The Informational Role of Stock and Option Volume

7/26/2019 The Informational Role of Stock and Option Volume

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The Informational Role of Stock and Option Volume

Kalok Chan

Department of Finance

Hong Kong University of Science and TechnologyClearwater Bay

Hong KongTel: 852-2358-7680

E-mail: [email protected]

Y. Peter Chung

A. Gary Anderson Graduate School of Management

University of CaliforniaRiverside, CA 92521

U.S.A.

Tel: 909-787-3906E-mail: [email protected]

Wai-Ming Fong

Department of Finance

The Chinese University of Hong KongShatin, N.T.

H K


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Hong Kong

The Informational Role of Stock and Option Volume

Abstract

This paper analyzes the intraday interdependence of price movements and order flows for actively traded

NYSE stocks and their CBOE-traded options. Stock net-buy volume (buyer-initiated volume minus

seller-initiated volume) has strong predictive ability for subsequent stock and option returns, but call or

put net-buy volume has little predictive ability. Furthermore, stock returns lead option returns more than

they lag even after controlling for net-buy volume. Therefore, our results indicate that order flows in the

stock market are informative but order flows in the option market are not, and suggest that informed

investors submit trades primarily in the stock market rather than in the option market. There is also some

evidence for the non-informational linkage between the two markets. Stock net-buy volume is positively

(negatively) related to lagged call (put) returns, suggesting that option dealers dynamically hedge their

outstanding short option positions when the option deltas change. However, call or put net-buy volume

is not correlated with stock net-buy volume or lagged stock returns, suggesting that option traders do not


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Introduction

In complete markets, option trading should convey no new information to market participants

because options are derivative securities. In the absence of market completeness, however, informed

traders may prefer to trade options instead of the underlying stocks for a couple of reasons. First, lower

transaction costs and greater financial leverage may induce informed traders to trade in the option market

instead of the stock market (Black (1975) and Mayhew, Sarin, and Shastri (1995)). Second, investors who

have private information about volatility of the underlying stock price can only make their bet on volatility

in the option market (Back (1993) and Cherian (1993)). For these reasons, the option market may not be

redundant and can play an important role in discovering the information. On the other hand, lower

liquidity of the option market may discourage informed traders from trading options. Easley, OHara, and

Srinivas (1998) characterize this scenario as a separating equilibrium where only uninformed traders

transact in the option market while all informed traders transact in the liquid, stock market. Furthermore,

Brennan and Cao (1996) show that in their noisy rational expectations model, the option market can be

dominated by noise traders. In both cases, option trading would convey little information.

Although numerous empirical studies address this issue and investigate the informational linkage


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Easley, OHara, and Srinivas (1998) suggest that certain types of option trades have some predictive

power for future stock price changes.

The two markets can be related for reasons other than information transmission. Very few studies,

however, provide evidence. One possible reason that investors participate in the option market is

hedging: it can provide a venue to hedge the risk from holding the underlying stocks. When underlying

stock prices move, it might be optimal for hedgers to adjust their option positions, and therefore there can

be a relationship between the price movements in the stock market and the order flows in the option

market. Furthermore, option dealers can reduce the delta exposure of their option positions by hedging

dynamically with the underlying stocks. If there is too much inventory risk in their option positions after

customer purchases or sales, option dealers can trade in the stock market to unload some of their inventory

risk. Consequently, there can be interdependence between the order flows in the two markets.

In this paper we provide a comprehensive analysis of the interrelationship between the stock and

option markets. We examine the dynamics of price movements and order flows for actively- traded New

York Stock Exchange (NYSE) stocks and their CBOE-traded options. We focus on three important

iss es First e in estigate hether order flo s in the stock (option) market ha e an incremental


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option price changes while Anthony (1988) examines the linkage between the daily trading volume in the

two markets. Although Stephan and Whaley (1990) investigate both price changes and volume in the two

markets, they analyze the price change relationship and the volume relationship separately. By examining

both price change and order flow variables together, this paper presents a more comprehensive study of

the informational linkage between the stock and option markets.

Second, unlike those previous studies (Anthony (1988) and Stephan and Whaley (1990)) that use

total trading volume, we make use of net-buy volume (buyer-initiated volume minus seller-initiated

volume) to represent order flows. Net-buy volume measures temporary order imbalance in the market. As

demonstrated by some asymmetric information models (Kyle (1985) and Admati and Pfleiderer (1988)),

net-buy volume provides useful information to the market makers for price revision. Since market

makers cannot distinguish whether a specific buy or sell order is from an informed trader or a liquidity

trader, a rational pricing strategy for them is to revise the price upward (downward) when the net-buy

volume is positive (negative). Such behavior is supported by empirical studies in market microstructure

(e.g., Glosten and Harris (1988), Madhavan, Richardson, and Roomans (1997), and Huang and Stoll

(1997)) Th fi d th t t d i di t i bl h b i iti t d d ll i iti t d t d it


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put), Easley, OHara, and Srinivas (1998) examine whether option trades are informative. They suggest

that option trades have predictive power about future stock price changes. However, both Vijh (1990)

and Easley, OHara, and Srinivas (1998) examine the information content of option trades only. This

paper extends their work by also including stock trades into analysis. As the current literature provides

well-documented evidence that intraday stock trading volume leads the intraday option trading volume

(e.g., Stephan and Whaley (1990)), it is possible that the information empirically inferred from option

trades actually originates from stock trades.

