trading costs for listed options
TRANSCRIPT
Journal of Financial Economics 8 (1980) 179-201. 0 North-Holland Publishing Company
TRADING COSTS FOR LISTED OPTIONS
The Implications for Market Efficiency*
Susan M. PHILLIPS
The University of Iowa, Iowa City, IA S2240, USA
Clifford W. SMITH, Jr.
Uniwrsity @‘Rochester, Rochester, NY 14627, USA
Received October 1979, final version received March 1980
This paper reexamines the anomalous evidence concerning the efficiency of the listed options exchanges. We focus on the structure of trading costs m that market, and note several costs which generally have been ignored, the largest of which is the bid-ask spread. When we adjust the published trading rules for our estimates of these trading costs, the reported abnormal returns are eliminated.
1. Introduction and summary
The efficiency of organized options exchanges is questioned in recent
studies by Galai (1977, 1978), Trippi (1977), Chiras/Manaster (1978) and Klemkosky/Resnick (1979a, b). Although these authors all conclude their evidence is inconsistent with market efficiency, none of their studies carefully examines trading costs. As Jensen (1978) indicates, market efficiency implies that economic profits from trading are zero, where economic profits are risk- adjusted returns net of all costs. In this paper we analyze the structure of costs facing traders in the options markets. We examine the costs for traders who have a comparative advantage in arbitrage to determine whether trading costs are sufficiently large to eliminate the reported abnormal returns; if they are, market efficiency cannot be rejected and the inefficiency conclusion is unjustified.
Oueruiew of the paper: In section 2, after summarizing the out-of-pocket costs of trading, we examine and estimate the transaction cost implicit in the
*This research was partially supported by the Managerial Economics Research Center, Graduate School of Management, University of Rochester. We thank M. Jensen, W. Schwert, L. Wakeman, J. Warner, R. Watts, and J. Zimmerman and the referee, M. Rubinstein for their comments and criticisms of this paper.
180 S.M. Phillips und C.W Smith, Jr., Trading costs and efficiency tests
bid-ask spread for both the options markets and the stock market. We detail the sources and implications of information costs in establishing the po- sitions required for tests of option market efficiency. Following Galai, we
distinguish between ex post and ex ante trading profits, recognizing that the prices which signal ex post profit opportunities will not necessarily generate
economic profits when a trading rule is implemented. In section 3, we indicate how the inclusion of the costs modifies the return to the Galai,
Trippi. Chiras/Manaster, and Klemkosky/Resnick trading rules. Since much of the previous evidence on options market efficiency concludes that only seatholders on the exchange can earn abnormal returns, in section 4 we examine the expenditures necessary to become a seatholder and the impli- cations of the opportunity cost of that investment for conclusions of options market inefficiency. In section 5 we present our conclusions.
2. Costs in options trading
Pricing of transactions services on most security exchanges involves two
components: commissions and other explicit fees, plus the bid-ask spread. Although the costs of floor trading and clearing fees are well documented, most examinations of market efficiency of security exchanges ignore the bid-~ ask spread. The bid-ask spread reflects the charge by market makers for assuming the trader’s undesired inventory position. Additionally, information costs are implicit in the specification of various trading rules. Both the explicit costs of commissions and the implicit costs of the bid ask spread and
information are relevant to questions of market efficiency since each must be
incurred in implementing a trading rule.
2.1. Summar!, qf explicit costs in trading listed options
We examine three groups ~ (1) options market makers, (2) arbitrageurs, and (3) non-member individual traders as low cost traders effecting
transactions in the options markets.’ A market maker is a member of the
exchange who contractually agrees to stand ready to buy and sell put and call options. Arbitrageurs are generally employees of a special trading division of one of the larger retail brokerage firms. Through the firm’s exchange memberships, arbitrageurs have direct access to the trading floors of both options and stock exchanges. Since individual non-member traders do not have direct access to exchange floors, they contract with exchange members to provide that access.
The cost structures facing these investors directly reflect the institutional,
‘Stock exchange specialists are not considered because they are prohibited by the exchanges from trading in options on stocks for which they make a market.
SM. Phillips and C.W Smirh, Jr., Trading costs and efficiency tests 181
regulatory, and contractual arrangements under which they trade. The different classes of traders generally have cost advantages in varying areas; the costs of stock and option executions and the financing and capital requirements of each type of trader are quite different. Arbitrageurs generally effect their own stock transactions, so their out-of-pocket cost of trading equity claims is generally lower than for options market makers. The reverse is true for options market makers: they execute their own options transac- tions but contract out their stock executions. Individual traders contract all executions. These differences in structure and regulation lead to different costs in various hedging activities.
In addition to commissions, other costs face all traders. These are SEC
transactions fees, net capital charges, the New York State transfer tax, and the cost of margin regulations. These costs are detailed in the appendix and their magnitudes are summarized in table 1.’
2.2. The bid usk spread
The bid--ask spread is the difference between the highest quote to buy and
the lowest offer to sell registered in the market. These recorded offers come from two sources: (1) quotes from market makers/specialists, and (2) customer’s limit orders recorded on the exchange’s limit order book. A market maker who performs the passive function of providing liquidity on the exchange continually quotes a higher price at which he is willing to sell than buy. Thus he expects to make a fraction of a point on each trade, and
protect himself from customers who have additional information.3 The size of
the spread depends on a number of variables specific to the security including price, trading activity, etc.4
Any trader who actively seeks to establish a hedge must deal with other market participants, and thus must incur the expense of the bid--ask spread. Clearly, an individual or arbitrageur incurs the expense of the spread, but (perhaps not so clearly) a market maker also does. Market makers obviously
‘In the appendix, we also examine regulatory constraints which affect the ability of traders to engage effectively in certain arbitrage activities. These provisions include exchange-Imposed limitations on aggregate position size, constramts on the timing of the exercise of options positions, trading restrictions on out-of-the-money options. requirements to separate traders’ transactions from transactions in which the trader acts as an agent of a customer. the short sale rule. and the so called ‘zone requirements’ and ‘affirmative and negative obligation requirements’ which limit market makers’ activities.
