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An empirical analysis of common stock call exercise: A note
Journalof BANKING & ELSEVIER
Journal of Banking & Finance 21 (1997) 563-571
FINANCE
An empirical analysis of common stock call exercise: A note Thomas J. Finucane * Syracuse University, School of Management, Syracuse, NY 13244, USA Received 10 September 1995; accepted 20 September 1996
Abstract This study tests the hypothesis that common stock call options are exercised rationally and in accordance with the commonly used frictionless markets boundary conditions. Using two years of historical early exercise data for common stock call options, the results show that contrary to the frictionless markets boundary conditions, approximately 20 percent of the early call exercise occurs at times other than ex-dividend dates. While most of the non-dividend related early exercise may be explained by transactions costs, a significant number of contracts appear to be exercised irrationally. These results suggest that failure to incorporate market frictions in option pricing models is likely to lead to specification error. JEL classification: G 13 Keywords: Options; Early exercise; Rationality
1. Introduction Of all exchange traded American options, the conditions for rational exercise of common stock call options are the most basic. Under the assumption of frictionless markets, Merton (1973) shows that common stock call options should optimally be exercised prior to maturity if and only if the underlying stock is about to pay a sufficiently large cash dividend. In practice, as Diz and Finucane (1993) show in their study of S &P 100 index option exercise, transactions costs and other market frictions may also induce optimal early exercise. While their findings suggest that
* Tel,: (+ 1) 315-443.2963; fax: (+ 1) 315-443.5389; e-mail: [email protected]. 0378-4266/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S 03 7 8-4266(96)00054-4
564
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563-571
market frictions may also influence early exercise decisions in other option markets, no one has examined early exercise behavior in the market of primary interest: options on common stock. The conditions for rational early exercise are simpler for common stock options than for index options. To empirically distinguish between wild card, dividend, and transaction cost induced early exercise, Diz and Finucane estimate dividend and wild card adjusted model prices, and compare those prices with option bid prices. Some ambiguity is, however, necessarily introduced in their classifications by using model prices. Besides the usual sources of measurement and specification error inherent in empirical tests of option pricing models, the post-closing index level is not directly observable and must be measured by proxy. One advantage to studying stock options is that because they are not cash settled, the wild card option is not relevant. A second, related, advantage is that the relatively low frequency of dividend payments makes it possible to distinguish between dividend and transaction cost induced exercise without estimating option model prices. This study applies the methodology developed by Diz and Finucane (1993) to common stock call options, and empirically tests the hypothesis that investors and traders exercise common stock call options rationally. Since all of the tests are model independent, the study provides a remarkably clean test of investor rationality and the viability of the assumptions that are universally incorporated in American option pricing models. The remainder of this paper is organized as follows. Section 2 discusses the theoretical factors that may trigger early exercise, and the data used in the study is described in Section 3. Section 4 contains the results of tests designed to assess the empirical relevance of the various factors, and conclusions are presented in the final section.
2. Theoretical factors influencing early exercise In the absence of taxes and other market frictions, rational investors will be indifferent to selling and exercising at maturity, but unless a sufficiently large dividend is about to be paid, selling should always be preferred to exercising prior to maturity. In the presence of transaction costs, early exercise may be optimal, even when the stock is not about to go ex-dividend. While the direct costs of selling and exercising are the same for nonmember traders, exercise allows the investor to avoid the indirect cost of the option b i d - a s k spread. If the option is exercised, the stock may be sold or held. ~ Since exercising and
i When individuals exercise common stock call options, capital gain taxes are deferred until the stock is sold. Holding the stock allows the investor to defer capital gain taxes and the cost of selling the stock, but taxes and stock transaction costs can also be deferred by holding the option to maturity, or by exercising at a future ex-dividend date.
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563-571
565
holding the stock creates a cash outflow and no cash inflows, waiting to exercise dominates exercising and holding the stock. Consequently, the only time transaction cost induced early exercise should occur is when an investor wants to convert a position to cash. Exercising early and deferring taxes by holding the stock will never be optimal unless a sufficiently large dividend is about to be paid. 2 If the loss of time value and cost of selling the stock exceeds the cost of the option spread, a long call position should be closed by selling the option. Otherwise, exercising prior to maturity may be optimal even in the absence of dividends. The after tax cash flow realized by selling a call at time t that was purchased at time 0 < t is
CF~ = Cb,-- ( Cbt-- C~0)7, - T( C, t)(1 - r,),
(1)
where Cb, is the bid (sale) price of the call received at time t, Cao is the ask (purchase) price of the call at time 0, T(C, t) is the before tax commission charged for selling or exercising the call, and 7, is the marginal tax rate at time t. The alter tax cash flow realized from exercising an option at time t that was purchased at time 0 is CFx
= Sb,
-
K-
-
K -
Cao)7,-
0(1
- 7,) -
t ) ( I - 7,). (2)
where Sb, is the stock bid price at the time of exercise, and y(S, t) is the before tax cost of selling the stock. Comparing Eq. (1) and Eq. (2), the cash flow from exercising the option exceeds the cash flow from selling when Cb,-- (Sb,-- K ) < - - y ( S , 0 ( 1 -- 7,).
