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Further evidence of the influence of option expiration on the underlying common stock
J BUSN RES 1987:15:291-302
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Further Evidence of the Influence of Option Expiration on the Underlying Common Stock Robert A. Strong
William P. Andrew
The University
The Pennsylvania
of Maine
State University
Over the past decade there has been increasing research into the interaction among the securities options markets and other institutions. Of particular interest in the earliest research was the extent to which social efficiency is enhanced by the trading of puts and calls. Since it is now well established that market-spanning opportunities are more complete when options are available, recent research has been directed toward such issues as the informational efficiency of the options exchanges and the relationship between an option premium and the behavior of the underlying common stock. Of interest to us in this research is the latter issue. We find significant new evidence that in the final two days of trading prior to the expiration of an option series, the presence of options influences some underlying stock prices. Previous
Research Prior research in this area has resulted in a variety of conclusions regarding the influence of options on the underlying stock. Shortly following the advent of listed options in 1973, the Chicago Board Options Exchange (CBOE) conducted, sponsored, or reviewed several examinations [5,6, 16, 171 of the impact of these option contracts on the behavior of stock prices. The first CBOE study [5] and the second Nathan study [17] found evidence that option trading decreased the price volatility of the underlying stock. Similarly, Hayes and Tennenbaum [9] found that the presence of listed options increases stock trading volume, which, ceteris paribus, should reducC price volatility. In addition, they report that respondents to a mail survey of the top management of the 43 firms listed on the CBOE in May 1973 felt that option listing did not influence the price of their securities. However, agreement on these issues is not as clear cut when stock behavior is examined during certain periods in the option’s life. For example, Gastineau [8] indicates that many observers believe that stocks with listed options are more volatile during
Address correspondence ME 04469. Journal of
to Dr. Robert A. Strong, University of Maine, South Stevens Hall, Orono,
Business Research 15, 291-302 (1987) 0 1987 Elsevier Science Publishing Co., Inc. 1987 52 Vanderbilt Ave., New York, NY 10017
0148-2963/87/$3.50
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the week or two preceding and following an expiration date. Branch and Finnerty [4] offer evidence that stocks with newly listed options tend to outperform the market prior to and just after the option-listing date. Exploration of the behavior of security prices around an option-expiration date was given further impetus when Fisher Black [2] wrote in 1976 that “Option trading may even have some slight effect on stock volatilities and on stock prices at the time the options expire.” The first major study of the impact of option expirations on stock prices was by Klemkosky [ll] in 1978. He concluded that in the week prior to expiration of an option series, stock prices show a 1% average residual decline, while in the subsequent week prices rise by 0.4%. Two other studies support Klemkosky’s results. Officer and Trennepohl [14] discovered a tendency for stocks to decline slightly in the few days prior to expiration. Hess [lo] finds similar results, with the most significant declines occurring on Thursday and Friday of the expiration week. Klemkosky offers several explanations for this price behavior. For example, he asserts that in the final week of trading, call options frequently sell at a slight discount from intrinsic value, enabling a noncommission-paying arbitrageur to exercise the call and sell the stock at a profit without benefit of a price uptick, thereby increasing downward pressure on the price of the underlying common stock. This and other explanations by Klemkosky imply that the presence of call options will bias the underlying stock price downward immediately prior to option expiration. However, in his study, Klemkosky makes no effort to test empirically for any differential impact due to in- or out-of-the-money calls on the expiration effects. One result of our research supports the hypothesis that such a differential effect exists. It should be noted that the previous research was conducted during a period when option contracts consisted primarily of call options. In the last few years, however, ‘put options have increased in both availability and popularity. Some researchers argue that if the presence of calls biases stock prices down prior to option expiration, then the presence of puts should have the opposite effect, with the two influences offsetting each other. For example, Hess’s research, which covered the period 1978-1981 (when the number of puts was increasing), led him to conclude “As put trading appears to offset the market inefficiencies caused by call option trading, the concern of regulators that options trading unduly effects stock prices seems unwarranted.” Like Klemkosky, however, Hess does not investigate whether the existence of put options affects the underlying stock differently depending on whether the nearest puts are in or out of the money. The existence of such a differential impact is supported by articles by Anders [l] and Lenzer [12]. The logic of such an effect is relatively straightforward. For a given option striking price, a put and a call cannot both have intrinsic value. If the call has intrinsic value, then Klemkosky’s explanations may be operative, while the put will expire worthless. If, however, it is the put which has intrinsic value, a comparable explanation would be that arbitrageurs buy stock and exercise puts, while short sellers of stock who have also written puts leave the market by buying the put back and covering their short position in the stock. Either of these last two activities could exert upward pressure on stock prices (in contrast to the effect when the call has intrinsic value).