%ee Bagehot (1971). ‘+The original derivation and estimation of the supply function for market-making services was
completed by Demsetz (1968) using NYSE securities. Tinic (1972), TinicjWest (1972, 1974) Benston/Hagerman (1974), Hamilton (1976, 1978). and Stall (1978) have since extended and further tested the Demsetz model using various segments of the securities markets. In general. all of these authors found that price, some measure of trading activity, and competition were significant Influences on the price charged by market makers for liquidity services.
Tab
le
1
Sum
mar
y of
tra
nsac
tions
co
sts
for
optio
ns
mar
ket
mak
ers,
ar
bitr
ageu
rs,
and
mdi
vidu
als
in t
he
optio
ns
mar
kets
.
Floo
r tr
adin
g an
d cl
eari
ng
Opt
ions
St
ock
New
Y
ork
Stat
e tr
ansf
er
tax
SEC
tr
ansa
ctio
ns
fee
Mar
gin
requ
irem
ents
Net
ca
pita
l ch
arge
s
Opt
ions
m
arke
t m
aker
A
rbitr
ageu
r In
divi
dual
-
_ .-
____
-
$O.S
0--l
.OO
/con
trac
t $l
.SO
-1.7
0/co
ntra
ct4
g10.
W6S
.OO
/con
trac
t 5.
0s12
.SO
/rou
nd
lot
1.00
--4.
OO
/rou
nd
lot
5.70
-48.
70/r
ound
lo
t
O.O
O-6
.25/
roun
d lo
t 0.
00-6
.25/
roun
d lo
t 0.
0&6.
2S/r
ound
lo
t
0.00
003
of s
ale
0.00
003
of s
ale
__a
Reg
ulat
ion
T
Reg
uiat
ron
T &
U
Reg
ulat
ion
T &
U
314
pom
t ab
ove
NY
ca
ll ra
te
-a
NY
ca
ll ra
te
‘Not
a
sepa
rate
ch
arge
(s
houl
d be
re
flec
ted
in t
he
com
mis
ston
).
S.M. Phillips und C.W Smith, Jr., Truding costs und efficiency tests 183
have the expense for trades on other exchanges; but to actively establish a position in his own security he must deal with the limit order book or, if on
the CBOE, a competing market maker.5 Although we believe the bid-ask spread is an important trading cost in
the options market, estimation of the appropriate magnitude of this cost is
no simple matter. The average bid-ask spread overstates the cost for three reasons. First, trades occur inside the spread. In Phillips/Roberts (1979), analysis of the quotations and transactions occurring in selected dually traded options classes on the AMEX and CBOE in March and April 1977 indicates that on average 57 to 62 percent of the transactions occur at the bid or ask, with approximately 40 percent inside the spread. Second, of the 60 percent, presumably a number of the trades reflect new information and, although coincident with the bid or ask, are close to the true price. And
third, if observed spreads are weighted by volume to complete the average spread, the weighted average would be lower than the simple average
because securities with high volume tend to have lower spreads. However, the average bid-ask spread understates the cost if trading rules systematically pick out transactions for which the bid-ask spread is large and if the bid-ask
spread differs across transactions. The problem of estimation of the appropriate transactions cost associated
with the bid-ask spread apparently is not easily solved. Data on prices alone would not allow one to infer which trades were initiated by buy or sell
orders. Even if the data were augmented with reported bid-ask quotes, trades inside the spread are direct evidence that the quotes do not represent the effective supply and demand prices.6 A pparently convincing establish- ment of the appropriate magnitude would require execution of the rule. Operationally, in this paper we employ the average bid-ask spread to adjust the reported returns to trading rules for trading costs.
To estimate the spread for stocks and options, we collected bid and ask quotations for options and underlying stocks. We then computed average
daily spreads as a percentage of price and on an absolute dollar basis. For stocks, the spreads (ask minus bid) were calculated from the bid and ask quotations which were in effect at 1 :OOam and 2:OOpm (EST) as reported in the July ‘1977 NYSE Transaction Journal. In addition, average percentage spreads were calculated by dividing the spread by the average of bid and ask prices, i.e., ((ask - bid)/(ask + bid)/2). Since there are five options exchanges which trade put options and each was allowed to trade put options on five
*Alternatively, if the market maker chooses to engage in arbitrage, he must expect to earn at least as much as if he continued to provide liquidity services. See section 4, below.
6Even if available, the use of bid and ask quotations would provide an underestimate of the returns to operating a trading rule. Given the direction of the bias, if abnormal returns were documented, market efftciency could be rejected.
184 S.M. Phillips and C.19: Smith, Jr., Trading costs and efficiency tests
stocks, our sample consisted of 1000 stock spread observations for the twenty trading days in July (two per stock per day).
In order to estimate the cost of liquidity to effect options transactions, the dollar and percentage spreads for the options classes in which both puts and
calls are available also were calculated from the observed 11 :OOam and 2 :00 pm (EST) bid and ask quotations in effect on the CBOE for the weeks of
June 27, 1977; September 19, 1977; December 5, 1977 and February 13, 1978.’
Table 2 contains the frequency distributions of the dollar and percentage spreads for the options traded on the CBOE and for stocks with listed options trading on organized exchanges. The options data are presented separately for puts and calls and for options whose prices are greater than $0.50.’ The percentage spreads for stocks are generally lower than for options - the average spread for stocks is less than 1 percent, while the
average spread for call options is 30 percent and for puts 15 percent. For options priced at more than $0.50, the spread drops to 4.5 percent for calls and 5.9 percent for puts. The dollar spreads for stocks and options are closer,
between $16.00 and $20.00.9
2.3. Information costs: Ex ante versus ex post profits
To demonstrate market inefficiency, an implementable trading rule (which generates economic profits) must be specified. Galai (1975, 1977, 1978) points
out that many of the tests of market efficiency, especially in the options markets, do not specify a trading strategy which a trader could have duplicated. Observing a set of prices which, ex post, would have allowed one to establish a position that generates abnormal returns does not imply market inefficiency. He argues that it must be further demonstrated that a trader observing those prices could have executed trades which yield profits. Thus Galai distinguishes between ex post and ex ante trading rules: an ex
post rule assumes that trades can be instituted at the same prices which
‘Four weeks were randomly selected for the examination of absolute and relative options premium spreads. Since put options were only opened for trading in July 1977, use of data for that month would not have allowed an examination of options spreads over several strike prices. That is, the put options trading in July 1977 all would have been at or near the money (i.e., the stock price would be approximately equal to the exercise price of the option).