(3)
In the absence of transaction costs, condition (3) becomes C b , - ( S b t - K) < 0.
(4)
3. Data
The number of common stock call contracts exercised each day from 1 / 1 / 8 8 to 1 2 / 3 1 / 8 9 are obtained from the Options Clearing Corporation's Historical Exercise Report for Common Stock Options. Closing option bid/ask quotes, together with daily trading volume and contemporaneous stock prices, are culled from the Berkeley Option tapes, and daily dividend dates for the underlying stocks are obtained from the CRSP tapes. Options on underlying stocks that are not found
2 Taxes may affect the investors' decision to close the position, but given that the decision has been made to close the position, exercising and holding the stock is dominated either by exercising and selling the stock or by selling the option.
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563 571
566 100000000
10000000
1000000
LU
100000
0 10000 C
-
-
1000
1 O0
10
I 0
25
50
75
I O0
125
I 50
175
200
225
250
Time to Maturity Fig. 1. Total contracts exercised for common stock call options by days to maturity: 1 / 1 / 8 8 to 1 2 / 3 1 / 8 9 . The vertical axis has been scaled logarithmically.
on the CRSP tapes, and options without quoted bids for the exercise date, are eliminated from the sample. 3 Fig. 1 summarizes the number of call contracts exercised from maturity to the earliest exercise time prior to maturity for the entire sample period. 4 An examination of Fig. 1 reveals that most of the observed exercise occurs at maturity: 6,574,097 call contracts are exercised at maturity, while 2,513,140 contracts are exercised early. The level of early exercise activity tends to decline as the number of days to maturity increases, with the earliest instance of exercise occurring 239 days before expiration, when 60 contracts are exercised. Fig. 1 also suggests the existence of a day-of-the-week effect for early exercise. There is a tendency for early exercise to be relatively low on Tuesdays (the fourth bar in each group) and
3 On business days prior to expiration Fridays, exercise notices for common stock options can be filed by clearing members between 9:00 a.m. and 7:00 p.m. While some brokers impose deadlines that are earlier than the 3:15 p.m. close of options trading, many allow options to be exercised after the close. Since the decision to exercise or sell should be made as late in the day as possible, closing option bid prices are the most accurate measure of the price at which an exercised option could have been sold. Using the last stock trade price recorded prior to the option bid to estimate the exercise value could create measurement error when the closing option bids are recorded early in the day. To test for this possibility, the sample was limited to observations with bids recorded after 2:30, 2:45, 3:00, and 3:10. Doing so does not alter any of the conclusions contained in this study. 4 Because of the large variation in the number of contracts exercised at different points in time, ranging from as many as 5,987,654 to as few as one, Fig. I uses logarithmic scaling for the number of contracts exercised.
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563 571
567
high on Thursdays. To the extent that early exercise is dividend induced, it is likely that the day-of-the-week exercise pattern can be explained by day-of-theweek patterns in dividend payments on the underlying stocks. While the majority of exercise does occur at maturity, early call exercise occurs frequently. The seasonal exercise patterns are consistent with dividend induced early exercise, but the instances of exercise that occur long before maturity suggest that other factors may influence early exercise decisions. In the following section, the relative importance of transaction costs and dividends are considered, and the hypothesis that investors consistently exercise common stock call options in a rational manner is tested.
