Stock Returns on Option Expiration Dates

<strong>Stock</strong> <strong>Returns</strong> on Option Expiration Dates
CHIN-HAN CHIANG
Columbia University
This version: January 2010
Abstract
This paper documents striking evidence that stocks with a suf ciently large amount of deeply in-the-
money call options earn signi cantly lower returns on option expiration dates, with a drop in average
daily returns of up to 1 percentage point. This price movement of stocks is followed by a short-term
reversal. On option expiration dates, option holders who exercise deeply in-the-money call options
have an increasing demand for immediacy to sell the acquired stocks in the stock market. I offer an
explanation of why this is not offset by option writers' purchases, based on the premise that most written
calls are covered either at inception or prior to maturity. When exercised open interest is suf ciently
large compared to the daily trading volume of the underlying stocks, the resulting selling pressure in the
stock market leads to a fall in expiration-date returns of the underlying stocks.
1 Introduction
Options were introduced into the Chicago Board Options Exchange (CBOE) on April 26, 1973. After 36
years, the option market has burgeoned, with the daily volume reaching 14 million contracts in 2008. As the
option market grew, the number of optionable stocks also increased. By 2008 nearly two thirds of all stocks
traded on the New York <strong>Stock</strong> Exchange were optionable. This large fraction gives rise to an intriguing
issue in the study of nancial markets—how options interact with the underlying stocks.
With a standardized contract, exchange-traded options expire at 10:59 pm Central Standard Time on the
third Saturday of each month. Since the option market stops trading after the market closes on the third
Friday and reopens on the following Monday, no transactions take place on the of cial option expiration
date. Therefore, investors treat the third Friday as the expiration date. The option expiration date has always
been a day with vibrant trading activities. In the option market, evidence shows (Figure 1) that total open
Email address: cc2538@columbia.edu. I would like to thank my advisor, Jialin Yu, for all the valuable discussions and constant
support. I am grateful to Michael Adler, Ailsa Roell, and Paul Tetlock for helpful advice. I also thank Jushan Bai, Vyacheslav Fos,
Louise Lusby, Yiqun Mou, Tomasz Piskorski, Stephanie Schmitt-Grohe, Jon Steinsson, Martin Uribe, Neng Wang, and seminar
participants from both Economics and Finance departments at Columbia University for their comments and suggestions. All errors
are mine.
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interest of options remains at a similar level in the expiration week, suggesting that most investors wait until
the expiration Fridays to close their positions.
As for the stock market on the expiration dates, researchers also nd an enormous increase in market
trading volume (Stoll and Whaley (1987), Stoll and Whaley (1990) and Chiang (2009)). In a related paper, I
show that this large increase in trading activities is generated by option expiration (Chiang (2009)). When an
option contract expires on Saturday, any position on this contract automatically disappears, and this change
in option position can trigger on the third Friday parallel trading in the stock market and offsetting trades to
close out the options themselves. For instance, an investor who hedges her options by purchasing (shorting)
the underlying stocks has to rebalance the stock position. In this paper I argue that a call option investor who
acquires stocks by exercising the option has an incentive to sell the shares immediately in the stock market.
Both examples indicate that a large number of transactions in the stock market are likely to be associated
with the expiration of options.
This paper seeks to investigate how trading activities in the stock market triggered by option expiration
can impact stock prices on the expiration dates. A small number of studies examine the relation between
option expiration and stock returns but obtain mixed results. Klemkosky (1978) investigates weekly returns
before and after 14 option expiration dates from 1975 to 1976, and he nds average abnormal returns of -1%
in the week before and +0.4% after the expiration dates. However, he focuses on the weekly returns instead
of returns on the expiration dates. Moreover, the positive returns in the week following option expiration are
signi cant for only three of the fourteen expiration dates. Cinar and Yu (1987) study the return behavior of
six stocks on the expiration dates and nd insigni cant results. The insigni cance could be due to a small
sample of stocks.
This paper, in contrast, uses daily returns with a longer sample period (1996-2006) and includes all
optionable stocks traded on the NYSE/AMEX. One of the distinctions of this paper is that, instead of using
individual stocks, I group stocks with similar option characteristics into portfolios. Option characteristics,
such as in- or out-of-the-moneyness, open interest and types, may affect investors' trading strategies and
therefore affect the direction and the size of the price change. If options provide useful information on the
returns of the underlying stocks, by sorting stocks into portfolios based on the option characteristics, there
should be dispersion in returns across portfolios.
Using these portfolio returns, this paper provides striking evidence that stocks with large amounts of
deeply in-the-money call options tend to earn signi cantly lower returns on option expiration dates. The
drop in average daily returns from the third Thursday to the expiration Friday, a day later, reaches 1:4%
per day. The returns remain signi cantly lower after adjusting for systematic risk. These abnormal returns
are con ned to stocks which have call options with a large degree of in-the-moneyness and with a large
amount of option contracts. Moreover, no particular pattern is observed in stock portfolios based on put
option characteristics.
The low returns are accompanied by strong reversals immediately in the following week. This reversal
phenomenon is consistent with the price-pressure hypothesis, according to which the price movement is
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generated by the selling pressure on the expiration dates, and it should appear only in the market of stocks
with low-returns. Under the price-pressure hypothesis, the non-information-motivated demand shift associ-
ated with large sales (purchases) of stocks can press down (push up) prices. The passive liquidity suppliers
are attracted by the associated price drop (rise), and they are afterward compensated for providing immedi-
ate liquidity when prices reverse to the original level. Previous literature nds that a stock price rises when
it is added into a stock index or when its weight in an index increases (Shleifer (1986), Harris and Gurel
(1986), and Wurgler and Zhuravskaya (2002)). They attribute this phenomenon to an increase in demand
for the stock, and the buying pressure pulls up the stock prices. Campbell, Grossman, and Wang (1993) also
propose a rational equilibrium framework in which liquidity providers absorb the buying or selling pressure
from liquidity traders but demand a higher future returns as compensation, and the compensation is provided
in the form of short-term reversals. Given the price reversals observed in the low-returned portfolios and
their association with the selling pressure, the next question is what produces this selling pressure on the
expiration dates.
A possible source of the selling pressure is from the investors who exercise deeply in-the-money call
options and sell the acquired stocks immediately. On option expiration dates, the evidence shows that a large
number of options are exercised. Firstly, there is a considerably wider bid-ask spread in the option market,
which makes exercising the option to close the position a dominant trading strategy for investors. Secondly,
the high differential between the market and exercise prices of in-the-money call options can also induce
investors to exercise. 1
Unlike index options, which are cash-settled, a distinctive feature of equity options is the requirement
of physical delivery. That is, call option writers need to deliver the underlying stocks to option buyers after
the option is exercised, while put option buyers must deliver the stocks to the writers. Therefore, investors
who exercise in-the-money call options will end up with stocks in hand. They then have a motive to sell
these acquired shares immediately in the stock market. Plausible reasons for this strong propensity to sell
the stocks includes: the shortage of capital for exercise the options, a need for recovery of the original cash
position, and portfolio rebalancing. All in all, these incentives to liquidate the newly acquired stock holdings
increase investors' demand for immediate liquidity. I do not test these conjectures in this paper.
The net selling pressure caused by this demand for liquidity has the effect of lowering the stock's price.
This, in turn, attracts passive liquidity suppliers. The key reason this statement is likely to be true is that
buying pressure from the call option writers tends to be relatively small, as a majority of the written call
options are covered at initiation. 2 Additionally, call option writers anticipating being assigned have an
incentive to reduce the uncertainty of their loss by purchasing the underlying stocks before the expiration
date. 3 Therefore, on option expiration dates, there tends to be negligible buying pressure, and the strong
1 See Poteshman and Serbin (2003).
2 When an option position is opened by selling an option, while simultaneously owning an equivalent position in the underlying
security, it is called a "covered" position. Calls are covered by owning the underlying security, and puts are covered by shorting the
underlying security.
3 To assign means to designate an option writer for ful llment of her obligation to sell stocks (call option writer) or buy stocks
3