*There are restrictions on trading in options whose closing price on the previous day was less than or equal to $0.50. See the appendix.
“Care should be employed in the interpretation of the data presented in table 2. While competing market makers on the CBOE provide strong incentives to keep the bid-ask quotes updated on a timely basis this is not the case for the specialists on the NYSE, AMEX, or PHLX. Thus, the reported bid-ask spreads for exchanges which use specialists are expected to be less accurate than those with competing market makers,
S.M. Phillips and C.W Smith, Jr., Trading costs and efficiency tests 185
Table 2
Frequency distribution of average percentage and absolute dollar spreads (per 100 shares or per contract) between bid and ask prices of NYSE optioned stocks and CBOE options for which both puts and calls are traded. The distrtbutions of spreads for options are reported
both including and excluding options whose prices are less than $0.50.
Percentage spreads NYSE
0.0-0.2 59 7 5 7 5 0.220.4 213 0 0 0 0 0.4 0.6 275 7 7 3 3 0.6 0.8 176 6 6 0 0 0% 1 .o 170 16 16 3 3 1.0-1.2 38 13 13 6 6 1.2 1.5 4s 50 50 6 6 I.5 2.0 23 49 49 I9 15 2.0 3.0 I 166 163 109 105 3.c-5.0 0 188 181 I81 161 5.0 8.0 0 116 112 132 127 8.0 12.0 0 55 49 70 66
12.B20.0 0 35 13 44 23 20.0-30.0 0 17 1 11 3 30.0 50.0 0 32 3 9 0 5o.c 100.0 0 21 2 6 3
100.0 200.0 0 9x 0 26 0
!I 1000 Mean ( “,) 0.62 Medran ( “$)) 0.56
876 29.85 4.23
~_
670 4.51 3.39
632 526 15.00 5.77 4.76 4.44
-___
CBOE calls CBOE puts Dollar spreads NYSE All c > $0.50 All P > $0.50
CBOE calls CBOE puts
All c 2 $0.50 All P > $0.50 _
0.000 6.250 0 311 145 169 145 6.25s 12.500 421 252 225 220 196
12.500-25.000 421 215 213 143 136 25.00@ 50.000 156 90 19 83 59
> 50.000 2 8 8 17 17
II 1000 876 670 632 526 Mean (S) 20.46 16.05 18.23 18.84 19.10 Medtum ($) 25.00 12.50 12.50 12.50 12.50
186 S.M. Phillips and C.W Smith, Jr., Trading costs and &kienc), tests
generate the profit signal, an ex ante rule implements the trades employing a subsequent set of prices.”
To implement a trading rule after observing the signal the arbitrageur (or market maker) frequently must place simultaneous orders in at least two but perhaps three or four different markets. If market orders are placed, a price change in any of the markets can eliminate the arbitrage opportunity.” Thus, as long as price changes can occur prior to execution of the orders, the trading rule is not riskless. If limit orders (rather than market orders) are placed, there is a positive probability that only part of a hedge will be
executed (e.g., he may get the stock, but not the call). Thus, his position is not hedged.‘*
The bid-ask spread and selection bias. Given the evidence presented in table 2 of a substantial bid-ask spread in the options market, the use of transactions prices in ex post trading rules leads to a subtle form of selection
bias; the use of ex ante tests reduces this. Most trading rules employed in the options literature involve a process of ‘looking for outliers’. If a trading rule attempts to pick out undervalued calls for purchase, and it is assumed that the call could be purchased at observed prices (i.e., an ex post test) then the
trading rule will systematically pick out, as undervalued, call prices from transactions initiated by orders to sell. In such a case, the trading rule is
simulated using prices to initiate the position which systematically deviate from the prices at which the trades could have been made; the rule systematically use prices from the wrong side of the bid-ask spread. If the
“Ex post tests which employ closing prices both to generate the signal of profit opportunities and to establish the initial position in the securities from which returns are measured raise the possibility of measured abnormal returns because of noncontemporaneous data. For example, if a stock price changes at 2:00pm but the last trade in an option on that stock was earlier, a trading rule which looks for mispriced options is more likely to identify that option as mispriced. If the trading rule IS simulated using the same closing prices to establish positions in the securities, abnormal returns are likely to be measured. These results are spurious because this test does not represent an implementable trading rule. This source of bias can be controlled either by employing an ex ante test or by using intra-day data to ensure that observed prices are contemporaneous.
If the trading rule only employs closing prices from the CBOE, this problem is probably not major. Prior to February 28, 1979, reported prices on the CBOE were determined by a closing rotation so they should have reflected the information at the close of business. However, the closing prices on the CBOE after February 1979 and the American Options Exchange, as well as the stock exchanges are simply the last trade.
“When an apparent profit opportunity is indicated, that signal can be based on incomplete or inaccurate prior information. For example, to check the market price of the stock, market makers and arbitrageurs generally must rely on the last-sale information from the consolidated transaction tape. This information is subject to transmission delays and errors by the employees of the exchange.
‘*Traders typically refer to simultaneous transactions in two options on the same stock (e.g., which differ in expiration date or exercise price) as a spread rather than a hedge. However, even if the trading rule can be executed by placing all orders on one exchange, unless the various parts can be negotiated simultaneously the same problems occur.
S.M Phillips and C.W Smith, Jr., Trading costs and efficiency tests 187
position is mechanically closed at a later date, that closing price will on
average be at the midpoint of the bid-ask spread. Thus, in addition to the cost of the full bid-ask spread, ex post trading rules which look for outliers are subject to a selection bias which should average half the bid-ask spread.
The selection bias can be avoided by employing an ex ante test, or reduced by using bid-ask quotes as signals for the trading rule. But if observations
on quotes (rather than prices) are to be used as a signal to implement the trading rule, it should be noted that the exchanges only require that the quote information be valid for 100 shares. Quote information ‘in size’ (i.e., for multiple contracts) is not necessarily available.