4. Empirical results The relative importance of dividends and transaction costs is assessed by classifying each case of early call exercise into one of three mutually exclusive categories. Defining D t as the dividend payment, Cbt as the bid price of the call, and Cxt = Sbr -- K as the exercise value of the call, the categories that are used are: I. D, > 0: Dividends are consistent with the observed case. 2. D, = 0 A Cb, < Cxt: Dividends are not consistent with the case, hut the cash flow from exercising exceeds the cash flow from selling. 3. D, = 0 ~ Cbt > Cxt: The case is not consistent with dividends or transaction costs. The classification system that is used is designed to provide a conservative test of rational exercise. Exercise is classified as dividend induced if the date of exercise is an ex-dividend date, even though it is possible that some of the dividends may he too small to induce optimal early exercise. Similarly, the second class is based on condition (4) and assumes the direct cost of selling the stock is zero. Furthermore, the last stock trade price is used to estimate the bid price of the stock in Eq. (5), providing an upper limit on the sale price of the stock. Table 1 contains the number of call contracts and percentage of contracts exercised in each category, together with some additional descriptive information concerning the observations in each class. The results show that at least 20 percent of the early exercise is inconsistent with the frictionless markets boundary conditions and cannot be explained by dividend payments on the underlying stock. Transaction costs may potentially explain 12 percent of the early exercise activity, and 8 percent of the contracts are exercised when no dividends are paid and the hid is higher than the exercise value of the contract. The most striking difference in the summary measures for the three classes in Table 1 is in the mean daily exercise. The number of contracts exercised on ex-dividend days tends to be much larger than the number of contracts exercised when dividends are not paid. This is true both in absolute terms and in relation to
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Table 1 Early call exercise explainedby dividendsand transactioncosts: 1/1/88-12/31/89 a Exercise condition
Number Numberof of cases contracts exercised
% of total Mean Mean Mean Mean early daily daily days to moneyexercise exercise volume maturity hess
Dt > 0 (dividends) 1,561 Dt = 0(? Cbt _ Cxt 1,549 (unexplained)
2,010,457 309,556
80.00 12.32
1,610 77
1,458 629
15 12
1.20 1.28
193,127
7.68
125
2,298
24
1.16
Totals
2,513,140 100.00
7,145
Early exercise is defined as exercise prior to the last day of trading. Cxt is the exercise value of the call, calculatedas (S t - K), where St is the closing stock price and K is the exercise price. D, is the ex-dividend amount, and Cbt is the last bid recorded during the trading day. Moneynessis defined as St /K. The sample is limited to observationsfor which underlyingstock prices, dividend information, and bid and ask option quotes are available.The mean daily volume,days to maturity,and moneyness are weighted by the number of contracts exercised.
daily trading volume. While 80 percent of the contracts exercised appear to be consistent with dividend induced early exercise, the cases of early exercise that are unexplained or consistent with transactions occur more frequently. Of the 7,145 cases considered in Table 1, 78 percent of the cases of early exercise are not dividend induced. Several other noteworthy differences across the three classes are found in the summary measures in Table 1. There is a tendency for the calls in each class to be exercised when they are deep in-the-money, but the unexplained cases are less deep in-the-money. These cases also occur the farthest from maturity. Mean daily trading volume is highest for the calls in the unexplained class, suggesting that low liquidity is not a valid explanation for the unexplained cases of early exercise. The lowest average daily trading volume is associated with the cases of exercise in the transaction cost class, which is consistent with the idea that low bid prices may induce early exercise and reduce trading volume. The cases in the transaction cost class tend to be the deepest in-the-money and closest to maturity. Transaction cost induced exercise therefore tends to occur when the difference between the value of the option and the exercise value is small. Although the results of the classification tests presented in Table 1 are generally consistent with the Diz and Finucane (1993) results for OEX options, dividends explain a larger percentage of the early exercise activity for common stock call options, while transaction costs are more important for index options. The relatively low level of dividend induced early exercise for index options may be explained by differences in the dividend streams for the underlying assets; dividend payments on the S & P 100 index are small compared with the dividend payments on individual stocks. The higher incidence of transaction cost related
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569
early exercise for index options is also expected. Stock transaction costs, which are not present for cash settled index options, reduce the gain from exercising and avoiding the cost of the option spread. The number of unexplained cases of early exercise in Table 1 that occur when no dividends are paid and when the option bid exceeds the exercise value suggests that at least some of the observed cases of early exercise are irrational. From Eq. (3), the value lost by exercising may be defined as E, ~ C b t - ( S b , -
K)
-+- " ~ ( S , 1 ) ( ]
-
Tt),
(5)
and the condition for rational early exercise is simply
<_<0.
(6)
The hypothesis that common stock call options are consistently exercised in a rational manner is tested by estimating values of E, for the two-year sample. A conservative measure of E, is constructed by setting the cost of selling the stock.