Third, this paper examines the extent to which the stock and option markets are interrelated for

non-informational reasons. Some recent studies document covariation in order flows for different stocks

due to liquidity reasons. For the theoretical literature, Subrahamanyam (1991), Chowdhry and Nanda

(1991), and Kumar and Seppi (1994) recognize that there are liquidity traders who have portfolio-wide

liquidity needs, so that liquidity trading activities in different stocks are highly correlated. For the

empirical literature, Chordia, Roll, and Subrahmanyam (1998), Hasbrouck and Seppi (1999), and

Huberman and Halka (1999) report evidence of commonality in liquidity and order flows among different

t k Whil th i t di f th l ti hi f li idit t di t k


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A. The Sample

The data are retrieved from two sources. The first is the Berkeley Options Database, which

contains a complete time-stamped history of quotes and trade prices of the options traded on the Chicago

Board Options Exchange (CBOE). The second is the Trade and Quote (TAQ) database of the New York

Stock Exchange (NYSE), which contains time-stamped data on all trades and quotes on the NYSE,

American Stock Exchange, and NASDAQ. Both databases contain the time to the nearest second, the

price and volume for each trade, and, for quotations, the time and the bid and ask prices. We obtain data

for the first quarter (58 trading days) of 1995.

We start with the sixty most actively-traded stocks on the NYSE (based on average daily trading

volume) that do not split during our sample period as stock splits tend to affect the trading activities of the

stocks. We exclude the stock trades and quotes that originate outside the NYSE. Each day the most

active CBOE-traded call and put contracts are selected for each stock. When the most active contract has

five days or less to maturity, we select the next most active contract to eliminate option expiration effects

documented elsewhere. Thus, each stock has at most 58 option days (days on which a matching sample

f t k d ti d t il bl ) T iti t th ff t f i ti t di d l t th ti


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(1991) and compare the trade price with the prevailing bid/ask quotes. 2 The trade is classified as buyer

(seller) initiated if the trade price occurs at the ask (bid). If the trade price lies within the spread, we

follow Harris (1989) and record the trade as buyer (seller) initiated if the trade price is closer to the ask

(bid). In the second approach, which we use only if we cannot determine the direction of a trade using

the first approach, we employ tick test to compare the trade price with the preceding trade price(s). The

test classifies each trade into four categories: an uptick, a downtick, a zero uptick, and a zero downtick.

A trade is an uptick (downtick) if the price is higher (lower) than the price of the previous trade. When

the price is the same as the previous trade (a zero tick) but the last price change was an uptick

(downtick), the trade is a zero uptick (zero downtick). A trade is classified as buyer (seller) initiated if it

occurs on an uptick (downtick) or a zero uptick (downtick). When a trade occurs on consecutive zero

ticks, it is not classified.

B. Summary Statistics

Table I presents our final sample of the CBOE options and their NYSE-traded underlying stocks.

IBM h th hi h t b f ti d (56 d ) i l d d i th l hil C ll G lf h th


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Motor to 0.9 million for Best Buy.3 The stock with the most active option trading activity in our sample

is IBM (a daily average of 9,047 contracts traded for all call options and a daily average of 4,391

contracts traded for all put options). It is notable that the trading volume of the most active call and put

accounts for 29% to 73% of the trading volume of all calls and puts. This suggests that the trading

activities of the most active call and put are good representatives of those of all calls and puts, and that

options other than the most active ones are often thinly traded. Our analyses initially focus on the most

active calls and puts, but later check the robustness of our results using all calls and puts.

The percentages of buyer-initiated and seller-initiated volume vary across the stocks and options.

For example, there are buying pressure for the stock of Sears Roebuck (49% buyer-initiated volume and

32% seller-initiated volume) during the sample option days, but selling pressure for the stock of Citicorp

(31% buyer-initiated volume and 41% seller-initiated volume). Since not all trades are classified4, the

sum of the percentages of buyer-initiated and seller-initiated volume is less than unity.

C. Autocorrelations and Cross-autocorrelations in Volume and Returns

W titi h ti d i t t i ht i 5 i t i t l h b th th


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minute interval. Net-buy volume is the difference between buyer-initiated volume and seller-initiated

volume during the 5-minute interval. We follow Easley, OHara, and Srinivas (1998) and standardize

return, total volume, and net-buy volume variables to control for their cross-sectional variations across

different stocks and options. Each option day we first calculate the mean and standard deviation for a

variable. The variable is then standardized by subtracting the mean and dividing by the standard

deviation. Such standardization allows us to pool the entire 231 option days for later analyses.

C.1. Total Volume Series

Table II presents the autocorrelations and cross-autocorrelations of the standardized 5-minute

total trading volume of stocks, the most active calls, and the most active puts.5 Several results are noted.

First, stock trading volume is positively autocorrelated up to six lags, whereas call and put trading volume

are less autocorrelated - up to three lags for calls and two lags for puts.6 Second, stock trading volume is

contemporaneously correlated with call and put trading volume. The contemporaneous correlation

coefficients (0.090 between stock volume and call volume and 0.063 between stock volume and put

l ) hi hl i ifi t fl ti th t th i t it f t di ti iti i th t k d ti


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C.2. Net-Buy Volume Series

Table III presents autocorrelations and cross-autocorrelations of the standardized 5-minute net-

buy volume series. The three net-buy volume series also display significant positive autocorrelation at the

first lag. This finding is consistent with previous studies that document serial dependence in the arrival of

buy and sell orders (e.g., Hasbrouck and Ho (1987)). The net-buy volume series are, however, less cross-

autocorrelated than the total trading volume series. In fact, stock net-buy volume is not correlated with

call net-buy volume even at the contemporaneous level. These findings suggest that although the total

trading volume in the stock and option markets are highly correlated, the directions of trades in the two

markets are largely independent.

C.3. Return Series

Table IV presents autocorrelations and cross-autocorrelations of the standardized 5-minute return

series. All three return series exhibit negative autocorrelations. Since returns are calculated using bid-

k id i t th ti t l ti b d t b tt ib t d t bid k b ( R ll


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Whaley (1990), who find that stock returns lead option returns more than vice versa.

