216.46
Average daily volume:
own account
customer
Dual-duals are floor traders who were classified as dual traders both before and after dual trading restrictions. The sample periods are May 1
to July 31, 1987 for the S&P 500 and April 1 to June 28, 1991 for the Japanese Yen.
40
Table 7
Dual Trader Personal Trading Quantities on their Exclusive Local Days
S&P 500 and Japanese Yen Futures
Dual-duals
Dual-brokers
Dual-locals
Dual-quitters
S&P 500
Mean Quantity
151.48
14.83
185.77
121.13
Standard
deviation
162.7
12.25
213.45
135.55
137
13
216.9
115
-0.9771
(0.4984 )
2.018Ú
(0.0435)
-2.7091Ú
(0.0068)
24
892
146
Median
Wilcoxon Z
Prob > Z
N
513
Japanese Yen
Mean Quantity
141.87
29.5
278.63
20
Standard
deviation
135.2
10.6
282.45
16.12
126
29.5
260
17
-0.6482
(0.7277 )
1.8693Ú
(0.0825)
-1.1376
(0.2556)
2
262
10
Median
Wilcoxon Z
Prob > Z
N
89
Dual traders' personal trading quantities on their exclusive local days are compared for the pre-rule period. Dual-duals are floor traders who
dual traded both before and after dual trading restrictions during our sample period. Dual-brokers (dual-locals) are floor traders who dual
traded before the restrictions but switched to trading only for their customers' (own) accounts following the restrictions. Dual-quitters are
floor traders who dual traded before the restrictions but quit trading in the affected contract month afterwards. The Z-statistic tests for
differences in the distribution of quantities between dual-duals and the other groups of dual traders. Significant differences are starred. N
is the number of observations. The sample periods are May 1 to June 20, 1987 for the S&P 500 and April 1 to May 19, 1991 for the Japanese
Yen.
41
Table 8
Dual Trader Personal Trading Revenues Per Contract on their Exclusive Local Days
S&P 500 and Japanese Yen Futures
Dual-duals
Dual-brokers
Dual-locals
Dual-quitters
S&P 500
Mean Profits
43
19.5
259.5
158
Standard deviation
486.5
477.5
1121.5
680
Median
17.5
17
50
38
-017173
(0.8636)
2.4753Ú
(0.0350)
24
892
146
Wilcoxon Z
(Prob > Z)
N
513
2.68627Ú
(0.0072)
Japanese Yen
Mean Profits
Standard deviation
Median
4.13
27.5
-0.0125
7.5
161.75
31.88
106.38
45.88
5.63
27.5
7.63
5
0.8798
(0.379)
0.74814
(0.4544)
0
(0.9999)
2
262
10
Wilcoxon Z
Prob > Z
N
89
Revenues per contract (in dollars) are calculated for dual traders' personal trades on their exclusive local days for the pre-rule period.
Dual-duals are floor traders who dual traded both before and after dual trading restrictions during our sample period. Dual-brokers (duallocals) are floor traders who dual traded before the restrictions but switched to trading only for their customers' (own) accounts following
the restrictions. Dual-quitters are floor traders who dual traded before the restrictions but quit trading in the affected contract month
afterwards. The Z-statistic tests for differences in the distribution of revenues between dual-duals and the other groups of dual traders.
Significant differences are starred. N is the number of observations. The sample periods are May 1 to June 20, 1987 for the S&P 500
and April 1 to May 19, 1991 for the Japanese Yen.
