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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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Reference
Amin, K., J. D. Coval, and H. Seyhun, 2004, Index Option Prices and Stock MarketMomentum,Journal of Business, 77, 835-873.
Baker, M. and J. Wurgler, 2006, Investor Sentiment and the Cross-section of Stock Returns,Journal of Finance, 61, 1645-1680.
Bakshi, G, N. Kapadia and D. Madan, 2003, Stock Return Characteristics, Skew Laws, andDifferential Pricing of Individual Equity Options,Review of Financial Studies, 16, 101-143.
Bao, J., J . Pan and J. Wang, 2010, The Illiquidity of Corporate Bonds,Journal of Finance,forthcoming.
Bates, D., 1991, The Crash of 87: Was It Expected? The Evidence from Options Markets,Journal of Finance, 46, 1009-1044.
Bates, D., 2000, Post-87 Crash Fears in S&P 500 Futures Options,Journal of Econometrics,94,181-238.
Black, F. and M. Scholes 1973, The Pricing of Options and Corporate Liabilities,Journal ofPolitical Economy, 81, 637-645.
Bollen, N. P., and R. E. Whaley, 2004, Does Net Buying Pressure Affect the Shape of ImpliedVolatility Functions?Journal of Finance, 59, 711-753.
Cherkes, M., J . S. Sagi and R. H. Stanton, 2009, A Liquidity-Based Theory of Closed-EndFunds,Review of Financial Studies, 22, 257-299.
Constantinides, G. M., J . C. Jackwerth, and S. Perrakis, 2009, Mispricing of S& P 500 Index
Options, Review of Financial Studies, 22,1247-1277.
Coval, Joshua, and Tyler Shumway, 2001, Expected Option Returns,Journal of Finance, 56,983-1009.
D J i Ch d J W i 2009 S t ti Ri k d th P i St t f I di id l
7/28/2019 SSRN-id1340762
38/51
Fama, Engene, 1970, Efficient Capital Markets, A Review of Theory and Empirical Work,Journal of Finance, 25, 383-417.
Figlewski, S., 1989, Options Arbitrage in Imperfect Markets,Journal of Finance, 44, 1289-1311.
Grleanu, N., L. H. Pederson and A. Poteshman, 2009, Demand-based Option Pricing,Reviewof Financial Studies, 22, 4259-4288.
Han, B., 2008, Investor Sentiment and Option Prices,Review of Financial Studies, 21,387-414.
Heston, S., 1993, A Closed-from Solution for Options with Stochastic Volatility withApplications to Bond and Currency Options,Review of Financial Studies, 6, 327-343.
Jackwerth, J., and M. Rubinstein, 1996, Recovering Probability Distributions from OptionPrices,Journal of Finance, 51, 1611-1631.
Kaplanski, G. and Levy H., 2010, Sentiment and stock prices: the case of aviation disasters,Journal of Financial Economics, 95(2), 174-201.
Kumar, A., and C. M.C. Lee, 2006, Retail Investor Sentiment and return comovements,Journal of Finance, 61, 2451-2486.
Lakonishok, J ., I. Lee, N. D. Pearson, and A. M. Poteshman, 2007, Option Market Activity,Review of Financial Studies, 20, 813-857.
LaPorta, R., J . Lakonishok, A. Shleifer, and R. Vishny, 1997, Good News for Value Stocks:Further Evidence on Market Efficiency,Journal of Finance, 62, 859874.
Lee, C. M. C., A. Shleifer and R. H. Thaler, 1991, Investment Sentiment and Close-end FundPuzzle, Journal of Finance, 46, 75-109.
Lemmon, M. and E. Portniaguina, 2006, Consumer Confidence and Asset Prices: SomeEmpiricalEvidence, Review of Financial Studies 19(4), 1499-1529.
7/28/2019 SSRN-id1340762
39/51
Newey, W. K., and K. D. West, 1987, A Simple Positive Semi-definite, Heteroskedasticity andAutocorrelation Consistent Covariance Matrix Estimator,Econometrica, 55, 703-708.
Pan, J., 2002, The Jump-risk Premia Implicit in Options: Evidence from an Integrated Time-Series Study,Journal of Financial Economics, 63, 3-50.
Pan, J., and A. M. Poteshman, 2006, The Information in Option Volume for Future StockPrices,Review of Financial Studies, 19, 871-908.
Pastor, L. and R. F. Stambaugh, 2003, Liquidity Risk and Expected Stock Returns, Journal ofPolitical Economy, 111, 642685.
Pontiff, J ., 1996, Costly Arbitrage: Evidence from Closed-End Funds, Quarterly Journal ofEconomics, 111, 1135-1151.
Poteshman, A. M. and V. Serbin, 2003, Clearly Irrational Financial Market Behavior: Evidencefrom the Early Exercise of Exchange Traded Stock Options,Journal of Finance, 58, 37-70.
Roll, R., E. Schwartz and A. Subrahmanyam, 2009, Relative Trading Activity in Options andStock,Journal of Financial Economics, forthcoming.
Shleifer, A. and R. W. Vishny, 1997, The Limits of Arbitrage,Journal of Finance, 52, 35-55.
Stambaugh, R. F., J. Yu and Y. Yuan (2011), The Short of It: Investor Sentiment andAnomalies, working paper, University of Pennsylvania, University of Minnesota and Universityof Iowa.
Stein, J., 1989, Overreactions in the Options Market,Journal of Finance, 44, 1011-1023.
Stein, E. and J. Stein, 1991, Stock Price Distributions with Stochastic Volatility,Review ofFinancial Studies, 4, 727-752.
Yan, S., 2010, Jump risk, stock returns, and slope of implied volatility smile,Journal ofFinancial Economics, 99 (1), 216-233.
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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