C.4. Between Returns and Net-Buy Volume

Table V presents cross-autocorrelations between returns and net-buy volume of the stocks, the

most active calls, and the most active puts. The table shows that stock net-buy volume is positively

correlated with stock and call returns, and negatively correlated with put returns. It indicates that when

there is an increase in stock net-buy volume, which signals good news about the stock, stock and call

prices react positively while put price reacts negatively. However, we cannot explain why call (put) net-

buy volume is negatively (positively) correlated with contemporaneous stock returns,7nor why call net-

buy volume and put net-buy volume are negatively correlated with the contemporaneous returns in their

own markets. Suppose there is informed trading in the option market. When call net-buy volume is

positive, it signals good news about the stock. So it should be accompanied by positive price reaction in

the stock and call market. Likewise, when put net-buy volume is positive, it signals bad news about the

stock. So it should be accompanied by negative price reaction in the stock and positive price reaction in

th t Thi li id th f t d bt ti t d i f ti t t b t th


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As results so far indicate that the returns and net-buy volume of the stocks, calls, and puts could

jointly affect one another, we further investigate their dynamic relationships with a system of six

regression equations as follows:

.v......vcv tptp1t1t ++++++++== (1)

where vt= [SRt,CRt,PRt,SNBt,CNBt,PNBt], SRt,CRt,andPRt are the standardized returns for the stocks,

calls, and puts for the interval t,and SNBt,CNBt, andPNBtare the standardized net-buy volume for the

stocks, call, and puts for the interval t; cis a (6 x 1) vector of intercepts; jis a (6x6) matrix of

autoregressive coefficients forj = 1, 2, ...,p; tis an (6 x 1) vector of residuals,

(( )) and,0E t ==

(( )) otherwise,=tfor0E'

t ==

where represents a (6x 6) symmetric positive definite matrix. The above system is very similar to a

VAR model where the lagged values of the dependent variables appear on the right hand side of the

equations. One advantage of our model is that the dynamic relationships among jointly endogenous


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values of the dependent variables on right hand side to capture serial dependency effects, the random

errors are likely to be independently distributed. Finally, the error terms in six equations are

contemporaneously correlated, but every equation has the same set of explanatory variables. So there is

no efficiency gain from using the seemingly unrelated regression estimation. We estimate all equations

separately by the ordinary least square method.

B. Hypotheses on Relationships among Returns and Net-Buy Volume

B.1 Effects of lagged net-buy volume on returns

If informed investors submit trades, market makers can attempt to infer the information from the

net-buy volume in the stock and option markets and adjust the quotes accordingly. If market makers

update the quotes instantaneously, there will be no impact of lagged net-buy volume on returns.

However, if there is a delay in quote adjustments, lagged net-buy volume would affect subsequent returns.

8 Suppose informed investors submit trades in the stock market. A positive (negative) stock net-buy

volume signals favorable (unfavorable) news to market makers in the stock and option markets. Then the

t k d ll t ld b i d d (d d) hil th t t i d d d


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Note that the inventory control model (Ho and Stoll (1983)) also predicts that quotes are adjusted

upward (downward) following an increase (a decrease) in net-buy volume, as market makers are expected

to revise the quotes to encourage offsetting orders. In the inventory model, however, the net-buy volume

can affect returns only in its own market. It should not affect returns in the other market.

B.2 Relationship among returns

If information is discovered mainly through trading activities of informed investors and market

makers update the quotes based on net-buy volume in the stock and option markets, net-buy volume

should subsume the informational role of returns. In other words, stock and option returns will not have

any incremental predictive ability for each other once we allow for the explanatory power of the net-buy

volume in both markets. However, it is likely that market makers do not observe the net-buy volume in

another market precisely, and therefore they may revise the quotes based on information inferred from

past price movements in another market.9 Furthermore, changes in quotes could contain some

information that is not contained in the net-buy volume. For example, Jones, Kaul, and Lipson (1993)

h th t t f NASDAQ t k ld h ith t t di ti th t k t


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purchases (sales) in order to encourage transactions that will equilibrate their inventory positions (Ho and

Stoll (1983)). When market makers raise the quotes, they induce more sell orders than buy orders

(negative net-buy volume). When market makers lower the quotes instead, they induce more buy orders

than sell orders (positive net-buy volume). Thus, the net buy-volume should be negatively related to the

lagged returns in its own market.

Lagged stock returns can also affect net-buy volume in the option market if investors use options

to dynamically hedge their long positions in the stock market. First, investors will either sell call options

or buy put options to reduce the risk exposure of their long stock positions. If the stock price increases,

the call delta increases and the put delta decreases. In order to remain hedged, investors must reduce their

short call position (buy call) or increase their long put position (buy put). Therefore, lagged stock returns

can be positively related to subsequent call net-buy volume and put net-buy volume.

On the other hand, lagged option returns can also affect stock net-buy volume if option dealers

use the underlying stocks to dynamically hedge the risk in their option positions. According to Vijh

(1990), option investors are more likely to be buyers rather than sellers, and therefore option dealers are

lik l b i f h ll d i If ll ( ) i i h ll ( ) d l


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a pooling equilibrium where informed traders may submit trades in both stock and option markets

(Easley, OHara and Srinivas (1988)), the net-buy volume in the two markets could be positively

correlated. If, for example, informed traders submit trades in the stock market prior to the option market,

stock net-buy volume could have predictive ability for call and put net-buy volume. It is, however,

unlikely that informed traders submit trades in the two markets sequentially, as they would be afraid that

the information could be leaked out from one market to another.

Net-buy volume in the two markets can also be related due to hedging behavior of option dealers.

