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The Effects of Investor Sentiment on Speculative Trading and Prices of Stock

and Index Options

Michael Lemmon

Sophie Xiaoyan Ni*

August 2011

JEL Classification Code: G1

Key Words: Options, Volatility Smile, Sentiment, Speculation, Hedging

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ABSTRACT

We find that the demand for stock option positions that increase exposure to the underlying is

positively related to measures of investor sentiment and past market returns, while the demand

for index options is invariant to these factors. These differences in trading patterns are reflected

in differences in the composition of traders in the different types of options---Options on stocks

are actively traded by individual investors, while trades in index options are more often

motivated by hedging demands of sophisticated investors. Consistent with a demand based view

of option pricing, we find that sentiment is related to time-series variation in the slope of the

implied volatility smile of stock options, but has little impact on the prices of index options. The

pricing impact is more pronounced in options with a higher concentration of unsophisticated

investors and in options with higher hedging costs. Our results provide new evidence factors not

related to fundamentals affect price of securities actively traded by noise traders.

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The traditional view on asset pricing posits that the price of a security closely reflects the

present value of its future cash flows. According to this efficient market hypothesis (EMH), price

movements are driven by changes in the asset fundamental values, with irrational sentiment

playing no role because the actions of arbitrageurs readily offset such shocks. An alternative

theory argues that the dynamic interplay between sentimental noise traders and rational

arbitrageurs establishes prices (Delong, Shleifer, Summers, and Waldman(1990) ). According to

this behavioral hypothesis (BH), in addition to innovations in fundamentals, factors such as

systematic sentiment of noise traders also induce movement of asset prices if assets are held

predominantly by noise trader, and arbitrage forces will not fully correct the prices.

A perfect setting to test the two alternative theories would be the existence of two

identical securities in a market with friction, of which the only difference is that one security is

traded by rational investors, and the other is held by noise traders. EMH would predict that the

two securities will have same price movements. While the behavioral view would foretell that

the prices of two assets will behave differently; the correlated sentiments of noise traders will

affect the security held predominantly by noise traders, but not the security traded mainly by

rational investors. Its difficult, however, to find this ideal setting in the stock market except for

the close end fund; the securities that traded mainly by noise traders are usually different from

securities that traded by rational investors. Because of the joint hypothesis problem (Fama

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Our main purpose is to test the two alternative views on asset pricing using stock and

index options as experimental objects. Stock options in aggregate and index options are close to

identical in the sense that their underlying securities are driven by the same fundamentals, and

that their prices are affected by jump and volatility risks in similar ways. If we assume individual

investors are noise traders, then individual investors trading stock options much more actively

than index options gives us an ideal setting to test the two alternative asset pricing theories. In

addition, high transaction costs, margin requirements, and difficulties in short selling are more

likely to impede arbitrage activities in option markets (Figlewski (1989), Pontiff (1996)).

In testing the two alternative asset pricing theories, we focus on whether stock and index

options respond to sentiment and past market return differently. In addition to barometers of

behavioral biases, sentiment and past return can also be interpreted as signals of shifts in risk

preference or changes of fundamentals (Lemmon and Portniaguina (2006)). Unlike other studies

drawing conclusion based on a definite interpretation of sentiment, our tests on the simultaneous

responses of stock and index options to the sentiment do not require any assumption about

economic meaning of sentiment. EMH predicts that stock options in aggregate and index options

will respond to the sentiment in a similar way regardless what sentiment stands for. While BH

predicts if the sentiment is associated with correlated noise trader biases, we will observe

different reactions from stock and index options, for stock options are traded actively by

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sentiment is an indicator of behavioral biases. On the other hand, no valid conclusion can be

drawn if same responses (including no response) of stock and index options to sentiments are

detected.

We begin our study by showing that prices of stock and index options are driven by same

risk factors. Adopting a model with stochastic volatility with return jumps, we simulate that the

implied volatility functions (IVFs) of stock and index options respond in similar ways to the

variations in jump and volatility risks.

We then pursue two strands of empirical investigation to examine the link between

sentiment, past market return and option market. In order for behavioral bias to impact asset

prices, it must be associated with the trading of that asset. Our first empirical investigation

examines how trading activities of stock and index options are influenced by sentiment and

previous month market returns. Our measure of sentiment is the index of consumer sentiment

(CS) from University of Michigan adjusted for macroeconomic factors and used in Lemmon and

Portnaiguina (2006)1. We believe consumer sentiment is likely to be a proxy for behavioral bias

of noise traders because it is based on a survey on individual households. Our use of stock return

is motivated by the fact that changes in stock valuations are also likely to be associated with the

potential for overreaction by unsophisticated traders.

In our data, trading by unsophisticated investors (defined as discount brokerage

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types of options we construct a measure we call the positive-exposure demand for individual

stock options (PDS), and positive-exposure demand for SP500 index options (PDI). The

variables PDS and PDI measure the monthly non-market maker net option demands with

positive exposure to the underlying stock and the index, respectively. We focus onPD rather

than net option demand because sentiment is more likely to drive investors to speculate on the

direction of underlying stock price movements.To the extent that stock option trading is related

to aggregate changes in investor sentiment we expect thatPDS will be positively related to

consumer sentiment and past stock returns, whilePDI, which is primarily dominated by rational

trades, will be unrelated to sentiment or past stock returns. The evidence is consistent with these

predictions. Over the period from 1990 through 2008, time-series variation inPDSis increasing

in consumer sentiment and lagged market return, whilePDI is unrelated to the sentiment or

market return. We also find that changes in PDS are most strongly related to changes in

sentiment and lagged returns for trades initiated by customers of discount brokers and in small

option trades.

Our second empirical investigation examines the pricing impact of sentiment and lagged

market return on stock and index options. The dependent variable is the slope of the IVF

computed as the difference in implied volatility between OTM calls and OTM puts. If consumer

sentiment and past returns are proxies for changes in fundamentals, the slopes of IVF of stock

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return than prices of index options. In multivariate regressions that control for the lagged

dependent variable, contemporaneous market returns, volatility, and a measure of institutional

investor sentiment, we find that both the consumer sentiment and lagged market return are

positively related to the slope of the implied volatility function for options on individual stocks.

In contrast, we find no evidence that past market return or consumer sentiment is related to the

slope of the implied volatility function for S&P500 index options. Similar to Han (2008), we do

find that the slope of the IVF for index options is related to a measure of institutional investor

sentiment, but that institutional investor sentiment is not significantly related to slope of

volatility smile for options on individual stocks.

Also consistent with the view that sentiment significantly affects option prices we find

evidence of positive abnormal returns from contrarian trading strategies that trade calls and puts

on individual stocks following large changes in sentiment and market returns. In some cases

these abnormal returns exceed option transactions costs.

Finally, we examine whether the effects of sentiment on stock option trading and prices

vary cross-sectionally. As predicted by models of limited arbitrage, we find that options with a

higher proportion of trading from less sophisticated investors, and those with higher underlying

volatility and volatility of volatility exhibit trading and prices that are more sensitive to

sentiment.

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systematic factors other than BH influence stock and index option prices differently, for

example, stock options are less liquid than index options. However, for our findings to be driven

by liquidity, it would need to be the case that liquidity is associated with trading and price of

stock options only. It is not easy to see why aggregate liquidity does not impact index options,

given Cherks, Sagi and Stanton (2009) and Bao, Pan and Wang(2010) documenting that liquidity

commoving more closely with VIX index than consumer sentiment. Indeed, we find that

liquidity is not an alternative explanation for the role of consumer sentiment.