Fable 2 Early exercise activity lot common stock call options classified by Et: 1 / 1 / 8 8 - 1 2 / 3 1 / 8 9
'~
Range of E t
No. of cases
Contracts exercised early
Cure. percentage exercise
Mean daily exercise
Percent. dividend related
Mean days to maturity
Mean moneyness
E'~ > 4.00 3.50 < E~ _< 4.00 3.00 < E t _< 3.50 2.50 < E~ _< 3.00 2.00 < E t < 2.50 1.50 < E, _< 2.00 1.00 < E t < 1.50 I).50 < Et _< 1.00 0.25 < E, _< 0.50 0.125 < E, <_ 0.25 0.00 < E r _< 0.125 0.125 < E~ .<_0.00 0 . 2 5 < E t _ < - 0.125 0.50 < E, _< - 0 . 2 5 - 1.00 < E, ~ - 0 . 5 0 .... 1.50 < E, _< - 1.00 l:'~ < 1.50
8 I 6 4 8 28 67 194 221 5(18 733 2,456 1,280 1,454 162 12 3
39 I 51 7 119 154 797 8,458 14,549 116,570 281,915 979,448 )3,,7_7 538,890 38,662 750 3
0.00 0.00 0.00 11.00 0.01 0.01 0.05 0.38 0.96 5.60 16.82 55.79 76.99 98.43 99.97 100.00 100.00
4.88 1.00 8.50 1.75 14.88 5.50 11.90 43.60 65.83 229.47 384.60 398.80 416.19 370.63 238.65 62.50 1.00
0.00 0.00 0.00 0.00 0.00 0.00 3.51 7.98 25. I 1 24.33 69.81 82.00 89.65 86.81 83.81 (1.00 0.00
59 91 75 51 29 33 55 36 29 20 18 14 15 15 8 6 2
I. 13 1.06 1.27 1.04 1.02 1.06 1.09 1.16 1.10 1.13 1.22 1.21 I ~'~ 1.20 1.26 1.3 I 1.19
Totals
7,145
2.513.140
"' Early exercise is defined as exercise prior to the last day of trading. E~ = Cb, - ( S t - K), where Cb, is the last bid recorded fi)r the call during the trading day, S r is the last stock trade price recorded prior to the call bid, and K is the exercise price of the call. Moneyness is defined as S,/K. The sample is limited to observations for which underlying stock prices, dividend information, and bid and ask option quotes are available. The mean days to maturity and moneyness are weighted by the nmnber of contracts exercised.
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T.J. Finucane / Journal of Banking & Finance 21 (1997) 563-571
T(S, t), to zero and by using the last stock trade price to estimate the stock bid, Sbt.
Table 2 contains the number of contracts exercised prior to maturity, together with additional descriptive information, classified by values of E z. Contrary to the hypothesis of consistent rational exercise, the results show that at least some of the observed early exercise decisions are not made rationally. Nearly 17 percent of the contracts are exercised when the bids exceed the exercise value. Although the estimates of E, are biased downward, the cases of early exercise with small positive values of E, may possibly be explained by measurement error or market imperfections. Asynchronous prices, lack of depth in the options market, and cutoff times imposed by brokers could conceivably account for some of the cases where E t is positive but less than 25 cents. The cases with higher values of E t are more difficult to justify. To test the possibility that the cases with large positive values of E t can be explained by measurement error, the bids and concurrent stock prices were checked throughout the trading day for all cases with E t > $1.00. With the exception of one case that occurred on an ex-dividend day, the bids were consistently above the exercise value. These results imply that at least some of the observed early exercise decisions are not made rationally.
5. Conclusions This study provides a direct test of the validity of the frictionless markets assumptions that are commonly used in option pricing and a test of investor rationality that is independent of any pricing model. The results show that one of the most basic tenets of option pricing theory does not hold in practice. Non-dividend related early exercise occurs for 20 percent of the contracts in the sample that are exercised prior to maturity. The majority of the non-dividend related early exercise appears to be induced by market frictions. For approximately 60 percent of the contracts exercised in the absence of dividend payments, the cash flows realized by exercising and avoiding the direct cost of the option spread are higher than the cash flows from selling the option. In these cases, early exercise appears to be rational. The remaining contracts are exercised when the cash flows from selling would have been higher than the cash flows from exercising. Since these contracts are not exercised on ex-dividend dates, a strong case can be made that these unexplained cases represent instances of irrational investment decisions.
Acknowledgements Funding provided by a Syracuse University School of Management Summer Research Grant and a grant from the Bennett Center for Tax Studies at Syracuse University is gratefully acknowledged.
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References Diz, F. and T.J. Finucane, 1993, The rationality of early exercise decisions: Evidence from the S&P 100 index options market, The Review of Financial Studies 6, 765 797. Merton, R.C., 1973, Theory of rational option pricing, Bell Journal of Economics 4, 141-183.