As a writer of the call option, the option dealer may hedge his/her position by buying the underlying

stock. The more positive call net-buy volume is, the more stock that the option dealer may want to buy,

and therefore the more positive stock net-buy volume. Similarly, as a writer of the put option, the option

dealer may hedge his/her position by selling the underlying stock. The more positive put net-buy volume

is, the more stock that the option dealer may want to sell, and therefore the more negative stock net-buy

volume. Note that the hedging by option dealers in this case is for their new option positions. It is

different from the dynamic hedging in response to delta changes discussed in Section II.B.3, which is for

h d l di i i i


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A.1. Effects of Lagged Net-Buy Volume on Returns

First, we find that stock returns are not affected by lagged call and put net-buy volume, but are

affected by lagged stock net-buy volume. The coefficient for the first lagged stock net-buy volume on

stock returns is 0.102 and is highly significant (with a t-statistic of 12.05). Thus, this evidence suggests

that only stock trades, not option trades, convey new information to the stock market.

Second, option returns are affected more by lagged stock net-buy volume than by lagged option

net-buy volume. In the equation for explaining call returns, the coefficient for stock net-buy volume of

the first lag is 0.052 (with a t-statistic of 6.13), while the coefficient for call net-buy volume of the first

lag is only 0.029 (with a t-statistic of 3.94) and the coefficients for put net-buy volume are insignificant.11

In the equation for explaining put returns, only the coefficient for stock net-buy volume of the first lag is

significant, while the coefficients for call and put net-buy volume are not. These findings suggest that

informed traders are more likely to trade in the stock market rather than in the option market, and stock

trades play a much more important role than option trades in conveying new information to the option

k


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have predictive ability for subsequent quote returns in the other market. This suggests that quote returns

contain some useful information that cannot be inferred from the net-buy volume. Consistent with

Stephan and Whaley (1990), stock returns lead option returns more than they lag. For example, while

only the first lag of call and put returns can explain subsequent stock returns, all three lags of stock

returns are significant in explaining subsequent call and put returns.

A.3. Effects of Lagged Returns on Net-Buy Volume

First, we find that the coefficients measuring the effect of first-lagged returns on own net-buy

volume in the option market are negative (-0.089 for calls and -0.087 for puts) and significant. These

results are again consistent with the prediction of the inventory model. After market makers revise the

quotes upward (downward) for inventory control, option traders are induced to sell (buy) than to buy

(sell), and therefore net-buy volume is negatively related to lagged returns in the option market. In

contrast, such inventory control effect is smaller in the stock market. The coefficient that measures the

effect of the first-lagged stock returns on own net-buy volume is -0.032, and is only marginally

i ifi 12


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however, should not be too surprising in view of previous papers (e.g., Vijh (1990)) that suggest options

are used for speculation rather than hedging.13

On the other hand, we find that lagged option returns have significant impacts on stock net-buy

volume. In the equation for explaining stock net-buy volume, the coefficient for call returns of the first

lag is 0.049 (with a t-statistic of 4.73) while the coefficient for put returns of the first lag is -0.033 (with a

t-statistic of -3.33). It is consistent with the hypothesis that option dealers dynamically hedge their

outstanding short option positions in the stock market. When the price of the call increases (the delta

usually also increases), the option dealer, who is a writer of the call, has to buy more stocks to

dynamically hedge his/her outstanding short position.14 Similarly, when the price of the put increases

(the delta usually increases also), the option dealer, a writer of the put, has to sell more stocks for

hedging.

A.4. Relationships among Net-Buy Volume

The net-buy volume in the stocks, calls, and puts are all positively autocorrelated, suggesting that

h i i l d d i h i l f b d ll i h k Th h b l


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A.5 Summary

We find that net-buy volume in the stock market has strong predictive ability for future stock and

option returns. On the other hand, net-buy volume in the call or put market has little impact on its own

returns as well as stock returns. Therefore, our results strongly suggest that stock net-buy volume is

informative and option net-buy volume is not, confirming that informed investors submit trades primarily

in the stock market rather than in the option market. Furthermore, we find that stock returns lead option

returns more than they lag even after controlling for net-buy volume. This suggests that quote returns

contain some useful information beyond those contained in net-buy volume, and that stock returns

incorporate such information faster than option returns. All in all, the informational linkage between the

stock market and the options market is overwhelmingly from the former to the latter.

Our results also show some evidence for the non-informational linkage between the two markets.

Stock net-buy volume is positively (negatively) related to lagged call (put) returns, suggesting that option

dealers dynamically hedge their outstanding short option positions when the deltas of options fluctuate.

H k b l i l d l d ll b l i h i


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B. Analysis based on 2.5-minute intervals

Oour analyses so far are based on 5-minute intervals. Since our regression models do not allow

for contemporaneous explanatory variables, we ignore any contemporaneous relationships among the

variables. Recall our earlier cross-autocorrelation results (Table V) show that call (put) net-buy volume is

negatively (positively) correlated with contemporaneous stock returns. Such observation is contrary to

our intuition, and deserves further analyses.

To understand the nature of this puzzling relationship, we redo our analyses using variables

constructed for 2.5-minute intervals. Note that a contemporaneous correlation between two variables

measured for 5-minute intervals can become a lead-lag correlation when 2.5-minute intervals are used.

Thus, we can learn more about causality between the two variables with finer intervals.

We first examine the cross-autocorrelations among standardized 2.5-minute returns and net-buy

volume for the stocks, calls, and puts. Table VII presents the results. Again, we find no evidence that

option trades affect subsequent stock returns. Also, although call (put) net-buy volume remains

i l ( i i l ) l d i h l d k ll d b l l


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lagged call and put net-buy volume on stock, call, and put returns are similar to those in Table VI, being

insignificant in most cases.

Tables VII and VIII show no evidence that option net-buy volume conveys new information to

the stock market at the contemporaneous level. In contrast, we find stronger evidence that stock trades,

not option trades, convey new information to the stock market and that stock trades play a much more

important role than option trades in conveying new information to the option market. Therefore, we

confirm that stock trades are information-related while option trades are not.