Influence of Option Expiration
J BUSN RES 1987:15:291-302
All of these potential activities have a similar result: Stock selling at slightly above an option striking price (call has intrinsic value) may be biased downward, while stock selling slightly below the striking price (put has intrinsic value) may be biased upward. This is what some practitioners refer to as the “convergence phenomenon,” where stock prices are believed to show an unusual tendency to close near the closest striking price on option-expiration day (e.g., see [l]). Further investigation of this alleged phenomenon is the intent of this paper. Methodology It is challenging to investigate security-price behavior that earlier research has shown to be fleeting. In constructing our methodology we relied on the discoveries and suggestions of our predecessors in this research area. From Klemkosky we adopt two suggestions. First, we accept the charge that “Future research should test for daily price change patterns” (his research looked at weekly data). And second, we recognize the limitation of the linear market model when residual error terms are expected to be nonzero because of bias around certain events. Previous research does suggest that a bias may exist around option expiration, and while it might be possible to remove the bias, the limitations of the market model with daily data concern us. Our concern is aggravated by the consistent conclusions of Black, Hess, and Officer and Trennepohl that unusual price behavior occurs primarily in the last two days of option trading. Another matter of potential concern is the nonsynchronous data arising from the cessation of option trading one hour before the close of the stock exchange. Here we subscribe to the view of Manaster and Rendleman [13] that “one would expect the within-day assessment of the equilibrium (stock) price to differ from the day-end equilibrium price in a purely random and unbiased fashion.” Consequently we assume that the nonsynchronous closing prices will introduce no bias in the results. The methodology we employ is based on the fact that if security prices follow a true random walk, then whether a security sells above (or below) the nearest option’s striking price should have no effect on its subsequent price behavior. If there is an expiration convergence effect, then it may be exhibited in several ways: 1) A tendency for a stock’s price to move in the direction of the nearest option striking price as the date of option expiration is reached (directional convergence); 2) A tendency for the random deviation of stock prices from the nearest option striking price to be smaller on expiration day than on an earlier day for the same striking price (proximal convergence). We investigate the existence of both of these phenomena. 1. Convergence based on movement of the underlying stock in the direction of the nearest option striking price (directional convergence), Using the same Manaster and Rendleman argument as stated previously, there is no reason to expect an end-of-week security price to differ from a within-week price in other than a purely random and unbiased fashion. If a sample is selected on the basis of the Thursday price, there is no a priori reason for a systematic relationship between the day before (Wednesday) and day after (Friday) price. On this basis, then, the fact that a stock is above or below its nearest option
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strike price on a particular day should give no indication of its future price movement. However, if there is a directional-convergence phenomenon, one would expect stocks priced above the nearest option strike price to exhibit a tendency to move in the direction of that strike price, that is, to fall in price. On the other hand, stocks priced below the nearest option strike price would be expected to exhibit a tendency to increase in price. To test for the existence or lack of existence of such a tendency, the Fisher Exact Probability Test was employed. The Fisher test is a nonparametric test that gives the probability that the sample outcomes would be observed given that no directionality exists (see [15, 181. Also see [3] for a related application of the Fisher Test.). Using Wednesday prices, stocks were categorized as being either above or below the nearest option-expiration price. Then, on the basis of Friday prices, these same stocks were categorized as having moved either in the direction of or away from the nearest option striking price. To make the test as conservative as possible, stocks above or below the nearest option striking price on Wednesday and exhibiting no change in price on Friday were categorized as moving away from the strike price (i.e., not converging). Stocks that were at a striking price on Wednesday and had moved away from the striking price on Friday were classified as nonconverging (i.e., above the strike price and moving up or below the strike price and moving down). Without question, these classifications should bias the data against the existence of convergence (i.e., as represented here, movement in the direction of the nearest option strike price). The only data omitted from the sample were stocks that were at a striking price on Wednesday and still at the same price Friday. One could argue that these stocks had already converged. In any case, they consisted of a very small number of observations in relation to the sample size. If the price movement from Wednesday to Friday is truly random, the null hypothesis under the Fisher test would predict approximately equal numbers of stocks moving in the direction of or away from the nearest striking price (omitting the no-price-change stocks) regardless of whether the stock was above or below the strike price on Wednesday. On the other hand, the alternative hypothesis (i.e., convergence) would predict that the sum of the number of observations of stocks above the strike price and moving down and those below the strike price and moving up significantly exceeds the sum of the other possible price movements. 2. Convergence based on a reduction in the random deviation of a stock price from its nearest striking price (Proximal Convergence). While the Fisher test looks at the direction of the movement of a stock price relative to its nearest option striking price, it does not tell us how close the stock price actually ends up being to the striking price. A stock classified above the striking price on Wednesday could move below and further away from the striking price on Friday and still be classified as exhibiting “directional convergence.” Thus, in order to test convergence in the sense of a security’s price being closer to the striking price on Friday than on Wednesday, the following test statistic (e) was utilized: let 0,
= IP, - SPI
0,
= EJ
A
= ef -8,
-_SPI
Influence of Option Expiration where P, P/. SP
.J BUSN RES 1987:15:291-302
295
= Wednesday stock price = Friday stock price = option striking price
Since the population of stock options is large, we can invoke the central-limit theorem and conclude that the sampling distribution of the mean of the statistic should be approximately normally distributed. Thus, a paired t test can be used to test the hypothesis that the difference (A) in the mean Wednesday deviation (&,) and the mean Friday deviation (e,) is equal to zero (as one would expect if there is no systematic bias around the option-expiration date). In order to comprehensively establish the significance of the above two tests, the analysis was performed on a test group of stocks with expiring options and with three control groups. The control groups included: 1) a nonexpiration option control group, comprised of securities whose options did not expire in the cycle of the test group; 2) a “first-week” option control group, comprised of security prices before the first Friday of the month rather than the third Friday (when options normally expire); and 3) a stock control group, comprised of securities on which options are not available but where the security otherwise passed the selection screen (see below for a discussion of the screen).
Data We selected our data by screening all expiring options over the period May 1980 to January 1982, and we admitted to our sample those whose underlying stock price was $50 or less and that were within $1 of a striking price at the Thursday close (one day before expiration). Stocks priced below $50 have option striking prices at $5 intervals, while higher-priced stocks normally have striking prices at $10 intervals. To eliminate any effects that might be caused by these unequal intervals, we eliminated all securities over $50 in price. The motivation for the $1 screen is twofold. First, the efficient use of resources was of major importance since data collection of the entire option universe would have been excessively costly and time consuming and the $1 screen yields a sufficient sample for testing purposes. Assuming a uniform price distribution, selecting all stocks priced within $1 of a multiple of $5 should collect about 40% of the entire population of optionable stocks selling below $50 (a $2-l/2 screen would collect the entire population). Second is Klemkosky’s impression that unusual stock-price behavior may appear when a put or a call has only slight intrinsic value. In discussions with other researchers we were unable to conceive of any bias such a screen might induce. Six-hundred-and-two test-group securities passed the selection screen. For the proximal-convergence test we trimmed 18 observations where the difference between the Wednesday closing and the Friday closing price was more than $2; we considered this price change extraordinary and likely to overwhelm any influence from expiring options. The control groups for the proximal convergence test are trimmed in similar fashion (and in a similar proportion). In order to identify other potentially interesting characteristics, the data are flagged according to the exchange on which they trade and whether both puts and calls or just calls were available on the stock. In Galai’s [7] test of market efficiency
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R. A. Strong and W. P. Andrew
1987:15:291-302
Results of the Test of Directional Convergence
Table 1.
Securities That Are: Below S.P. and Move Up
Sample
Below S.P. and Move Down
Above S.P. and Move Up
Above S.P. and Move Down
Significance (probability)
Test Group
A. Marketmaker exchanges B. Specialist exchanges
78
65
64
89
,019
85
63
60
82
,007
69
36
56
95
,001
75
62
49
92
,001
72
65
52
62
,167
66
55
58
69
,102
168
158
166
176
,243
Nonexpiration Control Group
A. Marketmaker exchanges B. Specialist exchanges First- Week Control Group
A. Marketmaker exchanges B. Specialist exchanges Stock Control Group
on the CBOE, he raises the important question of whether the marketmaker system (where prices are quoted by competitors, as on the CBOE and Pacific Exchanges) or the specialist system (where prices are quoted by noncompeting specialists, as on the AMEX and Philadelphia Exchanges) is socially more efficient. Our research provides some relevant information about this question. Results 1. Directional
Convergence
The hypothesis tested using the Fisher Exact Probability Test is: H,: H,:
During expiration week, the movement of a stock’s price from Wednesday to Friday with respect to the nearest strike price is random. Stock prices tend to move in the direction of the nearest option strike price from Wednesday to Friday during option-expiration week.
