The Effects of Investor Sentiment on Speculative Trading and Prices of Stock. and Index Options

Transcription

1 The Effects of Investor Sentiment on Speculative Trading and Prices of Stock and Index Options Michael Lemmon* Sophie Xiaoyan Ni October 2010 JEL Classification Code: G1 Key Words: Options, Volatility Smile, Sentiment, Speculation, Hedging Lemmon is at the University of Utah and the Hong Kong University of Science and Technology, Ni is at the Hong Kong University of Science and Technology, We benefited from the comments and support of Kalok Chan, John Griffin, Ohad Kadan (IDC Caesarea discussant), Jun Pan, Neil Pearson, Allen Poteshman, Maik Schmeling (EFA discussant), Mark Seasholes, Jason Wei, Ning Zhu and seminar and symposium participants at the Hong Kong University of Science and Technology. We bear full responsibility for any errors. The financial support from a Hong Kong RGC Research Grant (Project # ) is gratefully acknowledged.

2 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 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 a higher concentration of unsophisticated investors and in options with higher hedging costs. Our results provide new evidence that sentiment affects the demand for and prices of securities that are subject to speculation, but has little effect on the prices of securities in which demand is driven by hedging motives unrelated to sentiment.

3 Prior literature suggests that different types of options are used by different types of investors and serve different purposes. For example, Bollen and Whaley (2004) show that most trading in S&P500 index options (SPX) involves puts, while most trading in stock options involves calls. They attribute this fact to the hedging demands of institutional investors, who purchase index put options as portfolio insurance against market declines. Similarly, Lakonishok, Lee, Pearson and Poteshman (2007) document that hedging motivated trades account for only a small fraction of trading in stock options. They also show that apart from stock call writing, a majority of non-market maker stock option trading involves naked positions that appear to be motivated by views about the direction of future stock price movements. This study examines the extent to which speculative and hedging motivated trades differ in equity options and how factors that influence speculative trading affect option prices. We begin our analysis by examining how non-market maker demand for stock and index options responds to investor sentiment and lagged market returns. We rely on two measures of investor sentiment used in prior research investigating the effects of sentiment on stock prices; namely the index of consumer sentiment (CS) based on a survey conducted by University of Michigan and used in Lemmon and Portnaiguina (2006), and the sentiment measure of Baker and Wurgler (BW) (2006). 1 Our use of stock returns is motivated by the fact that changes in stock valuations are also likely to be associated with both hedging demands and with the potential for overreaction by unsophisticated traders. Consistent with the latter, Lakonishok, Lee, Pearson, 1 DeLong, Shleifer, Summers and Waldman (1990)) interpret sentiment as capturing the correlated beliefs of investors that are unrelated to fundamentals. A number of papers examine the relation between investor sentiment and security prices in the stock market. For example, Lee, Shleifer and Thaler (1991) propose that fluctuations in the discounts of closed-end funds are driven by changes in individual investor sentiment. Baker and Wurgler (2006) present evidence that investor sentiment has significant effects on the cross-section of stock prices. Lemmon and Portniaguina (2006), show that sentiment measured by consumer confidence predicts future returns for small stocks and for stocks with high levels of individual ownership. 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. 1

4 and Poteshman (2007) show that the least sophisticated investors increased their exposure to growth stocks through the options market during the stock-market bubble of the late 1990 s and early In our data, trading by unsophisticated investors (defined as discount brokerage customers/small trades) accounts for more than 18% of total non-market maker volume for stock options, but only 3% of index option volume. To measure investor demand for different 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 non-market maker net option demands with positive-exposure to the underlying stock and the index, respectively. To the extent that speculative trading is related to aggregate changes in investor sentiment we expect that PDS will be positively related to our sentiment measures and past stock returns, while PDI, which is primarily dominated by hedging motivated trades, will be unrelated to sentiment, and will potentially be negatively related to past stock returns (especially for index puts). The evidence is generally consistent with these predictions. Over the period from 1990 through 2008, time-series variation in PDS is increasing in both the level and change in investor sentiment, but PDI is unrelated to the sentiment measures. We also find that PDS and PDI respond differently to past stock returns. PDS is positively related to lagged market returns, while PDI is generally unrelated to past market returns. Finally, we also find that PDS is most strongly related to sentiment and lagged market returns for trades initiated by customers of discount brokers and in small option trades. Given the evidence that speculative trading is related to our measures of sentiment, we then examine whether sentiment also impacts the prices of stock and index options. Under the 2

5 Black-Scholes assumption of frictionless markets, market-makers in options can perfectly and costlessly hedge their positions resulting in supply curves that are flat. According to this perfect markets hypothesis, price movements are driven by changes in assets fundamental values, with demand shocks and irrational sentiment playing no role because arbitrageurs readily offset price deviations. In contrast, if arbitrage is limited (Shleifer and Vishny (1997)) or hedging is costly, then supply curves for options become upward sloping. In this case, as shown by Gârleanu, Pedersen, and Poteshman (2009) demand imbalances generated by the trades of end users of options can affect option prices. 2 Given that sentiment driven demand is concentrated in stock options, and because arbitrage activities are more costly in individual stock options (Figlewski (1989)), we expect the prices of stock options to respond more strongly to sentiment and lagged market returns than prices of index options. Alternatively, if our measures of investor sentiment instead proxy for changes in fundamentals (e.g., Lemmon and Portniaguina (2006) and Baker and Wurgler (2006)), then we expect both the prices of stock and index options respond to sentiment and lagged market returns in similar ways, because payoffs of stock options in aggregate and index options are driven by the same underlying fundamentals. The dependent variable in our pricing analysis is the slope of the implied volatility function (IVF), which is computed as the difference in implied volatility between OTM calls and OTM puts. Bollen and Whaley (2004) find that the slope of the IVF changes significantly from month to month. Our tests examine whether changes in sentiment and lagged market returns can explain the time-series variation in the slope of the implied volatility function. 2 Our focus is on how differences in demand for different types of options can affect prices. Nevertheless, a large literature exists that examines other determinants of option prices. For example, Bates (1991, 2000), Bakshi, Kapadia and Madan (2003), Bollen and Whaley(2004), Coval and Shumway (2001), Liu, Pan and Wang (2005), Jackwerth and Rubinstain (1996), and Pan(2002), among others. 3