Journal of Banking & Finance 21 (1997) 563-571
FINANCE
An empirical analysis of common stock call exercise: A note Thomas J. Finucane * Syracuse University, School of Management, Syracuse, NY 13244, USA Received 10 September 1995; accepted 20 September 1996
Abstract This study tests the hypothesis that common stock call options are exercised rationally and in accordance with the commonly used frictionless markets boundary conditions. Using two years of historical early exercise data for common stock call options, the results show that contrary to the frictionless markets boundary conditions, approximately 20 percent of the early call exercise occurs at times other than ex-dividend dates. While most of the non-dividend related early exercise may be explained by transactions costs, a significant number of contracts appear to be exercised irrationally. These results suggest that failure to incorporate market frictions in option pricing models is likely to lead to specification error. JEL classification: G 13 Keywords: Options; Early exercise; Rationality
1. Introduction Of all exchange traded American options, the conditions for rational exercise of common stock call options are the most basic. Under the assumption of frictionless markets, Merton (1973) shows that common stock call options should optimally be exercised prior to maturity if and only if the underlying stock is about to pay a sufficiently large cash dividend. In practice, as Diz and Finucane (1993) show in their study of S &P 100 index option exercise, transactions costs and other market frictions may also induce optimal early exercise. While their findings suggest that
* Tel,: (+ 1) 315-443.2963; fax: (+ 1) 315-443.5389; e-mail: [email protected]. 0378-4266/97/$17.00 Copyright © 1997 Elsevier Science B.V. All rights reserved. PH S 03 7 8-4266(96)00054-4
564
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563-571
market frictions may also influence early exercise decisions in other option markets, no one has examined early exercise behavior in the market of primary interest: options on common stock. The conditions for rational early exercise are simpler for common stock options than for index options. To empirically distinguish between wild card, dividend, and transaction cost induced early exercise, Diz and Finucane estimate dividend and wild card adjusted model prices, and compare those prices with option bid prices. Some ambiguity is, however, necessarily introduced in their classifications by using model prices. Besides the usual sources of measurement and specification error inherent in empirical tests of option pricing models, the post-closing index level is not directly observable and must be measured by proxy. One advantage to studying stock options is that because they are not cash settled, the wild card option is not relevant. A second, related, advantage is that the relatively low frequency of dividend payments makes it possible to distinguish between dividend and transaction cost induced exercise without estimating option model prices. This study applies the methodology developed by Diz and Finucane (1993) to common stock call options, and empirically tests the hypothesis that investors and traders exercise common stock call options rationally. Since all of the tests are model independent, the study provides a remarkably clean test of investor rationality and the viability of the assumptions that are universally incorporated in American option pricing models. The remainder of this paper is organized as follows. Section 2 discusses the theoretical factors that may trigger early exercise, and the data used in the study is described in Section 3. Section 4 contains the results of tests designed to assess the empirical relevance of the various factors, and conclusions are presented in the final section.
2. Theoretical factors influencing early exercise In the absence of taxes and other market frictions, rational investors will be indifferent to selling and exercising at maturity, but unless a sufficiently large dividend is about to be paid, selling should always be preferred to exercising prior to maturity. In the presence of transaction costs, early exercise may be optimal, even when the stock is not about to go ex-dividend. While the direct costs of selling and exercising are the same for nonmember traders, exercise allows the investor to avoid the indirect cost of the option b i d - a s k spread. If the option is exercised, the stock may be sold or held. ~ Since exercising and
i When individuals exercise common stock call options, capital gain taxes are deferred until the stock is sold. Holding the stock allows the investor to defer capital gain taxes and the cost of selling the stock, but taxes and stock transaction costs can also be deferred by holding the option to maturity, or by exercising at a future ex-dividend date.
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563-571
565
holding the stock creates a cash outflow and no cash inflows, waiting to exercise dominates exercising and holding the stock. Consequently, the only time transaction cost induced early exercise should occur is when an investor wants to convert a position to cash. Exercising early and deferring taxes by holding the stock will never be optimal unless a sufficiently large dividend is about to be paid. 2 If the loss of time value and cost of selling the stock exceeds the cost of the option spread, a long call position should be closed by selling the option. Otherwise, exercising prior to maturity may be optimal even in the absence of dividends. The after tax cash flow realized by selling a call at time t that was purchased at time 0 < t is
CF~ = Cb,-- ( Cbt-- C~0)7, - T( C, t)(1 - r,),
(1)
where Cb, is the bid (sale) price of the call received at time t, Cao is the ask (purchase) price of the call at time 0, T(C, t) is the before tax commission charged for selling or exercising the call, and 7, is the marginal tax rate at time t. The alter tax cash flow realized from exercising an option at time t that was purchased at time 0 is CFx
= Sb,
-
K-
-
K -
Cao)7,-
0(1
- 7,) -
t ) ( I - 7,). (2)
where Sb, is the stock bid price at the time of exercise, and y(S, t) is the before tax cost of selling the stock. Comparing Eq. (1) and Eq. (2), the cash flow from exercising the option exceeds the cash flow from selling when Cb,-- (Sb,-- K ) < - - y ( S , 0 ( 1 -- 7,).