Our paper is related to the literature examining the relation between investor sentiment

and security prices in the stock market. For example, Lee, Shleifer and Thaler (1991) and Pontiff

(1996) propose that fluctuations in the discounts of closed-end fund (CEF) are driven by changes

in individual investor sentiment, while Cherkes, Sagi and Stanton (2009) show that the CEF

discounts emerge from the tradeoff between the funds liquidity benefits and management fees.

Baker and Wurgler (2006) and Stambaugh, Yu and Yuan (2011) present evidence that investor

sentiment has significant effects on the cross-section of stock prices. Lemmon and

Portniaguina(2006) show that consumer confidence predicts returns of small stocks. Kumar and

Lee (2006) document that individual investor trades are systematically correlated and can explain

the return co-movements for stocks with high retail investor concentration. In more recent study,

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Our paper is also related to studies examining trading and pricing of equity options.

Bollen and Whaley (2004) document that the excess implied volatility of S&P500 index options

is much higher than that of stock options. They attribute this fact to the hedging demand for

index put options as portfolio insurance against market decline. Grleanu, Pedersen, and

Poteshman (2009) confirm their finding and model that demand imbalances generated by the

trades of end users can affect option prices. Bates (1991, 2000), Heston (1993) Jackwerth and

Rubinstain (1996), Pan (2002), and among others show IVF is driven by stochastic volatility and

jump risks. Amin, Coval and Seyhun (2004) document that SP100 index call (put) prices are

overvalued following large upside (downside) market movements. Bakashi, Kapadia and Madan

(2003) document that the risk neutral skewness in stock option prices is less negative than that

index option prices because of idiosyncratic component in stock returns.

Our paper is also related to the study examining differences in cross sectional trading and

pricing of options on individual stocks. Lakonishok, Lee, Pearson and Poteshman (2007) find

that stocks with high past returns have high option volumes of both purchased call and put, and

during the bubble of the late 1990s, the least sophisticated investors increased their purchase of

calls on growth stocks. However they do not systematic examine how sentiment and lagged

return relate to the aggregate trading and price of stock options, nor do they compare differences

in stock and index option. Poteshman (2006), Yan (2010), and Zhang, Zhao and Xing (2010)

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while our study is based on time series variations in aggregate trading and pricing of all stock

options. Roll, Schwartz and Subrahmanyam (2009) investigate the relative volume in options and

stock markets, and argue that the determinants of option volume are not well understood. Our

study partially answers this question.

Finally, our findings are related to studies that document behavioral biases in options

markets. Stein (1989) documents that longer term implied volatilities of S&P 100 index options

overreact to changes in short-term volatility. Poteshman and Serbin (2003) document option

investors early exercise American options irrationally. Constantinides, Jackwerth and Perrakis

(2009) find no evidence that prices in the S&P500 index options have become more rational over

time. Han (2008) documents a positive relationship between the risk-neutral skewness in

S&P500 index option prices and measures of institutional investor sentiment.

The remainder of the paper is structured as follows. Section 1 shows that risks affect

prices of stock and index option in similar ways. Section 2 presents data and variable

construction. Section 3 presents summary statistics and trading activity of different investors on

stock and index options. Section 4 shows the results and Section 5 concludes.

1. Index and Stock Option PricesIn this section, we show that risks affecting IVF of index option havesame impact on

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, 1

1 , 2

where is interest rate, , is a standard Brownian motion in , is index pricejump process with jump probability , jump volatility and average relative jump size conditional on jump occurs, is the premium for conventional return risks, and is the jumprisk premium. In this model, we set jump size premia time varying to reflect the time seriesvariation in jump risk. Eq.(2) models stochastic volatility with constant long-run mean , mean-reversion rate, instantaneous variance, volatility coefficient , and correlation coefficient ofthe return and the volatility

.

Suppose an individual stock has beta one on index excess returns. Its price has thefollowing data generating eproc ssunder physical probability measureP:

1

, (3) , (4) 1 , (5)

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, average relative jump size 0 and jump size volatility ,. We assume when index jumpoccurs, the stock price appreciates or depreciates by same return as the index price does.

As , and , are uncorrelated and stock market beta is one, Eq.(4)shows the change of stock variance is the sum of changes in index variance () and stockidiosyncratic variance (). Eq. (5) shows the stock idiosyncratic variance also follows a meanreversion stochastic process.

Based on the above setting, the corresponding dynamic of index priceIunder risk neutral

probability measu lreQ is as fo lows:

, 6 1 , (7)

where , is a Brownian motion under Q, and is the time varying volatilitypremium. The jump process has a distribution under Q that is identical to the distribution ofZunderP, except that under Q, the average jump size is .

The corresponding dynamic of stock price

under risk neutral probability measure is as

follows:

1

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We assume systematic risk influences option prices through time varying jump size

premium ( or variance premium (, and use simulation to investigate their impacts onoption implied volatility function (IVF).2 We omit the pricing impacts from changes in physical

jump size, jump probability or physical volatility because these changes have same effects as the

variations in jump size premium or variance premium.

We show in Figure 1 that the jump and volatility risks have same impacts on IVF of

index and stock options. When jump size premium increases,3 the slopes and the levels of IVF

become more negative for both index and stock options. Similarly, when the variance premium

increases,4 the levels of IV increase for both options. These patterns suggest that if a systematic

risk influences option prices, it must affect IVF of stock and index options in similar ways.

Figure 1 also shows that the slope of stock options IVF is flatter and more volatile than

that of index options. This result is consistent with that documented in Bakshi, Kapadia and

Madan (2003), who show idiosyncratic components in stock returns drive risk neutral skewness

of stocks to be less negative and more volatile than that of index.

2. Data and Variables

In this section we describe the option and sentiment data and provide summary statistics

forthemainvariablesusedinouranalyses

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The data used to compute option trading activity is obtained from the CBOE. The data

set contains daily non-market maker volume for all CBOE-listed options from January 1990

through September 2008. The number of stocks having CBOE traded options in each month

increases from 239 in January 1990 to 2,449 in December 2008, reflecting the dramatic growth

in the option market during the sample period.

For each option, the daily trading volume is divided into four types of trades: open-buy,

in which non-market markers buy options to open new long positions, close-buy, in which non-

market makers buy options to close out existing written option positions, open-sell, in which

non-market makers sell options to open new short positions, and close-sell, in which non-market

makers sell options to close out existing long options positions.

The data on option prices are compiled from the Berkeley Option Database and Ivy

OptionMetrics. The time period covered in this study is also from January 1990 to September

2008. We obtain option price data from the Berkeley Option Database for the period from 1990

to 1995. The option price data from 1996 to 2008 are obtained from OptionMetrics. For the first

part of the data period, we follow Bollen and Whaley (2004) and compute daily option implied

volatilities from the midpoint of the last bid-ask price quote before 3:00 PM Central Standard

Time.5 Starting in January 1996 we use the implied volatilities supplied by OptionMetrics.

We use the implied volatility on the last trading day of the month for options that meet

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option bid price is larger than zero and within standard no-arbitrage bounds6, (3) the time to

expiration of the option is within (including) 10 to 60 trading days, and (4) from the options

written on same stock satisfying conditions (1)-(3) we retain those that have more than 2 strike

prices for at least one maturity. For options on same underlying that meet the criteria above we

first choose the maturity with the highest number of strikes; if options of different maturities

have the same number of strike prices, we then choose the maturity with the highest trading

volume to ensure that we include the most actively traded options. The final sample for stock

options consists of 132,668 stock end-of-month days from 4,872 different firms, and the number

of stocks in each month increases from 90 in January 1990 to 1470 in September 2008.