net selling pressure from deep-in-the-money call option holders leads to a drop in returns on the underlying
stocks. To compensate the liquidity providers for bearing the corresponding risk, the price on average
subsequently reverses, generating a higher post expiration-date return.
As deep-in-the-money call options have a larger bid-ask spread and a greater amount of open interest
compared to the daily trading volume of the underlying stock, stocks with a suf ciently large amount of
deep-in-the-money calls tend to experience stronger net selling pressure and result in a deep drop in returns.
Unlike call options, put options have a much smaller amount of open interest throughout the option
duration. Additionally, Finucane (1997) and Overdahl and Martin (1994) report that a smaller proportion
of puts is exercised at maturity. As a result, the number of shares associated with put option exercise is not
large enough to have an impact on prices. I con rm this last result in this study.
Another distinction between calls and puts is that, with the obligation of physical settlement, the majority
of the call option writers already own stocks before option expiration dates and they keep holding the stocks
until the expiration dates for fear of having to deliver. This tends to be especially true for deep-in-the-money
call option writers, as the possibility for them of being assigned is larger. When writers deliver these shares
to call option holders who exercise the option, most investors have few incentives to hold on to the stocks.
As a consequence, investors mostly sell the shares and create downward selling pressure on the expiration
dates. For put options, however, neither the option buyers nor the writers have the need to hold stocks. This is
because in-the-money put option holders can always choose to close their option position by selling the puts
if they do not have stocks in hand on the expiration Fridays. Even when they ultimately choose to exercise,
they could have started purchasing stocks throughout the holding period instead of on the expiration date.
Given these asymmetries between puts and calls, I observe no price impact in stock portfolios based on put
options.
The price-pressure hypothesis also implies that the demand curve for stocks may be less than perfectly
elastic. In that case, the liquidity of stocks can play an important role in determining the magnitude of
short-term reversals. In the early study by Atkins and Dyl (1990) and Bremer and Sweeney (1991), they
document signi cant reversals after a large one-day price decline and partially attribute the reversals to
market illiquidity. This is further examined by Cox and Peterson (1994). By using rm size as a proxy
for liquidity, they nd a negative correlation between the magnitude of reversal returns and the rm size,
suggesting a stronger reversal for less liquid stocks. Avramov, Chordia, and Goyal (2006) also nd that ex-
treme price changes occur in stocks with low liquidity and high turnover, for which the demand for liquidity
from non-informational traders is higher. To further investigate the relationship between liquidity trading
and price change, I regress post-expiration returns of portfolios with abnormal expiration-date returns on
the Amihud illiquidity ratio (Amihud (2002)) and nd a positive correlation—less liquid stocks experience
stronger reversals after the option expiration dates.
The remainder of the paper is organized as follows: In the next section, I describe my samples. Section 3
(put option writer). Assignment is the receipt of an exercise notice by an option writer that obligates him to sell (in the case of a
call) or purchase (in the case of a put) the underlying security at the speci ed strike price.
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presents the portfolio formation methodology. Section 4 reports the main return results on option expiration
dates along with the reversals in Section 5. Section 6 provides possible interpretations of the expiration-date
returns. Section 7 presents some further empirical evidence. Section 8 tests the robustness of the return
results, and Section 9 is the conclusion.
2 Data
The two primary sample sets used in this paper are the stock data from Center for Research in Security
Prices (CRSP) and Ivy DB data from OptionMetrics LLC. Data on the U.S. stock market consist of all
common stocks traded on the NYSE and AMEX. The options data, including strike prices, types of options,
expiration dates, open interest, option trading volume and option prices, are from Ivy DB OptionMetrics.
Both samples are from January 1, 1996 to December 31, 2006, and recorded on a daily basis.
Exchange-listed options expire on the third Saturday of each month. Since markets are closed in the
weekend, all stock and option transactions related to option expiration should take place before the markets
close on the third Friday. Hence, I treat the third Friday of each month as the option expiration date.
There are 132 expiration dates from 1996 to 2006, with 130 of them falling on the third Friday. The
other two are on the third Thursday with the following Friday being an exchange holiday known as "Good
Friday." I only include the Friday expiration dates in the sample. On the given date, a stock is considered
optionable if there is at least one option contract listed on it. Among all NYSE/AMEX-traded stocks, nearly
two thirds of them are optionable. In general, there is an upward trend in the number of optionable stocks
from 1996 to 2006.
To eliminate the possible noise generated from stock delisting, every year a stock must have data for
more than 200 days (200 observations) to be included in the sample. Moreover, the stock must have price
greater than $5 at the end of each month. This is because returns on low-price stocks are greatly affected by
the minimum tick size of $1/16. 4 By removing stocks less than $5 I am also removing the effect of penny
stocks, which can also add noises to the return estimations. 5
3 Forming <strong>Stock</strong> Portfolios Based on Option Characteristics
This section discusses the methodology of forming stock portfolios based on the characteristics of options
listed on the relevant stocks. Instead of using individual stocks, as previous studies did, I group stocks into
portfolios based on their option characteristics. The idea is that different option characteristics may give
investors different trading strategies in the stock market. If options provide useful information on returns
of the underlying stocks, by grouping stocks into portfolios based on option characteristics, there should
4 Effective since June 24, 1997.
5 See Harris (1994) and Amihud (2002) for more detailed discussion.
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e dispersions in returns across portfolios. This allows me to investigate how options are linked to the
underlying stocks.
Options can affect the stock market in three folds—moneyness, open interest, and option types. Mon-
eyness is determined by the relative position of the option strike price and the current stock price. A call
option is said to be in the money (ITM) if its strike price is smaller than the underlying stock price; at the
money (ATM) if equal; and out of the money (OTM) if the strike is larger than the current stock price. For
put options, the relation reverses. Different degrees of moneyness tend to give investors different trading
strategies in both the stock and the option markets on the expiration dates. And these strategies may further
affect the direction of stock returns.
Open interest is de ned as the total number of option contracts that are not closed or delivered on
a particular day. If options carry useful information on the underlying stocks, options with larger open
interest, which is equivalent to a larger share volume in the stock market, should have a stronger impact than
options with smaller open interest.
As for the option types, calls and puts function in the opposite direction and thus should be considered
separately.
A double-sorting methodology is applied in forming the portfolios by rst sorting stocks based on the
moneyness of their options then on the amount of open interest. Portfolios are formed on the Thursday prior
to the expiration Friday, i.e. one day prior to the third Friday. That is, the closing price and open interest
on the Thursday of the third week are used to determine the moneyness and the amount of open interest of
a relevant option. Only expiring options are considered, and only stocks with at least one expiring option
on the following expiration date are incorporated into the portfolio. Portfolios are rebalanced every third
Thursday, and stocks can switch between portfolios every month.
Only in-the-money options are considered in the portfolio forming process. <strong>Stock</strong> portfolios based on
out-the-money (OTM) options are further discussed in the appendix. The following subsections present the
formation method in greater detail.
3.1 Degree of Moneyness
The degree of moneyness is determined by the percentage in-the-money, which is the difference between
the stock price and the strike price normalized by the underlying stock price:
Percentage ITM =
(
stock price - strike price
stock price
strike price - stock price
stock price
if for a call option
if for a put option
0 5% ITM options are considered slightly ITM; 5% 25% ITM are medium ITM; and options more than
25% ITM are classi ed as deeply ITM. The 5% and 25% cutting points are chosen so that for each stocks,
there are roughly one third of options in each ITM category. Different cutting points are explored in the
robustness checks.
6
)
.

