Options - Stock Returns during Option Expiration Weeks and the Option-Stock Volume Ratio.pdf

8/10/2019 Options - Stock Returns during Option Expiration Weeks and the Option-Stock Volume Ratio.pdf

1/33Electronic copy available at: http://ssrn.com/abstract=1571786

Stock Returns during Option Expiration Weeks

and the Option-Stock Volume Ratio1

Chris Stivers

Terry College of Business

University of Georgia

Athens, GA 30602

Licheng Sun

Department of Finance

College of Business

Old Dominion University

Norfolk, VA 23529

This version: March 15, 2010

1Comments welcome. Please address comments to Chris Stivers (e-mail: [email protected]; phone:

(706) 542-3648) or to Licheng Sun (e-mail: [email protected]; phone: (757) 683-6552).



Stock Returns during Option Expiration Weeks and

the Option-Stock Volume Ratio

Abstract

Over 1983 to 2008, we find that large-cap stocks with actively traded options tend to have

substantially higher average weekly returns during option-expiration weeks (ending on a months

third-Friday), with consistent subperiod results. This empirical regularity is also evident in large-

cap-dominated stock portfolios. Further, over the 1996 to 2008 period with available Option Metrics

data, we find that the average weekly stock returns for option-expiration weeks tend to be apprecia-

bly larger for option-expiration weeks that also experience a relatively high option trading volume,

relative to the underlying stock trading volume. In contrast, the average weekly returns for the

option-expiration week are not much different than other weeks for smaller-cap stock portfolios,

which contain stocks with relatively less option trading activity. Further, for our sample of large-cap

stocks, the average weekly stock returns for the third-Friday of a calendar month are not different

than other weeks for a pre-option-market sample over 1948 to 1972. We provide additional evidence

that, along with the option market evidence in Lakonishok, Lee, Pearson, and Poteshman (2007),

suggests that the sizable written call activity from non-market makers may contribute towards

understanding our empirical findings.

JEL Classification: G12, G13, G14

Keywords: Option Expiration, Stock Returns, Option and Stock Trading Volume



1. Introduction

The past three decades have experienced a dramatic growth in the size of the options market.

According to the Chicago Board Options Exchange (CBOE), in 2007 CBOE options contract

volume reached an all-time record of 944,471,924 contracts. The growth rates in CBOE options

contract volume were 33%, 44%, and 40% in 2005, 2006, and 2007 respectively.1 Further, recent

research indicates that option-related activity may have an influence on the underlying stock price

behavior (Ni, Pearson, and Poteshman (2005)), or may contain information about the subsequent

behavior of stock prices (Roll, Schwartz, and Subrahmanyam (2010)). Ni, Pearson, and Poteshman

(2005) document that the closing prices of optionable stocks tend to cluster at option strike prices

on option-expiration days. They attribute the pricing patterns to hedge rebalancing by option

market makers and stock price manipulation by firm proprietary traders.

Given the tremendous growth in option trading activities and this recent research, this paper

re-examines the behavior of stock returns during option-expiration weeks. A few older studies

examine stock returns around the expiration day with return horizons beyond the actual expiration

day. Klemkosky (1978) analyzes weekly stock returns before and after option expiration for a

limited sample of 14 expiration periods in 1975 and 1976. He finds that 12 of the 14 expiration

weeks have negative returns (10 of the 14 weeks are significantly negative) with an average return

of about 1% in the expiration week. The returns in the week after option expiration are largely

positive with an average return of 0.4%. Using a longer sample from January 1979 to June 1985,

Cinar and Vu (1987) examine the effect of option expiration on six large-cap stocks (IBM, GM,

Eastman Kodak, 3M, Sears and Exxon). They find that the mean returns of these stocks during

the expiration weeks are mostly statistically indistinguishable from zero.2 Mayhew (2000) surveys

the empirical evidence on expiration-day effects and concludes that although there appear to have

been specific instances of price movements on expiration days that appear to have been related to

1See the website http://cboe.com/AboutCBOE/History.aspx.2Other studies examine option-expiration effects on the expiration day or the end of the expiration day. For

example, Stoll and Whaley (1987, 1991) look at expiration-day effects by focusing exclusively on the trading activity

during the last hour of trading on triple-witching days (days on which index futures, index options and options on

index futures expire simultaneously) and first half-hour of the following day.

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traders unwinding their positions, there is little evidence of a strong, systematic price effect around

expiration.

With the huge growth in option trading activities in recent years and the much longer time-series

now available, these earlier studies seem both outdated and limited in their scope. In this article, we

re-examine stock returns over option-expiration weeks for both large individual stocks and various

stock indices. We focus on the weekly returns of large individual firms that have actively traded

options over the 1996 to 2008 period, corresponding to option-volume data availability from Option

Metrics. However, our study also examines a longer 1983 to 2008 period (with 1983 coinciding with

the introduction of stock index options) and a pre-option-market period over 1948 to 1972.

This article is also the first to examine whether the relative trading activity in options has a

role in understanding the return patterns during option expiration weeks. We follow from Roll,

Schwartz, and Subrahmanyam (2010), hereafter RSS, and examine the ratio of option trading vol-

ume to stock trading volume, or O/S. RSS study the time-series properties and cross-sectional

determinants of the O/S ratio. Their findings include that the O/S tends to be higher around earn-

ings announcements and that the O/S ratio is positively related to the absolute post-announcement

returns.

The intuition behind examining the O/S ratio is simple. If weekly returns appear to behave

differently during the option-expiration week (in contrast to the other weeks) and the behavior is

tied to option-related activity, then it seems likely that the associated patterns would be stronger

during option-expiration weeks that experience a relative large O/S. Accordingly, we also separately

examine the mean and volatility of returns for option-expiration weeks that have a relatively high

O/S value.3

In stark contrast to earlier studies, we present striking new empirical evidence that average

stock returns tend to be higher during option-expiration weeks as compared to average returns in

other weeks, at least for large-cap stocks with very active option trading. First, for our primary

sample of 28 large-cap individual stocks with active option activity over 1996 to 2008, the average

3We use a weekly O/S, defined as the average of the option trading volume for the five trading days concluding in

the last day of the calendar week (normally Friday) divided by the comparable average of stock trading volume over

the same five trading days.

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weekly return during option-expiration weeks is 45.0 basis points. In contrast, for the other weeks,

the average weekly return is only 11.8 basis points. This spread in means tends to be larger for

the stocks with more actively traded options. We note that the average return volatility for the

option-expiration weeks is only modestly higher than the return volatility of the other weeks, at

4.97% versus 4.57%. One-half subperiod results are consistent.

Second, for the same sample of 28 stocks over 1996 to 2008, we examine the option-expiration

weeks where the O/S volume ratio is relatively high (above the 75th percentile value of the O/S

ratio for each respective stock). For our sample of large individual stocks, about 7.5% of the weeks

meet the double conditioning of being an option-expiration week with a high O/S value. We find

that the spread in means is even more dramatic. For the option-expiration weeks with a high O/S,

the average weekly return is 82.5 basis points. For the remaining 92.5% of the weeks, the average

weekly stock return is only 14.0 basis points. We note that the average return volatility for the

option-expiration weeks with a high O/S is only modestly higher than the return volatility of the

other weeks, at 4.87% versus 4.64%. One-half subperiod results are again consistent.