C. Robustness Tests

Overall, our evidence indicates that there are informational and non-informational linkages

between the stock and option markets. Now, we discuss results from a variety of robustness tests.

C.1. Analysis with Positive-News and Negative-News Option Volume

Previous studies such as Easley, OHara, and Srinivas (1998) use positive-news option volume

(b i ll lli ) d i i l ( lli ll b i ) i f


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are insignificant. Thus, we confirm that option trades have no predictive power for future stock returns

even if we use another measure of informed option trading.16

C.2. Analysis Dropping Call and Put Returns

Since lagged option returns can explain stock returns as in Table VI, one may argue that the

predictive power of option trades for future stock price changes could be subsumed by the predictive

power of option returns. In other words, the reason for our previous finding that option trades have no

information content for the stock market is simply because all information has already been incorporated

into option returns. We do not think this conjecture is reasonable because we show earlier (Table V) that

option net-buy volume is not positively correlated with the contemporaneous returns in its own market.

To double check this possibility, however, we re-specify our regression models by dropping call returns

(CR)and put returns (PR)from the explanatory variables in the equation for explaining stock returns

(SR). The results, which are not reported here, show that the coefficients for lagged call net-buy volume

and put net-buy volume remain insignificant in explaining stock returns, while the coefficient for the first-

l d k b l i hi hl i ifi h fi h i d h di i


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we repeat our regression (1) with the call and put net-buy volume calculated from all call and put

contracts traded on the sample option days. To generate the series for call and put net-buy volume, we

aggregate the net-buy volume across all calls (puts) for a stock.17 The call and put net-buy volume series

are then standardized by subtracting the mean and dividing by the standard deviation for each option day.

Note that we still calculate the call and put returns based on the quotes of the most active call and put.

The results, not reported here, are virtually the same as Table VI.

C.4. Analysis with Different Screening Criteria for the Sample

We select the most actively-traded stocks and then match them with the most active option

contracts. One might argue that there is a selection bias because we select the most active stocks before

we select the options: the stocks included in our sample are thus more likely to be information-related

than the matching options. We think the bias is insignificant. It should be noted that the trading activities

(in terms of total trading volume) of stocks and options are highly correlated. In fact, when we select the

active option contracts first (based on daily total option volume) and then match them with the stocks, the


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IV. Conclusion

Although numerous studies have investigated the informational linkage between the stock market

and the option market, there is no conclusive evidence as to which market plays a greater role in

discovering the information. Furthermore, there is little evidence in the literature on reasons other than

the information transmission for the linkage between the two markets. In this paper we provide a

comprehensive analysis of the interdependence of price movements and net-buy volume (buyer-initiated

trading volume minus seller-initiated trading volume) for actively traded NYSE stocks and their CBOE-

traded options. We improve the understanding of linkage between the stock and option markets in two

important aspects. First, we provide comprehensive evidence on the price discovery role of the two

markets by investigating the distinct impacts of trades in one market on price movements in both markets.

Second, we examine whether the interdependence of price movements and net-buy volume in the two

markets is consistent with the hedging activities of investors and option dealers.

We find that net-buy volume in the stock market has strong predictive ability for future stock and


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Our results also provide some evidence for the non-informational linkage between the two

markets. Stock net-buy volume is positively (negatively) related to lagged call (put) returns, suggesting

that option dealers dynamically hedge their outstanding short option positions by trading in the stock

market when the deltas of options fluctuate. However, stock net-buy volume is not significantly related to

lagged call or put net-buy volume, suggesting that option dealers do not hedge their new short option

positions.

Our evidence also shows that call or put net-buy volume is not related to lagged stock net-buy

volume. Furthermore, the call or put net-buy volume is not related to lagged stock returns. These suggest

that option traders do not use options for hedging or at least do not readjust their hedged position

frequently. On balance, it does not appear that option traders trade on the basis of information. Perhaps,

as Vijh (1990) points out, trading in the option market reflects more of difference of opinion among

investors or speculation, rather than private information.


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References

Admati, A., and P. Pfleiderer, 1988, A theory of interday patterns: Volume and price variability, Review

of Financial Studies 1, 3-40.

Anthony, J., 1988, The interrelation of stock and options market trading-volume data,Journal of

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51


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Table I

Daily Trading Volume of Stocks, Calls, and PutsAverage daily trading volume of 14 actively traded NYSE stocks and their CBOE-traded options during sample days in the first quarter of 1995. For each stock,a trading day will be included in the sample when the stock, the most active call and put, have more than 20 trades for the day, respectively. The number of daysincluded in the final sample is reported. The daily trading volume of the stock (call and put) is in terms of shares (contracts). Buy (sell) volume is the buyer-initiated (seller-initiated) volume, and is expressed in terms of the percentage of the total trading volume. The trading volume of the most active call (put) isexpressed in terms of the percentage of the total trading volume of all the calls (puts).

Average Daily Stock Volume Average Daily Call Volume Average Daily Put Volume

Total Buy Sell All Most Buy Sell All Most Buy SellNo. of Volume Volume Volume Calls Active Call Volume Volume Puts Active Put Volume Volume

Firm Name days (in shares) (in %) (in %) (in contracts) (in %) (in %) (in %) (in contracts) (in %) (in %) (in %)