2.2 Option trading and price variables

For each month

in the sample, we use the CBOE volume data to compute a measure

that we call the positive-exposure demand for stock options ( ) and positive-exposuredemand for SP500 index options (). and measure the newly established netoption positions that have p iv erlying and are computed as follows:osit e exposure to the und

_ _, where (10.1)

_ ,,,

,,,

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_ _, where (10.2)_ ,,,

,,,

_ ,,, ,,,

where indexes stocks having traded options in month , is the th trading day in month , indexes the option maturities, and

indexes strike prices.

,,, is the number of call

contracts open purchased by non-market maker investors in month on stock across allmaturities and strike prices, and the remaining terms ,,, , ,,, , and,,, , are computed in an analogous manner.7 We do not use delta adjusted volumebecause (1)sentiment driven investors are more attracted to OTM options due to their high

liquidity and leverage, and (2) OTM index puts are the most heavily traded index options.

The measures ofPDS and PDI are simple measures of the net demand for option

positions that have positive exposure to the underlying stocks and SP500 index, respectively.

ThePDS andPDI are different from the proxies for option demand examined in Bollen and

Whaley (2004) and Grleanu, Pedersen, and Poteshman (2009), where the option demand is

measured as the difference between buy and sell option volume or open interest. PDSandPDI

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have positive exposure to volatility. We usePDSandPDI instead of option demand because

sentiment is more likely to drive investors to speculate on the direction of underlying stock price

movements.

The primary measure we use to examine the relation between sentiment and option prices

is the slope of the implied volatility smile, i.e., the implied volatility difference between OTM

calls and OTM puts.8 For individual stock options, the slope measure is the average slope across

all stocks. For index options, the slope measure is the slope of the implied volatility smile of

SP500 index options. Specifically, the slope measures for stock options (SlopeSt) and index

options (SlopeIt) in month tare given by:

1 _,, _,,

11.1

_,,

_,, ,

11.2whereNt is the number of stocks having traded OTM calls and puts on the last trading day of

month t,

_,,and

_,, are the implied volatilities of OTM calls and

OTM puts, respectively, with maturity Tand underlying stock i. The above slope measures are

similar to the ones used by Han (2008), and are essentially equivalent to the risk neutral

k b dd d i ti i (B k hi K di d M d (2003)) W th l f

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Madan (2003) because most stocks do not have a sufficient number of strike prices to generate

the integral necessary to compute the risk-neutral skewness; the median number of strike prices

for optionable stocks in our sample is only three.

2.3 Sentiment Measures

The main measure of sentiment here is the monthly index of Consumer Sentiment (CS)

collected by University of Michigan. We view CS is likely to be a proxy for systematic

behavioral bias of noise traders because it is based on a survey of households perceptions about

current and future financial conditions. Lemmon and Portniaguina (2006) find that the level of

consumer sentiment predicts returns on small stocks and those with low institutional ownership.

In the main test, we adjust CS after with a set of macroeconomic variables including credit

spread, unemployment rate, and corporation productivity.

In addition to the direct sentiment measures, we also use one month lagged market

returns to capture the idea that changes in stock valuations are likely to be associated with

hedging demand for index put and with the potential for overreaction by unsophisticated

traders.9 Consistent with the latter view, Lakonishok, Shleifer, and Vishny (1994) argue that the

value premium in stock returns arises from investors over-extrapolating past performance.

3. Index and stock option trading

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Table 1 presents summary statistics for the main variables. The level and monthly change

of positive-exposure demand for stock options (PDSand dPDS) are close to zero on average.

The level (PDS) has high autocorrelation, while the change (dPDS) has no significant

autocorrelation. The positive-exposure demand for stock calls (PDS_C) is positive, while the

positive-exposure demand for stock puts (PDS_P) is negative, implying that the average stock

option open buy volume exceeds the open sell volume in both calls and puts. The positive-

exposure demand for SP500 index options (PDI,PDI_CandPDI_P) are all negative, especially

for puts (PDI_P), suggesting put purchases comprise the bulk of index option trading (Bollen

and Whaley (2004)). The slope of the volatility smile for stock options (SlopeS) is -204 basis

points, indicating that the implied volatility of out-of-the-money calls lies below that of out-of-

the-money puts on average. The average slope of the IVF for index options (SlopeI) is -415

basis points, which is much more negative thanSlopeS.

Insert Table 1 around here

The Michigan consumer sentiment index (CS) has a mean value 90.19 and strong auto

correlation (0.93), while its monthly change dCS has a mean close to zero and near zero

autocorrelation. CS is the residuals after we regress CSon credit spread, unemployment rate

and corporation productivity; dCS is the residuals after we regress dCS on changes of those

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S&P500 index over the remaining life of the option contracts (or ), and the monthly excessreturn on the value-weighted CRSP index (Rm).

Table 2 reports the correlation coefficients for the main variables. The positive-exposure

demand (PD) for stock calls and puts, PDS_CandPDS_P, are positively correlated with each

other, and the PD for index calls, PDI_C, is positively correlated withPDS andPDS_P. In

contrast, the PD for index puts, PDI_P, is uncorrelated withPDS, PDS_CorPDS_P. These

correlations suggest PDI_P is driven by different forces from those that influencePDS_C,

PDS_PandPDI_C. The PD for stock options (PDS) is positively correlated with the slope of

the stock implied volatility smile (SlopeS) and with macro-economic factor adjusted consumer

sentiment (CS) and lagged market risk premium (Rm-1). In contrast, thePD for index puts

(PDI_P) has either negative or near zero correlations with these variables. The slope of stock

option smile, SlopeS, is positively correlated with both the levels and changes of the consumer

sentiment and lagged market returns. In contrast, the slope of the SP500 index option smile,

SlopeI, is negatively associated with CS, and exhibits a small positive correlation withdCSand

Rm-1. These correlation coefficients provide preliminary evidence consistent with the view that

consumer sentiment is positively associated with the demand for options that increases investors

exposures to the underlying stock and with the slope of the implied volatility smile for stock

options but that sentiment exhibits a different relation with the demand and pricing of index

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Figure 2 plots the time series ofPDS,PDI, the level of the S&P 500 index, and the raw

measure of consumer sentiment. The figure shows that investors tend to increase their exposure

to individual stocks through the options market (i.e buy stock calls and sell stock puts) in periods

of high market returns and when sentiment is high. The correlation ofPDSwith the level of

consumer sentiment is particularly evident. In contrast, there is some evidence that investors

reduce their exposure to the index when market returns have been high. The correlations

between the demand for index options and the sentiment measures are less evident.

Insert Figure 2 around here

3.2 Option trading behavior of different investor types

A number of studies associate noise traders with small unsophisticated individual

investors, while institutional investors are generally assumed to act as rational arbitrageurs (Lee,

Shleifer, and Thaler (1991), Kumar and Lee (2006), Lemmon and Portniaguina (2006)). To

examine the trading behavior of different investors in the options markets, we use non-market

maker option volume obtained from the CBOE for the time period from 1990 to 2008. The

Option Clearing Corporation divides non-market maker option transactions into trades from firm

proprietary traders and trades from public customers. An example of a firm proprietary trader

would bean employeeof Goldman Sachs trading for the banks own account From 1990 to

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customers, and clients of Merrill Lynch are an example of Full-service brokerage customers. For

the remaining part of the sample period from 2002 to 2008, the CBOE changed its classification

scheme and subdivides public customer volumes into volumes associated with small, medium

and large trades corresponding to orders for less than 100 contracts, between 100 and 199

contracts, and larger than 199 contracts, respectively.