Third, given the above patterns in the mean and volatility of the weekly stock returns, the

Sharpe ratio during the option-expiration weeks is much higher than the Sharpe ratio during the

other weeks. When examining all the option-expiration weeks, the average Sharpe ratio for the

option-expiration weeks is 0.57 versus an average Sharpe ratio of 0.07 for the other weeks.4 When

examining the option-expiration weeks that also experienced a relatively high O/S ratio, the average

Sharpe ratio for the high O/S option-expiration weeks is 1.25 versus an average Sharpe ratio of

0.11 for the other weeks.

Fourth, we examine the same set of 28 firms in the earlier 1983 to 1995 period and find quali-

tatively consistent results for the difference in means, as related to the option expiration week. We

do not examine the O/S results in this earlier period, since the Option Metrics data begins in 1996.

Fifth, for stock indices, we examine the S&P 500 and size-based decile stock portfolios. Over

1983 to 2008, the option-expiration spreads in means for the S&P 500 and the large-cap stock

portfolio are positive and statistically significant. However, the option-expiration spread in means

4For these Sharpe ratios, we annualize the weekly return statistics by multiplying the mean excess return by 52

and multiply the sample standard deviation by the square root of 52.

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is much smaller and statistically insignificant for the smaller-cap portfolios, presumably portfolios

composed of stocks with relatively much lower option activity.

Sixth, we examine our sample of large individual stocks over an earlier pre-option-market period

of comparable length, 1948 to 1972. For the 15 firms with available return history over the entire

earlier period, we find essentially no spread in means between the third-Friday weeks and other

weeks. The average spread in means between the third-Friday weeks and other weeks is only 0.4

basis points and none of the spreads are statistically significant. The same result holds for the S&P

500 index in the pre-1983 sample (preceding index option trading).

We also discuss possible explanations for these return patterns and present related evidence in

Section 6. The dramatically higher Sharpe ratios for the option-expiration weeks suggest that the

high average returns during the option-expiration weeks cannot be rationally attributed to an ex

ante risk-return tradeoff.

Lakonishok, Lee, Pearson, and Poteshman (2007) document that nonmarket maker investors

(in aggregate) have more written than purchased open interest, with written calls making up the

majority of this written open interest. This suggests three non-fundamental-value avenues that

could promote the observed option-expiration spread in weekly mean returns. First, retail investors

could be purchasing the stock to cover their uncovered written calls or be purchasing stock so that

they do not have to lower their position in the underlying stock in the event their covered calls

expires in the money. Second, especially during option-expiration weeks with stock price increases

for other reasons, retail investors may be offsetting their written call positions. Presumably, such

offsetting would serve to lower the net long call position of market makers. This, in turn, could

result in market makers reducing their short stock positions that they may have in place to delta

hedge their long call positions, which might exert some upward pressure on stock prices. Third,

since the market makers tend to have a net long call position, then they would benefit from stock

price increases during the option-expiration week for their long call positions that are not delta

hedged. Thus, market-makers might have an incentive to promote stock price appreciation during

the option-expiration week.

To examine the notion that the stock price might be driven up beyond the fair economic value

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during by the option expiration, we also examine the average weekly returns for the week following

the option expiration (under the assumption that non-fundamentals price movements would tend

to be reversed in the subsequent week). For our sample of 28 large individual stocks over 1996 to

2008, the average return for fourth-Friday weeks is -2.9 basis points versus an average return of

18.1 basis points for the other weeks that are not option-expiration weeks (referring to a months

first-Friday, second-Friday, and fifth-Friday weekly return). Recall that option-expiration weeks

have a mean of 45.0 basis points, so this result suggests a return reversal in the week following the

option expiration, which is consistent with the explanation suggested in the prior paragraph.

Finally, in regard to our O/S volume ratio results for option-expiration weeks, we acknowledge

that it is possible that option activity responds to an increasing stock price (rather than the option

activity contributing to the observed high average weekly returns for the option-expiration weeks).

If so, it seems likely that other non-option-expiration weeks that have a high O/S value would also

be associated with higher average weekly stock returns. We also investigate this possibility for

our sample of 28 large stocks over 1996 to 2008. For non-option-expiration weeks that also have a

relatively high O/S volume ratio (an O/S above the 75th percentile value of the firms respective

O/S distribution), the average weekly stock return is 38.7 basis points across our 28 stocks. While

sizably positive, this average weekly return is only about 47% as large as the average weekly returns

for the option-expiration weeks that also have a high O/S ratio (which have an average weekly

return of 82.5 basis points). We interpret this as additional circumstantial evidence that suggest

option-related trading activity tends to promote stock price increases in the option-expiration week.

This article proceeds as follows. Section 2 reviews related theory and other related empirical

evidence. Sections 3 and 4 present our results for large individual stocks with active option trading

and size-based stock portfolios, respectively. Section 5 extends the results to the S&P 500 index.

Finally, Section 6 concludes and also provides some exploratory analysis on the likely causes of the

documented patterns for option-expiration weeks.

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2. Additional Background and Literature Review

Why would trading activities in options have any impact on the underlying stock prices? After all,

in the Black-Scholes world, options are viewed as redundant assets whose payoffs may be replicated

using a dynamic trading strategy in stocks and cash, and therefore should have no impact on

underlying stock prices. A number of theoretical articles have offered some interesting perspectives

on this issue. For example, Detemple and Selden (1991) demonstrate that in incomplete markets,

the valuation of option prices and their underlying stock prices is a simultaneous pricing problem.

Although in general stock prices depend on the contractual characteristics of options available for

trading, they find that, in a mean-variance model, option trading activity can lead to an increase

in the equilibrium stock price as well as a reduction in the stocks volatility. Cao (1999) identifies a

similar effect under an alternative theoretical framework. His model predicts that the availability of

options contracts can incentivize investors efforts to collect information about asset payoffs, which

in turn leads to an increase in the expected prices of the underlying as well as positively correlated

assets, and a reduction in price volatility. Mayhew (2000) provides a comprehensive review on the

topic.

Other studies evaluates the pricing effects related to the introduction of option contracts; see

Conrad (1989), Detemple and Jorion (1990), and Sorescu (2000). These studies find that option

listing is associated with positive abnormal stock returns in early years (prior to 1981) but insignif-

icant or negative returns after 1981, which is likely due to some regulatory changes in 1981.

Given our primary empirical results that indicate option-expiration weeks have higher average

stock returns and much higher Sharpe ratios than other weeks for large-cap stock with activity

traded options, the results in Ni, Pearson, and Poteshman (2005) seem particularly relevant. They

consider pricing influences related to option activity that can be described as price movements not

strictly related to fundamental value information. Specifically, they attribute the pricing patterns

they uncover to hedge rebalancing by option market makers and to stock price manipulation by

firm proprietary traders.