I sort stocks into these three ITM classes based on the percentage ITM of their options. If a stock has
more than one option listed on it, I allocate the stock into the ITM class with the largest open interest. For
instance, stock XYZ has ve call option contracts. Two of them are slightly ITM, one is medium ITM and
the other two are deeply ITM. If the two deeply ITM options have the largest open interest in total compared
to that of the slightly and medium ITM ones, stock XYZ is considered to be in the deeply ITM class.
3.2 Open Interest
Within each ITM class, I further rank the stocks based on the total amount of open interest into another
three groups—small, medium and large. 40th and 70th percentiles of total open interest in each ITM class
are used as the cutting points (as shown the following gure).
3.3 Nine Portfolios based on Calls and Puts
By double-sorting the stocks dependently on the degree of ITM and the amount of open interest, I form
nine portfolios in total, as illustrated in the following gure. All portfolios are denoted with two letters.
The rst letter represents the degree of moneyness: s stands for slightly ITM; m is medium; and d is deeply
ITM. The second letter is the size of open interest: s denotes for a small size; m is medium; and l denotes a
large size. In particular, portfolio ss contains stocks which have a majority of their options as slightly ITM.
When comparing the size of open interest to portfolio sm and portfolio sl, the size of option open interest in
portfolio ss is the smallest.
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<strong>Stock</strong>s are sorted based on call options and put options separately. Therefore, there are nine portfolios
(call option portfolios) based on calls and another nine based on puts (put option portfolios). Different
cutting points of degrees of moneyness and open interest will be explored in the robustness checks, and the
return results are not sensitive to the cutting points chosen.
4 Portfolio <strong>Returns</strong> on Option Expiration Dates
This section of the paper investigates portfolio return pattern on option expiration dates. For each portfolio,
portfolio returns are constructed as the value-weighted averages across all individual stocks included in the
portfolio, using market capitalization as the weight. All daily returns are reported in percentages. Portfolio
mean returns on the expiration dates are captured using the following regression speci cation:
rp;t = expdateIexpdate;t + Mon_4IMon_4;t + T ue_4IT ue_4;t + ::: + T hu_3IT hu_3;t + "p;t; (1)
where rp;t is the portfolio return; Iexpdate;t is the expiration date dummy, which equals 1 when the given date
is an expiration date and 0 otherwise; and expdate is the coef cient of interest, which captures the portfolio
mean return on the expiration dates. IMon_4 IT hu_3 are date dummies from the forth Monday to the third
Thursday of the next calendar month. The third Thursday (T hu_3) is also the next formation day at which
portfolios are rebalanced. The standard errors are robust standard errors controlling for heteroskedasticity.
Equation (1) is applied to both call and put option portfolios, and regression results are discussed in the
following subsections.
4.1 ITM Call Option Portfolios
Panel A of Table 1 summarizes the expiration-date returns of ITM call option portfolios, with coef cients
plotted in Figure 2. Except for the deeply ITM portfolios, other six portfolios all have similar returns, in
an average of 0:1%. Conversely, stocks with a medium and a large amount of deeply ITM call options
appear to have signi cantly lower returns on the expiration dates, with 0:8% (-2.36) for Portfolio dm and
an extreme 1:4% (-2.32) for Portfolio dl. Moreover, within the deeply ITM class, returns decrease along
the amount of open interest.
Figure 3 compares portfolio returns on the expiration dates to those on non-expiration Fridays and non-
expiration dates. All nine portfolios on dates other than option expiration dates have similar returns. Only on
the expiration dates do stocks with a suf ciently large number of deeply ITM call options earn considerably
lower returns.
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Table 1: <strong>Returns</strong> of Nine ITM Option Portfolios on Option Expiration Dates
This table reports the regression coef cient ( expdate ) of nine ITM call option and put option portfolios on
option expiration dates. Panel A reports the nine call option portfolio returns, and Panel B reports the nine
put option returns. Coef cients are obtained by regressing portfolio value-weighted returns on the expiration
date dummy: rp;t= expdateIexpdate;t+ Mon_4IMon_4;t+ T ue_4IT ue_4;t+:::+ T hu_3IT :All returns are in
hu_3;t+"p;t
percentages. The t-statistics are adjusted for heteroskedasticity and reported in parentheses.
Panel A: ITM Call Option Portfolios
Degree of ITM
Open Interest Slight Medium Deep
Small -0.11 -0.11 -0.48
(-1.34) (-1.52) (-1.81)
Medium -0.20 -0.19 -0.78
(-2.42) (-2.21) (-2.36)
Large -0.12 -0.06 -1.45
4.2 Risk Adjustment
(-1.27) (-0.66) (-2.32)
Panel B: ITM Put Option Portfolios
Degree of ITM
Open Interest Slight Medium Deep
Small -0.04 -0.04 0.25
(-0.57) (-0.49) (1.61)
Medium -0.04 -0.06 -0.36
(-0.40) (-0.68) (-2.03)
Large -0.11 -0.17 -0.35
(-1.13) (-1.65) (-1.40)
Table 2 provides the rst piece of evidence of the possible source of the low returns by reporting the risk-
adjusted returns. Time-series regression based on the four-factor model is applied to each portfolio on the
expiration dates:
(rp;m rf;m) = p + bp(rmkt;m rf;m) + spSMBm (2)
+hpHMLm + mpMomentumm + "p;m;
where rp;m is the portfolio return on the expiration date on month m; (rmkt;m rf;m) is the market premium
factor; SMB is the Fama–French size factor; HML the Fama–French book-to-market factor; Momentum
is the momentum factor; and rf;m is the daily return on one-month treasury bills. Daily data of the four
factors from 1996 to 2006 are obtained from Kenneth French's website. bp, sp, hp, and mp are the cor-
responding factor loadings; and p is the intercept coef cient interpreted as the risk-adjusted return of
portfolio p. p can also be considered the return that cannot be explained by the systematic risk captured
by the four factors. 6 After adjusting for systematic risk, Portfolio dm and Portfolio dl consistently have
signi cantly negative intercepts, with t-statistics of 2:24, and 2:02, respectively.
6 For details on portfolio construction, see Fama and French (1993).
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Table 2: Risk Adjustments of ITM Call Option Portfolios
This table summarizes the risk-adjusted returns ( expdate) of nine ITM call option portfolios on
option expiration dates using the four-factor model: (rp;m rf;m)= p+bp(rmkt;m rft)+spSMBm+hpHMLm
+mpMomentumm+"p;m:The t-statistics are adjusted for heteroskedasticity and reported in parentheses.
4.3 ITM Put Option Portfolios
Degree of ITM
Open Interest Slight Medium Deep
Small -0.06 -0.07 -0.45
(-1.49) (-2.09) (-1.70)
Medium -0.11 -0.12 -0.69
(-2.67) (-3.19) (-2.24)
Large -0.01 0.07 -1.36
(-0.17) (2.03) (-2.17)
As shown in Panel B of Table 1 and Figure 4, put option portfolios except for Portfolio dm have insigni cant,
close to zero expiration-date returns. However, the magnitude of Portfolio dm's return appears much smaller
compared to the call option portfolios. After adjusting for systematic risk, the signi cance disappears.
Moreover, there is no particular return pattern across portfolios within each ITM class.
4.4 Seasonality of Expiration Dates or the Third Fridays?
Previous section provides evidence that expiration-date returns are lower in stocks with a large amount of
deeply ITM call options. However, are these low returns a product of the expiration dates or the third
Fridays? It is possible that the low returns are common third-Friday seasonality that can be found in all
stocks with many deeply ITM call options, regardless the options are expiring or not. If the low returns are
indeed a product of option expiration, it should not be observed in either stocks with non-expiring options or
nonoptionable stocks. Hence, I further examine these two alternative sets of stocks. Optionable stocks with
non-expiring options are double-sorted into nine portfolios, while nonoptionable stocks are grouped into a
single portfolio. The result shows that the third-Friday returns using these two samples are insigni cant.
This implies that the low returns are generated from activities that take place only in the expiring options
and only on the expiration dates.
In sum, on option expiration dates, stocks with a suf ciently large amount of expiring deeply ITM call
options tend to have signi cantly lower returns. Similar abnormal returns are observed in neither ITM put
option portfolios nor stocks without expiring options.
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5 Price Reversals
The ef cient market hypothesis (EMH) states that security prices re ect all publicly available information.
If the price movement follows the EMH, the drop in returns on the expiration dates should be associated with
the arrival of information, which shifts the fundamentals, and any amount of sales (purchases) cannot have
a price impact due to a perfectly elastic demand curve for securities. On the other hand, the price-pressure
hypothesis (PPH) predicts that a large sale (purchase) in stocks can result in price decreases (increases) even
though there is no new information associated with the transactions. Under PPH, the short-term demand
curve for securities may not be perfectly elastic. PPH further assumes that investors who accommodate the
trading pressure will be compensated for bearing the transaction costs and risks, and the compensation is
provided in the form of short-term price reversals. 7
The most observable distinction between informational (EMH) and non-informational trading (PPH) is
the reversal phenomenon after a price movement. To further investigate whether the drop in returns on the
expiration date is associated with informational or liquidity trading, I calculate the 1 to 15-day holding-
period returns of each portfolio, assuming a long position on the formation Thursday. Holding returns are
value-weighted averages across all stocks included in the relevant portfolios, using market capitalization on
the formation day as the weight. The holding return results are plotted in Figure 5.
The low-returned portfolios (Portfolio dm and Portfolio dl) exhibit short-term reversals immediately
after the drop on the expiration Friday. The reversals are particularly strong on the following Monday, and
these accumulative returns gradually converge to the formation-day level.
The reversal result supports the price-pressure hypothesis, suggesting the drop in returns on the expira-
tion dates is associated with the selling pressure. This result also raises the question of what produces the
selling pressure on the expiration dates.
6 Sources of Low <strong>Returns</strong>
The expiration-date low returns are con ned to deeply ITM call option portfolios, the selling pressure should
take place only in the market of those portfolios. A plausible interpretation is that, on option expiration dates,
call option holders tend to exercise the option. With physical settlement, they acquire stocks from option
writers, and they immediately sell the acquired shares in the stock market.
There are several justi cations for their motives to sell the stocks immediately. First of all, to exercise
call options, investors require capital to purchase the shares from option writers. With a possible capital
constraint, investors need to sell the stocks simultaneously to raise suf cient capital to exercise the options.
Second, some investors might want to recover the cash position when their call options expire, and they
can do so through selling the acquired stocks. Third, some investors hold a diversi ed portfolio with a xed
7 For further discussion on the price-pressure hypothesis and the associated price reversals, see Harris and Gurel (1986), Camp-
bell, Grossman, and Wang (1993), Andrade, Chang, and Seasholes (2008) and Avramov, Chordia, and Goyal (2006).
11