Among public customers, we consider discount brokerage customer or small size trade as

most likely to be associated with unsophisticated investors, and full service customer or large

trade size as more likely to be associated with relatively more sophisticated investors (for

example, hedge funds trade through full service brokerages). Further evidence that discount

brokerage customers are less sophisticated is provided in Pan and Poteshman (2005), who show

that full-service brokerage customers and other public customers have a greater propensity than

discount brokerage option traders to open purchased call (put) positions before stock price

increases (decreases). However, it is worthy to note that some investors in full service category

are also individual investors and subject to irrational behavioral, as shown in Poteshman and

Serbin (2003), customers of full-service brokers also engage irrational early exercise of

American options.

Figure 3 depicts the monthly percentage of total non-market maker volume attributable to

each classof investors. Thepercentagevolume is computedas thesumof buy and sell option

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traders of both stock and index options. Trading generated from discount brokerage customers

constitutes 14% of total non-market maker trading of stock options, but only 2% of SPX index

options. Trading from small trades shows the same patter, small trades constitute 32% of trading

of stock options, but only 4% of SPX index options. Full service customers make up around 60%

of both stock and index trading, and large trades make up 41% of stock option trading and 53%

of index option.

Insert Figure 3 around here

4. Results

In this section we examine how consumer sentiment and lagged market returns are

related to option demand. We then investigate the associations of sentiment and past return with

the pricing of stock and index options and the profitability of a trading strategy. We also present

several robustness tests and conclude with an examination of the cross-sectional effects of

sentiment on positive-exposure demand and price of stock options and stock option prices.

4.1. Determinants of stock and index option trading

The first part of our empirical analysis investigates the determinants of positive-exposure

demand for stock and index options. Based on our prior analysis, we argue that the positive

exposure demand for index options (PDI) is more likely to bedriven by rational investors In

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investigate how the demand for options is influenced by sentiment, we estimate the following

time-series regression specifications:

, (12.2)

(12.1)

wherePDSt andPDIt are computed from Eq.(10.1-10.2). In the analysis, we also break down

PDStandPDIt into the components associated with call and put options separately. BecausePDS

and PDI have high autocorrelations, we also use their monthly changes in some model

specifications. Senttis sentiment measured either by the level of Michgan Consumer Sentiment

adjusted for macroeconomic factors (CS) or the change of consumer sentiment adjusted for

change of macroeconomic factors (dCS). The lagged market return, Rm-1, is used to examine

how option demand responds to past market movements. The regressions also include

contemporaneous market returns,Rm,and the lagged dependent variable as controls.10

The results are presented in Table 3. When the dependent variable is the level of positive-

exposure demand for stock options (PDS), the coefficient estimates on the level (CS) and the

change (dCS) of consumer sentiment and market returns are all positive and statistically

significant. The estimates on lagged market returns are approximately twice as large as those on

contemporaneous market returns. When the dependent variable is the monthly change of

positive-exposure demand for stock options (dPDS) the coefficient estimates on dCS and the

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16% of the unconditional standard deviation ofdPDS. And a one standard deviation change in

the lagged market return is associated with a eight unit change in dPDS, amounting to more than

one third of standard deviation ofdPDS.

Insert Table 3 around here

Panels C and D present the results based on the positive-exposure demand for stock

options from puts (dPDS_P) and calls (dPDS_C) separately. The results show that changes in

consumer sentiment are more strongly related to dPDS_Pthan to dPDS_C. For put demand, the

coefficient estimate on dCS is 0.53 with a t-statistic of 2.32, while for call demand, the

coefficient estimate is 0.34 with a t-statistic of 1.39. In addition, dPDS_Pand dPDS_Care both

positively related to lagged market returns, indicating that investors increase their exposure to

stocks by selling puts and buying calls after high market returns.

In contrast, as seen in the right hand side of Panel A, the positive-exposure demand for

index options (PDI) is not related to either sentiment or lagged market returns; all the estimates

of coefficients on consumer sentiment measures and past market returns are insignificant when

PDIor dPDI is the dependent variable. Breaking down dPDI into the demands from puts and

calls separately shows the similar pattern.

The results presented in Table 3 confirm the visual observations in Figure 2 The

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puts. On the other hand, the demand for SPX index options that increase exposure to the index is

not related to investor sentiment or past market returns.

Referring back to Figure 3, a significant portion of the volume in stock option trading is

attributable to discount brokerage customers/small trades, while only a small fraction of the

volume in index options is generated from this group of investors. These figures suggest that

relatively unsophisticated investors are important participants in the stock option market, but not

in the index option market. If unsophisticated investors are more prone to be sentiment driven,

then we expect that their demands for options that increase their exposure to underlying stocks

will be more sensitive to changes in sentiment and past returns compared to the demands of other

investors.

Table 4 reports the results where the dependent variables are the monthly changes of

positive-exposure demand for stock or index options from different types of investors. Panel A

is for the period 1990-2001 and panel B is for the period 2001 to 2008, corresponding to the

change in the reporting of trader types by the CBOE. When the dependent variable is dPDS, the

coefficient estimates on dCS is positive and statistically significant for discount, small and

medium investors. The estimates on lagged market returns are positive and statistically

significant for discount and small investors, and remain positive but insignificant for full, other,

and medium investors. While the coefficient estimates on lagged returns are negative for firm

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discount and small investors, and remain negative and statistically significant for firm

proprietary traders.

Insert Table 4 around here

Overall, the results suggest that less sophisticated investors (proxied by discount and

brokerage customers and small trade size) in particular tend to increase their exposures to

individual stocks through options trading when sentiment is high and following high past returns.

In contrast, firm proprietary traders trades appear to act more like market makers and take the

opposite side of these trades.

4.2. Sentiment and Option Prices

The previous section documents that the consumer sentiment and past market returns are

positively related to the positive-exposure demand for stock options, but are generally unrelated

to positive-exposure demand for index options. To the extent that market-makers in options

cannot perfectly and costlessly hedge their positions, supply curves for options become upward

sloping. In this case, systematic demand imbalances generated by the trades of end users of

options can affect option prices (Garleneau, Pedersen, and Poteshman (2007)). If sentiment and

market returns reflect changes in the aggregate demand for stock options as indicated by our

results in the last section, then we expect that changes in these variables will also be reflected in

optionprices

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that demand for high strike options will be larger than demand for low strike options following

increases in sentiment or high market returns. Based on this argument, we expect the slope of

the IVF of stock options, measured as the implied volatility difference between OTM (high

strike) calls and OTM (low strike) puts, to be positively associated with sentiment and past

market returns.11 In contrast, we expect sentiment to be unrelated to the prices of index options,

which, as we have shown, are largely immune from demand imbalances associated with changes

in aggregate sentiment.

On the contrary, if consumer sentiment and past returns are proxies for changes in

fundamentals such as jump or volatility risks, as shown in Section 1, the slopes of IVF of stock

and index options will respond to sentiment and lagged market return in similar ways.

The empirical specification used to investigate the impact of sentiment on option prices is

as follows:

13.1 , 13.2where SlopeSt and SlopeIt are slope of IVF of stock and index options and are calculated based

on Eqs. (11.1) and (11.2), Sentt is sentiment measured either by Michgan index of Consumer

Sentiment adjusted for macroeconomic factors (CS) or monthly change of Consumer Sentiment

adjusted for change of macroeconomic factors (dCS) and are previous and

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option prices through changes in demand, then the coefficients and will be positive andsignificant, and the coefficient and will be insignificant. Alternatively, if sentiment andpast returns instead influence option prices because they proxies for changes in risk preferences

or fundamentals, as shown in Section 1, the coefficients and , or and will be similarin sign and significance, as innovations in risk or fundamentals should affect prices of both index

and stock options in similar ways.