Best Buy 9 924,556 42.3 41.3 1,500 33.0 41.6 42.4 2,526 45.8 43.3 47.4Chrysler 24 2,835,046 33.3 41.7 5,471 35.0 45.9 45.8 2,063 48.2 40.7 43.1Citicorp 12 2,700,717 31.2 41.3 1,911 45.9 46.7 44.6 2,250 47.4 43.7 49.4Callaway Golf 5 1,437,380 41.3 42.7 2,139 31.9 42.1 46.2 1,777 38.9 50.8 43.9EMC Corp 20 2,770,615 40.2 40.0 2,143 34.1 48.0 40.6 958 48.1 34.5 56.3Ford Motor 9 3,472,967 38.5 43.2 2,130 36.3 48.8 30.8 659 56.8 38.2 52.0General Electric 7 1,880,529 46.1 33.9 1,777 37.8 48.2 43.6 818 48.4 41.8 38.7General Motor 32 2,458,747 38.1 34.1 3,890 36.8 42.7 43.4 1,589 40.7 37.6 42.8Hewlett Packard 14 1,008,050 46.1 32.0 1,752 34.9 41.6 53.1 1,162 42.5 43.7 44.4IBM 56 1,992,134 47.5 35.1 9,047 32.2 47.7 45.3 4,391 34.1 47.2 41.4Merck 11 2,257,382 45.1 36.3 3,311 29.1 39.9 47.3 1,226 58.9 39.0 32.0Micron Technology 11 2,716,045 42.8 36.4 1,746 42.1 48.7 41.0 2,054 39.5 44.7 47.0Sears Roebuck 7 2,951,443 48.7 31.9 5,284 73.2 44.1 50.5 5,166 55.4 43.1 49.3Texas Instruments 14 1,255,257 40.9 30.4 2,720 42.9 45.3 48.7 1,304 47.7 46.9 46.6


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Table II

Autocorrelations and Cross-Autocorrelations

of Standardized 5-Minute Volume of Stocks, Calls, and Puts

Volume series are standardized by subtracting the mean and dividing by the standard deviation of the day.

Reported below are Pearson correlation coefficients () with * indicating significance at the 0.1 percentlevel.

Panel A: Autocorrelation

Stock Volume Call Volume Put Volume

Lag (SV) (CV) (PV)

1 0.197 * 0.131 * 0.115 *

2 0.143 * 0.063 * 0.048 *

3 0.113 * 0.030 * 0.0234 0.097 * 0.024 0.0225 0.088 * 0.006 0.006

6 0.068 * -0.001 0.008

Panel B: Cross-autocorrelation

Lag k (SVt, CVt-k) (SVt, PVt-k) (PVt, CVt-k)

-6 0.047 * 0.040 * 0.017


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Table III


of Standardized 5-Minute Net-Buy Volume of Stocks, Calls, and Puts

Net-buy volume equals buyer-initiated volume minus seller-initiated volume. Net-buy volume series arestandardized by subtracting the mean and dividing by the standard deviation of the day. Reported below

are Pearson correlation coefficients () with * indicating significance at the 0.1 percent level.


Stock Net-Buy Volume Call Net-Buy Volume Put Net-Buy Volume

Lag (SNB) (CNB) (PNB)

1 0.066 * 0.055 * 0.073 *

2 0.005 -0.017 0.001

3 0.006 -0.015 -0.0084 -0.019 -0.012 0.0025 -0.005 -0.011 -0.022

6 -0.003 -0.023 -0.022


Lag k (SNBt, CNBt-k) (SNBt, PNBt-k) (PNBt, CNBt-k)

-6 -0.002 0.009 0.003


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Table IV


of Standardized 5-Minute Returns of Stocks, Calls, and Puts

Returns are computed with the midpoint of the prevailing bid and ask quotes at the end of each 5-minuteinterval. Return series are standardized by subtracting the mean and dividing by the standard deviation of

the day. Reported below are Pearson correlation coefficients () with * indicating significance at the 0.1percent level.


Stock Returns Call Returns Put ReturnsLag (SR) (CR) (PR)

1 -0.026 * -0.031 * -0.047 *

2 -0.031 * -0.029 * -0.038 *3 -0.012 -0.023 -0.047 *4 -0.021 -0.014 -0.003

5 -0.003 -0.007 -0.0086 -0.008 -0.002 -0.017


Lag k (SRt, CRt-k) (SRt, PRt-k) (PRt, CRt-k)


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Table V

Cross-Autocorrelations Between Standardized 5-Minute Returns of Stocks, Calls,

and Puts and Standardized 5-Minute Net-Buy Volume of Stocks, Calls and Puts

Returns are computed with the midpoint of the prevailing bid and ask quotes at the end of each 5-minute interval. Return series are standardized by

subtracting the mean and dividing by the standard deviation of the day. Stock (call and put) returns are denoted SR(CR andPR). Net-buy volume equalsbuyer-initiated volume minus seller-initiated volume. Net-buy volume series are similarly standardized. Stock (call and put) net-buy volume is denoted

SNB(CNB andPNB). Reported below are Pearson correlation coefficients () with * indicating significance at the 0.1 percent level.

Stock Returns (SR) vs. Call Returns (CR) vs. Put Returns (PR) vs.

Stock Net-Buy Call Net-Buy Put Net-Buy Stock Net-Buy Call Net-Buy Put Net-Buy Stock Net-Buy Call Net-Buy Put Net-Buy

(SNB) (CNB) (PNB) (SNB) (CNB) (PNB) (SNB) (CNB) (PNB)

Lag k (SRt, SNBt-k) (SRt, CNBt-k) (SRt, PNBt-k) (CRt, SNBt-k) (CRt, CNBt-k) (CRt, PNBt-k) (PRt, SNBt-k) (PRt, CNBt-k) (PRt, PNBt-k)

-6 0.012 0.014 0.000 0.008 0.014 0.002 -0.002 -0.010 0.004

-5 0.002 0.010 0.006 0.003 -0.001 0.010 0.002 -0.004 -0.017-4 0.002 0.021 0.002 0.003 0.017 -0.003 0.000 -0.011 -0.002-3 0.018 0.026 * -0.014 0.013 0.023 -0.014 -0.023 -0.017 0.021