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3. Weekly Returns for Large Stocks with Active Option Trading

3.1. Sample Selection

We desire to examine a set of individual stocks that have actively traded options. Further, we

wish to examine large-cap stocks, because of their economic importance and because large-cap

stocks account for most option activity, see Lakonishok, Lee, Pearson, and Poteshman (2007).

Additionally, we elect to limit the number of firms in our initial investigation so that we may report

results on each of the important stocks, firm by firm. Finally, our initial firm-level investigation is

limited to 1996 through 2008, based on availability of option trading volume from Option Metrics.

Given our goals and data limitations, we initially investigate the following set of 28 large-capstocks with actively traded options: International Business Machines (IBM), Texas Instruments

(TXN), 3M (MMM), Eastman Kodak (EK), Hewlett-Packard (HPQ), Coca-Cola (KO), Boeing

(BA), General Electric (GE), Wal-Mart(WMT), Merck (MRK), Halliburton (HAL), Schlumberger

(SLB), Alcoa (AA), Bristol-Myers Squibb (BMY), Johnson & Johnson (JNJ), McDonalds (MCD),

International Paper (IP), Occidental Petroleum (OXY), Honeywell (HON), Xerox (XRX), Ford (F),

Pepsico (PEP), Black & Decker (BDK), Dow Chemical (DOW), Gap (GPS), Baxter International

(BAX), Avon Products (AVP), and HJ Heinz (HNZ) (ticker in parentheses, with the firms ordered

based on the firms 75th percentile value of their respective weekly O/S volume ratio). These 28

firms are a subset of the 50 individual stocks from Dennis, Mayhew, and Stivers (2006) (DMS);

where the 50 firms from DMS are the 50 individual firms that have the largest option trading

volume over 1988 to 1995. These 28 firms are chosen (out of the 50) because they have both a

complete return history over 1996 through 2008 and available option trading volume from Option

Metrics. Using a sample of firms that were chosen for their high option trading activity over the

prior 1988 to 1995 period provides a set of firms that are expected to have high option activity

and provides ob jectivity to our firm selection. We note that these firms continue to have actively

traded options over our later sample period, but that there is a sizable cross-sectional dispersion

in the firms average O/S volume ratio across the 28 firms.

Table 1 reports summary statistics on these firms weekly stock returns, average daily stock

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This spread in means tends to be larger for the stocks with a high O/S volume ratio. For the

top 10 O/S stocks (ranked by the 75th percentile O/S volume ratio for each respective stock), the

average weekly return during option-expiration weeks is 58.3 basis points, versus 6.6 basis points

for the other weeks.

For the 28 stocks, we also find that the average return volatility for the option-expiration weeks

is only modestly higher than the return volatility of the other weeks, at 4.97% versus 4.57%. This

modest different in return volatility casts doubt on a risk-return tradeoff explanation for the high

average returns during the option-expiration weeks. Given these patterns in the mean and volatility

of the weekly stock returns, the Sharpe ratio during the option-expiration weeks is much higher

than the Sharpe ratio during the other weeks. The average Sharpe ratio for the option-expiration

weeks across the 28 stocks is 0.57 versus an average Sharpe ratio of 0.07 for the other weeks.

We also examine the option-expiration weeks in a GARCH system, since the volatility of the

weekly returns during the option-expiration weeks tends to be a little higher than for the other

weeks and to control for heteroskedasticity in general. We evaluate the mean and weekly volatility

of the third-Friday weekly returns in a GARCH framework that allows both the weekly mean and

volatility to be different for the third-Friday week (as compared to the other weeks). We estimate

the following model:

Ri,t= 0+ 1DumFr3t + t (2)

vi,t= 0+ 12

t1+ 2vi,t1+ 3DumFr3t (3)

where vi,t is the conditional variance oft from equation (2) for week t; 2t1 is the lagged squared

return shock; the s are coefficients to be estimated for the conditional variance equation; and the

other terms are as defined for equation (1). We estimate the GARCH system, given by equations

(2) and (3), simulataneously, using maximum likelihood with a conditional normal distribution. We

compute T-statistics for each estimated coefficients, based on heteroskedastic- and autocorrelation-

consistent standard errors.

We find the following. The conclusions for the conditional mean equation are the same as

depicted in Table 2. The estimated 1 coefficients indicates that the conditional mean for the

option-expiration weeks is 38.4 basis points higher than the conditional mean for the other weeks,

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with seven of the 1 estimates being positive and statistically significant across the 28 firms. Next,

for the variance equation, we find that the estimated 3 coefficients are positive for 21 of the 28

firms and positive and statistically significant for 2 of the 28 firms (versus negative and statistically

significant for 0 of the 28 firms). This indicates that the third-Friday volatility also tends to be

modestly higher than that for the other weeks, as indicated by the summary volatility results

reported earlier.

3.3. Average Weekly Returns for Option-Expiration Weeks with a Relatively

High O/S Volume Ratio

We next investigate whether the spread in mean returns between the option-expiration weeks and

other weeks is stronger when the option-expiration week also has a relatively high O/S option

volume ratio.

Here, we first estimate the following model to calculate the spread in weekly mean returns:

Ri,t= 0+ 1(DumFr3t Dum

HiOSt ) + t (4)

WhereDumHiOSt is a dummy variable that equals one if a weeks O/S volume ratio is above the 75th

percentile value of the weekly O/S distribution for each respective stock. The other terms are as

defined for equation (1). Thus, the product of the two dummy variables indicates option-expiration

weeks that also have a relatively high O/S volume ratio. We calculate and report T-statistics in

parentheses, based on heteroskedastic- and autocorrelation-consistent standard errors, to indicate

whether the estimated1 is reliably different than zero.

Table 3 reports the results. For our primary sample of 28 large-cap individual stocks over

1996 to 2008, the average weekly return is 82.5 basis points for option-expiration weeks that also

experience a relatively high O/S volume ratio. In contrast, for the other weeks, the average weekly

return is only 14.0 basis points. This spread in means is pervasive and sizable, with 11 of the 28

stocks having a spread in the weekly mean returns of 100 basis points or larger. For nine of the

individual stocks, the return spread is statistically significant with a 10% p-value or greater. Also,

as shown in Table 4, Panel B, one-half subperiod results are consistent with the return patterns in

Table 3.

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This spread in means tends to be larger for the stocks with a high O/S volume ratio. For the

top 10 O/S stocks (ranked by the 75th percentile weekly O/S for each respective stock), the average

weekly return is 129.1 basis points, versus 8.6 basis points for the other weeks and the return spread

is positive for all 10 stocks.

For the 28 stocks, we also find that the average return volatility for the option-expiration weeks

with a high O/S volume ratio is only modestly higher than the return volatility of the other weeks,

at 4.87% versus 4.64%. Again, in our view, this very modest difference in return volatility casts

doubt on a risk-return tradeoff explanation for the high average returns during the option-expiration

weeks. Given these patterns in the mean and volatility of the weekly stock returns, the Sharpe

ratio during the option-expiration weeks is much higher than the Sharpe ratio during the other

weeks. The average Sharpe ratio for the option-expiration weeks across the 28 stocks is 1.25 versus

an average Sharpe ratio of 0.11 for the other weeks.