The regressions also control for a number of other factors related to the slope of the

volatility smile. Han (2008) finds that institutional investor sentiment proxied by the level of

bull-bear spread (BB) is related to the prices of SPX index options. Li and Pearson (2006),

Dennis and Mayhew (2002), and Han (2008) find that volatility is negatively related to the slope

of the volatility smile. We control for volatility using the average realized volatility of the

underlying stock or index returns measured over the remaining life of the option contracts ( or).12 We also control forRm, the contemporaneous market returns, because Amin, Coval andSeyhun (2004) document that S&P 100 index call (put) prices are overvalued following large

upside (downside) market movements. Finally, we include the past months slope measure to

control for serial dependence in the slope.

Table 5 reports the results. For stock options (Panel A), the coefficient estimates on CS,

dCS and lagged market returns are all positive and significant In economic terms a one

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unconditional standard deviation of SlopeS. And a one standard deviation change in lagged

market returns is associated with a 35.5 basis point increase in the slope of the implied volatility

of stock options.

The results for index options (Panel B) exhibit a different pattern. None of the coefficient

estimates on the consumer sentiment or lagged market returns are statistically significant. These

findings show that sentiment affects stock options and index option prices in a manner consistent

with the idea that fluctuations in speculative demand driven by changes in aggregate sentiment

affect the prices of options on individual stocks but are unrelated to prices of index options.

As seen in Table 5, the coefficient estimate onBB (a measure of institutional investor

sentiment) is positive and significantly related to the slope of IVF for index options, which is

consistent with the empirical findings of Han (2008). The coefficient estimates on BB are

positive but not statistically significant for stock options. The coefficient estimates on realized

volatility ( or ) are negative in most specifications. The negative relation between volatilityand slope is consistent with the theoretical prediction of Bakshi, Kapadia and Madan (2003), and

with the empirical findings of Li and Pearson (2006). There is no consistent relation between

contemporaneous market returns (Rm) and the slope of the volatility smile for either stock or

index options.

InsertTable5aroundHere

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4.3. Trading Strategy

The results in previous section suggests that stock OTM calls are more (less) expensive

than OTM puts when sentiment and lagged market returns are high (low). To provide further

evidence on how sentiment and past returns affect the relative prices of options, we compute

returns from a trading strategy that trades calls and puts conditional on sentiment and lagged

returns. In particular, we sell OTM calls and buy OTM puts in last three trading days of the

month if change of consumer confidence (dCS) in that month is larger than 1 or 2 points and the

previous months market risk premium minus 0.5% (Rm-1-0.5%) is larger than 1% or 2%, and we

buy OTM calls and sell OTM puts when dCSis less than -1 or -2 andRm-1-0.5% is less than -1%

or -2%. We choose 0.5% because average market risk premium is around 0.5% per month. In

selecting the OTM call and put pairs for each underlying stock, we require options to have: (i)

same maturity of less than 60 trading days; (ii) non-zero trading volume; (iii) larger than $0.125

bid price, and (iv) bid ask spread below 15% of the mid price. If more than one call or put

satisfy above conditions for a pair, we choose the call (or put) with the largest trading volume.

For each call and put pair, we then compute the returns from holding the options to maturity with

and without delta hedging. The return without delta hedging is the profit of holding the position

to maturity scaled by the average call and put prices. The return with delta hedging is the

proceeds from the delta hedged position divided by theaveragecall and put prices. To estimate

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As seen in the table 6, all of the strategies yield significant positive abnormal returns

before accounting for option transactions costs. For example, the strategy that conditions

|dCS|>1, and |Rm-0.5|>1% has returns of 12.42% before delta hedging and returns of 6.36% after

delta hedging based on realized volatility. The returns increase further to 35.72% and 20.32%,

respectively, when we condition on |dCS|>2, and |Rm-0.5|>2%. Even after accounting for

transactions costs, all of the unhedged strategies and those of the hedged strategies conditioned

on |Rm-0.5|>2% yield positive and statistically significant returns. For example, the strategy that

conditions on |dCS|>2, and |Rm-0.5|>2% yields returns of 32.08% before delta hedging and

10.50% after delta hedging based on realized volatility. Finally, Table 6 also shows that the

average delta hedged return with realized volatility is higher than that with historical volatility.

This result suggests that mismeasurement of volatility does not upward bias returns of the delta

hedged strategies.

Insert Table 6 Here

To summarize, the results from the trading strategies show that positive returns are

generated by strategies that sell options that end users demand. The analysis provides additional

evidence that sentiment and past returns alter the time-series variation in the slope of the implied

volatility function of stock options, reflect changes in relative option prices as predicted by the

demand-basedviewofoptionpricing

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are driven by same fundamentals. It is possible that some factors influence prices of options on

stocks differently from options on index. For example, stock options are less liquid than index

options. However, for our findings to be driven by liquidity, it would need to be the case that

liquidity is associated with trading and slope of IVF of stock options. To examine if it is the case,

we use liquidity factor developed in Pastor and Stambaugh (2003) as a control and re-estimate

the coefficients of sentiment and past market returns.Another alternative explanation is that sentiments or market returns are correlated proxies

for future physical jump information in individual stocks which does not captured in prices of

index options. To investigate this hypothesis, we re-estimate the regressions controlling for

future realized return skewness (Skew) as a proxy for physical jump information. Future

skewness is a reasonable proxy for physical jumps, because a stock with high return jumps must

also exhibit high return skewness. We estimate Skew using daily returns from one trading day

after when we record the option price, to the last trading day of the following month.

Table 7 explores whether liquidity or skewness information can explain the relations

between sentiment (lagged returns) and trading or pricing of stock options, and shows that

neither liquidity nor future skewnss has power of explaining the positive exposure demand for

stock options (dPDS), and slope of stock option IVF (SlopeS). The coefficient estimates on

sentiment and lagged market returns remain statistically significant when liquidity or realized

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4.5. Sentiment and Lagged Returns versusPDS

If option demand is the only channel through which sentiment and lagged returns

influence option prices, then after controlling forPDS, sentiment and lagged returns should have

little power to explain the slope of the implied volatility function. Table 8 reports the results of

this investigation with SlopeS as the dependent variable. The coefficient estimate onPDS is

positive statistically significant, indicating that demand fluctuations have a direct effect on

option prices in the manner predicted. Nevertheless, after controlling for demand, sentiment

continues to have some explanatory power for option prices. For example, after controlling for

PDS, the coefficient estimate on dCSis 8.35 (t-statistic =2.82), while, in the absence ofPDS,

(See Table 5, Panel A), the coefficient estimate on dCS is 10.23 (t-statistic =3.27). These

results suggest that although consumer sentiment does affect relative option prices through

demand, it is not the only channel. In contrast, addingPDS to the regression wipes out the

predictive power of lagged market returns.13

Insert Table 8 around here

3.6 Cross-Sectional Analysis

Finally, we investigate the relation between sentiment and positive-exposure demand for

stock options (PDS) and the slope of the implied volatility function (SlopeS) for stocks with

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sentiment and the slope of the IVF is stronger for stocks in which trading by investors who are

prone to be sentiment driven is more concentrated and in stocks where market-makers face

higher arbitrage and hedging costs. As proxies for the costs of arbitrage we use volatility and the

volatility of volatility.