fraction allocated to certain stocks, and they are exposed to a larger risk if the fraction on one stock suddenly
rises. For risk consideration, they rebalance their portfolio holdings by selling the additional stocks.
The increase in demand for immediate liquidity from ITM call option holders results in strong selling
pressure, which leads to a drop in returns on option expiration dates. The passive liquidity suppliers are,
in turn, attracted by the price drops. This price movement subsequently reverses as a compensation for the
liquidity providers, as documented in the previous section.
To summarize the possible interpretation on the low returns in stocks with a suf ciently large amount
of deeply ITM call options on option expiration dates: Investors with deeply ITM call option positions
tend to exercise the option on the expiration dates and sell the acquired stocks immediately in the stock
market. When the open interest is large enough compared to the daily trading volume of the underlying
stocks, they generate downward selling pressure in the stock market. As a majority of the option writers
are hedged by writing covered calls, the buying pressure from the writers is relatively small. Due to this
non-synchronization between buying and selling the underlying stocks, there is "net selling pressure" in the
stock market on the expiration dates which results in a drop in returns.
6.1 Do Investors Exercise at Maturity?
The rst assumption of this interpretation is that investors need to exercise in-the-money call options on
the expiration dates. Evidence shows (as in Figure 1) that the total open interest of in-the-money call
option remains stable throughout the expiration week. Investors do not liquidate the option position in the
expiration week before the third Friday, and most of the open interest is carried to the expiration dates. This
is true even for options which are already deeply in-the-money before the expiration Friday. 8 With these
carried-over in-the-money call option contracts, investors have two alternatives to close the position on the
expiration dates—exercising it or selling it. The following subsections provide supporting evidence that a
large number of option contracts on the expiration dates are exercised instead of being sold.
6.1.1 Market Frictions
Finucane (1997) and Overdahl and Martin (1994) study the exercise behavior and show that investors tend to
exercise the option with the existence of market frictions, such as a large option bid-ask spread. Accordingly,
if there is a comparably larger spread in the option market than in the stock market, investors would have
incentives to exercise the option and trade the underlying stocks in the stock market.
8 By calculating the change in total in-the-money option open interest in the expiration week, call option open interest decreases
by only 4.12% (41,600 contracts) from the third Thursday to the expiration Friday. As for deeply ITM call options (determined
as deeply ITM on Thursday), the decrease is only 5%. This suggests that most of the open interest is carried to the expiration
dates. ITM put options have a even smaller change in open interest, with only a 1.98% decrease from Thursday to the third Friday.
The change in open interest is much smaller from the third Wednesday to the third Thursday, with a 1.62% decrease for calls and
a 1.14% decrease for puts. This evidence shows that investors wait until the expiration dates, even though the option is already
deeply in the money before the expiration Fridays.
12