3. Adjusting previous studies for estimated transactions costs
3.1. Gulai’s hedge and spreud tests
Galai (1977) examines the pricing of listed call options on the Chicago
Board Options Exchange and bases his tests of these prices on the Black/Scholes (1973) call pricing model. He replicates the Black/Scholes (1972) hedging strategy, in which a position in an option is matched with a
position in the underlying stock to eliminate the risk of the aggregate position. Specifically, Galai compares the observed call price, C, with the
Black/Scholes model value, C,,,
c
BS =SN lnCW)+(r+~2/2)T
i ~ T }_Xe_,TN(ln(WJ; (r;n2!2)T}
(1) where
C BS = Black/Scholes model value of the call, S =market price of the stock, X =exercise price of the call, T =time to expiration of the call, o2 =variance rate on the stock,
= riskless rate, Lt.1 = cumulative standard normal distribution function.
Galai then classifies options as overvalued or undervalued, compared with the Black/Scholes model.
In his ex post hedging test, Galai uses data from April, 1973 to November,
1973. He simulates the purchase of undervalued options (i.e., C <CBS) while selling short the appropriate amount of stock and lending, and the writing of overvalued options while purchasing stock and borrowing. Galai finds that by adjusting this hedge daily, he can make abnormal returns of $10 per
188 S.M. Phillips and C.W Smith, Jr., Trading costs and ejjiciency tests
hedge per day. In his ex ante hedging test Galai establishes the hedge at
closing prices from the next day’s trading. l3 Again by adjusting prices daily, Galai’s ex ante hedging test generates an abnormal return of F.00 per hedge per day before transactions costs.
A return of $5.00 per hedge per day is insufficient to generate economic profits from trading. Galai’s hedge requires purchasing one call contract while selling a fraction, ?C/aS( < l), of a round lot of stock. As we reported in section 2, the average bid--ask spread for a call contract is $16.00 and for a
round lot of stock is $20.00; thus our estimated bid--ask spread for the call alone more than eliminates Galai’s $5.00 average prolit.”
Galai also considers a spreading strategy, where call options which differ only in expiration dates are simultaneously bought and sold by buying undervalued and writing overvalued calls.i5 With daily data, Galai finds that
the ex post spreading strategy yields approximately $8.20 per spread per day before transactions costs. The returns to his ex ante test are lower,
approximately $4.00 per spread per day. Again he concludes that the market
does not seem perfectly efficient to market makers. Employing this strategy requires daily round-trip transactions in two call
option series. I6 But our estimated bid -ask spread of $16.00 for one call is sufficient to offset Galai’s $4.00 average profit.
Galai’s (1978) tests of CBOE call prices are based on Merton’s (1973) dominance conditions. Merton establishes that in a perfect market the call price must be greater than the stock price minus the discounted exercise
price minus the sum of the discounted dividend payments,
(2)
where D, is the dividend to be paid in T periods (r< T).
‘“Galai (lY77, 1978) IS careful to tndtcate the potential data problems from using closmg prices. Galai (1977, p. 172) warns: ‘In analyzing the results, one should keep in mmd the following problems: (1) The closing prices for opttons are not necessarily transactions prices. (2) Closing prtces are sometimes arttticial. (3) Closing prices do not always reflect a synchronization of the transactions on the CBOE and NYSE.’
“Whtle the bid ask spread eliminates Galat’s reported average profit. the questton of hts largest reported profits remains an open question. We cannot tell whether abnormal returns would be available if, instead of using as a signal all over or underprtced options, the signal were requtred to exceed $20, for example. To test this, different stgnal levels could be examined to find an ‘optimum’ which could then be tested on a hold out sample of prices.
‘5Specitically, comparing two calls, i and ,j, if i is undervalued Galai buys (writes) one call i and writes (buys) a quantity (r?C,/c~S)/(c~C,/c?S) of call j. This procedure eliminates the systematic risk of the spread.
16Note that since the spread ratio can be different from 1; Galai’s spread tests can involve purchases or sales of multiple contracts.
S.M. Phillips and C.W Smith, Jr., Trading costs and eficiency tests 189
If eq. (2) is violated then by buying the call, selling the stock and lending, profits are assured, ignoring trading costs. Galai finds that of the 16,327 observations on calls and stock, 482 violations were observed. The average profit before transactions costs associated with the ex post test of dominance
violations was $36.30. In his ex ante test, Galai repeats the trading rule, but establishes the position using closing prices from the next day’s trading. He finds an average profit of $12.00.
To exploit the apparent profit opportunities from violations of Merton’s lower boundary condition, round-trip transactions in both call and stock must be undertaken. From table 2, the average transaction cost for Galai’s
strategy implicit in the bid-ask spread is between $35 and $40. Again, this would appear to eliminate the $12.00 reported average profit.
3.3. Trippi’s trading rule
Trippi (1977) devises a trading rule based on deviations in implied variance rates across call series written on the same stock. Following
LatanC/Rendleman (1976) Trippi notes that if the observed call price is employed on the left-hand side of eq. (1) an implicit function for the implied variance rate, s2, results
2 =f(C, s, x, IT; r).
Although a closed form solution for eq. (3) has not been derived, Trippi uses numerical techniques to solve eq. (1) for ri’. He then uses the average implied
variance rate from different call options on a stock to calculate an expected market value for each option.
Trippi’s trading strategy consists of the following steps: (1) Compute the
average implied variance rate over different calls for each stock each week. (2) Using the average implied variance rate compute the implied value of the call, C, using eq. (1). (3) Purchase options where the market price, C, is less than the implied market value, C’, by more than fifteen percent (i.e., C <C/1.15); and write options where C> 1.15 C.
Trippi uses weekly closing stock and option prices from August 30, 1974, through March 14, 1975. He excludes options where: (1) the call price is less
than $1.00; (2) time to expiration is less than three weeks; or (3) call prices are less than 1.3 times the stock price minus the exercise price. Application of his trading rule selects 403 options, 201 short and 202 long positions. On average, Trippi earns 11.4 percent per option per week.