Some readers might be concerned that an increasing time trend in the O/S volume ratio might

result in essentially all of the high O/S realizations occurring later in our sample. If so, then the

O/S might not be informative, but rather our O/S results could just indicate a a higher average

weekly return for option-expiration weeks later in our sample. Our investigation indicates this is

not a material concern for the following reasons. First, as shown in Table 4, our O/S results are

reliably evident for both one-half subperiods separately (the January 1996 to June 2002 and July

2002 to December 2008 periods). Second, when estimating the O/S model over our entire 1996

to 2008 period, we tabulate what proportion of the high O/S weeks occur in the first one-half

subperiond versus the second one-half subperiod. Across our 28 stocks, 40% of the high O/S weeks

occur in the first one-half subperiod and 60% in the second one-half subperiod, and 8 of the 28

stocks have more high O/S weeks in the first half of our sample. We conclude that our O/S results

are not due to an increasing time-trend in the O/S.

We also examine the option-expiration weeks in a GARCH system, since the volatility of the

weekly returns during the option-expiration weeks tends to be a little higher than for the other

weeks and to control for heteroskedasticity in general. We evaluate the mean and weekly volatility

of weekly returns in a GARCH framework that allows both the weekly mean and volatility to be

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different for third-Friday weeks that also have a high O/S realization (as compared to the other

weeks). We estimate the following model:

Ri,t= 0+ 1(DumFr3t Dum

HiOSt ) + t (5)

vi,t= 0+ 12

t1+ 2vi,t1+ 3(DumFr3t Dum

HiOSt ) (6)

where vi,t is the conditional variance oft from equation (4) for week t; 2t1 is the lagged squared

return shock; the s are coefficients to be estimated for the conditional variance equation; and the

other terms are as defined for equation (4). We estimate the GARCH system, given by equations

(5) and (6), simulataneously, using maximum likelihood with a conditional normal distribution. We

compute T-statistics for each estimated coefficients, based on heteroskedastic- and autocorrelation-

consistent standard errors.

We find the following. The conclusions for the conditional mean equation are the same as

depicted in Table 3. The estimated 1 coefficients indicates that the conditional mean for the

option-expiration weeks is 73.4 basis points higher than the conditional mean for the other weeks,

with 12 of the 1 estimates being positive and statistically significant across the 28 firms. Next,

for the variance equation, we find that the estimated 3 coefficients are positive for 13 of the 28

firms and positive and statistically significant for only one of the 28 firms (versus negative and

statistically significant for 0 of the 25 firms). This indicates that the volatility for option-expiration

weeks with a high O/S tends to be little different than the volatility for the other weeks, as indicated

by the summary volatility results reported earlier.

3.4. Individual Stock Results for other Sample Periods

Next, we examine our sample of 28 firms over two alternate earlier periods. First, we examine the

1983 to 1995 period. We choose this period because it is the same length as our primary 1996 to

2008 period (13 years). Also, 1983 was the year that trading in stock-index options commenced,

which we examine later in this study. We do not examine the O/S volume ratio results in this

earlier period, since the Option Metrics data begins in 1996.

Column two of Table 5 reports the results for the 1983 to 1995 period for our sample of 28

individual stocks. We find that the spread in means between the option-expiration weeks and the

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other weeks also tends to be positive, with an average spread in means of 26.4 basis points and

with a positive spread observed for 22 of the 28 firms. This finding supports our earlier evidence

that indicates average weekly returns tend to be higher for option-expiration weeks for individual

stocks with activity traded options.

For comparison, we also evaluate the spread in means for our sample of 28 firms over the entire

26 year period from 1983 to 2008. Column one of Table 5 reports the results. For this case, we find

that the average spread in means is 29.8 basis points and the option-expiration spread is positive

for 26 of the 28 stocks.

Over our primary sample of 1996 to 2008, 2008 is noteworthy as a dramatic bear market with

the S&P 500 down over 38% for the year and with extreme day to day return volatility. Readers

might wonder whether this year has a strong influence on our results. Accordingly, we also re-

estimate our primary models over the 1996 to 2007 period (omitting the 2008 data). The results

are quite similar to those reported in Tables 2 and 3.

Finally, we also evaluate 1948 to 1972 as a period that predates the opening of option trading on

the Chicago Board Option Exchange. This 25 year period is essentially the same length as our 1983

to 2008 period. Column four of Table 5 reports the results for the 1948 to 1972 period. For this

earlier period, our evaluation only includes 15 of the 28 individual stocks in our primary sample,

because we only include the stocks that have the full stock return history back to January 1948.

Over 1948 to 1972, the average weekly stock return for the third-Friday weeks is essentially the same

as for the other weeks. The average spread in means is only 0.4 basis points and only about half

the stocks have positive spreads. None of the 15 stocks have a spread in means that is statistically

significant. This finding provides additional circumstantial evidence that option-related activity

may be important for understanding our primary results.

To conclude, over 1983 to 2008 and for inclusive subperiods, the weekly stock return for option-

expiration weeks tends to be higher for large, individual firms with actively traded options; with the

difference being sizable and statistically reliable in many cases. Further, the average weekly return

is even higher for option-expiration weeks that also experience a relatively high option trading. In

contrast, over the pre-option period, the weekly stock returns for the 3rd Friday-week of a calendar

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month is essentially the same as the other weekly returns.

4. Option-Expiration Weekly Returns for Size-based Portfolios

If option-related activity is a factor behind the patterns documented in Tables 2 through 5, then

it seems that the return patterns would be stronger for firms with actively traded stock options.

The comparisons in Tables 2 and 3 for stocks with a higher O/S volume ratio versus stocks with

a lower O/S ratio suggest the degree of option activity may be important. If so, then the return

patterns seem likely to be stronger in large-cap stock portfolios, as compared to smaller-cap stock

portfolio, since large firms have more actively traded options and many small firms have very little

option trading or may not even have publicly-traded options.

Accordingly, we investigate the weekly returns of size-based stock portfolio and report the results

in Table 6. We evaluate the weekly returns of the value-weighted, size-based, decile stock portfolios

from the French data library. The results are reported in rows one through ten of the table.

We find that the largest size-based decile exhibits a statistically reliable spread between the

average weekly returns for the option-expiration weeks and the average weekly return of the other

weeks. The spread in weekly returns for the largest size-based decile is 27.5 basis points, with an

average option-expiration weekly return of 41.7 basis points versus an average weekly return for

the other weeks of only 14.2 basis points. The spread in means is statistically significant at a 10%

p-value.

For the other nine size-based decile portfolios, the spread between the average weekly return

for the third Friday versus the other weeks is also positive for all cases. However, the magnitude

is appreciably lower, as compared to the largest size-based decile, and none of the spreads are

statistically reliable for the smaller nine size-based deciles.

To further investigate the differences between the largest size-based decile and the smaller

firms, we calculate a weekly return spread defined as the difference between the weekly return for

the largest size-based decile and the average return for that week for the smallest five size-based

decile portfolios. Then, we evaluate the average of this weekly return spread to see if it is reliably

different for the third-Friday of a calendar month. The results are reported in row 11 of Table 6.