I calculate the bid-ask spread of in-the-money call options from 90 days before expiration to the expira-
tion date, along with the average spread of the underlying stocks. The option bid and ask prices are the best
bid and the best ask of the day. The spreads are normalized by the midpoints, and Figure 6 plots the pattern
of spreads in both markets.
There is a dramatic increase in option spread, close to 37:65%; the expiration date approaches. The
spread is even wider for deeply ITM call options, which reaches up to 60:67%. In contrast, the average
stock spread is stable and relatively small, around 1:48%. The wide option spread suggests a much less
liquid option market, which makes option trading comparably expensive. Given these market frictions,
investors have motives to exercise the option rather than selling it in the option market.
6.1.2 Higher Pro t from Exercise and Sell than Close by Selling
With the existence of a wide option spread, it might be more pro table for investors to exercise the option
and trade the stocks. Therefore, I further compare the pro ts from two of the following trading strategies on
the expiration dates:
1. Exercise and Sell: exercise the ITM call (put) option on the expiration date at the strike price and sell
(buy) the underlying stocks at the expiration-date closing price. The pro t ( 1) of this strategy is
1 =
( (closing price strike price) if for a call option
(strike price closing price) if for a put option
2. Close by Selling: close the ITM option position by selling the option at the best bid of the day, and
the pro t ( 2) is
2 = option best bid:
I then calculate the difference between 1 and 2, denoted by diff , and the results are presented in
Table 3. diff is normalized by the close price of the underlying stock and is reported in percentages.
In Table 3, diff is signi cantly positive for all options in the three ITM classes, especially for deeply
ITM options. Exercise and Sell can generate 0:76% higher pro ts per share for deeply ITM calls and 1:29%
for deeply ITM puts. This is partly due to a larger percentage in-the-moneyness and partly due to a wider
option spread. Even the least in-the-money options (slightly ITM) have positive diff , with 0:27% higher
pro t per share for call options and 0:2% higher for puts.
With market frictions, "Exercise and Sell" strategy strictly outperforms the "Close by Selling," and in-
vestors should have incentives to exercise the call options on the expiration dates.
13
)

Table 3: Pro t from Two Trading Strategies on Option Expiration Dates
This table reports the difference in trading pro t ( diff ) from two trading strategies on option
expiration dates—Exercise and Sell and Close by Selling. is de ned as the difference
diff
between 1 and 2 , where 1 is the pro t from the Exercise and Sell strategy, and 2 is
that from the Close by Selling strategy.
6.1.3 High <strong>Stock</strong> Prices
ITM Type diff t-statistics
Slight Call 0.27% 108.98
Medium Call 0.45% 217.16
Deep Call 0.76% 59.47
Slight Put 0.20% 81.7
Medium Put 0.39% 158.32
Deep Put 1.29% 19.22
Poteshman and Serbin (2003) point out when investors become involved in irrational early exercise of call
options, more often the underlying stock is attaining a historically high price or is earning a high return. This
suggests a high price of the underlying stocks can trigger an exercise. For deeply ITM call options, being
deeply ITM implies that the underlying stocks are reaching a relatively higher price, which can provoke
investors to exercise the call option.
6.1.4 A Large Number of Contracts are Exercised at Maturity
Other supporting evidence includes the market statistics obtained from the Option Clearing Corporation
(OCC) and ratios from the previous literature. According to the OCC 2006 annual report, 303 millions
of contracts are exercised in 2006. After adjusting for market shares, the ratio of ITM call options to put
options, and the percentage of calls and puts being exercised at maturity, there are roughly 5:3 millions of
calls and 1:6 millions puts being exercised at each monthly expiration date in 2006. 9 Given these numbers
are larger than the total ITM open interest in my sample, 10 we can believe that a large portion of the open
interest in the sample is exercised.
To summarize, in the expiration week, few contracts are closed before the expiration date. While on the
expiration dates, investors face a higher transaction cost in the form of a wider spread in the option market.
The large spread makes it a dominant trading strategy to exercise the option and sell the stocks. In addition,
9 Assumptions and detailed calculation are shown in the appendix.
10 Portfolios are formed using the close price before the expiration day. Thus, to serve as a good proxy for the total ITM open
interest on the expiration dates, options determined as ITM must stay ITM, more speci cally, in the same moneyness class on the
expiration dates. By counting the number of stocks in each ITM class on both the formation Thursday and the expiration Friday, a
majority of the options remains in the same ITM class. For detailed results, please see appendix.
14

for deeply ITM call options, there is also a higher price to trigger an exercise. With additional support of the
market statistics, there is a suf ciently large amount of option contracts being exercised on the expiration
Fridays.
6.2 Net Selling Pressure
Given a large number of contracts being exercised on the expiration dates, how do these exercised contracts
impose a negative impact on stock prices?
After investors exercise the option, due to capital constraints, recovery of cash positions, risk considera-
tion and portfolio rebalance, investors have motives to sell acquired shares immediately and generate selling
pressure in the stock market.
However, as selling pressure generates a negative price impact, the corresponding buying pressure from
the writer must be negligible. If a majority of the option writers need to purchase stocks in order to deliver,
this buying pressure could offset the selling pressure.
Merton, Myron, and Gladstein (1978) report that according to CBOE, 85% of all options written are
covered, 11 meaning that most of the writers simultaneously purchase the underlying stocks while writing a
call option. Moreover, for deeply ITM calls, the writers can anticipate before the expiration dates that the
option will be exercised with great possibility. Their purchase of stocks can spread out across days before
option expiration instead of concentrating on the expiration dates. Therefore, the buying pressure from the
writers on the expiration dates should be relatively small compared to the selling pressure from the option
holders. That is, there is net selling pressure in the stock market which can push down the prices.
6.3 How Selling Pressure Impacts Price
With strong net selling pressure, stocks returns are pushed down on option expiration dates. However, low
returns are only observed in deeply ITM call option portfolios with a suf ciently large amount of option
open interest. This can be explained by the following:
1. Deeply ITM call options, on average, have a wider spread (as in Figure 6). Combined with a relatively
higher price, it gives investors a stronger motive to exercise the option.
2. Deeply ITM options are de ned as more than 25% ITM. With a wider gap between the current price
and the purchasing price (strike price), there is more space for investors to lower the selling pricing to
attract potential liquidity providers. On the other hand, for stocks with options with smaller degrees
of moneyness, even investors lower the price, the magnitude should be small.
3. Option open interest needs to be large compared to the daily trading volume of the underlying stock
to move the market. With a standardized contract, one call option contract gives investors the right
11 This number is further supported by a senior option practitioner.
15

to purchase 100 shares of the underlying stock. Therefore, when investors exercise the option, one
contract will be converted into 100 times of stock shares. To generate suf cient pressure to drive
the price down, the number of shares being sold must be large enough compared to the daily trading
volume. For instance, if call option XYZ is 50% ITM, and the investors lower the selling price of
underlying stock by 20%. The total option interest of XYZ, however, is only 1 contract, while the
daily trading volume of the underlying stock is 1 million shares. Selling these 100 shares clearly is
unable to affect the market price. Panel A of Table 4 shows the ratios of call option open interest
dollar value to the daily dollar trading volume of the underlying stocks. Open interest dollar value is
calculated by rst converting open interest into stock shares (one option contract is worth 100 shares
of the underlying stock), and then multiplying the stock shares by the closing price. Dollar volume is
the daily trading volume of the underlying stock multiplied by the closing price.
Portfolios without low expiration-date returns have not only smaller degrees of moneyness but also
much smaller open interest compared to the daily trading volume. As for the low-returned portfolios
(Portfolio dm and Portfolio dl), both of them have a considerably larger open-interest-to-volume ratio
while compared to other portfolios. Moreover, as the ratio increases from 4:53% of Portfolio dm to
40:06% of Portfolio dl, the returns documented in the previous sections also decrease, indicating a
stronger negative impact on prices. This result is also consistent with the hypothesis that a drop in
returns can only be observed in stocks with deeply in-the-money call options.
As a result, the selling pressure can generate a decrease in returns on the expiration dates, but it can only
be observed in stocks with a large amount of deeply in-the-money call options.
Table 4: Ratio of Open Interest Dollar Value to Daily Dollar Trading Volume
This table reports the ratio of the open interest dollar value to the daily dollar volume of the underlying stock. Ratios
are reported by portfolios. Open interest dollar value is calculated by rst converting open interest into shares (one
option contract is worth 100 shares of the underlying stock), and then multiplying the stocks shares by the closing price.
Dollar trading volume is the daily trading volume of the underlying stock multiplied by the closing price.
Panel A: Dollar Value of Call Option Open Interest to Expiration-date Dollar Volume
Portfolios ss sm sl ms mm ml ds dm dl
Deeply ITM 0.01% 0.10% 0.58% 0.02% 0.20% 2.41% 0.77% 4.53% 40.06%
Panel B: Dollar Value of Put Option Open Interest to Expiration-date Dollar Volume
Portfolios ss sm sl ms mm ml ds dm dl
Deeply ITM 0.00% 0.02% 0.14% 0.00% 0.03% 0.72% 0.15% 1.63% 13.13%
16