-2 0.023 0.020 0.002 0.017 0.013 0.007 -0.012 -0.029 * 0.010

-1 0.038 * -0.033 * 0.043 * 0.064 * -0.059 * 0.043 * -0.058 * 0.028 * -0.086 *

0 0.441 * -0.032 * 0.037 * 0.322 * -0.039 * 0.038 * -0.308 * 0.044 * -0.058 *1 0.075 * -0.006 0.008 0.093 * 0.033 * 0.007 -0.084 * 0.004 0.019

2 0.003 0.001 -0.014 0.023 0.002 -0.003 -0.009 -0.009 0.026 *

3 0.000 0.006 -0.002 0.003 0.000 0.001 -0.001 0.005 0.0144 -0.011 0.009 -0.003 0.004 0.002 -0.006 -0.001 0.000 0.003

5 -0.004 -0.011 0.002 -0.007 0.004 0.005 0.004 0.004 0.004

6 0.002 0.012 0.001 0.003 0.008 -0.003 0.004 -0.007 -0.002


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34

Table VI

Regression Analysis of the Relationships Among Standardized 5-Minute Returns and

Standardized 5-Minute Net-Buy Volume of Stocks, Calls and Puts

A system of six regression equations are estimated: .v......vcv tptp1t1t ++++++++== where vt= [SRt,CRt,PRt,SNBt,CNBt,PNBt], SRt,CRt,PRt,

are standardized returns for the stocks, calls, and puts for the 5-minute interval t,and SNBt,CNB

t, andPNB

tare standardized net-buy volume for the stocks,

calls, and puts for the 5-minute interval t. Returns are computed with the midpoint of the bid and ask quotes at the end of each 5-minute interval. Net-buy volume equals buyer-initiated volume minus seller-initiated volume. All return and volume series are standardized by subtracting the mean and

dividing by the standard deviation of the day. We impose six lags for the explanatory variables, and report the regression coefficients for the first three

lags (the intercepts and lags 4 through 6 are not shown to save space) and t-statistics (in italics) with * indicating significance at the 0.1 percent level.

Explanatory Variables

Lagged Lagged Lagged Lagged Lagged Lagged

Stock returns Call returns Put returns Stock net-buy volume Call net-buy volume Put net-buy volume

Dependent

Variable Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3

Stock -0.162 -0.082 -0.044 0.077 0.018 0.017 -0.058 -0.008 -0.015 0.102 0.015 0.015 -0.003 0.001 0.002 0.002 -0.007 -0.003

returns -15.40* -7.32* -3.87* 7.95* 1.84 1.73 -6.29* -0.85 -1.56 12.05* 1.76 1.83 -0.39 0.13 0.22 0.33 -0.93 -0.42

Call 0.227 0.157 0.122 -0.218 -0.153 -0.106 -0.047 0.006 0.004 0.052 0.002 -0.004 0.029 0.010 0.005 -0.003 -0.003 0.002

returns 21.64* 14.12* 10.76* 22.64* 15.34* 10.58* -5.09* 0.64 0.45 6.13* 0.21 -0.43 3.94* 1.32 0.62 -0.37 -0.38 0.30

Put -0.190 -0.136 -0.113 -0.059 -0.007 -0.005 -0.214 -0.151 -0.130 -0.047 0.007 0.007 0.004 -0.008 0.006 0.009 0.017 0.016

returns -18.15* 12.16* 10.00* -6.11* -0.67 -0.54 23.13* 15.87* 13.69* -5.61* 0.85 0.84 0.51 -1.15 0.77 1.27 2.30 2.16

Stock -0.032 0.017 0.020 0.049 0.010 0.008 -0.033 0.000 -0.009 0.054 -0.017 -0.006 -0.001 -0.002 -0.009 0.011 -0.006 0.001

net-buy volume -2.89 1.46 1.61 4.73* 0.90 0.76 -3.33* -0.05 -0.93 6.03* -1.91 -0.71 -0.07 -0.23 -1.18 1.35 -0.81 0.17

Call -0.006 0.039 0.028 -0.089 -0.024 -0.016 -0.006 -0.019 -0.007 0.028 0.011 0.018 0.049 -0.013 -0.011 0.002 0.006 0.006

net-buy volume -0.56 3.27 2.28 -8.52* -2.27 -1.47 -0.57 -1.90 -0.72 3.08 1.18 2.01 6.17* -1.68 -1.41 0.25 0.78 0.79

Put -0.012 -0.005 0.001 0.010 0.005 -0.002 -0.087 0.009 0.019 0.008 -0.006 0.008 0.002 0.010 -0.004 0.069 0.003 -0.006

net-buy volume -1.08 -0.43 0.08 0.93 0.45 -0.21 -8.73* 0.91 1.85 0.88 -0.65 0.91 0.28 1.30 -0.56 8.77* 0.32 -0.73


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35

Table VII

Cross-Autocorrelations Between Standardized 2.5-Minute Returns of Stocks, Calls,

and Puts and Standardized 2.5-Minute Net-Buy Volume of Stocks, Calls and Puts

Returns are computed with the midpoint of the prevailing bid and ask quotes at the end of each 2.5-minute interval. Return series are standardized by

subtracting the mean and dividing by the standard deviation of the day. Stock (call and put) returns are denoted SR(CR andPR). Net-buy volume equalsbuyer-initiated volume minus seller-initiated volume. Net-buy volume series are similarly standardized. Stock (call and put) net-buy volume is denoted

SNB(CNB andPNB). Reported below are Pearson correlation coefficients () with * indicating significance at the 0.1 percent level.

Stock Returns (SR) vs. Call Returns (CR) vs. Put Returns (PR) vs.