The results, presented in Table 1, were consistent with an option-influenceddirectional-convergence effect, that is, a rejection of the null hypothesis. The only apparent anomaly in the results was observed in the option control group. However, as explained below, the option-control-group results are not necessarily inconsistent with an option-influenced-directional-convergence effect.
Influence of Option Expiration
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Test Group.. On both marketmaker and specialist option exchanges, the tendency of stock prices to move in the direction of the nearest strike price was significant at .05 level (on the specialist exchanges at the .Ol level). These results are consistent with the existence of a directional-convergence effect. Nonexpiration Control Group.. The results of this test raise some interesting possibilities of other convergence phenomena related to the one under investigation. Both marketmaker and specialist option exchange stocks exhibited directional convergence at a significance level of better than 0.001. Recall that these are stocks with options that are not currently expiring. One possible explanation of these results is that as investors unwind positions in expiring options, they assume positions in other more distant options not necessarily on the same stock or in the same expiration cycle. For example, as the February option-expiration date approaches, speculators may close out their positions and look for opportunities with securities in the March or April cycles. Puts and calls can be purchased without the posting of margin, and the leverage associated with a small option premium means that a limited investment can produce very large gains on modest price movements in the underlying stock. As opening transactions, such inexpensive options may be attractive purchases to the speculator, but they are not attractive sales since the writing of options does involve a margin requirement, and the maximum possible gain with the writing of an option is the option premium. Consequently, it is likely to be the marketmakers or specialists who must, by virtue of their responsibility on the exchange, take the other side of the market for the speculators. They will then hedge their involuntary positions in these options by buying stock if they have to write calls or by shorting stock if they have to write puts. These activities will promote convergence as described in the introductory pages of this article. First- Week Control Group.. The results for this control group (stock-price movement in the first week of the month rather than expiration week) were not significant at the 10% level. This offers further evidence that the observed directionalconvergence behavior is at least partly a function of activities related to option expiration. Stock Control Group.. For stocks without options there appeared to be no significant directional convergence during the option-expiration period. This offers further evidence that the observed directional convergence is related to option expiration.
2.
Proximal
Convergence
This test complements the directionality test because while directional convergence indicates movement toward a particular strike price, it does not give any indication of how much closer the stock price is to the strike price. It is quite possible that a stock could move in the direction of the striking price and end up further away than when it started (having moved past the striking price).
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J BUSN
Table 2.
Option Test Group
RES 1987:15:291-302
Stratum All securities
Marketmaker (CBOE
Specialist (AMEX
Specialist
exchanges
& Pacific)
exchanges & Philly)
exchanges
with calls only
Specialist
R. A. Strong
Variable
Mean
t Stat
Prob>t
and W. P. Andrew
N”
o
ew
0.6346
30.03
0.0001
584
0.5107
%
0.5606
27.22
0.0001
584
0.4976
A
- 0.0741
- 2.82
0.0050
584
0.6350
Gv
0.6246
20.65
0.0001
294
0.5186
Gf
0.5850
19.43
0.0001
294
0.5163
A
- 0.0395
- 1.08
0.2798
294
0.6261
6,
0.6418
21.73
0.0001
283
0.4969
6,
0.5353
18.75
0.0001
283
0.4804
A
- 0.1064
- 2.77
0.0060
283
0.6468
e,
0.5691
7.58
0.0001
38
0.4629
6,
0.5000
7.76
0.0001
38
0.3971
A
- 0.0691
- 0.89
0.3806
38
0.4799
exchanges
6,
0.6531
20.36
0.0001
245
0.5020
with puts and calls
6,
0.5408
17.19
0.0001
245
0.4925
A
- 0.1122
- 2.62
0.0092
245
0.6695
“Securities
dually listed are not reported
in the exchange
breakdowns
Thus, the following hypothesis relating to proximal convergence
was tested:
In most instances, the results were similar to those with the test of directional convergence. There were several differences, however, in regard to proximal convergence with specialist and with marketmaker option exchange stocks. While both had exhibited similar directional-convergence results, when proximal convergence is examined, only the specialist option exchange stocks showed significant results. A discussion of these results and their summary statistics is given below and in Tables 2-5. Test Group.. For the reasons outlined above, one would not expect the mean deviation e,,, to differ significantly from G? Table 2 presents the results of testing this hypothesis for the test group and its various strata. For the entire test group, the mean deviation on Friday is significantly less than the mean deviation on Wednesday; there is less than a 1% probability that the value of the test statistic would be observed by chance. We find no significance in the marketmaker stratum but continued high significance in the specialist group. Within the specialist group, the significance disappears if only calls are traded. (The presence of puts does not add significance in the marketmaker stratum.) The reason that significance disappears when only calls are traded might be due
Influence
J BUSN RES 1987:15:291-302
of Option Expiration
Table 3. Nonexpiration Stratum
Option Control Group Mean
Variable
%
All securities
Marketmakerexchanges (CBOE & Pacific)
Specialist exchanges (AMEX & Philly)
Specialist exchanges with calls only
Specialist exchanges with puts and calls
299
t Stat
Prob>t
N”
u
5,
0.6709 0.6095
29.64 30.29
0.0001 0.0001
547 547
0.5294 0.4706
A
- 0.0615
- 2.24
0.0255
547
0.6417
5, e,
0.6788 0.6453
20.71 20.86
0.0001 0.0001
258 258
0.5264 0.4970
A
- 0.0334
- 0.79
0.4283
258
0.6768
5,. 5,
0.6667 0.5776
21.10 21.76
0.0001 0.0001
282 282
0.5307 0.4458
A
- 0.0891
- 2.47
0.0142
282
0.6065
e,, @
0.5399 0.5319
8.40 8.86
0.0001 0.0001
47 47
0.4409 0.4117
A
- 0.0080
- 0.12
0.9059
47
0.4599
e,. e,
0.6920 0.5867
19.50 19.87
0.0001 0.0001
235 235
0.5442 0.4526
A
- 0.1053
- 2.56
0.0112
235
0.6313
“Securities dually listed are not reported in the exchange breakdowns.
to the fact that if convergence results from differential effects of puts and calls (depending on whether a stock is above or below the nearest strike price), when there are no puts the effect may be in one direction only and exist only if the stock is above the nearest strike price. These effects, however, would be obscured by the random movement of stocks below the nearest strike price (since there would be no upward bias due to the presence of puts). Nonexpiration Control Group.. As with the directional-convergence test, this control group shows results that mirror those of the test group. The test statistic is significant for the entire sample and for the specialist exchange group, but is not significant for the marketmaker stratum. When the specialist group is split into “calls only” and “both options” subgroups, significance disappears in the “calls only” group. First- Week Control Group..