6.4 Asymmetries between Calls and Puts
As for put option portfolios, with the inherent asymmetries between puts and calls, no price impact is
observed.
In general, put options have much smaller open interest than calls throughout the entire option duration.
This is shown in Figure 7, which plots the total open interest of calls and puts from 180 days before ex-
piration to the expiration date using the 1996-2006 sample. Put options start with a smaller open interest
than calls, and the gap widens as the expiration date approaches. The same pattern follows by using only
the 2006 sample. Additionally, a smaller fraction of put options than calls are exercised on the expiration
date (40% compared to 70%), 12 giving rise to an even smaller proportion of shares from put options in the
stock market. This is also consistent with the option pricing theory, according to which call options should
optimally be exercised prior to maturity if and only if the underlying stock is about to pay a suf ciently large
cash dividend. The same is not true for put options. Therefore, the exercise of put options spreads out across
the option duration.
Another distinction between in-the-money calls and in-the-money puts is that, for put options, neither
the option buyers nor the writers have the need to hold stocks. This is because if the put option holders do
not have stocks in hand on the expiration dates, they can always choose to close their option position by
selling the puts. Even if put option holders choose to exercise the option, they can start purchasing stocks
throughout the holding period instead of solely on the expiration dates. Therefore, there tend to be small
buying pressure from put options holders on the expiration dates. As for the writers, to hedge the potential
risk, they tend to cover the put option position by shorting the stocks before the expiration dates. Once the
put options are exercised, writers purchase the underlying stocks and offset the original short position. This
leads to a seemingly negligible selling pressure in the stock market.
However, this is not true for calls. Whether a call option is exercised depends on the option holders, and
once the option is exercised, the writers have the obligation to deliver the stocks. As a consequence, most of
the call option writers hold stocks in hand until the expiration dates in preparation for the possible delivery.
This should be particularly true for deeply in-the-money call option writers, as the possibility of them being
assigned is greater. When writers deliver these shares to option holders who exercise the call option, there
is a release of stocks in the stock market on option expiration dates. The release of stocks generates the net
selling pressure in the stock market and results in a negative price impact.
For further evidence, Duf e, Liu, and Poteshman (2009) nd the propensity to exercise put options
is decreasing in option moneyness, suggesting investors tend to exercise less in-the-money puts instead of
deeply ITM ones. As all less in-the-money put options (slightly and medium ITM) have a fairly small size of
open interest compared to the daily trading volume (Panel B of Table 4), there should not be price pressure
in the stock market.
Based on these asymmetric features between the calls and the puts, no price pressure is observed in stock
12 The percentages are documented in Finucane (1997) and Overdahl and Martin (1994).
17

portfolios based on put options.
7 Further Results
This section provides some further evidence to support the interpretation that the selling pressure results in
the decline in returns on option expiration dates.
7.1 Do Wider Option Spreads Accompany Lower <strong>Returns</strong>?
Since a wide option spread motivates investors to exercise the option instead of selling the option in the
option market and at the end results in downward selling pressure, a wider spread should accompany stronger
selling pressure and a deeper drop in returns. By regressing expiration-date portfolio returns on the average
deeply ITM call option spreads:
rp;m = spreadp;m + "p;m;
where rp;m is the portfolio return on the expiration date of month m, I obtain negative 0 s for all portfolios,
suggesting a stronger price impact on the expiration date as the option bid-ask spread becomes wider.
7.2 <strong>Stock</strong> Liquidity and Short-term Reversals
Under the Campbell, Grossman, and Wang (1993) setup, the demand curve for stocks may not be perfectly
elastic, and trade pressure can thus induce a price impact. More illiquid stocks should have a steeper demand
curve and accordingly experience stronger reversals, as indicated in Avramov, Chordia, and Goyal (2006).
In this subsection, I follow Cox and Peterson (1994) who conduct a cross-sectional regression by regress-
ing post-drop cumulative returns for stock i on event-day abnormal returns and rm size. The regression
coef cient of rm size captures the relation between stock liquidity and reversal, while that of the event-day
abnormal returns captures the overreaction effect. Instead of using rm size as a liquidity proxy, I apply the
Amihud illiquidity ratio (Amihud (2002)) to measure stock illiquidity. The Amihud illiquidity ratio for stock
i at date t, ILLIQit, is de ned as the ratio of its daily absolute returns to its daily dollar trading volume
ILLIQit = jritj
:
V OLit
Portfolio illiquidity ratio is constructed as the value-weighted average across all individual stocks included
in the portfolio, similar as the portfolio returns. Moreover, with more than one expiration date (event day), I
apply the time-series regression on each low-returned portfolios with regression speci cation expressed as
where
post expdate
Rp;t+k = 0 + 1AR expdate
p;t + 2ILLIQ expdate
p;t + "p;t+k; (3)
18

post expdate
Rp;t+k = the value-weighted cumulative post expiration-date returns. These returns are
calculated for 1 to 5 holding days from the expiration dates, k = 1, 2,..., 5.
AR expdate
p;t = the expiration-date abnormal returns after adjusting for systematic risk using
the four-factor model.
ILLIQ expdate
p;t = the expiration-date illiquidity ratio calculated as its past-month average.
Only deeply ITM portfolios (Portfolio ds, dm and dl) are included in the regression. Regression results
are reported in Table 5, with dollar volume (V OLit) expressed in millions.
For portfolios with abnormal returns on the expiration dates (Portfolio dm and dl), all coef cients on the
illiquidity ratio (ILLIQ) are positive. This positive coef cients are consistent with both Cox and Peterson
(1994) and Avramov, Chordia, and Goyal (2006), indicating that less illiquid stocks experience stronger
reversals after the expiration-date prices decline. In contrast, expiration-date abnormal returns for all holding
days have negative coef cients. The deeper the return drops on option expiration dates, the stronger the
subsequent reversal. However, I do not consider this investor overreaction effect as in Atkins and Dyl
(1990). The negative relation should simply be generated from different degrees of selling pressure on the
expiration dates.
The panel data approach is also explored by pooling all portfolios into one panel regression, with portfo-
lio xed effects as a control. The standard errors are clustered-robust standard errors. The result is consistent
with the one using equation (4), with positive coef cient for the illiquidity ratio (ILLIQ expdate
p;t ).
8 Robustness Checks
This section explores the robustness of the ITM call option portfolio return results through several exercises.
8.1 Controlling for Bid-ask Bounce
If the formation-day closing price hits the ask while the expiration-date closing price hits the bid, the daily
expiration-date returns picks up the bid-ask bounce instead of the actual price movement. 13 If the spread
is wide, the low returns on the expiration date can be misleading. Thus, I apply the midpoint of the daily
closing bid and closing ask price to construct the daily returns, and a similar result follows. Portfolio dm and
dl continue to demonstrate strikingly lower returns ( 0:76 and 1:49), with both of them being statistically
signi cant ( 2:32 and 2:48).
13 This is as suggested in Cox and Peterson (1994).
19