42
Table 9
Customer Trading Costs on Broker Days Before and After Restrictions
For Different Groups of Dual Traders
Dual-duals
Dual-brokers
Non-brokers
All brokers1
Before
Before
Before
After
S&P 500
Mean costs
58.21
56.48
35.27
62.09
Standard deviation
293.05
315.21
334.41
341.6
Median
41.24
36.43
38.64
59.49
Wilcoxon Z
(Prob>Z)
1.4963
(0.16)
1.6254
(0.1042)
1.7953i
(0.07)
N
439
102
44
2661
Japanese Yen
Mean costs
45
8.75
51.5
10.75
Standard deviation
172.88
156.25
506.25
308.8
Median
34.13
19.13
10.38
21.88
Wilcoxon Z
(Prob>Z)
0.7635
(0.45)
0.6742
(0.5)
1.3232
(0.186)
N
308
42
18
785
Customer trading costs (in dollars) are calculated for broker days of dual traders for the pre-rule period (before) and for broker days of all
brokers (dual traders and pure brokers) in the post-rule period (after). Dual-duals are floor traders who dual traded both before and after dual
trading restrictions during our sample period. Dual-brokers are floor traders who dual traded before the restrictions but traded only for their
customers' accounts following the restrictions. Non-brokers are floor traders who dual traded before the restrictions but quit brokerage in
the affected contract month afterwards. The Z-statistic measures differences in the distribution of customer trading costs between the three
groups in the pre-rule period and all brokers in the post-rule period. P-values are in parentheses. Significant differences are starred. N is
the number of observations. The sample periods are May 1 to June 20, 1987 for the S&P 500 and April 1 to May 19, 1991 for the Japanese
Yen.
1. All-brokers include both dual traders and pure brokers in the post-rule period.
43
Table 8
Dual Trader Personal Trading Quantities on their Exclusive Local Days:
Brokers and Non-brokers
S&P 500 and Japanese Yen Futures
Dual traders' personal trading quantities on their exclusive local days are compared for the pre-rule period. After-brokers
include both dual-duals (i.e., floor traders who dual traded both before and after dual trading restrictions during our sample
period) and dual-brokers (i.e., floor traders who dual traded before the restrictions but switched to trading only for their
customers' accounts following restrictions). After-locals are dual-locals (i.e., floor traders who dual traded before the
restrictions but switched to trading only for their own accounts following restrictions). After-quitters are dual-quitters (i.e.,
floor traders who dual traded before the restrictions but quit trading in the affected contract month afterwards). The zstatistic tests for differences in median quantities between after-brokers and the other two groups of dual traders. The sample
periods are May 1 to June 20, 1987 for the S&P 500 and April 1 to May 19, 1991 for the Japanese Yen.
After-brokers
After-locals
After-quitters
S&P 500
Mean Quantity
145.37
185.77
121.13
Standard deviation
160.3
213.45
135.55
Minimum
1
3
2
1st Quartile
20
127
55
Median
124
216.9
115
3rd Quartile
157
274
192
Maximum
483
468
313
92.9Ú
-9Ú
Difference in medians
2.0054Ú
(0.0466)
Wilcoxon z-statistic
N=537
-2.5156Ú
(0.0095)
N=892
N=146
Japanese Yen
Mean Quantity
139.34
278.63
20
Standard deviation
134.1
282.45
16.12
Minimum
1
3
1
1st Quartile
19
145
6
Median
124
260
17
3rd Quartile
219
587
45
Maximum
426
587
45
136
-107
1.869Ú
(0.0822)
-1.1376
(0.2556)
Difference in medians
Wilcoxon z-statistic
44
N=91
N=262
N=10
Table 9
Dual Trader Personal Trading Revenues Per Contract on their Exclusive Local Days:
Brokers and Non-brokers
S&P 500 and Japanese Yen Futures
Revenues per contract (in dollars) are calculated for dual traders' personal trades on their exclusive local days for the pre-rule
period. After-brokers include both dual-duals (i.e., floor traders who dual traded both before and after dual trading
restrictions during our sample period) and dual-brokers (i.e., floor traders who dual traded before the restrictions but switched
to trading only for their customers' accounts following restrictions). After-locals are dual-locals (i.e., floor traders who dual
traded before the restrictions but switched to trading only for their own accounts following restrictions). After-quitters are
dual-quitters (i.e., floor traders who dual traded before the restrictions but quit trading in the affected contract month
afterwards). The z-statistic tests for differences in median revenues between after-brokers and the other two groups of dual
traders. The sample periods are May 1 to June 20, 1987 for the S&P 500 and April 1 to May 19, 1991 for the Japanese Yen.