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We find that the average difference between the large-firm and small-firm portfolio is 0.177% for

the third-Friday week, as compared to a -0.042% for the other weeks. The difference of 0.220% is

statistically reliable, indicating that there a reliable difference between the behavior in the large-firm

and small-firm stock portfolios.

To conclude, for the large-firm portfolio in Table 6, we find that the spread between the average

weekly return for the third-Friday and the average weekly return for the other Fridays is sizable and

statistically significant. Further, we find that the third-Friday spread behavior is reliably stronger

in the large-firm portfolios, as compared to the smaller-firm portfolios. This behavior is consistent

with the notion that option-related activity influences the prices of large firms that have more

actively traded stock options.

5. Weekly S&P 500 Index Returns and Option Expiration

5.1. Discussion of Main Results

Given the evidence that large-cap firms with actively traded stock options exhibit particular strong

returns during the option expiration weeks, we inquire if such a trading pattern is limited only to

these particular stocks or do they spill over to the broad market in general? In particular, we are

interested in the the performance of the S&P 500 index during option expiration weeks for two

major reasons. First, it is the most widely used benchmark index for many mutual funds as well as

hedge funds. Second, some of the most actively traded futures and option contracts are based on

the prices the S&P 500 index. Therefore if we find a similar trading pattern in the S&P 500 index,

this indicates that our empirical findings carry broad-based economic significance to all investors.

We collect daily S&P 500 index prices from the Center for Research in Security Prices (CRSP)

and convert them to weekly returns. The data is available from 1962 to 2008. Similar to what

we did in previous sections, we focus on the sample period from July 1983 to December 2008 for

our main results. It should be noted that the CBOE introduces the trading of S&P 500 index

options in July 1983. We calculate weekly S&P 500 index returns using Friday-to-Friday prices. If

the stock market closes on a Friday and therefore the price on Friday is not available, then we use

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Thursdays prices instead, and so on.

To contrast with our main sample period, we also include the results calculated from an earlier

sample period that spans from July 1962 to the week ended on July 1st, 1983 (which is a Friday).

It should be noted that during the first half of this earlier sample period (1962 to 1972), there were

no listed option contracts available for trading. In the second half (1973 to 1983), listed option

contracts were available for some individual equities but the overall size of the option market is

quite small compared to the cash market.

Panel A of Table 7 reports the mean return, standard deviation, and return spread for the S&P

500 index during the third Friday week of a calendar month. To calculate the return spread, we

run the same regression as shown in equation (1), but for the S&P 500 index return. The estimated

coefficient 1 captures the return spread between the option expiration week and other weeks of

a calendar month. For comparison, we also include the results for the full sample (both option

expiration week and other weeks of a calendar month).

We find that the mean return for the third Friday week is 37 basis points, more than double the

average return for the full sample average of 15 basis points for all weeks. Meanwhile the volatility

during the third Friday week is about the same as the full sample average. The return spread

between third Friday week and other weeks is also significantly positive at 28 basis points.

Further, we find the results are strikingly different for the pre-1983 sample. Here the third

Friday weekly returns do not appear to be different from other weeks. The mean return for third

Friday weeks is 11 basis points, nearly identical to the full sample average of 12 basis points. The

return spread between option expiration weeks and non-expiration weeks is -1 basis points and

statistically insignificant. In terms of return standard deviations, option expiration weeks and

other weeks are also very similar (1.95% vs. 1.99%).

Hence our results indicate that there appear to have been a change in the markets trading

activity during the option expiration weeks in the two sample periods. When trading in option

contracts are either not available or relatively unimportant due to a small market size, returns in

the third Friday weeks are not dissimilar to other weeks. However as options market become more

active in the more recent sample, returns in the third Friday weeks become pronouncedly more

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value-weighted and equal-weighted indexes are very strong around the turn of a month, defined

as the last trading day of a month plus the first three trading days of a month, and weak during

other trading days of a month. Lakonishok and Smidt (1988) also confirms this turn of month

effect using 90 years of data on the Dow Jones Industrial Average. Since the third-Friday weeks

do not coincide with turn of the month days, our results are unlikely to be driven by this effect.

Nevertheless it is interesting to know what our results will look like after controlling for this effect.

To this end, we exclude the weekly S&P 500 returns that do not belong to the third-Friday week

or the two weeks adjacent to it. In other words, for every calendar month, we only examine the

returns from the three weeks around option expiration. In Panel D of Table 7, we find that by

excluding the weeks not neighboring the option expiration, the sample mean return is reduced by

about two thirds from 0.15% to only 0.05% in our 1983 to 2008 sample. This shows that the turn

of month effect continues to be significant in our sample period. Meanwhile excluding the turn of

month effect also strengthens our main result. We find the spread between third Friday weeks and

other weeks now increases to 48 basis points with a t-statistic of 3.

Overall we find the third-Friday returns for the S&P 500 exhibit similar patterns as those stocks

with actively traded options and large-cap stock portfolios. The pattern is consistent across the

subperiod samples and robust after accounting for the 1987 market crash, September 11, 2001

terrorist attack, as well as the turn of the month effect. Further the lack of a similar pattern in the

pre-1983 sample indicates that it likely to be attributable to option market trading activities.

6. Conclusions and Additional Evidence towards Interpretation

We document that large-cap stocks with actively traded options tend to have higher average weekly

returns during third-Friday weeks of the month over 1983 to 2008, with consistent subperiod results.

This empirical regularity is also evident in several large-cap-dominated stock portfolios that we

examine. Further, over the 1996 to 2008 period with available Option Metrics data, we find that

the average weekly stock return for option-expiration weeks tends to be appreciably larger for

option-expiration weeks that also experience a relatively high option trading volume, relative to

the underlying stock trading volume.

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In contrast, for our sample of large-cap stocks, the average weekly stock return for the third-

Friday of a calendar month is not different than other weeks for a pre-option-market sample over

1948 to 1972. Further, over our recent sample period of 1983 to 2008, the third-Friday average

weekly returns are not much different than other weeks for smaller-cap stock portfolios, which

contains stocks with relatively less option trading activity.

In our view, this collective evidence provides solid circumstantial evidence that suggests option

activity tends to contribute to higher average returns during the option-expiration week, at least

for stocks with relatively high option trading activity. Further, the much higher Sharpe ratios for

option-expiration weeks suggest that the high average returns during the option-expiration weeks

cannot be rationally attributed to an ex ante risk-return tradeoff.

However, it is unclear what types of option-related activity might contribute to understanding

the documented effect in option expiration weeks. While our aggregated option volume data limits

us on what we can determine in this area, we do discuss some limited exploratory analysis in this

direction in this concluding section.

With access to a unique option data set, Lakonishok, Lee, Pearson, and Poteshman (2007)

document that nonmarket maker investors (in aggregate) have more written than purchased open

interest, with written calls making up the majority of this written open interest. Further, they

note (page 841) that call writing is the most important category of option trade, based on open

interest, and the second most important, based on open volume. In our view, their summary

of option market activity suggests three non-fundamental-value avenues that could promote the

observed option-expiration spread in weekly mean returns.