Stock Net-Buy Call Net-Buy Put Net-Buy Stock Net-Buy Call Net-Buy Put Net-Buy Stock Net-Buy Call Net-Buy Put Net-Buy

(SNB) (CNB) (PNB) (SNB) (CNB) (PNB) (SNB) (CNB) (PNB)

Lag k (SRt, SNBt-k) (SRt, CNBt-k) (SRt, PNBt-k) (CRt, SNBt-k) (CRt, CNBt-k) (CRt, PNBt-k) (PRt, SNBt-k) (PRt, CNBt-k) (PRt, PNBt-k)

-6 0.012 0.013 -0.006 0.011 0.012 -0.011 -0.016 -0.016 0.004

-5 0.001 0.018 * -0.005 -0.001 0.019 * -0.007 -0.011 -0.007 0.015-4 0.018 * 0.017 -0.001 0.014 0.010 0.004 -0.002 -0.021 * 0.001-3 0.011 0.004 0.007 0.014 -0.010 0.017 -0.007 -0.004 -0.011

-2 0.028 * -0.018 * 0.025 * 0.032 * -0.020 * 0.025 * -0.030 * 0.011 -0.035 *

-1 0.027 * -0.039 * 0.039 * 0.058 * -0.075 * 0.033 * -0.050 * 0.029 * -0.093 *

0 0.369 * -0.014 0.017 0.251 * -0.010 0.016 -0.232 * 0.032 * -0.021 *1 0.137 * 0.000 0.007 0.105 * 0.026 * 0.010 -0.106 * 0.000 0.016

2 0.013 -0.005 0.005 0.030 * 0.012 0.004 -0.027 * 0.003 0.010

3 0.006 0.001 -0.006 0.014 0.000 -0.003 -0.012 -0.004 0.0064 -0.003 -0.003 0.000 0.015 0.006 0.003 -0.005 -0.002 0.010

5 -0.007 0.001 -0.014 -0.007 -0.004 -0.003 -0.007 0.000 0.010

6 0.000 0.005 0.005 0.004 0.005 0.001 0.005 -0.008 0.013


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36

Table VIII

Regression Analysis of the Relationships Among Standardized 2.5-Minute Returns and

Standardized 5-Minute Net-Buy Volume of Stocks, Calls and Puts

A system of six regression equations are estimated: .v......vcv tptp1t1t ++++++++== where vt= [SRt,CRt,PRt,SNBt,CNBt,PNBt], SRt,CRt,PRt,

are standardized returns for the stocks, calls, and puts for the 2.5-minute interval t,and SNBt,CNB

t, andPNB

tare standardized net-buy volume for the

stocks, call, and puts for the 2.5-minute interval t. Returns are computed with the midpoint of the bid and ask quotes at the end of each 2.5-minuteinterval. Net-buy volume equals buyer-initiated volume minus seller-initiated volume. All return and volume series are standardized by subtracting the

mean and dividing by the standard deviation of the day. We impose six lags for the explanatory variables, and report the regression coefficients for the

first three lags (the intercepts and lags 4 through 6 are not shown to save space) and t-statistics (in italics) with * indicating significance at the 0.1 percentlevel.

Explanatory Variables

Lagged Lagged Lagged Lagged Lagged Lagged

Stock returns Call returns Put returns Stock net-buy volume Call net-buy volume Put net-buy volume

Dependent

Variable Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3 Lag 1 Lag 2 Lag 3

Stock -0.141 -0.089 -0.056 0.093 0.036 0.026 -0.047 -0.031 -0.005 0.141 0.027 0.013 0.000 -0.005 -0.001 0.003 0.004 -0.003

returns -21.10* 12.70* -7.86* 14.75* 5.60* 3.91* -7.66* -4.95* -0.84 24.49* 4.64* 2.15 -0.07 -0.94 -0.24 0.54 0.73 -0.65

Call 0.193 0.136 0.103 -0.184 -0.131 -0.088 -0.039 -0.018 -0.001 0.069 -0.005 -0.004 0.022 0.015 0.002 0.006 -0.002 -0.003

returns 29.15* 19.66* 14.62* 29.34* 20.28* 13.44* -6.42* -2.84 -0.12 12.10* -0.86 -0.69 4.15* 2.83 0.38 1.22 -0.47 -0.56

Put -0.162 -0.102 -0.082 -0.074 -0.024 -0.024 -0.175 -0.112 -0.095 -0.063 0.004 0.004 0.000 0.004 -0.002 0.009 0.008 0.004

returns -24.53* 14.73* 11.60* 11.92* -3.79* -3.71* 28.77* 17.94* 15.15* 11.09* 0.68 0.76 -0.07 0.78 -0.33 1.67 1.60 0.80

Stock -0.034 -0.013 -0.008 0.047 0.025 0.016 -0.032 -0.021 0.000 0.057 0.017 0.007 0.006 0.002 -0.012 0.003 0.006 0.005

net-buy volume -4.78* -1.72 -1.13 6.99* 3.60* 2.34 -4.84* -3.08 -0.01 9.24* 2.72 1.20 1.07 0.36 -2.13 0.52 1.08 0.96

Call -0.009 0.002 0.031 -0.092 -0.042 -0.043 -0.004 -0.006 -0.007 0.010 0.023 0.004 0.080 0.008 0.004 -0.002 -0.001 0.013

net-buy volume -1.21 0.22 4.03* 13.62* -6.00* -6.19* -0.65 -0.87 -0.97 1.59 3.63* 0.64 14.29* 1.39 0.63 -0.44 -0.14 2.35

Put 0.004 -0.018 -0.023 0.002 0.007 0.009 -0.099 -0.046 -0.018 0.003 -0.008 0.006 -0.002 -0.001 -0.001 0.080 0.011 0.017

net-buy volume 0.60 -2.38 -3.01 0.34 0.96 1.28 14.99* -6.88* -2.64 0.42 -1.28 0.95 -0.43 -0.24 -0.24 14.31* 1.89 3.03


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37

Documents

The Informational Role of Stock and Option Volume