After-brokers
After-locals
After-quitters
S&P 500
Mean Profits
41.5
259.5
158
Standard deviation
486
1121.5
680
-3565
-1075
-2624.5
1st Quartile
-9.5
-217.5
-23
Median
17
50
38
3rd Quartile
55
84.5
175
3650
3308.5
3712.5
33Ú
21Ú
2.4755Ú
(0.0352)
2.684Ú
(0.0070)
N=892
N=146
Minimum
Maximum
Difference in medians
Wilcoxon z-statistic
N=537
Japanese Yen
Mean Profits
46.38
-0.125
75
Standard deviation
1615
1063.75
458.75
7412.5
-5487.5
-475
100
-137.5
-300
Median
56.25
76.25
50
3rd Quartile
193.75
226.25
625
Maximum
10500
4781.25
708.75
20
-6.25
Minimum
1st Quartile
Difference in medians
45
Wilcoxon z-statistic
N=91
46
0.7481
(0.4543)
0
(0.9999)
N=262
N=10
Table 10
Dual Trader Daily Personal Trading Revenues on their Exclusive Local Days:
Brokers and Non-brokers
S&P 500 and Japanese Yen Futures
Average daily revenues (in dollars) are calculated for dual traders' personal trades on their exclusive local days for the prerule period. After-brokers include both dual-duals (i.e., floor traders who dual traded both before and after dual trading
restrictions during our sample period) and dual-brokers (i.e., floor traders who dual traded before the restrictions but switched
to trading only for their customers' accounts following restrictions). After-locals are dual-locals (i.e., floor traders who dual
traded before the restrictions but switched to trading only for their own accounts following restrictions). After-quitters are
dual-quitters (i.e., floor traders who dual traded before the restrictions but quit trading in the affected contract month
afterwards). The z-statistic tests for differences in median revenues between after-brokers and the other two groups of dual
traders. The sample periods are May 1 to June 20, 1987 for the S&P 500 and April 1 to May 19, 1991 for the Japanese Yen.
After-brokers
After-locals
After-quitters
2,450.00
13,000.00
7,900.00
241,900.00
560,750.00
340,000.00
(1,782,500.00)
(1,620,000.00)
(1,312,250.00)
(4,550.00)
(10,900.00)
(11,500.00)
Median
8,500.00
25,000.00
19,000.00
3rd Quartile
23,750.00
42,250.00
87,500.00
1,825,000.00
1,654,250.00
1,856,250.00
16,500.00Ú
10,500.00
1.6705Ú
(0.1056)
0.684
(0.4271)
N=892
N=146
5,800.00
7,812.50
9,375.00
202,925.00
132,975.00
57,350.00
(3,706,250.00)
(685,937.50)
(59,375.00)
1st Quartile
6,250.00
(68,750.00)
(37,500.00)
Median
7,037.50
9,537.50
6,250.00
3rd Quartile
24,387.50
28,287.50
78,125.00
1,312,500.00
597,662.50
88,600.00
Difference in medians
2,500.00
(787.50)
Wilcoxon z-statistic
1.0545
(0.1462)
-0.859
(0.6227)
N=262
N=10
S&P 500
Mean Profits
Standard deviation
Minimum
1st Quartile
Maximum
Difference in medians
Wilcoxon z-statistic
N=537
Japanese Yen
Mean Profits
Standard deviation
Minimum
Maximum
N=91
47
48
Table 9
Dual Trader Personal Trading Revenues Per Contract on their Exclusive Local Days:
Brokers and Non-brokers
S&P 500 and Japanese Yen Futures
Revenues per contract (in dollars) are calculated for dual traders' personal trades on their exclusive local days for the pre-rule
period. After-brokers include both dual-duals (i.e., floor traders who dual traded both before and after dual trading
restrictions during our sample period) and dual-brokers (i.e., floor traders who dual traded before the restrictions but switched
to trading only for their customers' accounts following restrictions). After-locals are dual-locals (i.e., floor traders who dual
traded before the restrictions but switched to trading only for their own accounts following restrictions). After-quitters are
dual-quitters (i.e., floor traders who dual traded before the restrictions but quit trading in the affected contract month
afterwards). The z-statistic tests for differences in median revenues between after-brokers and the other two groups of dual
traders. The sample periods are May 1 to June 20, 1987 for the S&P 500 and April 1 to May 19, 1991 for the Japanese Yen.