First, retail investors could be purchasing the stock to cover their uncovered written calls or be

purchasing stock so that they do not have to lower their position in the underlying stock in the

event their covered calls expires in the money. Such stock demand could tend to promote a stock

price increase during the option-expiration week. Presumably, such activity would be amplified if

the stock price were increasing during the option-expiration week for fundamentals reasons.

Second, especially during option-expiration weeks with stock price increases for fundamentals

reasons, retail investors may be generating sizable option volume by offsetting their existing written

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call positions. Presumably, such offsetting would serve to lower the net long call position of market

makers. This, in turn, could result in market makers lowering their short stock positions that they

may have in place to delta hedge their long call positions. Market makers covering their short stock

positions could promote further stock price increases during the option-expiration week.

Third, since the market makers tend to have a net long call position, then they would benefit

from stock price increases during the option-expiration week for their long call positions that are not

delta hedged. Thus, market-makers might have an incentive to promote stock price appreciation

during the option-expiration week.

If upward stock price movements during option-expiration weeks tend to have a partial non-

fundamental-value component, then one would presumably expect to see lower average returns

during the week following option expiration, as prices revert to their fundamental value. Accord-

ingly, we also examine the average weekly returns for the week following the option expiration. For

our sample of 28 large individual stocks over 1996 to 2008, the average return for fourth-Friday

weeks is -2.9 basis points (with a median of -4.8 basis points) versus an average return of 18.1 basis

points (with a median of 12.8 basis points) for the other weeks that are not option-expiration weeks

(referring to a calendar months first-Friday, second-Friday, and fifth-Friday weekly return). Recall

that option-expiration weeks have a mean of 45.0 basis points (with a median of 48.4 basis points

across our 28 stocks), so this result suggests a return reversal in the week following the option

expiration, which is consistent with the explanation suggested in the prior paragraph.6

Next, recall that the average weekly stock returns for option-expiration weeks are especially

large when the option-expiration week also experiences a relatively high O/S volume ratio. As we

pointed out in our introduction, we acknowledge that it is possible that option activity responds

to an increasing stock price (rather than the option activity contributing to the observed high

average weekly returns for the option-expiration weeks). If so, it seems likely that other non-

option-expiration weeks that have a high O/S value would also be associated with higher average

weekly stock returns. We investigate this possibility for our sample of 28 large stock over 1996

6The same analysis over the earlier 1983 to 1995 period yield consistent results. For this earlier period, the average

weekly stock return for fourth-Friday weeks is -9.2 basis points versus an average weekly stock return of 55.9 basis

points for the option-expiration weeks.

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to 2008. For non-option-expiration weeks that also have a relatively high O/S volume ratio, the

average weekly stock return is 38.7 basis points (with a median of 32.1 basis points for the 28

stocks) across our 28 stocks.7 While sizably positive, this average weekly return is only about 47%

as large as the average weekly returns for the option-expiration weeks that also have a high O/S

ratio (which have an average weekly return of 82.5 basis points with a median of 86.6 basis points

for the 28 stocks).

Finally, our above discussion and the supplementary results suggest that written calls held by

non-market makers may have a role in understanding our primary findings. If so, then activity

related to written calls (such as offsetting written calls that may otherwise expire in the money)

should be stronger following periods of up movement in the underlying stock prices. If so, then

option-related influences on the underlying stock price during option-expiration weeks may be

stronger following recent stock price appreciation. To investigate this possibility, we calculate the

average returns for third-Friday weeks following positive prior three-week returns and negative

prior three-week returns. We conjecture that average option-expiration week stock returns may be

higher when the prior three-week returns are positive (as contrasted to the case when the prior

three-week returns are non-positive). The evidence in Panel D of Table 7 supports this conjecture.

We find that for the S&P 500 index, the third-Friday weekly average return following positive

prior three-week returns is almost twice as much as the mean return conditional on negative prior

three-week returns. In addition, volatility is lower and the proportions of positive returns are also

higher following positive prior three-week returns.

Overall, we interpret this sections additional evidence as supportive of the notion that option-

related activity contributes to the high average stock returns that we document for the option-

expiration week. In later revisions to this study, we hope to further probe the potential explanations

that may be behind our intriguing empirical findings tied to the option-expiration weeks.

7Recall that we define a high O/S value as an O/S realization above the 75th percentile value of the firms respective

O/S distribution.

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Cao, H. Henry, 1999, The effect of derivative assets on information acquisition and price behavior

in a rational expectations equilibrium, Review of Financial Studies12, 131163.

Cinar, E. Mine, and Joseph Vu, 1987, Evidence on the effect of option expirations on stock prices,

Financial Analysts Journal43, 5557.

Conrad, Jennifer, 1989, The price effect of option introduction, The Journal of Finance44, 487499.

Dennis, Patrick, Stewart Mayhew, and Chris Stivers, 2006, Stock returns, implied volatility in-

novations, and the asymmetric volatility phenomenon, Journal of Financial and Quantitative

Analysis41, 381406.

Detemple, Jerome, and Philippe Jorion, 1990, Option listing and stock returns: An empirical

analysis, Journal of Banking and Finance14, 781801.

Detemple, Jerome, and Larry Selden, 1991, A general equilibrium analysis of option and stock

market interactions, International Economic Review32, 279303.

Klemkosky, Robert C., 1978, The impact of option expiration on stock prices, Journal of Financial

and Quantitative Analysis13, 507518.

Lakonishok, Josef, Inmoo Lee, Neil D. Pearson, and Allen M. Poteshman, 2007, Option market

activity,Review of Financial Studies20, 813857.

Lakonishok, Josef, and Seymour Smidt, 1988, Are seasonal anomalies real? a ninety-year perspec-

tive, Review of Financial Studies1, 403425.

Mayhew, Stewart, 2000, The impact of derivatives on cash markets: What have we learned?,

Working paper, Unversity of Georgia.

Ni, Sophie Xiaoyan, Neil D. Pearson, and Allen M. Poteshman, 2005, Stock price clustering on

option expiration dates, Journal of Financial Economics78, 4987.

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Roll, Richard, Eduardo Schwartz, and Avanidhar Subrahmanyam, 2010, O/S: The relative trading

activity in options and stock, Journal of Financial Economics96, 117.

Sorescu, Sorin M., 2000, The effect of options on stock prices: 1973 to 1995,The Journal of Finance

55, 487514.

Stoll, Hans R., and Robert E. Whaley, 1987, Program trading and expiration-day effects,Financial

Analysts Journal43, 1628.

, 1991, Expiration-day effects: What has changed?, Financial Analysts Journal47, 5872.

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Table 2: Average 3rd Friday Weekly Returns for 28 Large Individual Stocks

This table reports the average weekly returns for 3rd-Friday weeks (the option-expiration week) for

our sample of 28 large-cap stock with active option trading. The weekly returns are five-day Monday-

through-Friday returns, ending on a Friday. The sample period is 1996 to 2008, corresponding to the data

availability from Option Metrics. Column one reports the ticker for each individual large stock. Column

two reports the average return on the 3rd-Friday weeks when options expire. Column three reports the

average return for the remaining weekly returns. Column four reports the spread in the mean returns

between columns two and three, with t-statistics in parenthesis that are calculated with heteroskedastic

and autocorrelation consistent standard errors. For the t-statistics in parentheses for column four, 1, 2,

3, indicate 1%, 5%, and 10% p-values, respectively.