(3)
In the absence of transaction costs, condition (3) becomes C b , - ( S b t - K) < 0.
(4)
3. Data
The number of common stock call contracts exercised each day from 1 / 1 / 8 8 to 1 2 / 3 1 / 8 9 are obtained from the Options Clearing Corporation's Historical Exercise Report for Common Stock Options. Closing option bid/ask quotes, together with daily trading volume and contemporaneous stock prices, are culled from the Berkeley Option tapes, and daily dividend dates for the underlying stocks are obtained from the CRSP tapes. Options on underlying stocks that are not found
2 Taxes may affect the investors' decision to close the position, but given that the decision has been made to close the position, exercising and holding the stock is dominated either by exercising and selling the stock or by selling the option.
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563 571
566 100000000
10000000
1000000
LU
100000
0 10000 C
-
-
1000
1 O0
10
I 0
25
50
75
I O0
125
I 50
175
200
225
250
Time to Maturity Fig. 1. Total contracts exercised for common stock call options by days to maturity: 1 / 1 / 8 8 to 1 2 / 3 1 / 8 9 . The vertical axis has been scaled logarithmically.
on the CRSP tapes, and options without quoted bids for the exercise date, are eliminated from the sample. 3 Fig. 1 summarizes the number of call contracts exercised from maturity to the earliest exercise time prior to maturity for the entire sample period. 4 An examination of Fig. 1 reveals that most of the observed exercise occurs at maturity: 6,574,097 call contracts are exercised at maturity, while 2,513,140 contracts are exercised early. The level of early exercise activity tends to decline as the number of days to maturity increases, with the earliest instance of exercise occurring 239 days before expiration, when 60 contracts are exercised. Fig. 1 also suggests the existence of a day-of-the-week effect for early exercise. There is a tendency for early exercise to be relatively low on Tuesdays (the fourth bar in each group) and
3 On business days prior to expiration Fridays, exercise notices for common stock options can be filed by clearing members between 9:00 a.m. and 7:00 p.m. While some brokers impose deadlines that are earlier than the 3:15 p.m. close of options trading, many allow options to be exercised after the close. Since the decision to exercise or sell should be made as late in the day as possible, closing option bid prices are the most accurate measure of the price at which an exercised option could have been sold. Using the last stock trade price recorded prior to the option bid to estimate the exercise value could create measurement error when the closing option bids are recorded early in the day. To test for this possibility, the sample was limited to observations with bids recorded after 2:30, 2:45, 3:00, and 3:10. Doing so does not alter any of the conclusions contained in this study. 4 Because of the large variation in the number of contracts exercised at different points in time, ranging from as many as 5,987,654 to as few as one, Fig. I uses logarithmic scaling for the number of contracts exercised.
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563 571
567
high on Thursdays. To the extent that early exercise is dividend induced, it is likely that the day-of-the-week exercise pattern can be explained by day-of-theweek patterns in dividend payments on the underlying stocks. While the majority of exercise does occur at maturity, early call exercise occurs frequently. The seasonal exercise patterns are consistent with dividend induced early exercise, but the instances of exercise that occur long before maturity suggest that other factors may influence early exercise decisions. In the following section, the relative importance of transaction costs and dividends are considered, and the hypothesis that investors consistently exercise common stock call options in a rational manner is tested.