49
Table 5
Differences in Dual Traders' Execution Skills
in the S&P 500 and Japanese Yen Pits
Trading costs are calculated for dual traders' customers on the dual traders' broker days for the pre-rule period. Continuing dual traders are floor traders
who dual traded both before and after dual trading restrictions during our sample period. Dual-brokers (dual-locals) are floor traders who dual traded
before the restrictions but switched to trading only for their customers'(own) accounts following the restrictions. Dual-quitters are floor traders who dual
traded before the restrictions but quit trading in the affected contract month afterwards. The F-statistic measures differences in customer trading costs
between continuing and other groups of dual traders. For the Japanese Yen, costs have been multiplied by 10,000. P-values are in parentheses. N is the
number of observations. The sample periods are May 1 to June 20, 1987 for the S&P 500 and April 1 to May 19, 1991 for the Japanese Yen.
Continuing dual traders
Dual-brokers
Dual-locals
Dual-quitters
S&P 500
Mean costs
21.62
-8.81
0.31
2.69
Standard deviation
22.53
34.38
35.89
50.3
Standard error
3.81
5.81
6.61
9.87
-2.31
(0.0076)
-1.41
(0.2392)
-0.89
(0.1261)
N=35
N=35
N=26
Wilcoxon Z S tatistic
(Prob>Z)
N=35
Japanese Yen
Mean costs
3.09
-2.46
-4.35
-3.63
Standard deviation
4.44
6.00
16.45
16.05
Standard error
0.75
0.21
4.75
5.08
-0.42
(0.55)
-0.58
(0.3904)
1.27
(0.1369)
N=12
N=8
N=10
Wilcoxon Z-statistic
(Prob>Z)
N=35
50
51
Table 9
Adverse Selection Costs Faced by Marketmakers Executing for Dual Trading
Customers in the S&P 500 Pit
Adverse selection costs faced by marketmakers for the pre-rule period are estimated using SUR from the following regression system:
(1) Ct = a0 + a1 (Qt - Qt-1 ) + a2 (Vt Qt ) + a3Mt + et
(2) Ct,j = b0 + b1 (Qt, j - Qt-1, j ) + b2 (Vt, j Qt, j ) + b3Mt + et,j for j=1, 2, 3
where (1) is for continuing dual traders. In (2), the index j=1 for dual-locals, 2 for dual-brokers, and 3 for dual-quitters. For group j,
Ct, j is the price difference between intervals t and t-1, and in interval t,
Qt, j is a buy/sell indicator, Vt, j is the net (unsigned) customer trading volume and Mt is the number of floor brokers trading for their own accounts. Dual-brokers (dual-locals) are floor traders who dual
traded before restrictions but switched to trading only for customers'(own) accounts following restrictions. Dual-quitters are floor traders who dual traded before restrictions but quit trading in the affected
contract month afterwards. The chi-square statistic tests for a2=b2. T-statistics are shown in parentheses. N is the number of observations. The sample periods are May 1 to June 20, 1987 for the S&P 500.