1. Ticker 2. Mean 3. Mean 4. Spread of

3rd

Friday Other Weeks Means(Col. 2 - Col 3.)

IBM 0.758% 0.161% 0.597% (1.30)

TXN 0.553% 0.288% 0.266% (0.43)

MMM 0.496% 0.092% 0.404% (1.16)

EK 0.141% -0.271% 0.412% (0.84)

HPQ 1.080% 0.047% 1.033% (1.87)3

KO 0.596% -0.013% 0.608% (1.65)3

BA 0.274% 0.108% 0.166% (0.35)

GE 0.747% -0.011% 0.758% (1.91)3

WMT 0.471% 0.296% 0.175% (0.43)

MRK 0.708% -0.039% 0.747% (1.84)

3

HAL 0.342% 0.292% 0.050% (0.08)

SLB 0.633% 0.183% 0.450% (0.91)

AA 0.113% 0.163% -0.050% (-0.10)

BMY 0.131% 0.181% -0.050% (-0.12)

JNJ 0.746% 0.080% 0.665% (1.97)2

MCD 0.061% 0.295% -0.234% (-0.66)

IP 0.606% -0.210% 0.817% (1.86)3

OXY 0.662% 0.317% 0.346% (0.86)

HON 0.371% 0.143% 0.228% (0.44)

XRX 0.470% -0.015% 0.485% (0.66)

F 0.184% 0.000% 0.184% (0.30)

PEP 0.157% 0.212% -0.055% (-0.17)

BDK 0.657% 0.016% 0.641% (1.39)

DOW -0.007% 0.172% -0.179% (-0.44)

GPS 0.296% 0.301% -0.005% (-0.01)

BAX 0.532% 0.193% 0.339% (0.81)

AVP 0.312% 0.280% 0.032% (0.08)

HNZ 0.513% 0.031% 0.482% (1.79)3

average(all 28) 0.450% 0.118% 0.333%

average(1st 10) 0.583% 0.066% 0.517%

average (last 10) 0.348% 0.133% 0.215%

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Table 3: Average 3rd Friday Weekly Returns when Option Trading is High: Large Individual Stocks

This table reports the average weekly returns for 3rd-Friday weeks (the option-expiration week) when

the option trading volume is relatively high for our sample of 28 large-cap stocks. Weeks are categorized as

having a relatively high option trading volume when the option volume is high relative to the underlying

stock trading volume, as explained in Table 1. The sample period is 1996 to 2008. Column one reports

the ticker for each individual large stock. Column two reports the average return on the 3rd-Friday weeks

that have a relatively high O/S option-stock volume ratio. Column three reports the average return for

the remaining weekly returns. Column four reports the spread in the mean returns between columns two

and three, with t-statistics in parenthesis that are calculated with heteroskedastic and autocorrelation

consistent standard errors. For the t-statistics in column four, 1, 2, 3, indicate 1%, 5%, and 10% p-values,

respectively. Column five reports the number of weekly returns that meet the column-two conditions for

each stock.

1. Ticker 2. Mean 3. Mean 4. Spread of 5. Number

3rd Friday Other Weeks Means of Weeks

High Opt. Vol. (Col. 2 - Col 3.) Col. 2

IBM 1.403% 0.177% 1.226% (1.70)3 67

TXN 1.267% 0.266% 1.000% (1.02) 56

MMM 0.532% 0.158% 0.373% (0.72) 49

EK 1.551% -0.296% 1.847% (2.61)1 44

HPQ 1.341% 0.184% 1.157% (1.37) 59

KO 1.430% -0.004% 1.434% (2.85)1 62

BA 0.803% 0.097% 0.706% (1.07) 47

GE 1.756% 0.017% 1.738% (2.90)1

57WMT 1.044% 0.278% 0.765% (1.38) 51

MRK 1.779% -0.018% 1.797% (3.21)1 57

HAL 0.006% 0.325% -0.319% (-0.38) 47

SLB 0.905% 0.229% 0.676% (0.84) 58

AA -0.071% 0.165% -0.237% (-0.34) 40

BMY 0.564% 0.139% 0.425% (0.67) 48

JNJ 1.370% 0.121% 1.249% (2.76)1 61

MCD 1.057% 0.180% 0.876% (1.72)3 47

IP 1.005% -0.103% 1.108% (1.45) 49

OXY 0.688% 0.376% 0.311% (0.40) 43

HON 0.153% 0.199% -0.046% (-0.05) 52

XRX 0.387% 0.074% 0.313% (0.20) 49

F 0.554% 0.006% 0.548% (0.62) 45

PEP 0.309% 0.191% 0.118% (0.21) 44

BDK 0.068% 0.171% -0.103% (-0.19) 50

DOW 0.317% 0.117% 0.200% (0.32) 46

GPS 0.373% 0.294% 0.079% (0.09) 51

BAX 1.253% 0.198% 1.055% (2.10)2 47

AVP 0.104% 0.300% -0.196% (-0.26) 43

HNZ 1.152% 0.062% 1.090% (2.70)1 50

average(all 28) 0.825% 0.140% 0.685%

average(1st 10) 1.291% 0.086% 1.204%average (last 10) 0.467% 0.161% 0.306%

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Table 4: 3rd Friday Weekly Returns: One-Half Subperiod Results

This table reports the comparable results from Tables 2 and 3 for one-half subperiod analysis for our

sample of 28 large individual stocks. Panel A reports on the same analysis as for Table 2 for the 3rd

-Fridaymean weekly returns. Panel B reports on the same analysis as for Table 3 for the 3 rd-Friday mean weekly

returns for weeks with a relatively high option volume (high O/S ratio). The two subperiods run from

January 1996 to June 2002 and from July 2002 to December 2008, with 339 weeks in each subperiod.

Column four reports the spread in the mean returns between columns two and three, with the number

in parenthesis, (), indicating the number of stocks with a positive spread, and the number in brackets, [],

indicating the number of stocks where the spread is positive and statistically significant at a 10% p-value

or better. As in Tables 2 and 3, the individual stocks are ranked from 1 to 28, based on each stocks O/S

volume ratios 75th

percentile value.

Panel A: 3rd Friday Weekly Returns - Subperiods


3rd Friday Other Weeks Means

(Col. 2 - Col 3.)