4. Empirical results The relative importance of dividends and transaction costs is assessed by classifying each case of early call exercise into one of three mutually exclusive categories. Defining D t as the dividend payment, Cbt as the bid price of the call, and Cxt = Sbr -- K as the exercise value of the call, the categories that are used are: I. D, > 0: Dividends are consistent with the observed case. 2. D, = 0 A Cb, < Cxt: Dividends are not consistent with the case, hut the cash flow from exercising exceeds the cash flow from selling. 3. D, = 0 ~ Cbt > Cxt: The case is not consistent with dividends or transaction costs. The classification system that is used is designed to provide a conservative test of rational exercise. Exercise is classified as dividend induced if the date of exercise is an ex-dividend date, even though it is possible that some of the dividends may he too small to induce optimal early exercise. Similarly, the second class is based on condition (4) and assumes the direct cost of selling the stock is zero. Furthermore, the last stock trade price is used to estimate the bid price of the stock in Eq. (5), providing an upper limit on the sale price of the stock. Table 1 contains the number of call contracts and percentage of contracts exercised in each category, together with some additional descriptive information concerning the observations in each class. The results show that at least 20 percent of the early exercise is inconsistent with the frictionless markets boundary conditions and cannot be explained by dividend payments on the underlying stock. Transaction costs may potentially explain 12 percent of the early exercise activity, and 8 percent of the contracts are exercised when no dividends are paid and the hid is higher than the exercise value of the contract. The most striking difference in the summary measures for the three classes in Table 1 is in the mean daily exercise. The number of contracts exercised on ex-dividend days tends to be much larger than the number of contracts exercised when dividends are not paid. This is true both in absolute terms and in relation to
568
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Table 1 Early call exercise explainedby dividendsand transactioncosts: 1/1/88-12/31/89 a Exercise condition
Number Numberof of cases contracts exercised
% of total Mean Mean Mean Mean early daily daily days to moneyexercise exercise volume maturity hess
Dt > 0 (dividends) 1,561 Dt = 0(? Cbt _
2,010,457 309,556
80.00 12.32
1,610 77
1,458 629
15 12
1.20 1.28
193,127
7.68
125
2,298
24
1.16
Totals
2,513,140 100.00
7,145
Early exercise is defined as exercise prior to the last day of trading. Cxt is the exercise value of the call, calculatedas (S t - K), where St is the closing stock price and K is the exercise price. D, is the ex-dividend amount, and Cbt is the last bid recorded during the trading day. Moneynessis defined as St /K. The sample is limited to observationsfor which underlyingstock prices, dividend information, and bid and ask option quotes are available.The mean daily volume,days to maturity,and moneyness are weighted by the number of contracts exercised.
daily trading volume. While 80 percent of the contracts exercised appear to be consistent with dividend induced early exercise, the cases of early exercise that are unexplained or consistent with transactions occur more frequently. Of the 7,145 cases considered in Table 1, 78 percent of the cases of early exercise are not dividend induced. Several other noteworthy differences across the three classes are found in the summary measures in Table 1. There is a tendency for the calls in each class to be exercised when they are deep in-the-money, but the unexplained cases are less deep in-the-money. These cases also occur the farthest from maturity. Mean daily trading volume is highest for the calls in the unexplained class, suggesting that low liquidity is not a valid explanation for the unexplained cases of early exercise. The lowest average daily trading volume is associated with the cases of exercise in the transaction cost class, which is consistent with the idea that low bid prices may induce early exercise and reduce trading volume. The cases in the transaction cost class tend to be the deepest in-the-money and closest to maturity. Transaction cost induced exercise therefore tends to occur when the difference between the value of the option and the exercise value is small. Although the results of the classification tests presented in Table 1 are generally consistent with the Diz and Finucane (1993) results for OEX options, dividends explain a larger percentage of the early exercise activity for common stock call options, while transaction costs are more important for index options. The relatively low level of dividend induced early exercise for index options may be explained by differences in the dividend streams for the underlying assets; dividend payments on the S & P 100 index are small compared with the dividend payments on individual stocks. The higher incidence of transaction cost related
T.J. Finucane/ Journal of Banking & Finance 21 119971 563-571
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early exercise for index options is also expected. Stock transaction costs, which are not present for cash settled index options, reduce the gain from exercising and avoiding the cost of the option spread. The number of unexplained cases of early exercise in Table 1 that occur when no dividends are paid and when the option bid exceeds the exercise value suggests that at least some of the observed cases of early exercise are irrational. From Eq. (3), the value lost by exercising may be defined as E, ~ C b t - ( S b , -
K)
-+- " ~ ( S , 1 ) ( ]
-
Tt),
(5)
and the condition for rational early exercise is simply
<_<0.
(6)
The hypothesis that common stock call options are consistently exercised in a rational manner is tested by estimating values of E, for the two-year sample. A conservative measure of E, is constructed by setting the cost of selling the stock.