Continuing dual traders
a0
a1
Discontinuing dual traders
a2
a3
b0
b1
b2
b3
0.879
(0.256)
-0.047
(-1.14)
-0.06
(-0.87)
j ' 1 : adverse selection costs faced by marketmakers executing for customers of continuing dual traders and dual-locals
11.96
(1.03)
5.21
(1.449)
N=
H0: a2 = b2
-0.083
(-6.728)
-0.065
(-1.01)
12.42
(1.048)
I Chi-square = 26.0734; df = 8
I
Prob>chi-square = 0.001
j ' 2 : adverse selection costs faced by marketmakers executing for customers of continuing dual traders and dual-brokers
8.704
(0.585)
2.899
(0.868)
N=
H0: a2 = b2
-0.076
(-6.65)
-0.033
(-0.628)
1.842
(0.214)
I Chi-square = 26.71; df = 8
-0.534
(-0.167)
-0.045
(-1.20)
0.005
(0.094)
0.144
(0.388)
0.078
(0.615)
I
Prob>chi-square = 0.0008
j ' 3 : adverse selection costs faced by marketmakers executing for customers of continuing dual traders and dual-qutters
-4.79
(-0.21)
5.794
(1.249)
N=
H0: a2 = b2
-0.079
(-5.42)
0.0198
(0.172)
I Chi-square = 24.68; df = 8
-13.2
(-0.54)
Prob>chi-square = 0.0018
Table 9
Table 9
2.816
(0.6)
I
Adverse Selection Costs Faced by Marketmakers Executing for Dual Trading
Customers in the Japanese Yen Pit
52
Adverse selection costs faced by marketmakers for the pre-rule period are estimated using SUR from the following regression system:
(1) Ct = a0 + a1 (Qt - Qt-1 ) + a2 (Vt Qt ) + a3Mt + et
(2) Ct,j = b0 + b1 (Qt, j - Qt-1, j ) + b2 (Vt, j Qt, j ) + b3Mt + et,j for j=1, 2, 3
where (1) is for continuing dual traders. In (2), the index j=1 for dual-locals, 2 for dual-brokers, and 3 for dual-quitters. For group j,
Ct, j is the price difference between intervals t and t-1, and in interval t,
Qt, j is a buy/sell indicator, Vt, j is the net (unsigned) customer trading volume and Mt is the number of floor brokers trading for their own accounts. Dual-brokers (dual-locals) are floor traders who dual
traded before restrictions but switched to trading only for customers'(own) accounts following restrictions. Dual-quitters are floor traders who dual traded before restrictions but quit trading in the affected
contract month afterwards. The chi-square statistic tests for a2=b2. T-statistics are shown in parentheses. N is the number of observations. The sample periods are April 1 to May 19, 1991 for the Japanese Yen.
Continuing dual traders
a0
a1
Discontinuing dual traders
a2
a3
b0
b1
b2
b3
-15.49
(0.827)
0.162
(0.075)
0.656
(0.246)
j ' 1 : adverse selection costs faced by marketmakers executing for customers of continuing dual traders and dual-locals
22.29
(0.36)
32.05
(3.00)
N=
H0: a2 = b2
-0.203
(-3.041)
-0.69
(-0.34)
-33.42
(-0.377)
I Chi-square = 12.781; df = 8
I
Prob>chi-square = 0.1196
j ' 2 : adverse selection costs faced by marketmakers executing for customers of continuing dual traders and dual-brokers
34.15
(0.863)
0.064
(0.064)
N=
H0: a2 = b2
-0.15
(-2.01)
-0.628
(-0.514)
-4.56
(-0.12)
I Chi-square = 10.7; df = 8
-22.62
(-2.27)
0.252
(1.728)
0.725
(0.636)
-0.547
(-2.29)
-0.51
(0.481)
I
Prob>chi-square = 0.2193
j ' 3 : adverse selection costs faced by marketmakers executing for customers of continuing dual traders and dual-qutters
21.33
(0.755)
0.227
(0.035)
N=
H0: a2 = b2
-0.105
(-1.82)
-1.232
(-1.41)
20.67
(0.591)
I Chi-square = 12.63; df = 8
Prob>chi-square = 0.1252
53
0.635
(0.08)
I
Table 10
Dual Traders' Trading Skills Before and After Dual Trading Restrictions
in the S&P 500 Pit
Dual traders' personal trading revenues on their local days before and after dual trading restrictions are compared. The z statistc tests for the difference in median revenues before and after dual trading restrictions.