As with the directionality
test, this group shows no
significance in any category. Stock Control Group.. This control group shows no statistically significant difference in the mean deviations of the stock price from the phantom striking price on Wednesday and Friday. In other words, there is no evidence of unusual behavior. As with the directional-convergence tests, the above results are consistent with
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J BUSN RES 1987:15:291-302
Table 4.
First-Week Option Control Stratum
R. A. Strong and W. P. Andrew
Variable
Group Mean
t Stat
Prob>t
N”
o
a+
0.6260
28.55
0.0001
510
0.4951
e,
0.6500
29.28
O.oool
510
0.5014
A
0.0240
0.86
0.3877
510
0.6275
e,
0.6304
19.51
0.0001
254
0.5149
i%
0.6526
24.70
0.0001
254
0.5226
A
0.0222
0.53
0.5952
254
0.6634
e,.
0.6285
20.78
0.0001
250
0.4782
5,
0.6485
21.34
0.0001
250
0.4806
A
0.0200
0.54
0.5927
250
0.5903
s.
0.6500
7.97
O.OWl
30
0.4470
6,
0.6542
8.05
0.0001
30
0.4449
A
0.0042
0.05
0.9606
30
0.4578
exchanges
S”
0.6256
19.20
O.OWl
220
0.4832
with puts and calls
6,
0.6477
19.76
O.OWl
220
0.4862
A
0.0221
0.54
0.5887
220
0.6070
All securities
Marketmaker (CBOE
Specialist (AMEX
exchanges
& Pacific)
exchanges & Philly)
Specialist
exchanges
with calls only
Specialist
“Securities
dually listed are not reported
in the exchange
breakdowns.
an option-expiration-induced-proximal-convergence effect. Support for option expiration as a causal factor is indicated by the lack of the observed effect in the firstweek and stock control groups. Conclusions
and Implications
The results of our analysis lead us to the conclusion that when specialist-traded options (both puts and calls) are available on common stock, those stock prices show a significant tendency to move in the direction of and closer to the nearest option striking price in the final two days of trading before option expiration. A potential explanation for these results lies in hedging activities by the option specialist. By virtue of his or her obligation to make a market in assigned securities, a specialist may have to involuntarily purchase either puts or calls that are only slightly in the money. If the specialist buys a quantity of expiring calls with slight intrinsic value, his or her firm may choose to hedge this “investment” by causing Table 5.
Stock Control Group Stratum
All securities
t Stat
Prob>t
N
5,
0.6490
36.61
O.OWl
678
0.4616
e,
0.6340
36.90
0.0001
678
0.4474
A
- 0.0150
- 0.75
0.4551
678
0.5203
Variable
Mean
is
Influence of Option Expiration
J BUSN RES 1987:15:291-302
301
a representative on the stock exchange to sell short an equivalent number of shares. Similarly, if puts must be purchased, the specialist’s member firm may consider it prudent to hedge by buying stock. In addition, with regard to Galai’s question about social efficiency of specialists and marketmakers, we do find evidence that options traded via the specialist system have a monthly expiration influence on stock prices, while there appears to be a directional-convergence effect but not a proximal-convergence effect when a marketmaker system is used. While it is not completely clear why these differences should exist, they may relate to differences in the hedging activities undertaken by marketmakers and specialists. There are potentially many more exchange members making a market in a single security on the CBOE and Pacific Exchange than on the specialist exchanges. On the Chicago Board Options Exchange, for instance, there are approximately 1,800 members (nonspecialist “broker/dealers”) making a market in options on 420 securities. These members trade in “crowds” ranging in size from 7 people to over 500. On the other hand, the American Stock Exchange has 29 specialist units dealing in about 106 securities, or about four options per specialist. A public order for 250 inexpensive, soon-to-expire option contracts on a particular common stock might be an unacceptable risk to a specialist, and he or she might hedge this risk in the stock market as described earlier. However, on the CBOE this risk could be distributed throughout the crowd, and make an individual’s need for such a hedge less pronounced. This is certainly an area worthy of further research. The magnitude of the observed convergence effect on the specialist exchanges is small; it is unlikely that it can be profitably exploited by a commission-paying investor. However, social efficiency in the Pareto optimal sense is reduced if a market participant is able to systematically exploit the economic system to the detriment of another participant. Although it is unclear from these results that such is the case, the results are thought provoking, and further research is also indicated in this area. The discovery that the convergence tendency appears in stocks with nonexpiring options was initially unexpected. However, when considering the various strategies employed by option traders, the results can be viewed as a reasonable result of trading activity. What this indicates is that the existence of option-related “events” may have a more pervasive impact than previously suspected on common stock not directly related to the option in question. This also appears to be an interesting area for further research. References 1. Anders, George, Option Trading at Expiration Might Influence Prices of Underlying Stock, Studies Indicate, Wall Street Journal (April 15, 1982):55.
Black, Fischer, What Happens When Options Start Trading, Options Newsletter (April 19, 1975). Bowen, Robert M., Daley, Lane A., and Huber, Charles C., Jr., Evidence on the Existence and Determinants of Inter-Industry Differences in Leverage, Financial Management (Winter 1982):10-20. Branch, Ben, and Finnerty, Joseph, The Impact of Option Listing on the Price and Volume of the Underlying Stock, Financial Review 10 (Spring 1975):1-15.
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R. A. Strong and W. P. Andrew
5. Chicago Board Options Exchange, Analysis of Volume and Price Patterns in Stock Underlying CBOE Options from December 30, 1974 to April 30, 197.5, Chicago (July
1975). 6. -,
Analysis of Volume and Price Patterns in Stock Underlying CBOE Options from December 31, 1975 to January 16, 1976, Chicago (February 1976).