Table 5: Relation between Reversals, Illiquidity and Expiration-date Abnormal <strong>Returns</strong>
This table reports the regression coef cients of post expiration-date portfolio holding returns on the Amihud illiquidity
ratio and the expiration-date portfolio abnormal returns: post expdate
Rp;t+k = 0+ 1AR expdate
p;t + 2ILLIQ expdate
p;t
post expdate is the value-weighted cumulative post expiration-date returns calculated for 1-5 holding days from the
Rp;t+k expiration dates; expdate is the expiration date abnormal returns after adjusting for systematic risk using the four
ARp;t factor model, with k = 1, 2,..., 5; expdate is the expiration-date illiquidity ratio calculated as its past-week
ILLIQp;t average. The t-statistics are adjusted for heteroskedasticity and reported in parentheses.
Abnormal <strong>Returns</strong> Illiquidity Ratio
ds dm dl ds dm dl
Day 1 -0.71 -0.77 -1.00 0.03 1.37 0.43
(-14.3) (-19.7) (-14.7) (-0.27) (1.89) (-0.72)
Day 2 -0.85 -0.86 -1.12 0.18 1.38 0.58
(-15.5) (-17.7) (-14.0) (-1.14) (2.51) (-1.04)
Day 3 -0.91 -0.91 -1.20 0.12 1.15 0.98
(-17.1) (-19.2) (-14.8) (-0.84) (2.48) (1.90)
Day 4 -0.96 -0.95 -1.28 0.15 0.7 1.21
(-16.2) (-19.9) (-15.7) (-0.92) (-1.48) (2.34)
Day 5 -0.99 -0.98 -1.31 0.09 0.61 0.77
(-17.5) (-20.5) (-15.7) (-0.56) (-1.38) (-1.52)
8.2 Expiration of Index Futures—the Triple-witching Day
+"p;t+k, where
Index futures also expire on the third Fridays. However, instead of a monthly expiration date, index futures
expire on a quarterly basis. To ensure the low returns are not generated from the expiration of index futures,
I remove all quarterly expiration dates before forming the portfolios. 14 The result remains the same, with
substantially lower returns for portfolios with large amounts of expiring deeply ITM call options.
8.3 Expiration of LEAPS
LEAPS (Long-Term Equity Anticipation Securities), known as long-term equity option contracts, expire
only in January. After removing the January expiration dates, all portfolios show a similar expiration-date
return pattern as in section 4.1, suggesting the low-return effect is not con ned to the LEAPS expiration
dates, but is a widespread phenomenon for stocks with equity options.
14 Index futures contract expires on the third Friday of March, June, September and December, the so-called triple-witching day.
20

8.4 Different Cutting Points of Degree of ITM
This subsection provides evidence of expiration-date portfolio returns using different cutting points of the
degree of moneyness. Since the low returns are observed only in deeply ITM portfolios, I start from 15%
ITM. Instead of three ITM classes, I allocate stocks into ve ITM classes. Within each ITM category, I sort
the stocks into another two portfolios based on the amount of open interest. Ten double-sorted portfolios are
formed, and portfolio returns are reported in Panel A of Table 6.
Low returns are observed in portfolios with more than 35% in-the-money call options. As open interest
increases, return decreases, similar to the previous results.
8.5 Different Cutting Points of Open Interest
Instead of forming three open interest classes, this subsection sorts stocks within each ITM class into four
portfolios based on the amount of call option open interest. Cutting points of each open interest class are
the three quartiles. As shown in the following gure, there are twelve call option portfolios in total.
Panel B of Table 6 summarizes the portfolio returns on the option expiration dates. Low returns are only
observed in deeply ITM portfolios. Also, portfolio returns decease along with the size of open interest.
9 Conclusion
This paper rst investigates stock returns on monthly option expiration dates. By double-sorting the stocks
into portfolios with similar option characteristics, stocks with a suf ciently large amount of expiring deeply
21

Table 6: Different Cutting Points of Degree of ITM & Open Interest
This table reports the regression coef cient ( expdate ) of nine ITM call option returns on the expiration dates using
different cutting points to sort the stocks into portfolios. Panel A reports nine call option portfolio returns using
different cutting points of degrees of ITM in the rst stage of sorting. Panel B shows the nine call option portfolio
returns using different cutting points of open interest in the second stage of sorting. Cutting points of open interest
are the three quartiles (Q1, Q2 and Q3). Coef cients are obtained by regressing the value-weighted returns of
each portfolio onto the expiration date dummy: rp;;t= expdate Iexpdate;t+ Mon_4 IMon_4;t+ T ue_4 IT ue_4;t+:::
+ T hu_3IT :All returns are in percentages. The t-statistics are adjusted for heteroskedasticity and reported
hu_3;t+"p;;t
in parentheses.
Panel A: Different Cutting Points of the Degree of ITM
Degree of ITM
Open Interest 15 - 20% 20 - 25% 25 - 30% 30 - 35% > 35%
Small 0.01 -0.04 0.27 0.12 -1.14
(0.05) (-0.38) (1.29) (0.49) (-2.43)
Large -0.08 0.02 -0.32 -0.14 -2.20
(-0.61) (0.13) (-1.80) (-0.44) (-1.87)
Panel B: Different Cutting Points of Open Interest
Degree of ITM
Open Interest Slight Medium Deep
< Q1 -0.17 -0.14 -0.55
(-2.12) (-1.81) (-1.69)
Q1 - Q2 -0.10 -0.16 -0.61
(-1.20) (-2.05) (-1.92)
Q2 - Q3 -0.17 -0.16 -1.19
(-2.05) (-1.87) (-2.42)
> Q3 -0.14 -0.06 -1.27
(-1.40) (-0.62) (-2.12)
in-the-money call options earn signi cantly lower returns on option expiration dates. The negative returns
are in a strikingly large magnitude, with an average daily drop of up to 1.4%. These negative returns remain
signi cant after adjusting for systematic risk.
The drop in returns is followed by a strong reversal. This price reversal supports the price-pressure
hypothesis, according to which the low returns are generated from the large selling pressure. On option
expiration dates, option holders tend to exercise their deeply in-the-money call options and sell the acquired
shares immediately in the stock market. This increasing demand for immediacy results in selling pressure
22

in the stock market. As a majority of the option writers are hedged by writing covered calls, the buying
pressure from the writers is relatively small. Due to this non-synchronization between buying and selling
the underlying stocks, there is net selling pressure in the stock market on the expiration dates which results
in a drop in returns.
The price subsequently reverses, generating higher future returns as a compensation for liquidity sup-
pliers. A similar price impact cannot be observed in put option portfolios due to the asymmetries between
calls and puts.
Appendix
A.1 How Many Option Contracts are Exercised at Maturity?
According to the Option Clearing Corporation 2006 annual report, there are 303 million contracts being
exercised in total. Using the data from OptionMetrics, around 46% of the total option contracts are listed
under NYSE/AMEX-traded stocks. It is reasonable to assume that most of the exercised contracts are ITM
option contracts, and among all ITM options, 65% are calls while 35% are puts. I further assume that both
call and put option holders have the same propensity to exercise the option under the same market condition.
Moreover, from the studies by Finucane (1997) and Overdahl and Martin (1994), among all exercised call
options, 70% are exercised on the expiration dates, while for all exercised put options, 40% are exercised on
the expiration dates.
By applying the information from market statistics, OptionMetrics data and the ratios from the past
ndings, I infer the number of call and put option contracts exercised at each expiration date in 2006:
Total option contracts exercised at 2006 = 303 millions
Option on NYSE/AMEX stocks exercised = 303 46% = 140 millions
NYSE/AMEX call options exercised = 140 65% = 91 millions
NYSE/AMEX put options exercised = 140 35% = 49 millions
NYSE/AMEX call options exercised at maturity = 91 70% = 63:7 millions
NYSE/AMEX put options exercised at maturity = 49 40% = 19:6 millions
NYSE/AMEX call options exercised at each expiration date = 63:7=12 = 5:3 millions
NYSE/AMEX call options exercised at each expiration date = 19:6=12 = 1:6 millions
9.1 A.2 Total Open Interest in the Sample
Table 7 summarizes the total open interest of options in the three ITM classes on each expiration date of
2006 in my sample.
23