P values are in parentheses. The mean, median and standard deviation of revenues for the Japanese Yen have been multiplied by 10,000. The sample periods are May 1 to July 31, 1987 for the S&P 500.
Local days of all dual traders
Local days of continuing dual traders
Before
After
S&P 500
Mean
0.06
0.051
Standard deviation
0.98
0.535
1st Quartile
-0.019
-0.018
Median
0.034
0.031
3rd Quartile
0.09
0.081
Maximum
7.3
3.35
Minimum
Difference in medians
-0.003
Test z-statistic
(prob. value)
-0.893
( )
N=1322
N=830
54
Table 11
Dual Traders' Trading Skills Before and After Dual Trading Restrictions
in the Japanese Yen Pit
Dual traders' personal trading revenues on their local days before and after dual trading restrictions are compared. The z statistc tests for the difference in median revenues before and after dual trading restrictions.
P values are in parentheses. The mean, median and standard deviation of revenues for the Japanese Yen have been multiplied by 10,000. The sample periods are April 1 to June 28, 1991 for the Japanese Yen.
Local days of all dual traders
Local days of continuing dual traders
Before
After
Japanese Yen Futures
Mean
-0.0073
-10
9.73
6.15
1st Quartile
-1.2
-1.1
Median
0.53
0.26
3rd Quartile
1.7
1.18
Maximum
84
10.59
Standard deviation
Minimum
Difference in medians
-0.27
Test z-statistic
(prob. value)
-1.482
( )
N=367
N=100
55
Table 12
Customer Trading Costs Before and After Dual Trading
Restrictions in the S&P 500 and the Japanese Yen Pits
Changes in customer trading costs on account of dual trading restrictions are estimated from the following regression:
(1) St = a0 + a1Vt + a2VOLt + a3Mt + a4Dt + et
where, for day t,
accounts, and
St is customers' trading costs, Vt, is customer trading volume, VOLt is the standard deviation of buy prices for customer trades, Mt is the number of floor brokers trading for their own
Dt =1 in the pre-rule period and 0 otherwise. For the Japanese Yen, the coefficients have been multiplied by 100, 000. T-statistics are shown in parentheses. N is the number of observations. The
sample periods are May 1 to June 20, 1987 for the S&P 500 and April 1 to May 19, 1991 for the Japanese Yen.
S&P 500 Futures
a0
a1
a2
a3
b0
20.21
(3.44)
-0.0005
(-2.007)
0.168
(4.128)
-0.03
(-0.81)
4.74
(1.304)
N=63
F=11.083
0.04
(1.25)
0.07
(0.079)
I Prob>F = 0.001
Japanese Yen Futures
-1.62
(1.334)
-0.0001
(0.332)
N=63
F=5.036
1129.3
(2.47)
I Prob>F = 0.0015
56
Table 13
The Effect of Dual Trading Restrictions on Marketmakers' Personal Trading Revenues
in the S&P 500 Pit
Before (after) refers to floor traders' personal trading revenues per contract before (after) dual trading restrictions. The z statistc tests for the difference in median revenues before and after dual trading restrictions.
P values are in parentheses. The sample periods are May 1 to July 31, 1987 for the S&P 500.