7. Galai, Dan, Tests of Market Efficiency of the Chicago Board Options Exchange, Journal of Business 50 (April 1977):167-197. 8. Gastineau, Gary, The Stock Options Manual. McGraw-Hill, New York, Appendix D, p. 354. 9. Hayes, Samuel L., and Tennenbaum, Michael E., The Impact of Listed Options on the Underlying Stock, Financial Management 8 (Winter 1979):72-76. 10. Hess, Dan W., The Impact of Option Expiration on Underlying Stock Prices and the Determinants of the Size of the Impact, unpublished Ph.D. dissertation, The University of Arizona, 1982. 11. Klemkosky, Robert C., The Impact of Option Expiration on Stock Prices, Journal of Finance and Quantitative Analysis 13 (September 1978):507-517. 12. Lenzner, Robert, Call of the Wild: Options--Despite Denials-Influence Movements in Stocks, Barron’s (May 3, ‘1976):5. 13. Manaster, Steven, and Rendleman, Richard J., Jr., Option Prices as Predictors of Equilibrium Stock Prices, Journal of Finance 37 (September 1982):1043-1057. 14. Officer, Dennis T., and Trennepohl, Gary L., Price Behavior of Corporate Equities Near Option Expiration Dates, Financial Management 10 (Summer 1981):75-80. 15. Pierce, Albert, Fundamentals of Nonparametric Statistics. Dickenson, Belmont California, 1970, chapter 8. 16. Robert R. Nathan Associates, Inc., Public Policy Aspects of a Futures-Type Market in Options in Securities, Chicago (November 1969). 17. -. Review of Initial Trading Experience at the Chicago Board Options Exchange, Chicago (December 1974). 18. Siegel, Sidney, Nonparametric Statistics for the Behavioral Sciences. McGraw-Hill, New York, 1956, chapter 6.
291
Further Evidence of the Influence of Option Expiration on the Underlying Common Stock Robert A. Strong
William P. Andrew
The University
The Pennsylvania
of Maine
State University
Over the past decade there has been increasing research into the interaction among the securities options markets and other institutions. Of particular interest in the earliest research was the extent to which social efficiency is enhanced by the trading of puts and calls. Since it is now well established that market-spanning opportunities are more complete when options are available, recent research has been directed toward such issues as the informational efficiency of the options exchanges and the relationship between an option premium and the behavior of the underlying common stock. Of interest to us in this research is the latter issue. We find significant new evidence that in the final two days of trading prior to the expiration of an option series, the presence of options influences some underlying stock prices. Previous
Research Prior research in this area has resulted in a variety of conclusions regarding the influence of options on the underlying stock. Shortly following the advent of listed options in 1973, the Chicago Board Options Exchange (CBOE) conducted, sponsored, or reviewed several examinations [5,6, 16, 171 of the impact of these option contracts on the behavior of stock prices. The first CBOE study [5] and the second Nathan study [17] found evidence that option trading decreased the price volatility of the underlying stock. Similarly, Hayes and Tennenbaum [9] found that the presence of listed options increases stock trading volume, which, ceteris paribus, should reducC price volatility. In addition, they report that respondents to a mail survey of the top management of the 43 firms listed on the CBOE in May 1973 felt that option listing did not influence the price of their securities. However, agreement on these issues is not as clear cut when stock behavior is examined during certain periods in the option’s life. For example, Gastineau [8] indicates that many observers believe that stocks with listed options are more volatile during
Address correspondence ME 04469. Journal of
to Dr. Robert A. Strong, University of Maine, South Stevens Hall, Orono,
Business Research 15, 291-302 (1987) 0 1987 Elsevier Science Publishing Co., Inc. 1987 52 Vanderbilt Ave., New York, NY 10017
0148-2963/87/$3.50
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R. A. Strong and W. P. Andrew
the week or two preceding and following an expiration date. Branch and Finnerty [4] offer evidence that stocks with newly listed options tend to outperform the market prior to and just after the option-listing date. Exploration of the behavior of security prices around an option-expiration date was given further impetus when Fisher Black [2] wrote in 1976 that “Option trading may even have some slight effect on stock volatilities and on stock prices at the time the options expire.” The first major study of the impact of option expirations on stock prices was by Klemkosky [ll] in 1978. He concluded that in the week prior to expiration of an option series, stock prices show a 1% average residual decline, while in the subsequent week prices rise by 0.4%. Two other studies support Klemkosky’s results. Officer and Trennepohl [14] discovered a tendency for stocks to decline slightly in the few days prior to expiration. Hess [lo] finds similar results, with the most significant declines occurring on Thursday and Friday of the expiration week. Klemkosky offers several explanations for this price behavior. For example, he asserts that in the final week of trading, call options frequently sell at a slight discount from intrinsic value, enabling a noncommission-paying arbitrageur to exercise the call and sell the stock at a profit without benefit of a price uptick, thereby increasing downward pressure on the price of the underlying common stock. This and other explanations by Klemkosky imply that the presence of call options will bias the underlying stock price downward immediately prior to option expiration. However, in his study, Klemkosky makes no effort to test empirically for any differential impact due to in- or out-of-the-money calls on the expiration effects. One result of our research supports the hypothesis that such a differential effect exists. It should be noted that the previous research was conducted during a period when option contracts consisted primarily of call options. In the last few years, however, ‘put options have increased in both availability and popularity. Some researchers argue that if the presence of calls biases stock prices down prior to option expiration, then the presence of puts should have the opposite effect, with the two influences offsetting each other. For example, Hess’s research, which covered the period 1978-1981 (when the number of puts was increasing), led him to conclude “As put trading appears to offset the market inefficiencies caused by call option trading, the concern of regulators that options trading unduly effects stock prices seems unwarranted.” Like Klemkosky, however, Hess does not investigate whether the existence of put options affects the underlying stock differently depending on whether the nearest puts are in or out of the money. The existence of such a differential impact is supported by articles by Anders [l] and Lenzer [12]. The logic of such an effect is relatively straightforward. For a given option striking price, a put and a call cannot both have intrinsic value. If the call has intrinsic value, then Klemkosky’s explanations may be operative, while the put will expire worthless. If, however, it is the put which has intrinsic value, a comparable explanation would be that arbitrageurs buy stock and exercise puts, while short sellers of stock who have also written puts leave the market by buying the put back and covering their short position in the stock. Either of these last two activities could exert upward pressure on stock prices (in contrast to the effect when the call has intrinsic value).