We estimate individual trading activity on options on a particular stock by the total trading

volume of discount investors/small trade sizes divided by the trading volume of all non-market

makers. For each month, we estimate volatility and its volatility with daily returns, where the

volatility of volatility is measured as the standard deviation of daily absolute returns. We first

sort stocks into quintiles based on the characteristic of interest, and then computePDSand the

average of SlopeS across stocks in each quintile for every month. We then sort months into

quintiles based on the level of the consumer sentiment and compare PDS or SlopeS during

periods of high and low sentiment across stock characteristic quintiles.

The results are reported in Table 9. As seen in Panel A, the difference inPDSduring

periods of high and low sentiment is 34.46 units for stocks with the lowest concentration of

trading by individual investors and 82.49 units for stocks in the highest quintile of individual

investor trading, and the difference is statistically significant. Consistent with these differences

in demand, the right hand side of Panel A also shows a similar effect onSlopeS; the difference in

SlopeS between high and low sentiment periods is 366.70 basis points for stocks in the lowest

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market maker-hedging costs. In both cases there is a positive association between the proxies for

hedging costs and the effects of sentiment on speculative demand and the slope of the IVF in the

predicted direction.

Insert Table 9 Here

5. Conclusion

We show that the demand for stock option positions that increase exposure to the

underlying is positively related to measures of investor sentiment and past market returns, while

the demand for index options is invariant to sentiment and returns. These differences in trading

patterns are reflected in differences in the composition of traders in the different types of

options---Options on individual stocks are actively traded by unsophisticated investors who

appear to use options largely to speculate on future stock-price movements, while trades in index

options are more often motivated by hedging demands of sophisticated investors. Consistent

with a demand based view of option pricing, we find that sentiment is related to time-series

variation in the slope of the implied volatility smile of stock options, but has little impact on the

prices of index options. The pricing impact is more pronounced in options with higher

concentration of speculative trading, higher stock return volatility, and those with higher

volatility of volatility. Our results provide new evidence that sentiment and lagged market

returns as behavioral biases affect the demand for and prices of securities traded actively by

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Table 1 Summary Statistics

Mean Std Min Max Auto

Positive-exposure demand for stock options (PDS) -2.61 34.05 -128.49 82.57 0.79

Change ofPDS(dPDS) 0.15 21.71 -54.70 96.45 -0.05

PDS from call (PDS_C) 13.73 22.57 -35.79 73.77 0.75

Change ofPDS_C (dPDS_C) 0.21 15.57 -75.53 62.65 -0.29

PDS from put (PDS_P) -16.34 24.86 -112.88 41.82 0.76

Change ofPDS_P (dPDS_P) -0.06 16.54 -68.89 73.09 -0.15

Positive-exposure demand for index options (PDI) -37.35 22.00 -134.14 1.32 0.61

Change ofPDI (dPDI) 0.25 18.53 -64.41 60.88 -0.35

PDIfrom call (PDI_C) -8.30 16.05 -74.46 21.17 0.61

Change ofPDI_C (dPDI_C) 0.11 13.41 -46.57 44.14 -0.42

PDIfrom put (PDI_P) -29.04 13.56 -68.56 0.94 0.49Change ofPDI_P (dPDI_P) 0.14 12.45 -52.80 51.26 -0.44

Slope of smile for stock options (SlopeS) (bp) -204.15 269.12 -1122.39 773.42 0.29

Slope of smile for index options (SlopeI)( bp) -415.90 248.34 -1611.04 364.57 0.58

Consumer sentiment (CS) 90.19 11.33 56.40 112.00 0.93

Change ofCS (dCS) -0.10 4.09 -12.20 17.30 -0.01

Consumer sentiment macro adjusted (CS) 3.36 23.28 -45.37 49.90 0.97

Change ofCSmacro adjusted (dCS) -0.10 4.10 -12.29 16.97 -0.00Bull-bear spread (BB) 14.72 14.55 -26.70 41.05 0.71

Volatility of Stocks (S)(bp) 4709.31 1556.57 2501.69 11801.61 0.83

Volatility of SP500 index (I) (bp) 1481.57 726.03 486.62 5419.19 0.51

Monthly market excess return Rm 0.48 4.12 -16.20 10.30 0.02The positive-exposure demand for stock options (PDS) is the monthly sum of the non-market makeropen buy call and sell put volumes minus the sum of open sell call and buy put volumes across all

stock options, where volumes are in logarithm. PDS_CorPDS_PisPDScomputed form stock callsor stock puts only.PDI,PDI_CandPDI_Pare similar variables for SP500 index options. SlopeSisthe cross sectional average slope of IVF for stock options, computed as the difference betweenimplied volatilities of OTM calls and implied volatilities of OTM puts. SlopeIis the slope of impliedvolatility of S&P500 index options. Consumer sentiment (CS) is based on monthly household surveyconducted by theUniversity of Michigan. dCS is its monthly change. CS and dCS are the maro-

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Table 2 Correlation Coefficients

PDS PDS_C PDS_P PDI PDI_C PDI_P SlopeS SlopeI CS dCS BB S I

PDS_C 0.74

PDS_P 0.79 0.32

PDI 0.11 -0.08 0.24

PDI_C 0.18 -0.13 0.38 0.80

PDI_P -0.03 0.02 -0.06 0.68 0.11

SlopeS 0.42 0.36 0.29 0.02 0.07 -0.04

SlopeI 0.12 0.14 0.04 -0.15 -0.10 -0.13 0.15

CS 0.46 0.12 0.56 0.13 0.20 -0.06 0.44 -0.19

dCS 0.17 0.07 0.19 -0.01 0.02 -0.03 0.16 0.06 0.22

BB 0.12 0.08 0.23 0.30 0.23 0.22 0.10 0.16 0.19 -0.05

S

0.08 -0.07 0.17 0.07 0.28 -0.17 0.19 -0.41 0.49 -0.09 0.05

I -0.09 -0.15 0.00 0.13 0.19 -0.02 -0.03 -0.51 0.20 -0.16 0.18 0.66

Rm-1 0.39 0.36 0.27 0.02 -0.04 0.08 0.18 0.06 0.12 0.28 0.06 -0.17 -0.21PDSis the positive-exposure demand for stock options, measured as the monthly sum of the non-market maker open buy call and sell putvolumes minus the sum of open sell call and buy put volumes across all stock options.PDS_CandPDS_ParePDSfrom stock calls andstock puts.PDI,PDI_CandPDI_Pare similar variables for SP500 index options. SlopeSis the cross sectional average slope of IVF forstock options, computed as the difference between implied volatilities of OTM calls and implied volatilities of OTM puts. SlopeI is the

slope of implied volatility of S&P500 index options. CS and dCS are level and change of Consumer sentiment adjusted for macro-economic factors.BB is bull bear spread, a proxy for institutional sentiment. Sand I are realized volatility for stocks and SPX.Rm-1 isprevious month market risk premium. Variables are monthly and for the period of January 1990 to September 2008.