Table 7: Average Total Open Interest on Each Option Expiration Date in 2006
This table summarizes the total open interest of options in the three ITM classes on each expiration date in 2006. Call
option portfolios and put option portfolios are reported in Panel A and Panel B, respectively.
Panel A: Option Open Interest of Three ITM Classes in Each Call Option Portfolio
Degree of Moneyness ss sm sl ms mm ml ds dm dl Total
Slightly ITM 5,222 46,793 831,912 2,679 9,818 309,094 93 337 19,238 1,225,185
Medium ITM 947 13,423 313,654 6,260 49,032 1,210,020 183 1,054 69,594 1,664,166
Deeply ITM 60 1,314 34,015 206 2,928 136,254 532 3,044 122,183 300,537
Panel B: Option Open Interest of Three ITM Classes in Each Put Option Portfolio
Degree of Moneyness ss sm sl ms mm ml ds dm dl Total
Slightly ITM 3,664 32,220 598,093 1,207 5,004 94,625 59 24 4,494 739,391
Medium ITM 354 4,748 135,622 2,300 16,416 468,060 65 335 11,540 639,439
Deeply ITM 25 411 12,523 55 728 52,890 233 1,444 28,855 97,162
A.3 Options Moneyness on the Formation and the Expiration Day
Table 8 compares the option moneyness on the formation Thursday to that on the expiration Friday. A large
percentage of the options remain in the same moneyness categories on both days. Therefore, open interest in
the nine portfolios formed on the third Thursdays can relevantly serves as a proxy for the total open interest
in each moneyness category on the expiration Fridays.
Table 8: Percentage of Options in each Moneyness Class on the Formation and Expiration Day
A.4 OTM Option Portfolios
Expiration day
Formation day OTM Slightly ITM Medium ITM Deeply ITM
OTM 98.43% 1.39% 0.07% 0.11%
Slightly ITM 7.00% 86.23% 6.67% 0.10%
Medium ITM 0.08% 2.55% 96.12% 1.25%
Deeply ITM 0.27% 0.10% 1.11% 98.52%
Both OTM call and OTM put portfolios are formed using the same double-sorting method. As reported
in Table 9, returns of nine OTM call option portfolios appear insigni cantly different than zero. On the
24

contrary, stocks with a large amount of open interest on deeply OTM puts perform poorly on the expiration
dates, similar to deeply ITM call portfolios. This is because the deeply OTM put portfolios simultaneously
pick many of the same stocks as in the deeply ITM call option portfolios.
The duality between OTM puts (calls) and ITM calls (OTM puts) is straight-forward. A stock with
many deeply in-the-money call options tends to have a relatively higher price, and the put options listed
on this high-priced stock are more likely to be out of the money. By checking the stocks in both ITM and
OTM portfolios, I con rm that OTM put and ITM call option portfolios simultaneously pick many identical
stocks. Similar return patterns of ITM call (put) portfolios and OTM put (call) portfolios are shown in Figure
8.
Since stocks with a large number of deeply ITM calls also includes a large amount of deeply OTM puts,
to rule out the possibility that the low returns are resulted from deeply OTM puts rather than deeply ITM
calls, I remove stocks contained in the deeply ITM call portfolios (Portfolio ds, dm and dl) and repeat the
same exercise. The low returns originally found in deeply ITM put portfolios disappear. This concludes that
the low return is exclusive in stocks with deeply ITM calls.
Table 9: <strong>Returns</strong> of Nine OTM Option Portfolios on Option Expiration Dates
This table reports the regression coef cient ( expdate ) of nine OTM call option and put option portfolio returns
on option expiration dates. Panel A reports the nine call option portfolio returns, and Panel B shows the nine
put option returns. Coef cients are obtained by regressing each portfolio value-weighted returns on the
expiration date dummy: rp;t= expdateIexpdate;t+ Mon_4IMon_4;t+ T ue_4IT ue_4;t+:::+ T hu_3IT :All returns
hu_3;t+"p;t
are in percentages. The t-statistics are adjusted for heteroskedasticity and reported in parentheses.
Panel A: OTM Call Option Portfolios
Degree of OTM
Open Interest Slight Medium Deep
Small -0.02 -0.02 -0.03
(-0.28) (-0.21) (-0.25)
Medium -0.00 0.01 -0.55
(-0.03) (0.09) (-1.55)
Large -0.05 -0.18 -0.21
(-0.48) (-1.89) (-1.02)
Panel B: OTM Put Option Portfolios
Degree of OTM
Open Interest Slight Medium Deep
25
Small -0.15 -0.08 -0.44
(-1.97) (-1.04) (-2.28)
Medium -0.17 -0.10 -0.34
(-1.89) (-1.28) (-1.62)
Large -0.22 -0.11 -1.10
(-2.22) (0.98) (-1.96)

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27

Figure 1: Total Open Interest of ITM Call Options in the Expiration Week. This gure plots the average
total open interest of in-the-money call options in each expiration week of 2006. Open interest is in numbers of
option contracts.
Figure 2: <strong>Returns</strong> of Nine ITM Call Option Portfolios on Option Expiration Dates. This gure plots the
value-weighted average returns of nine ITM call option portfolios on option expiration dates. All returns are in
percentages. Portfolio returns are obtained from Panel A of Table I.
28

Figure 3: <strong>Returns</strong> of Nine ITM Call Option Portfolios on Expiration and Non-expiration Dates. This
gure plots the ITM call option returns on the expiration dates, non-expiration Fridays and non-expiration
dates. Regression coef cients are obtained by regressing portfolio returns on three sets of date dummies. All
returns are in percentages.
Figure 4: <strong>Returns</strong> of Nine ITM Put Option Portfolios on Option Expiration Dates. This gure plots the
regression coef cients of value-weighted portfolio returns of nine ITM put option portfolios on option expiration
dates. Regression coef cients are obtained from Panel B of Table I.
29

Figure 5: Price Reversal. This gure plots the 1 to 15-day holding period returns of nine ITM call option
portfolios by longing the portfolios on the formation Thursday.
Figure 6: Option and <strong>Stock</strong> Spreads. This gure plots both the call option spreads and stock spreads.
Both spreads are calculated as the bid-ask spread normalized by the midpoint. Option spreads are
plotted from 90 days before expiration to the expiration dates. <strong>Stock</strong> spreads are spreads in the
expiration week (Monday through the expiration Friday).
30

Figure 7: Total Open Interest. This gure plots the path of total open interest of call options and put options
from 180 days before expiration to the expiration date. Open interest is in numbers of option contracts.
Figure 8: Duality of ITM Call (Put) and OTM Put (Call). This gure plots returns of both ITM call (put)
option portfolios and OTM put (call) option portfolios on the expiration dates.
31