Fable 2 Early exercise activity lot common stock call options classified by Et: 1 / 1 / 8 8 - 1 2 / 3 1 / 8 9
'~
Range of E t
No. of cases
Contracts exercised early
Cure. percentage exercise
Mean daily exercise
Percent. dividend related
Mean days to maturity
Mean moneyness
E'~ > 4.00 3.50 < E~ _< 4.00 3.00 < E t _< 3.50 2.50 < E~ _< 3.00 2.00 < E t < 2.50 1.50 < E, _< 2.00 1.00 < E t < 1.50 I).50 < Et _< 1.00 0.25 < E, _< 0.50 0.125 < E, <_ 0.25 0.00 < E r _< 0.125 0.125 < E~ .<_0.00 0 . 2 5 < E t _ < - 0.125 0.50 < E, _< - 0 . 2 5 - 1.00 < E, ~ - 0 . 5 0 .... 1.50 < E, _< - 1.00 l:'~ < 1.50
8 I 6 4 8 28 67 194 221 5(18 733 2,456 1,280 1,454 162 12 3
39 I 51 7 119 154 797 8,458 14,549 116,570 281,915 979,448 )3,,7_7 538,890 38,662 750 3
0.00 0.00 0.00 11.00 0.01 0.01 0.05 0.38 0.96 5.60 16.82 55.79 76.99 98.43 99.97 100.00 100.00
4.88 1.00 8.50 1.75 14.88 5.50 11.90 43.60 65.83 229.47 384.60 398.80 416.19 370.63 238.65 62.50 1.00
0.00 0.00 0.00 0.00 0.00 0.00 3.51 7.98 25. I 1 24.33 69.81 82.00 89.65 86.81 83.81 (1.00 0.00
59 91 75 51 29 33 55 36 29 20 18 14 15 15 8 6 2
I. 13 1.06 1.27 1.04 1.02 1.06 1.09 1.16 1.10 1.13 1.22 1.21 I ~'~ 1.20 1.26 1.3 I 1.19
Totals
7,145
2.513.140
"' Early exercise is defined as exercise prior to the last day of trading. E~ = Cb, - ( S t - K), where Cb, is the last bid recorded fi)r the call during the trading day, S r is the last stock trade price recorded prior to the call bid, and K is the exercise price of the call. Moneyness is defined as S,/K. The sample is limited to observations for which underlying stock prices, dividend information, and bid and ask option quotes are available. The mean days to maturity and moneyness are weighted by the nmnber of contracts exercised.
570
T.J. Finucane / Journal of Banking & Finance 21 (1997) 563-571
T(S, t), to zero and by using the last stock trade price to estimate the stock bid, Sbt.
Table 2 contains the number of contracts exercised prior to maturity, together with additional descriptive information, classified by values of E z. Contrary to the hypothesis of consistent rational exercise, the results show that at least some of the observed early exercise decisions are not made rationally. Nearly 17 percent of the contracts are exercised when the bids exceed the exercise value. Although the estimates of E, are biased downward, the cases of early exercise with small positive values of E, may possibly be explained by measurement error or market imperfections. Asynchronous prices, lack of depth in the options market, and cutoff times imposed by brokers could conceivably account for some of the cases where E t is positive but less than 25 cents. The cases with higher values of E t are more difficult to justify. To test the possibility that the cases with large positive values of E t can be explained by measurement error, the bids and concurrent stock prices were checked throughout the trading day for all cases with E t > $1.00. With the exception of one case that occurred on an ex-dividend day, the bids were consistently above the exercise value. These results imply that at least some of the observed early exercise decisions are not made rationally.
5. Conclusions This study provides a direct test of the validity of the frictionless markets assumptions that are commonly used in option pricing and a test of investor rationality that is independent of any pricing model. The results show that one of the most basic tenets of option pricing theory does not hold in practice. Non-dividend related early exercise occurs for 20 percent of the contracts in the sample that are exercised prior to maturity. The majority of the non-dividend related early exercise appears to be induced by market frictions. For approximately 60 percent of the contracts exercised in the absence of dividend payments, the cash flows realized by exercising and avoiding the direct cost of the option spread are higher than the cash flows from selling the option. In these cases, early exercise appears to be rational. The remaining contracts are exercised when the cash flows from selling would have been higher than the cash flows from exercising. Since these contracts are not exercised on ex-dividend dates, a strong case can be made that these unexplained cases represent instances of irrational investment decisions.
Acknowledgements Funding provided by a Syracuse University School of Management Summer Research Grant and a grant from the Bennett Center for Tax Studies at Syracuse University is gratefully acknowledged.
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References Diz, F. and T.J. Finucane, 1993, The rationality of early exercise decisions: Evidence from the S&P 100 index options market, The Review of Financial Studies 6, 765 797. Merton, R.C., 1973, Theory of rational option pricing, Bell Journal of Economics 4, 141-183.