Before
After
S&P 500
Mean
0.048
0.029
Standard deviation
0.775
0.517
Minimum
-7.342
-6.16
1st Quartile
-0.023
-0.012
Median
0.038
0.029
3rd Quartile
0.113
0.073
Maximum
7.791
16.35
Difference in medians
-----
-0.009
Test z-statistic
(prob. value)
-----
-8.466
(0.0001)
N=11379
N=9567
57
Table 14
The Effect of Dual Trading Restrictions on Marketmakers' Personal Trading Revenues
in the Japanese Yen Pit
Before (after) refers to floor traders' personal trading revenues per contract before (after) dual trading restrictions. The z statistc tests for the difference in median revenues before and after dual trading restrictions.
P values are in parentheses. The mean, median and standard deviation of revenues for the Japanese Yen have been multiplied by 10,000. The sample periods are April 1 to June 28, 1991 for the Japanese Yen
futures.
Before
After
Japanese Yen
Mean
-0.6
0.12
Standard deviation
11.38
8.04
Minimum
-114.4
-80.6
1st Quartile
-1.2
-0.7
Median
0.55
0.5
3rd Quartile
1.85
1.47
104.22
76.64
Difference in medians
-----
-0.38
Test z-statistic
-----
-0.3411
(0.7330)
N=2580
N=1426
Maximum
58
Table 2
Activity of Floor Traders Before and After Dual Trading Restrictions in the S&P 500
and Japanese Yen Futures Pits at the Chicago Mercantile Exchange
Own account (customers) refers to floor traders who traded exclusively for their own (customers) account during the sample period. Both refers to floor traders who traded both for their own and their customers'
accounts on the same day at least once during the sample period. There are 35 days before and 29 days after the dual trading restrictions for both contracts. The sample periods are May 1 to July 31, 1987 for the S&P
500 futures and April 1 to June 28, 1991 for the Japanese Yen futures.
Own account
Number of:
Before
Customers
After
Before
Both
After
Before
All
After
Before
After
S&P 500
Traders
484
477
205
176
252
197
941
850
7,339
7,426
912
1,025
5,416
4,268
13,667
12,719
own account only
7,339
7,426
1,595
1,563
8,934
8,989
customer only
-----
-----
912
1,025
648
1,668
1,560
2,693
dual
-----
-----
-----
-----
3,173
1,037
3,173
1,037
Active days per trader:
15.16
15.57
4.45
5.82
21.49
21.66
14.52
14.96
own account only
15.16
15.57
-----
-----
6.33
7.93
9.49
10.58
customer only
-----
-----
4.45
5.82
2.57
8.47
1.66
3.17
dual
-----
-----
-----
-----
12.59
5.26
3.37
1.22
Active traders per day:
209.69
256.07
26.06
35.34
154.74
147.17
390.49
438.59
own account only
209.69
256.07
-----
-----
45.57
53.9
255.26
309.97
customer only
-----
-----
26.06
35.34
18.51
57.52
44.57
92.86
dual
-----
-----
-----
-----
90.66
35.76
90.66
35.76
Trading days:
Japanese Yen
Traders
129
116
106
81
53
35
288
232
1,867
1,310
588
403
1,320
767
3,775
2,480
own account only
1,867
1,310
-----
-----
374
125
2,241
1,435
customer only
-----
-----
588
403
383
507
971
910
dual
-----
-----
-----
-----
563
135
563
135
14.47
11.29
5.55
4.98
24.91
21.91
13.11
10.69
Trading days:
Active days per trader:
59
own account only
14.47
11.29
-----
-----
7.06
14.49
7.78
7.83
customer only
-----
-----
5.55
4.98
7.23
3.57
3.37
2.28
dual
-----
-----
-----
-----
10.62
3.86
1.95
0.58
53.34
45.17
16.8
13.9
37.71
26.45
107.86
85.52
own account only
53.34
45.17
-----
-----
10.69
17.48
64.03
62.66
customer only
-----
-----
16.8
13.9
10.94
4.31
27.74
18.21
dual
-----
-----
-----
-----
16.09
4.66
16.09
4.66
Active traders per day:
60
@FedFRASER