Influence of Option Expiration
J BUSN RES 1987:15:291-302
All of these potential activities have a similar result: Stock selling at slightly above an option striking price (call has intrinsic value) may be biased downward, while stock selling slightly below the striking price (put has intrinsic value) may be biased upward. This is what some practitioners refer to as the “convergence phenomenon,” where stock prices are believed to show an unusual tendency to close near the closest striking price on option-expiration day (e.g., see [l]). Further investigation of this alleged phenomenon is the intent of this paper. Methodology It is challenging to investigate security-price behavior that earlier research has shown to be fleeting. In constructing our methodology we relied on the discoveries and suggestions of our predecessors in this research area. From Klemkosky we adopt two suggestions. First, we accept the charge that “Future research should test for daily price change patterns” (his research looked at weekly data). And second, we recognize the limitation of the linear market model when residual error terms are expected to be nonzero because of bias around certain events. Previous research does suggest that a bias may exist around option expiration, and while it might be possible to remove the bias, the limitations of the market model with daily data concern us. Our concern is aggravated by the consistent conclusions of Black, Hess, and Officer and Trennepohl that unusual price behavior occurs primarily in the last two days of option trading. Another matter of potential concern is the nonsynchronous data arising from the cessation of option trading one hour before the close of the stock exchange. Here we subscribe to the view of Manaster and Rendleman [13] that “one would expect the within-day assessment of the equilibrium (stock) price to differ from the day-end equilibrium price in a purely random and unbiased fashion.” Consequently we assume that the nonsynchronous closing prices will introduce no bias in the results. The methodology we employ is based on the fact that if security prices follow a true random walk, then whether a security sells above (or below) the nearest option’s striking price should have no effect on its subsequent price behavior. If there is an expiration convergence effect, then it may be exhibited in several ways: 1) A tendency for a stock’s price to move in the direction of the nearest option striking price as the date of option expiration is reached (directional convergence); 2) A tendency for the random deviation of stock prices from the nearest option striking price to be smaller on expiration day than on an earlier day for the same striking price (proximal convergence). We investigate the existence of both of these phenomena. 1. Convergence based on movement of the underlying stock in the direction of the nearest option striking price (directional convergence), Using the same Manaster and Rendleman argument as stated previously, there is no reason to expect an end-of-week security price to differ from a within-week price in other than a purely random and unbiased fashion. If a sample is selected on the basis of the Thursday price, there is no a priori reason for a systematic relationship between the day before (Wednesday) and day after (Friday) price. On this basis, then, the fact that a stock is above or below its nearest option
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strike price on a particular day should give no indication of its future price movement. However, if there is a directional-convergence phenomenon, one would expect stocks priced above the nearest option strike price to exhibit a tendency to move in the direction of that strike price, that is, to fall in price. On the other hand, stocks priced below the nearest option strike price would be expected to exhibit a tendency to increase in price. To test for the existence or lack of existence of such a tendency, the Fisher Exact Probability Test was employed. The Fisher test is a nonparametric test that gives the probability that the sample outcomes would be observed given that no directionality exists (see [15, 181. Also see [3] for a related application of the Fisher Test.). Using Wednesday prices, stocks were categorized as being either above or below the nearest option-expiration price. Then, on the basis of Friday prices, these same stocks were categorized as having moved either in the direction of or away from the nearest option striking price. To make the test as conservative as possible, stocks above or below the nearest option striking price on Wednesday and exhibiting no change in price on Friday were categorized as moving away from the strike price (i.e., not converging). Stocks that were at a striking price on Wednesday and had moved away from the striking price on Friday were classified as nonconverging (i.e., above the strike price and moving up or below the strike price and moving down). Without question, these classifications should bias the data against the existence of convergence (i.e., as represented here, movement in the direction of the nearest option strike price). The only data omitted from the sample were stocks that were at a striking price on Wednesday and still at the same price Friday. One could argue that these stocks had already converged. In any case, they consisted of a very small number of observations in relation to the sample size. If the price movement from Wednesday to Friday is truly random, the null hypothesis under the Fisher test would predict approximately equal numbers of stocks moving in the direction of or away from the nearest striking price (omitting the no-price-change stocks) regardless of whether the stock was above or below the strike price on Wednesday. On the other hand, the alternative hypothesis (i.e., convergence) would predict that the sum of the number of observations of stocks above the strike price and moving down and those below the strike price and moving up significantly exceeds the sum of the other possible price movements. 2. Convergence based on a reduction in the random deviation of a stock price from its nearest striking price (Proximal Convergence). While the Fisher test looks at the direction of the movement of a stock price relative to its nearest option striking price, it does not tell us how close the stock price actually ends up being to the striking price. A stock classified above the striking price on Wednesday could move below and further away from the striking price on Friday and still be classified as exhibiting “directional convergence.” Thus, in order to test convergence in the sense of a security’s price being closer to the striking price on Friday than on Wednesday, the following test statistic (e) was utilized: let 0,
= IP, - SPI
0,
= EJ
A
= ef -8,
-_SPI
Influence of Option Expiration where P, P/. SP
.J BUSN RES 1987:15:291-302
295
= Wednesday stock price = Friday stock price = option striking price
Since the population of stock options is large, we can invoke the central-limit theorem and conclude that the sampling distribution of the mean of the statistic should be approximately normally distributed. Thus, a paired t test can be used to test the hypothesis that the difference (A) in the mean Wednesday deviation (&,) and the mean Friday deviation (e,) is equal to zero (as one would expect if there is no systematic bias around the option-expiration date). In order to comprehensively establish the significance of the above two tests, the analysis was performed on a test group of stocks with expiring options and with three control groups. The control groups included: 1) a nonexpiration option control group, comprised of securities whose options did not expire in the cycle of the test group; 2) a “first-week” option control group, comprised of security prices before the first Friday of the month rather than the third Friday (when options normally expire); and 3) a stock control group, comprised of securities on which options are not available but where the security otherwise passed the selection screen (see below for a discussion of the screen).
Data We selected our data by screening all expiring options over the period May 1980 to January 1982, and we admitted to our sample those whose underlying stock price was $50 or less and that were within $1 of a striking price at the Thursday close (one day before expiration). Stocks priced below $50 have option striking prices at $5 intervals, while higher-priced stocks normally have striking prices at $10 intervals. To eliminate any effects that might be caused by these unequal intervals, we eliminated all securities over $50 in price. The motivation for the $1 screen is twofold. First, the efficient use of resources was of major importance since data collection of the entire option universe would have been excessively costly and time consuming and the $1 screen yields a sufficient sample for testing purposes. Assuming a uniform price distribution, selecting all stocks priced within $1 of a multiple of $5 should collect about 40% of the entire population of optionable stocks selling below $50 (a $2-l/2 screen would collect the entire population). Second is Klemkosky’s impression that unusual stock-price behavior may appear when a put or a call has only slight intrinsic value. In discussions with other researchers we were unable to conceive of any bias such a screen might induce. Six-hundred-and-two test-group securities passed the selection screen. For the proximal-convergence test we trimmed 18 observations where the difference between the Wednesday closing and the Friday closing price was more than $2; we considered this price change extraordinary and likely to overwhelm any influence from expiring options. The control groups for the proximal convergence test are trimmed in similar fashion (and in a similar proportion). In order to identify other potentially interesting characteristics, the data are flagged according to the exchange on which they trade and whether both puts and calls or just calls were available on the stock. In Galai’s [7] test of market efficiency
J BUSN RES
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R. A. Strong and W. P. Andrew
1987:15:291-302
Results of the Test of Directional Convergence
Table 1.