40

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Table 3 Determinants of positive-exposure demand for stock options (PDS) andpositive-exposure demand for index options (PDI)

Sent Sent Rm-1 Rm Lag obs/R2 Sent Rm-1 Rm Lag obs/R

2

Panel A Positive-exposure demand

Dependent: PDS(stocks) Dependent: PDI(S&P500 index)

CS 0.26 2.05 0.82 0.71 224 0.11 0.06 -0.22 0.61 224

(2.38) (8.20) (3.54) (6.40) 0.71 (1.05) (0.16) (-0.61) (2.98) 0.38

dCS 0.69 1.93 0.79 0.75 224 0.02 0.10 -0.20 0.62 224

(2.41) (7.69) (3.24) (6.95) 0.71 (0.08) (0.29) (-0.56) (2.82) 0.37

Panel B Change of positive-exposure demand

Dependent: change ofPDS (dPDS) Dependent: change ofPDI (dPDI)

dCS 0.75 2.02 0.96 -0.24 224 -0.05 0.11 -0.09 -0.34 224

(2.56) (7.18) (3.47) (-1.65) 0.27 (-0.11) (0.32) (-0.26) (-1.59) 0.10

Panel C Change of positive exposure demand for puts

Dependent: change ofPDS_P (dPDS_P) Dependent: change ofPDI_P (dPDI_P)

dCS 0.53 0.84 0.84 -0.33 224 0.02 0.22 -0.37 -0.47 224

(2.32) (4.09) (3.94) (-1.84) 0.20 (0.09) (1.04) (-1.63) (-2.06) 0.23

Panel D Change of positive exposure demand for calls

Dependent: change ofPDS_C (dPDS_C) Dependent: change ofPDI_C (dPDI_C)

dCS 0.34 1.29 0.14 -0.38 224 0.09 -0.15 0.31 -0.39 224

(1.39) (7.64) (0.77) (-2.07) 0.27 (0.26) (-0.68) (1.36) (-2.13) 0.15

PDSis positive exposure demand for stock options, measured as the sum of stock option openbuy call and sell put volume minus the sum of open buy put and sell call volume, dPDS is itsmonthly changes, anddPDS_Por dPDS_C is the monthly change of PDS for stock calls or putsonly. PDI, dPDI, dPDI_P and dPDI_C are similar variables for S&P500 index options.Sentiment (Sent) is either CSor dCS,the level or the change of Michigan consumer sentimentadjusted for macro-economic factors. Lag is the lagged dependent variable.Rm-1 andRm are pre

and contemporaneous market premium. The parentheses contain Newey-West t-statistics thatcorrect for serial correlation and heteroscedasticity. Variables are monthly and for the period ofJanuary 1990 to September 2008.

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Table 4 Determinants of positive exposure demand for stock (PDS) and indexoptions (PDI) from different types of investors or trades

Dependent: dPDS(Stocks) Dependent: dPDI(S&P500 index)

dCS Rm-1 Rm Lag dCS Rm-1 Rm lag

Panel A: 1990 2001

Discount customers

2.29 3.78 2.63 -0.31 1.18 2.09 -1.75 -0.38(2.91) (5.78) (3.58) (-1.21) (0.57) (1.82) (-1.28) (-1.65)

Full service customers

1.23 0.19 1.82 -0.29 0.54 -3.04 2.61 -0.36

(1.32) (0.31) (2.45) (-1.23) (0.22) (-1.61) (1.68) (-1.63)

Other customers

0.49 1.26 -4.02 -0.50 -0.38 2.14 -2.04 -0.45

(0.80) (1.60) (-6.21) (-2.46) (-0.34) (1.72) (-1.77) (-2.65)Firm proprietary traders

-0.36 -2.77 0.26 -0.21 -0.45 -2.07 3.92 -0.49

(-0.59) (-5.01) (0.54) (-0.77) (-0.50) (-2.41) (4.19) (-2.83)

Panel B: 2002 2008

Small trades

1.29 4.04 0.06 -0.47 -0.20 0.62 0.04 -0.48

(2.09) (6.08) (0.08) (-2.17) (-0.61) (0.92) (0.07) (-1.68)Medium trades

1.12 1.44 1.11 -0.37 0.74 -2.21 0.13 -0.30

(2.84) (1.21) (2.08) (-1.30) (0.80) (-2.49) (0.27) (-1.30)

Large trades

-0.76 -0.07 -3.48 -0.46 -0.48 0.69 -2.77 -0.37

(-1.47) (-0.07) (-4.35) (-1.74) (-0.63) (1.02) (-4.48) (-1.40)

Firm proprietary traders0.39 -3.48 -0.05 -0.39 -0.68 -1.61 1.26 -0.28

(0.75) (-5.74) (-0.10) (-1.34) (-0.96) (-2.44) (1.81) (-1.16)

dPDS is the monthly change of positive exposure, andPDSis the sum of stock option open

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Table 5 Slope of implied volatility smile for stock and index options

Panel A: Dependent: slope of stock option implied volatility smile (SlopeS)

CS' dCS' Rm-1 Rm BB S lag obs/R2

7.28 8.34 -2.84 0.91 -0.02 0.38 224

(4.55) (2.27) (-0.51) (1.23) (-1.95) (3.41) 0.3410.23 8.56 -2.65 1.71 0.00 0.50 224

(3.27) (2.59) (-0.46) (1.58) (0.40) (4.82) 0.30

Panel B: Dependent: slope of SPX option implied volatility smile (SlopeI)

CS' dCS' Rm-1 Rm BB I lag obs/R2

-0.58 2.35 1.93 3.12 -0.12 0.54 224

(-0.65) (0.66) (0.84) (1.97) (-5.90) (6.00) 0.69

-2.23 2.76 2.08 2.92 -0.13 0.54 224 (-1.06) (0.76) (0.86) (1.91) (-5.88) (5.96) 0.69

SlopeS is the cross sectional average slope of IVF for stock options, computed as thedifference between implied volatilities of OTM calls and implied volatilities of OTM puts.SlopeIis the slope of implied volatility of S&P500 index options. CSor dCS,is the level orthe change of Michigan consumer sentiment adjusted for macro-economic factors.Rm-1 andRm are pre and contemporaneous market returns, respectively. BB is the bull bear spread.

Lag is the lagged dependent. S or I is the volatility of stocks or index. The parenthesescontain t-statistics computed from Newey-West standard errors that correct for serialcorrelation and heteroscedasticity. The time period covers 1990 to September 2008.

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Table 6 Returns of trading strategy on stock options

Return without delta hedge (%) Return with daily delta hedge (%)

Historical volatility Realized volatility

buy: mid

sell: mid

buy: ask

sell: bid

buy: mid

sell: mid

buy: ask

sell: bid

buy: mid

sell: mid

buy: ask

sell: bid

No. of

months/obs|dCS|>1, |Rm-1-0.5|>1%

12.42 5.13 3.58 -6.32 6.36 -2.54 85

t-stats (2.79) (1.15) (1.88) (-3.32) (3.49) (-1.94) 43,916

|dCS|>1, |Rm-1 -0.5|>2%

15.87 13.24 7.51 2.58 8.47 3.55 69

t-stats (6.12) (4.90) (5.78) (2.33) (6.06) (3.38) 34,373

|dCS|>2, |Rm-1-0.5|>1% 16.06 11.26 6.5 -3.34 7.92 -2.92 65

t-stats (3.18) (2.16) (3.01) (-1.54) (3.81) (-0.92) 34,471

|dCS|>2, |Rm-1-0.5|>2%

35.72 32.08 19.80 10.02 20.32 10.50 54

t-stats (6.31) (5.45) (6.00) (3.04) (6.61) (3.45) 27,218A strategy of sell OTM calls and buy OTM puts in the end of the month is employed ifdCS >1 or 2 andRm-1-0.5 >1% or 2% , and astrategy of buying OTM calls and selling OTM puts is employed ifdCS

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Table 7 L iquidity and skewness information interpretations for the role ofsentiment

dCS Liquidity Skew Rm-1 Rm BB S Lag obs/R2

Dependent: change of positive exposure demand for stock options (dPDS)