This trading rule requires weekly round-trip transactions in calls. Moreover, Trippi’s reported return is likely to be overstated because of selection bias. Since Trippi’s ex post test uses the same prices to identify over- and under-priced calls in establishing his position, he will systemati-
190 S.M. Phillips und C.W Smith, Jr., Truding costs and efliciency tests
tally have to purchase calls when the observed price resulted from a sell order and sell calls when the observed price resulted from a buy order. However, in closing the position at the next week’s price, he will on average be at the midpoint of the bid-ask spread. The transactions cost associated with the spread can be as high as 1.5 times the bid-ask spread. As reported in table 1, the bid-ask spread for calls selling at prices greater than $0.50 is 4.5 percent. Thus, this trading cost will be approximately 6.75 percent. The addition of commissions would appear to eliminate average abnormal returns to non-exchange-member traders; however the average abnormal
returns to market makers and arbitrageurs still appear positive.17
3.4. Chiras/Manaster’s truding rule
Chiras/Manaster (1978) employ Merton’s (1973) adjustment for dividend payments to the Black/Scholes call pricing model,
C =SeeaTN M
(4)
where
C, = Merton dividend adjusted model value of the call, 6 = (assumed constant and continuously paid) dividend yield.
Like Trippi, they use numerical solution techniques to find the implied standard deviation (ISD) which makes the right-hand side of eq. (4) equal to the observed market price of the call, C. Since many options are traded on each stock, Chiras/Manaster have an average of 6.3 implied standard
deviations for each stock on each month. They calculate a weighted average of the implied standard deviations (WISD) for each stock. Their trading strategy is:
(1) An ‘implied market value’ (IMV) is calculated for each option by using the value of its associated WISD in the evaluation equation.
(2) The observed option price is compared to the IMV.
“Trippi’s methods are not explained in great detail, and thus his results should be interpreted with some care. For example, although his inclusion criteria are quite specific, he does not report how many alternative criteria were examined prior to that set which generated returns in excess of 11 percent. Since he reports no results from a hold-out sample, his results could be attributed to selection bias associated with searching for a trading strategy. This possibility is made more plausible because of the similarity between the Chiras/Manaster and Trippi tests and the differences in reported magnitudes. Finally, Trippi only reports raw returns, he makes no adjustment for risk.
(3)
(4)
(5)
(6)
S.M. Phillips and C.W Smith, Jr., Trading costs and @ciency tests 191
Options whose price exceeds the IMV by at least 10 percent are selected as ‘eligible short positions’ (ESPs). Options for which the IMV exceeds the price by 10 percent or more are selected as ‘eligible long positions’ (ELPs). A risk-free hedge is created between an ESP and an ELP for each stock having at least one of each type of option. For stocks having several ESPs or ELPs the two options with the maximum percentage difference from their IMVs are selected for the hedge. The amount of each option included in the hedged position is determined by the value of its hedge ratio (derivation shown below) so that each pair of options will produce offsetting gains and losses from an in- stantaneous movement in the underlying stock price. All option positions are closed one month later.
The hedge ratio is the reciprocal of the derivative of (4) with respect to the
stock price, (KY/aS)- ‘,
(5)
The hedge ratio, (?C/?S) ‘, gives the number of options that must be sold in order to offset the instantaneous unexpected change in the stock price and thus establish a riskless hedge. Using monthly data from June, 1973, to April, 1975, the Chiras/Manaster procedure generates an average return of 9.7 percent per hedge per month.
The Chiras/Manaster trading rule requires monthly opening and closing of both long and short positions in selected call options; moreover, it requires purchasing and writing multiple contracts to establish each hedge, since each
hedge ratio is greater than one. Specifically, Chiras/Manaster calculated the return to their hedge as
R = IQLtCl- C, I- Qs(C; - cs)llCQ~C,_ + Qscsl~ (6)
where the subscripts L and S refer to the quantities (Q) and prices (C) of the
long (undervalued) and short (overvalued) calls. Primes (‘) indicate prices one month later. Chiras/Manaster report abnormal returns as a percentage of the total dollar value of the hedge (i.e., they assume a 100 percent margin requirement in writing calls). With positive trading costs, the prices Chiras/Manaster used are biased; the purchase prices, C, and Cs, are too low, and the sale prices, CL and C,, are too high. Furthermore, their trading rule suffers from the same selection bias problem as Trippi’s procedure, since they calculate implied variance rates, look for overvalued and undervalued
192 S.M. Phillips and C.W Smith, Jr., Trading costs and eficienc~ tests
options, and then trade on the same set of prices. Because their test is for ex post profit opportunities the appropriate adjustment can be as high as 1.5 times ‘the bid-ask spread. These adjustments appear to eliminate Chiras/Manaster’s reported average profits.‘*
3.5. KlemkoskylResnick’s trading rule
Klemkosky/Resnick (1979a, b) adjust the Gould/Galai (1974) put<all parity model for dividend payments. They check whether
where
(C-P-S)erT+X+ C D,e-'cT-T)~O, r<T
(7)
P =value of the put, D, = dividend payment z periods in the future (t < 7).
They also check the Merton (1973) and Roll (1977) sufficient condition for
no premature exercise of a call on a dividend paying stock,
(8)
Using intraday prices from the options and stock exchanges for twelve trading days between July 1977 and June 1978, Klemkosky/Resnick (1979a) require that the observed prices occur within one minute of each other. They
find 147 instances where the left-hand side of (7) was positive and greater than $20 (their estimate of transactions costs). The average appears to be approximately $35. In their ex ante test, Klemkosky/Resnick (1979b) use violations of the put-call parity restriction in (7) as a signal to institute a trade. The trade is established at market prices after imposing both 5 and 15 minute lags. By only acting on signals for which the indicated ex post profit
would exceed $40, the trading rule earns an average of $58 per hedge. Simultaneous transactions in put, call and stock markets are necessary to
exploit the apparent abnormalities found by Klemkosky/Resnick; to imple- ment their procedure, one must write a call, buy a put, and buy stock. Thus
‘*Using data provided by Chiras/Manaster, we modified the returns to their trading rule for estimated average costs reported m table 2. The dollar return per hedge fell from a profit of $133 to a loss of $68 per hedge when we used the $18.23 per contract cost and adjusted for selection bias. We also calculated the return to their trading rule using the 4.51 percent estimated spread; the dollar return fell from $133 to $51 per hedge. The difference in the estimated returns between the adjustments reflects the fact that options selected by the Chiras/Manaster trading rule tend to have prices below the mean for all listed options. If there are economies of scale in trading costs, the dollar adjustment will tend to overestimate, while the percentage adjustment will tend to underestimate, the costs for options priced below the mean.
S.M. Phillips and C.W Smith, Jr., Trading costs and efjclency tests 193
the sum of bid-ask spreads for each type of security must be included. Using averages, this exceeds $50 per hedge.”