Securities That Are: Below S.P. and Move Up
Sample
Below S.P. and Move Down
Above S.P. and Move Up
Above S.P. and Move Down
Significance (probability)
Test Group
A. Marketmaker exchanges B. Specialist exchanges
78
65
64
89
,019
85
63
60
82
,007
69
36
56
95
,001
75
62
49
92
,001
72
65
52
62
,167
66
55
58
69
,102
168
158
166
176
,243
Nonexpiration Control Group
A. Marketmaker exchanges B. Specialist exchanges First- Week Control Group
A. Marketmaker exchanges B. Specialist exchanges Stock Control Group
on the CBOE, he raises the important question of whether the marketmaker system (where prices are quoted by competitors, as on the CBOE and Pacific Exchanges) or the specialist system (where prices are quoted by noncompeting specialists, as on the AMEX and Philadelphia Exchanges) is socially more efficient. Our research provides some relevant information about this question. Results 1. Directional
Convergence
The hypothesis tested using the Fisher Exact Probability Test is: H,: H,:
During expiration week, the movement of a stock’s price from Wednesday to Friday with respect to the nearest strike price is random. Stock prices tend to move in the direction of the nearest option strike price from Wednesday to Friday during option-expiration week.
The results, presented in Table 1, were consistent with an option-influenceddirectional-convergence effect, that is, a rejection of the null hypothesis. The only apparent anomaly in the results was observed in the option control group. However, as explained below, the option-control-group results are not necessarily inconsistent with an option-influenced-directional-convergence effect.
Influence of Option Expiration
J BUSN RES 1987:15:291-302
Test Group.. On both marketmaker and specialist option exchanges, the tendency of stock prices to move in the direction of the nearest strike price was significant at .05 level (on the specialist exchanges at the .Ol level). These results are consistent with the existence of a directional-convergence effect. Nonexpiration Control Group.. The results of this test raise some interesting possibilities of other convergence phenomena related to the one under investigation. Both marketmaker and specialist option exchange stocks exhibited directional convergence at a significance level of better than 0.001. Recall that these are stocks with options that are not currently expiring. One possible explanation of these results is that as investors unwind positions in expiring options, they assume positions in other more distant options not necessarily on the same stock or in the same expiration cycle. For example, as the February option-expiration date approaches, speculators may close out their positions and look for opportunities with securities in the March or April cycles. Puts and calls can be purchased without the posting of margin, and the leverage associated with a small option premium means that a limited investment can produce very large gains on modest price movements in the underlying stock. As opening transactions, such inexpensive options may be attractive purchases to the speculator, but they are not attractive sales since the writing of options does involve a margin requirement, and the maximum possible gain with the writing of an option is the option premium. Consequently, it is likely to be the marketmakers or specialists who must, by virtue of their responsibility on the exchange, take the other side of the market for the speculators. They will then hedge their involuntary positions in these options by buying stock if they have to write calls or by shorting stock if they have to write puts. These activities will promote convergence as described in the introductory pages of this article. First- Week Control Group.. The results for this control group (stock-price movement in the first week of the month rather than expiration week) were not significant at the 10% level. This offers further evidence that the observed directionalconvergence behavior is at least partly a function of activities related to option expiration. Stock Control Group.. For stocks without options there appeared to be no significant directional convergence during the option-expiration period. This offers further evidence that the observed directional convergence is related to option expiration.
2.
Proximal
Convergence
This test complements the directionality test because while directional convergence indicates movement toward a particular strike price, it does not give any indication of how much closer the stock price is to the strike price. It is quite possible that a stock could move in the direction of the striking price and end up further away than when it started (having moved past the striking price).
298
J BUSN
Table 2.
Option Test Group
RES 1987:15:291-302
Stratum All securities
Marketmaker (CBOE
Specialist (AMEX
Specialist
exchanges
& Pacific)
exchanges & Philly)
exchanges
with calls only
Specialist
R. A. Strong
Variable
Mean
t Stat
Prob>t
and W. P. Andrew
N”
o
ew
0.6346
30.03
0.0001
584
0.5107
%
0.5606
27.22
0.0001
584
0.4976
A
- 0.0741
- 2.82
0.0050
584
0.6350
Gv
0.6246
20.65
0.0001
294
0.5186
Gf
0.5850
19.43
0.0001
294
0.5163
A
- 0.0395
- 1.08
0.2798
294
0.6261
6,
0.6418
21.73
0.0001
283
0.4969
6,
0.5353
18.75
0.0001
283
0.4804
A
- 0.1064
- 2.77
0.0060
283
0.6468
e,
0.5691
7.58
0.0001
38
0.4629
6,
0.5000
7.76
0.0001
38
0.3971
A
- 0.0691
- 0.89
0.3806
38
0.4799
exchanges
6,
0.6531
20.36
0.0001
245
0.5020
with puts and calls
6,
0.5408
17.19
0.0001
245
0.4925
A
- 0.1122
- 2.62
0.0092
245
0.6695
“Securities
dually listed are not reported
in the exchange
breakdowns
Thus, the following hypothesis relating to proximal convergence
was tested:
In most instances, the results were similar to those with the test of directional convergence. There were several differences, however, in regard to proximal convergence with specialist and with marketmaker option exchange stocks. While both had exhibited similar directional-convergence results, when proximal convergence is examined, only the specialist option exchange stocks showed significant results. A discussion of these results and their summary statistics is given below and in Tables 2-5. Test Group.. For the reasons outlined above, one would not expect the mean deviation e,,, to differ significantly from G? Table 2 presents the results of testing this hypothesis for the test group and its various strata. For the entire test group, the mean deviation on Friday is significantly less than the mean deviation on Wednesday; there is less than a 1% probability that the value of the test statistic would be observed by chance. We find no significance in the marketmaker stratum but continued high significance in the specialist group. Within the specialist group, the significance disappears if only calls are traded. (The presence of puts does not add significance in the marketmaker stratum.) The reason that significance disappears when only calls are traded might be due
Influence
J BUSN RES 1987:15:291-302
of Option Expiration
Table 3. Nonexpiration Stratum
Option Control Group Mean
Variable
%
All securities
Marketmakerexchanges (CBOE & Pacific)
Specialist exchanges (AMEX & Philly)
Specialist exchanges with calls only
Specialist exchanges with puts and calls
299
t Stat
Prob>t
N”
u
5,
0.6709 0.6095
29.64 30.29
0.0001 0.0001
547 547
0.5294 0.4706
A
- 0.0615
- 2.24
0.0255
547
0.6417
5, e,
0.6788 0.6453
20.71 20.86
0.0001 0.0001
258 258
0.5264 0.4970
A
- 0.0334
- 0.79
0.4283
258
0.6768
5,. 5,
0.6667 0.5776
21.10 21.76
0.0001 0.0001
282 282
0.5307 0.4458
A
- 0.0891
- 2.47
0.0142
282
0.6065
e,, @
0.5399 0.5319
8.40 8.86
0.0001 0.0001
47 47
0.4409 0.4117
A
- 0.0080
- 0.12
0.9059
47
0.4599
e,. e,
0.6920 0.5867
19.50 19.87
0.0001 0.0001
235 235
0.5442 0.4526
A
- 0.1053
- 2.56
0.0112
235
0.6313
“Securities dually listed are not reported in the exchange breakdowns.