0.71 -3.85 2.02 0.96 -0.24 224

(2.51) (-0.14) (7.18) (2.17) (-4.92) 0.270.71 -8.85 2.06 0.97 -0.24 224

(2.52) (-1.00) (7.29) (3.55) (-4.43) 0.27

Dependent: Slope of stock option implied volatility smile (SlopeS)

9.98 -396.67 8.34 -2.30 1.87 0.00 0.50 224

(3.18) (-1.10) (2.46) (-0.39) (1.69) (0.40) (4.81) 0.29

10.03 212.61 6.93 -3.24 1.98 0.00 0.48 224

(3.21) (1.68) (1.97) (-0.56) (1.78) (0.20) (4.74) 0.30

dPDSis the monthly change ofPDS, wherePDSis the sum of stock option open buy call and sellput volumes minus the sum of open buy put and sell call volumes. SlopeSis the cross sectionalaverage slope of IVF for stock options, computed as the difference between implied volatilities ofOTM calls and implied volatilities of OTM puts. dCS is the monthly changes of consumersentiment adjusted forchanges in macroeconmic factors.Liquidity is traded liquidity factor usedin Pastor and Stambaugh (2003). Skew is the realized physical skewness of the underlying stocksduring the remaining life of option contracts. The parentheses contain t-statistics computed fromNewey-West (1997) standard errors that correct for serial correlation and heteroscedasticity. Thetime period covers 1990 to September 2008.

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Table 8 Slope of implied volatility smile for stock option: sentiment versus optiondemand

PDS dCS Rm-1 Rm BB S Lag obs/R2

2.19 8.35 3.86 -3.61 1.13 0.00 0.43 225

(4.10) (2.82) (1.14) (-0.66) (0.87) (-0.13) (4.23) 0.33

The dependent is the slope of stock option implied volatility, computed as the cross sectionalaverage difference between implied volatility of OTM calls and implied volatility OTM puts.PDSis the sum of stock option open buy call and sell put volumes minus the sum of openbuy put and sell call volumes, dCS is the monthly change of consumer sentiment adjustedfor change of macroeconomic factors, and Rm-1 and Rm are pre and contemporaneousmonthly returns, respectively. The parentheses contain t-statistics computed from Newey-West (1997) standard errors that correct for serial correlation and heteroscedasticity. The

time period covers J anuary 1990 to September 2008.

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Table 9 Cross sectional stock portfolio analysis

PDS SlopeS

Small 2 3 4 Large L-S Small 2 3 4 Large L-S

Panel A: Discount Investor Stock Option Trading Activity Measured by Open Interest

LowCS -47.24 -47.21 -24.12 -11.39 -11.94 35.31 -455.37 -510.51 -413.69 -452.70 -427.17 28.20

HighCS -12.79 13.24 23.81 45.85 70.56 83.34 -88.67 -166.82 -83.35 -40.53 100.88 189.55

H L 34.46 60.45 47.93 57.24 82.49 48.04 366.70 343.69 330.34 412.17 528.05 161.36t-stats (3.21) (4.96) (4.97) (5.08) (5.78) (3.80) (6.45) (5.99) (5.29) (5.98) (7.20) (2.46)

Panel B: Stock Volatility

LowCS -23.85 -29.83 -20.01 -27.47 -8.69 15.16 -282.36 -382.13 -444.67 -426.19 -504.19 -221.83

HighCS 0.80 13.78 30.80 35.54 37.11 36.31 -18.04 -61.62 -30.60 -92.08 45.73 63.77

H L 24.66 43.61 50.81 63.01 45.80 21.15 264.33 320.51 414.07 334.12 549.92 285.59

t-stats (2.42) (4.28) (4.70) (5.38) (4.85) (2.15) (5.71) (8.87) (12.24) (7.50) (8.95) (5.25)

Panel C: Volatility of VolatilityLowCS -30.89 -27.22 -19.39 -16.77 -6.36 24.52 -284.58 -288.22 -443.60 -400.70 -458.81 -174.23

HighCS -5.42 17.67 26.62 37.23 40.14 45.56 -86.74 -57.61 -88.87 -35.04 10.02 96.76

H L 25.47 44.89 46.01 54.00 46.51 21.04 197.84 230.62 354.74 365.66 468.83 270.99

t-stats (3.11) (4.85) (4.89) (5.48) (5.59) (2.55) (3.55) (3.75) (4.33) (4.38) (5.19) (4.06)PDSis the positive exposure demand for stock options, computed as the sum of open buy call and sell put volumes minus the sum of open buy putand sell call volumes. SlopeS is the cross sectional average slope of IVF for stock options, computed as the difference between impliedvolatilities of OTM calls and implied volatilities of OTM puts. CS is the consumer sentiment adjusted for macro-economic factors. ThePDSor SlopeSdifferences between high and low sentiment periods are reported on rows started with H L; their cross sectional difference betweenstocks with large and small quintile categories are reported in column headed with L S. The parentheses contain t-statistics computed fromNewey-West (1997) standard errors that correct for serial correlation and heteroscedasticity.

47

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0 0.1 0.2 0.3 0.4 0.5-0.2

-0.15

-0.1

-0.05

0

J ump Size Premium

Slo

peofIVF

0 0.1 0.2 0.3 0.4 0.5

0.2

0.3

0.4

0.5

J ump Size Premium

IVof

ATMoptions

index

stock

Figure 1 IVF of index and stock options with various jump and variance risk premia. Slope of IVF is the average IV of OTMcalls minus average IV of OTM puts. Options are OTM if 0.1250.375or0.3750.125,and ATM if0.3750.626or0.6250.375. IV and delta are computed using Black-Scholes model and the volatility used for computing delta is theaverage risk neutral variance in one volatility path.

0 2 4 6 8 10 12-0.2

-0.15

-0.1

-0.05

0

Variance Premium

SlopeofIVF

0 5 10

0.2

0.3

0.4

0.5

Variance Premium

IVofATMopt

ions

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Figure2 SP500 Index Level, PDS, PDI and Consumer SentimentPDSis the positive-exposure demand for stock options, calculated as the monthly sum of the nonmarket maker open buy call and sell putvolumes minus sum of open sell call and buy put volumes across all stock options, andPDIis the net positive-exposure demand for S&P500index options. The level of SP500 index is indicated by the dashed line.

Oct90 Jan94 J an00 J an04 J un08-4

-20

24

x 106 PDS and SP500

PDS

400

800

1200

1600

SP500

Oct90 Jan94 J an00 J an04 J un08-10

-5

0

5x 10

5

PDI and SP500

400

800

1200

1600

SP500

Oct90 Jan94 J an00 J an04 J un0850

100

Consumer Sentiment (CS)

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50

J an1990 J ul1992 Jan1995 J ul1997 Jan2000 J ul2002 J an2005 J ul20070

20

40

60

80Stock Option Trading

Volume%

J an1990 J ul1992 Jan1995 J ul1997 Jan2000 J ul2002 J an2005

20

0J ul2007

40

60

80Index Option Trading

Volume%

Discount/Small

Full/Large

Other/Medium

Figure 3 Stock and SP500 index option trading of different types of investors or trade sizes.

The monthly percentage trading volume of discount brokerage customers, full service customers, and the other public customersbefore 2002, and percentage trading volume of small, large and medium trade from 2002 onwards. Percentage trading volume ismeasured as the total volume originated from specific investor or trade group divided by total non-market maker volume. Thepercentage trading volume of firm proprietary traders