4. The market for exchange seats and market efficiency
When examining the evidence on options market efficiency, Galai, Trippi, Chiras/Manaster, and Klemkosky/Resnick conclude that exchange members could earn abnormal returns employing their trading rules. We have indicated that when the bid-ask spread is explicitly included as a cost of trading, the profits are generally eliminated; however even if the profits remained, we believe there is a logical problem with their argument.
If the market for exchange seats is efftcient,2” the price of a seat reflects the capitalized value of the expected future net cash flows to the marginal
seatholder.” Thus, the investment in the exchange seat establishes an opportunity cost. Without accounting for that oppotunity cost one would
expect to observe ‘abnormal’ returns to seatholders; alternatively, only if the returns exceed that opportunity cost are security markets inefficient.
There are still a number of unanswered questions about the specific nature of the opportunity cost reflected in the seat price. First. the available evidence on arbitrage opportunities for market makers only documents the
magnitudes of the anomalous price relationships; the frequency with which they occur, especially intraday, has yet to be examined. Both dimensions of the distribution are important. Second, we do not understand the nature of the trade-offs between engaging in arbitrage activities and the provision of liquidity services. The extant work on the market making function by
Garman (1976) and Amihud/Mendelson (1980) restricts the analysis to liquidity motivated trades; the impact of the investment in information either by traders or market makers and its implications for the market making function has not been examined.
5. Conclusions
Jensen (1978, p. 95) points out that:
We seem to be entering a stage where widely scattered and as yet incohesive evidence is arising which seems to be inconsistent with the
“Since their (1979 a) test is for ex post profit opportunltles and 1s sublect to selectlon bias. the appropriate transactlons cost is 1.5 times the bid-ask spread. However by employing intraday data, KlemkoskyiResnick avoid the selectlon bias problems associated with the use of closing prices.
“See Schwert (1977a, b) for evidence on the efliciency of the market for seats on the NYSE and AMEX from 19261972.
“Dann/Mayers/Rabb (1977, p. 19, fn. 28) point out to the extent that cash flows from arbitrage ever exceed those from the provision of liquidity services (either from acting as agent for non-seatholders and accomplishing their trades, or from acting as a market maker) the seat price will be higher to reflect the capitalized incremental cash flows.
194 S.M. Phillips and C.H! Smith, Jr., Truding costs and efliciency tests
theory. As better data become available and as our econometric sophistication increases we are beginning to find inconsistencies that our cruder data and tests missed in the past.
In attempting to resolve some of these inconsistencies, we have examined the structure of transactions costs facing traders in the organized options markets. Our major conclusions are: (1) There are several sources of direct and indirect costs associated with trading which have been generally ignored in previous studies of trading rules/market efficiency; the largest of these is the bid-ask spread. (2) When trading rules involving options markets are employed, a subtle form of selection bias arises from looking for outliers. With positive bid-ask spreads, the trading rule tends to pick security prices
generated by orders from ‘the wrong side of the market’. (3) To decide if abnormal returns are available to a seatholder, the opportunity cost as- sociated with the use of the seat must be computed. However, if markets for
exchange seats are efficient, then the capitalized rents available from the ability to trade at lower cost will be reflected in the price of the seat.
We believe these conclusions go far in explaining the reported incon- sistencies with the efficient markets hypothesis.
Appendix: Costs in trading options
In addition to the direct incremental transactions costs facing efficient traders, there are indirect transactions costs generated by SEC and self- regulatory organization rules which constrain the trading activities of market participants. Only if the regulatory constraints are completely ineffective do they not impose costs. On the other hand, if market participants must find alternative means of effecting transactions to reduce the impact of the
regulations, search costs are incurred ~ fixed, not incremental, per trade. The full cost of regulatory constraints is composed of loss of income atrributable
to the inability to effect transactions as desired and/or search costs incurred in avoidance activities. Finally there are fixed costs associated with exchange membership which must be covered in order to earn a normal return to the
investment in a seat. In this appendix we identify these sources of direct and indirect costs to traders.
A.1. Floor trading und clearing fees: Option exchunges
On May 1, 1975, the commission structure in the securities industry
became negotiated. Prior to that time, commissions were fixed by the exchange on which the security was traded. Table A.1 gives the basic commission schedules which were in force on the Chicago Board Options Exchange prior to deregulation. Although discounts are sometimes available,
SM. Phillips and C.W Smith, Jr., Trading costs and efficiency tests 195
this schedule provides a benchmark for the commissions which individuals
can expect. When the options exchanges were first permitted by the Securities and
Exchange Commission (SEC) to begin the trading of standardized options, the Options Clearing Corporation (OCC) was formed. The OCC is directly regulated by the SEC and all transactions in options must be cleared through the OCC. Since the capital requirements for membership in the
OCC are fairly stringent, many potential members of the options exchanges have elected to clear through a few OCC members.22 Over a period of time, the institutional and contractual arrangements have developed so that now options market makers are able to contract with the clearing firms for services involving clearing, bookkeeping, regulatory compliance and pro- vision of financial and pricing information.
Floor trading and clearing fees are paid by market makers to their clearing firms for these services. Depending on individual contractual arrangements between the clearing firm and the market maker, floor trading and clearing
fees range from $0.50 to $1.00 per contract. These fees are negotiable and generally lower for market makers who have high trading volumes, establish
low-risk portfolio positions, and are well capitalized. Although retail brokerage firms, for whom arbitrageurs work, could elect
to belong to the OCC and therefore clear for themselves. most arbitrageurs contract their options transactions to OCC member firms by having market makers execute their options orders. Therefore, their fees for this service are somewhat higher than those incurred by market makers. Arbitrageurs’ floor
trading fees generally range from $1.50 to $1.70 per contract.23
A.2. Floor truding and clearing fees: Stock exchanges
Table A.1 also contains the basic commission schedules which were in force on the New York Stock Exchange prior to deregulation on May 1, 1975. The SEC (1978) reports that for individuals the average discount from these commissions was 18.3”/:, in December 1977; average commissions per share ranged from 5.7 cents for trades greater than ten thousand shares to
48.7 cents for trades less than two hundred shares. Options market makers generally are not members of any stock exchanges,
so must act as customers to effect transactions.‘” Usually the clearing firms
“For example, one clearing firm, First Options Corp., clears for over one third of the market makers on the CBOE.