to the fact that if convergence results from differential effects of puts and calls (depending on whether a stock is above or below the nearest strike price), when there are no puts the effect may be in one direction only and exist only if the stock is above the nearest strike price. These effects, however, would be obscured by the random movement of stocks below the nearest strike price (since there would be no upward bias due to the presence of puts). Nonexpiration Control Group.. As with the directional-convergence test, this control group shows results that mirror those of the test group. The test statistic is significant for the entire sample and for the specialist exchange group, but is not significant for the marketmaker stratum. When the specialist group is split into “calls only” and “both options” subgroups, significance disappears in the “calls only” group. First- Week Control Group..
As with the directionality
test, this group shows no
significance in any category. Stock Control Group.. This control group shows no statistically significant difference in the mean deviations of the stock price from the phantom striking price on Wednesday and Friday. In other words, there is no evidence of unusual behavior. As with the directional-convergence tests, the above results are consistent with
300
J BUSN RES 1987:15:291-302
Table 4.
First-Week Option Control Stratum
R. A. Strong and W. P. Andrew
Variable
Group Mean
t Stat
Prob>t
N”
o
a+
0.6260
28.55
0.0001
510
0.4951
e,
0.6500
29.28
O.oool
510
0.5014
A
0.0240
0.86
0.3877
510
0.6275
e,
0.6304
19.51
0.0001
254
0.5149
i%
0.6526
24.70
0.0001
254
0.5226
A
0.0222
0.53
0.5952
254
0.6634
e,.
0.6285
20.78
0.0001
250
0.4782
5,
0.6485
21.34
0.0001
250
0.4806
A
0.0200
0.54
0.5927
250
0.5903
s.
0.6500
7.97
O.OWl
30
0.4470
6,
0.6542
8.05
0.0001
30
0.4449
A
0.0042
0.05
0.9606
30
0.4578
exchanges
S”
0.6256
19.20
O.OWl
220
0.4832
with puts and calls
6,
0.6477
19.76
O.OWl
220
0.4862
A
0.0221
0.54
0.5887
220
0.6070
All securities
Marketmaker (CBOE
Specialist (AMEX
exchanges
& Pacific)
exchanges & Philly)
Specialist
exchanges
with calls only
Specialist
“Securities
dually listed are not reported
in the exchange
breakdowns.
an option-expiration-induced-proximal-convergence effect. Support for option expiration as a causal factor is indicated by the lack of the observed effect in the firstweek and stock control groups. Conclusions
and Implications
The results of our analysis lead us to the conclusion that when specialist-traded options (both puts and calls) are available on common stock, those stock prices show a significant tendency to move in the direction of and closer to the nearest option striking price in the final two days of trading before option expiration. A potential explanation for these results lies in hedging activities by the option specialist. By virtue of his or her obligation to make a market in assigned securities, a specialist may have to involuntarily purchase either puts or calls that are only slightly in the money. If the specialist buys a quantity of expiring calls with slight intrinsic value, his or her firm may choose to hedge this “investment” by causing Table 5.
Stock Control Group Stratum
All securities
t Stat
Prob>t
N
5,
0.6490
36.61
O.OWl
678
0.4616
e,
0.6340
36.90
0.0001
678
0.4474
A
- 0.0150
- 0.75
0.4551
678
0.5203
Variable
Mean
is
Influence of Option Expiration
J BUSN RES 1987:15:291-302
301
a representative on the stock exchange to sell short an equivalent number of shares. Similarly, if puts must be purchased, the specialist’s member firm may consider it prudent to hedge by buying stock. In addition, with regard to Galai’s question about social efficiency of specialists and marketmakers, we do find evidence that options traded via the specialist system have a monthly expiration influence on stock prices, while there appears to be a directional-convergence effect but not a proximal-convergence effect when a marketmaker system is used. While it is not completely clear why these differences should exist, they may relate to differences in the hedging activities undertaken by marketmakers and specialists. There are potentially many more exchange members making a market in a single security on the CBOE and Pacific Exchange than on the specialist exchanges. On the Chicago Board Options Exchange, for instance, there are approximately 1,800 members (nonspecialist “broker/dealers”) making a market in options on 420 securities. These members trade in “crowds” ranging in size from 7 people to over 500. On the other hand, the American Stock Exchange has 29 specialist units dealing in about 106 securities, or about four options per specialist. A public order for 250 inexpensive, soon-to-expire option contracts on a particular common stock might be an unacceptable risk to a specialist, and he or she might hedge this risk in the stock market as described earlier. However, on the CBOE this risk could be distributed throughout the crowd, and make an individual’s need for such a hedge less pronounced. This is certainly an area worthy of further research. The magnitude of the observed convergence effect on the specialist exchanges is small; it is unlikely that it can be profitably exploited by a commission-paying investor. However, social efficiency in the Pareto optimal sense is reduced if a market participant is able to systematically exploit the economic system to the detriment of another participant. Although it is unclear from these results that such is the case, the results are thought provoking, and further research is also indicated in this area. The discovery that the convergence tendency appears in stocks with nonexpiring options was initially unexpected. However, when considering the various strategies employed by option traders, the results can be viewed as a reasonable result of trading activity. What this indicates is that the existence of option-related “events” may have a more pervasive impact than previously suspected on common stock not directly related to the option in question. This also appears to be an interesting area for further research. References 1. Anders, George, Option Trading at Expiration Might Influence Prices of Underlying Stock, Studies Indicate, Wall Street Journal (April 15, 1982):55.
Black, Fischer, What Happens When Options Start Trading, Options Newsletter (April 19, 1975). Bowen, Robert M., Daley, Lane A., and Huber, Charles C., Jr., Evidence on the Existence and Determinants of Inter-Industry Differences in Leverage, Financial Management (Winter 1982):10-20. Branch, Ben, and Finnerty, Joseph, The Impact of Option Listing on the Price and Volume of the Underlying Stock, Financial Review 10 (Spring 1975):1-15.
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J BUSN RES 1987:15:291-302
R. A. Strong and W. P. Andrew
5. Chicago Board Options Exchange, Analysis of Volume and Price Patterns in Stock Underlying CBOE Options from December 30, 1974 to April 30, 197.5, Chicago (July
1975). 6. -,
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