First Half: Jan:1996 to Jun:2002

average(all 28) 0.488% 0.241% 0.247% (19) [1]

average(1st 10) 0.719% 0.175% 0.544% (9) [1]

average (last 10) 0.351% 0.326% 0.025% (6) [0]

Second Half: Jul:2002 to Dec:2008

average(all 28) 0.412% -0.006% 0.418% (22) [4]

average(1st 10) 0.368% 0.029% 0.339% (7) [3]

average (last 10) 0.364% -0.062% 0.426% (9) [0]

Panel B: 3rd Friday Weekly Returns with High Option Volume- Subperiods


3rd Friday Other Weeks Means

High Opt. Vol. (Col. 2 - Col 3.)First Half: Jan:1996 to Jun:2002

average(all 28) 0.913% 0.234% 0.679% (22) [6]

average(1st 10) 1.248% 0.198% 1.050% (9) [3]

average (last 10) 0.619% 0.302% 0.317% (7) [2]

Second Half: Jul:2002 to Dec:2008

average(all 28) 0.742% 0.035% 0.707% (23) [11]

average(1st 10) 0.741% 0.053% 0.668% (9) [4]

average (last 10) 0.446% -0.001% 0.448% (6) [3]

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Table 5: Average 3

rd

Friday Weekly Returns for 28 Large Individual Stocks: Other Periods

This table reports how the mean weekly returns ending on the 3rd Friday of a calendar month are

different than other Friday weekly returns for a sample of large individual stocks. This table reports

results for the following periods: 1983 to 2008, 1985 to 1995, 1996 to 2008, and 1948 to 1972. Over 1983

to 2008, our sample includes the following 28 large individual stocks: AA, AVP, BA, BAX, BDK, BMY,

DOW, EK, F, GE, GPS, HAL, HNZ, HON, HPQ, IBM, IP, JNJ, KO, MCD, MMM, MRK, OXY, PEP,

SLB, TXN, WMT, and XRX (by ticker). Over 1948 to 1972, our sample includes the following 15 large

firms, which are the firms from our 1983 to 2008 sample that have return data over the entire 1948 to 1972

period: BA, BDK, BMY, DOW, EK, GE, HNZ, HON, IBM, IP, JNJ, KO, MMM, MRK, and PEP (by

ticker). T-statistics are in parentheses, based on heteroskedastic- and autocorrelation-consistent standard

errors. For row 6 (8), we report the number of the estimated coefficients that are positive (negative) and

statistically significant at a 10% p-value, or better.

1. 2. 3. 4.

Sample Period: 1983 - 2008 1983 - 1995 1996 - 2008 1948 - 1972

1. Average Weekly Return, 0.505% 0.559% 0.450% 0.341%

3rd

Friday Weeks

2. Average Weekly Return, 0.206% 0.295% 0.118% 0.337%

Other Weeks

3. Average Spread, 0.298% 0.264% 0.333% 0.004%

3rd Friday less Others

4. Median Spread, 0.267% 0.254% 0.342% 0.039%

3rd Friday less Others

5. Positive Spreads 26 of 28 22 of 28 22 of 28 8 of 15

6. Positive & Significant Spreads 8 of 28 4 of 28 7 of 28 0 of 15

7. Negative Spreads 2 of 28 6 of 28 6 of 28 7 of 15

8. Negative & Significant Spreads 0 of 28 0 of 28 0 of 28 0 of 15

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Table 6: Option-Expiration Weekly Returns for Size-based Portfolios

This table reports how the mean weekly returns ending on the 3rd Friday of a calendar month are

different than other Friday weekly returns for size-based portfolios returns. The weekly returns are

five-day Monday-through-Friday returns, ending on a Friday. To calculate the spreads, we estimate the

same model as in Table ??. The size-based decile portfolios in rows 1 through 10 are the value-weighted

portfolios from the French data library. In row 11, the [10 minus (Mean of 1 to 5)] is the difference

between the weekly return of the largest decile-10 portfolio and the average of the weekly returns of

the smallest five size-based deciles. The sample period is 1983 to 2008. T-statistics are in parentheses,

based on heteroskedastic- and autocorrelation-consistent standard errors.

Portfolios: 1. Mean 2. Mean 3. Spread 4. T-stat.

Size Deciles of 3rd Friday of Other between Col. 1 on

& Other Weekly Returns Weekly Returns & Col. 2 the Spread

1. Decile-1 0.185% 0.168% 0.017% (0.13)

2. Decile-2 0.234% 0.181% 0.054% (0.36)

3. Decile-3 0.269% 0.192% 0.078% (0.50)

4. Decile-4 0.259% 0.179% 0.080% (0.51)

5. Decile-5 0.249% 0.202% 0.047% (0.30)

6. Decile-6 0.254% 0.200% 0.054% (0.36)

7. Decile-7 0.278% 0.208% 0.069% (0.46)

8. Decile-8 0.280% 0.196% 0.085% (0.54)

9. Decile-9 0.317% 0.195% 0.123% (0.82)

10. Decile-10 0.417% 0.142% 0.275% (1.81)

11. 10 minus 0.177% -0.042% 0.220% (2.09)

(Mean of 1 to 5)

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Table 7: 3rd Friday Weekly Returns: S&P 500 Index

This table reports how the mean weekly returns ending on the 3 rd Friday of a calendar month are

different from other weekly returns for the S&P 500 index. We report the mean return, standard

deviation, and return spread for various sample periods. Panel A shows the main results from July

1983 to December 2008. To contrast, we also include the earlier sample results from 1962 to 1983.

Panel B report the results for two half-sample subperiods from July 1983 to April 1996 and April

1996 to December 2008. Panel C shows the results after excluding the weeks during October 1987

market crash and the September 11, 2001 terrorist attack. Panel D accounts for the turn of the

month effect and the triple-witching weeks. Panel E reports the results conditional on positive or

non-positive prior three-week returns. The results are shown in percentage form. The return spreads

are calculated from equation (1). T-statistics are reported in parentheses.

Panel A: S&P 500 Index Weekly Returns and Option Expirations

1983 to 2008 1962 to 1983

Mean Return Std Dev Spread Mean Return Std Dev Spread

3rd Friday Weeks 0.3702 2.3415 0.2838 0.1121 1.9512 -0.0108

(2.77) (1.94) (0.91) (-0.08)

All Weeks 0.1517 2.2494 0.1204 1.9925

(2.46) (2.00)

Panel B: Subperiod Evidence

July 1983 to April 1996 April 1996 to December 2008


3rd Friday Weeks 0.3844 1.8807 0.2110 0.3560 2.7253 0.3568

(2.53) (1.21) (1.62) (1.51)

All Weeks 0.2219 1.8902 0.0813 2.5571

(3.03) (0.82)

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33/33

Table 7: (continued)

Panel C: 1987 Market Crash and September 11, 2001

Excluding 1987 Market Crash Excluding September 11, 2001


3rd Friday Weeks 0.3702 2.3415 0.2718 0.4094 2.2425 0.3236

(2.77) (1.88) (3.19) (2.23)

Full Sample 0.1609 2.2246 0.1601 2.2278

(2.64) (2.62)

Panel D: Third Friday Week Returns Conditional on Prior 3-Week Returns

Positive Prior 3-Week Returns Non-Positive Prior 3-Week Returns

Mean Return Std Dev %> 0 Mean Return Std Dev %> 0

3rd Friday Weeks 0.5154 1.5992 64.34 0.2644 2.7546 55.93

(3.66) (1.27)

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Options - Stock Returns during Option Expiration Weeks and the Option-Stock Volume Ratio.pdf

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