‘%ince these fees are negotiable, it is possible that a few arbitrage arrangements result in lower fees. However, fees must be htgh enough to allow market makers a normal return for the services they provide.
?Some CBOE members are beginning to purchase seats on the Midwest Stock Exchange to lower the cost of stock executions, but with the advent of negottated floor commissions many market makers believe that the cost of a nonmember NYSE execution does not justify the purchase of a stock exchange seat.
Tab
le
A.1
Mrn
rmum
co
mm
issi
on
sche
dule
s fi
xed
by
the
New
Y
ork
Stoc
k E
xcha
nge
(NY
SE
) an
d th
e C
hica
go
Boa
rd
Opt
mns
E
xcha
nge
ICB
OE
) pr
ior
to
May
1,
197
5.
.-.--
_-
~__
-._.
__._
____
_-
--
--_
Mon
ey
invo
lved
H
I th
e or
der
(S)
Min
imum
co
mm
isio
n sc
hedu
le
----
.- --
-__
- -_
--__
~_._
__
__I
____
-.-.
.. --
.-_
Typ
e of
ord
er
At
leas
t B
ut
less
th
an
Stoc
ks
(NY
SE
) O
ptio
ns
(CB
OE
) :
----
__
___.
._
---..
__
_-_
____
____
----
-_
___.
._
..__I
__
---.-
-.
Smgl
e tr
adin
g un
rt
orde
rs
0 80
0 2.
0”,,
of m
oney
i
S 6.
40
f.3yf
0 of
mon
ey+S
12.0
0 s %
(s
hare
s an
d op
ttons
80
0 2,
500
I .3
‘I<,
of m
oney
+
S 12
.00
I .3
‘!.c
of m
oney
+
$12.
00
‘J,
prrc
ed
at
$1 a
nd
abov
e)
2.50
0 an
d ab
avc
0.9
“i,
of m
oney
f
$22.
00
0.9
:‘;
of m
oney
+
$22.
00
%
Nor
rt
The
co
mm
issi
on
on
a N
ote:
T
he
com
mis
sion
on
a
: si
ngle
tr
adin
g un
it or
der
sing
le
trad
mg
unit
orde
r $
shal
l no
t ex
ceed
S6
5.00
. sh
all
not
exce
ed
$65.
00
Nor
r:
Odd
lo
ts.
$2 l
ess.
no
r be
le
ss
than
$2
5.00
. 2 .g
0 2,
500
1.3”
/, of
mon
eyff
12
.00
1.3?
:, of
mon
ey+$
l2.0
0 c >y
2,
500
20,0
00
0.9
2,
of m
oney
f
$ 22
.00
0.9
9:, o
f m
oney
+
$22.
00
2o.O
OO
30
,000
0.
6 “/
, of
mon
ey
+ S
82.0
0 0.
6”;
of m
oney
+
$82.
00
7
30,0
00
300,
000
0.4
“:,
of m
oney
+
$142
.00
As
mut
ually
ag
reed
9
300,
000
and
abov
e A
s m
utua
lly
agre
ed
As
mut
ually
ag
reed
J:
a
Mul
trpl
e tr
adin
g un
it or
ders
(s
hare
s an
d op
tions
pr
rced
at
$1
and
ab
ove)
Sing
le
and
mul
trpl
e tr
adin
g um
t or
ders
(s
hare
s an
d op
tions
pr
iced
be
low
St
)
0 1,
000
10,0
00
and
abov
e
1,00
0 10
.000
Add
: S6
.00
per
trad
ing
umt
for
1st
to
10th
tr
adrn
g un
it,
$4.0
0 pe
r 5
trad
ing
unit
for
I It
h tr
adm
g un
it an
d ab
ove.
N
ote:
In
no
ca
se
shal
l th
e co
mm
issi
on
per
trad
mg
umt
on
a m
ultip
le
B
trad
ing
unit
orde
r ex
ceed
th
e co
mm
issi
on
for
a si
ngle
tr
adm
g un
it or
der.
9 1.
8.4
“(, o
f m
oney
A
s m
utua
lly
agre
ed.
3
5.0”
,, of
mon
ey
+ S
34.0
0 So
urce
ap
plie
s st
ock
2
4.0”
,, of
mon
ey
+S13
4.00
sc
hedu
le
in b
ox
to
the
left
. 2 Y
;
“For
al
l st
ock
orde
rs
$5.0
00
and
belo
w
m
valu
e:
Add
lo
”,
to
com
mrs
sron
ca
lcul
ated
ab
ove.
Fo
r al
l st
ock
orde
rs
abov
e $5
,000
m
va
lue:
A
dd
24.2
96
to
com
mrs
sion
ca
lcul
ated
ab
ove.
S.M. Phillips and C.W Smith, Jr., Trading costs und efjiciency tests 197
effect the stock transactions for their market makers as members of stock exchanges or through correspondent arrangements. The cost to market makers for executing stock transactions ranges from $5.00-$12.50 per round lot. Since floor commissions are negotiable, the cost of the execution is usually a function of the size of the transaction and the frequency of orders
placed by the clearing firm. The arbitrageurs, as employees of firms which generally are NYSE
members, have direct access to the floors of the stock exchanges and can execute their stock transactions directly through their floor representatives. Floor commission rates for the NYSE range from $1.0&$4.00 per round lot. The average appears to be $2.00 per round lot.
A.3. Position und exercise limits
The exchanges all have specified limitations on the sizes of positions that
members (and their customers) can take and on the number of contracts that can be exercised within a specified time period. The maximum position limit restriction in effect for all options exchanges is 1000 contracts (long or short) of the put and call class on the same side of the market covering the same underlying security. Depending on existing portfolio composition,
traders can be prohibited from acting on profit signals which are based on the put--call parity or other dominance restrictions. In addition, traders are prohibited from exercising more than 1000 option contracts of a particular class within five consecutive business days.
A.4. Trading restrictions on out-of-the-money options
A number of restrictions limit trading activity when options are more than $5 out-of-the-money, based on the previous day’s closing price in the primary
market, or when the previous day’s closing price of the option was less than $0.50 per unit of trading.25 These restrictions on out-ot-the-money options
constrain entry. Consequently, option arbitrage hedging based on the put-call parity relationship is restricted to at-the-money put and call options series. If the put (call) is deep in the money then a corresponding call (put) with the same exercise price is likely to be subject to the exchange restrictions governing out-of-the-money options.
A.S. Short sale rule
Both arbitrageurs and options market makers are subject to the SEC’s short sale rule: short sales may only be executed on an uptick. This
25Allowed trades include: (1) transactions to close existing posltions: (2) writing covered options (i.e., the writer owns the underlying stock), (3) one-for-one spreads (i.e., the writer simultaneously purchases and writes calls on the same stock), and (4) options written by market makers.
198 S.M. Phillips and C.W Smith, Jr., Trading costs and eflciencg tests
provision increases the cost of executing short sales. Both market makers and arbitrageurs experience delays in executing short sale orders and before the order is executed the price of the stock can change. The arbitrage hedge position then is at risk both because of the price change and the delay.
A.6. Murket maker truding restrictions
Market makers are subject to various exchange-specific rules which serve to inhibit their trading activity. First, defined proportions of market makers’
transactions must be effected in certain physical exchange locations called ‘trading zones’. Market makers are assigned to these zones by the exchange which nominally wishes to assure continuous quotations for all options traded on that exchange.26 Furthermore, zone requirements provide one basis for granting market makers exemptions from the usual customer margin requirements.
A second series of restrictions on options market makers’ activities can be collectively called ‘affirmative and negative obligations’. Affirmative obli- gations imply that when a market maker is in a crowd where a particular security is traded, he must respond to a request from another member for a
quote on that security. Further, that quote must be close to the last sale based on an exchange-specified formula. Negative obligations generally imply that the market maker cannot displace customer orders: that is, customer orders must be filled before those of a market maker.
A final group of restrictions limiting market makers’ trading activities center around the traditional separation of principal and agency transactions.
These transactions are separated because of the alleged conflict of interest which is believed to exist if a trader acting in a fiduciary capacity on behalf
of a public customer executes that customer’s order from his own account. For market makers, the separation of agency and principal transactions is accomplished by exchange regulations. Some exchanges have different classes of members while other exchanges require that a member cannot act as broker and a dealer on the same day. In the latter case, an exchange member acting as a broker on any one day cannot effect arbitrage hedges or spreads for his own account when a signalled profit opportunity is observed.
In addition to the exchange rules, arbitrageurs have developed their own procedures to assure separation of agency and principal transactions. If the security is listed on two or more exchanges, the retail firms generally direct customer orders to one exchange and principal orders to another. If the
security is not dually listed, arbitrage firms generally do not execute their own transactions on the exchange floor, but rather execute through other
26All options written on a specific stock trade at a particular post or pit. A zone frequently encompasses more than one post.
S.M. Phillips and C.W. Smith, Jr.. Trading costs and efficiency tests 199
market makers (or specialists). This contracting arrangement has been developed particularly in the options area because crossing an arbitrageur’s order with a firm customer’s order creates a potential liability to the firm
(breach of fiduciary responsibility) greater than the cost of contracting out the execution.
A.7. Margin requirements
Option market makers, arbitrageurs, and individuals are all subject to margin requirements. This legislation specifies maximum percentages of assets value which can be financed with debt. The real cost of the margin requirements is related to the degree to which the constraint on the choice of financing is binding. If margin requirements are nonbinding constraints, and if less debt than the maximum allowable would be chosen, then the cost of
the margin regulation is zero. Options market makers are exempt from the Federal Reserve Board’s
margin requirements for options transactions, but not for their stock positions. Any position in a specialty security taken by a specialist or a
market maker is exempt from the margin requirements. Traditionally, the FRB has allowed this exemption, arguing that specialists and market makers as part of their market making obligations are likely to assume undesired inventory positions; if they must stand ready to buy and sell securities, they should not be hampered by financing restrictions. Regulation T governs the extension of credit by broker-dealers for the purpose of purchasing and
carrying securities and the extension of credit by the clearing corporations for effecting stock transactions. Although some margin relief for stock positions is allowed market makers who acquire certain hedge positions, the inventory carrying cost of stock positions is higher than for options positions. The interest rate on the load for stock positions is the N.Y. call rate (the cost to the clearing firm) plus 3/4 point.
Arbitrageurs generally are subject to the margin requirements under Regulation U, governing the extension of credit for financing and carrying securities by banks. Depending on the composition and commitment of the assets of the retail firm, the arbitrageur has access to unused customer debit
balances to execute stock-option hedges. Arbitrageurs are subject to the same uniform margin requirements for options positions as customers under either Regulation T or U. The brokerage firms can typically borrow at the N.Y. call rate.
A.8. Exchange seats
Exchange members or seatholders own the assets of the exchange; thus seats are equity claims in the exchange. The markets for seats on various
200 S.M. Phillips and C.W Smith, Jr., Trading costs and ejkiency tests
stock and options exchanges are essentially similar in form. Each exchange maintains an anonymous auction market. Whenever a new bid or ask price is brought to the market all interested participants are informed. (In general, seats can only be purchased by individuals, not partnerships or corpo- rations.) Generally, there are no direct out-of-pocket trading costs in the
market for seats beyond the costs. of applying for exchange membership. Although reported bid-ask spreads for seats are large, trades regularly occur within the spread. Thus trading costs associated with the scale of seats appear to be relatively small. Table A.2 summarizes the cost associated with seats for various exchanges.
Table A.2
Prices of seats on the stock and options exchanges, March 1979.
Exchange Seat price (%) Exchange dues (S)
New York Stock Exchange (NYSE) Chicago Board Options Exchange (CBOE) American Stock Exchange (AMEX) Philadelphia Stock Exchange (PHLX)
Stock Options
Midwest Stock Exchange (MSE) Stock & options Options
Pacific Stock Exchange (PSE)
125,000 115,000 62,500
500 5,000
6,900 6,900 4,300
1,5OO/year 800/year 800/year
1 ,OOO/year 1 ,OOO/year
2,200Jyear l,OOO/year
“Exchange dues on the Pacific Stock Exchange depend on the value of the transactions per month:
$ OM-IOM $O.l325/thousand SlOMm 15M $0,0880/thousand $50Mp $O.O660/thousand
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