6 Consistent with the demand based view of option pricing, investor sentiment and lagged market returns have a significant effect on stock option prices, but have no effect on index option prices. In multivariate regressions that control for the lagged dependent variable, contemporaneous market returns, realized volatility and a measure of institutional investor sentiment, we find that both lagged market returns and investor sentiment are positively related to the slope of the implied volatility function for options on individual stocks. In contrast, we find no evidence that past returns or our measures of investor sentiment are related to the slope of the implied volatility function for index SPX 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 has no effect on the slope of the 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 sell call options and purchase put options following large changes in sentiment and high past returns. In some cases these abnormal returns exceed option transactions costs. Further analysis explores whether our results might be driven by the fact that our sentiment measures proxy for time variation in physical jump information in underlying stock returns or any time-series variation in macroeconomic conditions. 3 We do not find that this is the case. Finally, we examine whether the effects of sentiment on speculative trading and option 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 3 In the models of Bates (1991, 2000) and Pan (2002), the risk neutral jump size is the single factor that drives timeseries variation in the slope of the option implied volatility function. 4

7 underlying volatility and volatility of volatility (as proxies for hedging costs) exhibit demands and prices that are more sensitive to sentiment. Our paper is related to several studies on option trading. 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 finding that positiveexposure demand for stock options (PDS) exhibits significant time-series variation related to investor sentiment is consistent with the results in Lakonishok et al.(2007), who document that during the bubble period in the late 1990 s, unsophisticated investors increased their purchases of growth stock calls. However, they do not systematically examine how investor sentiment is related to speculative and hedge trading, nor do they investigate whether investor sentiment affects option prices. Pan and Poteshman (2006) document that stock option put-call ratios contain information about future stock returns. Their study is based on cross sectional differences in option trading, while our study focuses on time-series differences in aggregate option volume. Our findings are also related to a number of studies that document behavioral biases in options markets. Stein (1989) finds that longer term implied volatilities of S&P 100 index options overreact to changes in short-term volatility. Poteshman (2001) documents both underreaction and over-reaction to volatility fluctuations in the market for S&P500 index options. Constantinides, Jackwerth and Perrakis (2009) find no evidence that prices in the option markets have become more rational over time. Han (2008) finds a positive relationship between the riskneutral skewness in S&P500 index option prices and measures of institutional investor sentiment. In contrast to these papers, our study links measures of investor sentiment and past market returns to variation in demand for speculative positions in stock options, and to variation in pricing of options both in time-series and in the cross-section. 5

8 The remainder of the paper is structured as follows. Section 1 describes the data sources and variable construction. Section 2 presents summary statistics and describes the trading activity of different types of investors in stock and index option markets. Section 3 presents the main empirical results and Section 4 concludes with a brief summary. 1. Data and Variables In this section we describe the option and sentiment data and provide summary statistics for the main variables used in our analysis Option trading and price data 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 over the period January 1990 through September 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 nonmarket 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 Over the period from January 1990 to December 1995, we obtain option price data from the Berkeley Option Database, and from January 1996 through September 2008, the option price 6

9 data 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 bidask price quote before 3:00 PM Central Standard Time. 4 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 the following four conditions: (1) the option has above zero trading volume on that day, (2) the option bid price is larger than zero and within standard no-arbitrage bounds 5, (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 Option trading and price variables For each month t in the sample, we use the CBOE volume data to compute a measure that we call the positive-exposure demand for stock options (PDS t ) and positive-exposure demand for SP500 index options (PDI t ). PDS t and PDI t measure the newly established net option positions that have positive-exposure to the underlying stocks and index and are computed as follows: 4 For American-style stock options we use the dividend-adjusted binomial method with the actual dividends paid over the life of an option as a proxy for the expected dividends. For SPX index options, which are European, we compute implied volatilities by inverting the Black-Scholes (1973) formula. Linearly interpolated LIBOR is used as the risk free rate. 5 For a call, the ask price is not less than S-K-PV(D), and the bid price is not larger than S; for a put, the ask price is not less than K-S+PV(D), and the bid price is not larger than K. For the European SPX options, we adjust the arbitrage bound by replacing K with Ke -rt. 7

10 =_ +_, where (1.1) _ =,,,,,, _ =,,,,,, =_ +_, where (1.2) _ =,,,,,, _ =,,,,,, where i indexes stocks having traded options in month t, τ is the τth trading day in month t, T indexes the option maturities, and K indexes strike prices.,,, is the number of newly opened call contracts purchased by non-market maker investors in month t on stock i across all maturities and strike prices, and where the remaining terms,,,,,,,, and,,,, are computed in an analogous manner. 6 We do not use delta adjusted number of contracts, which weights more on ITM options, because that OTM options are more liquid and attractive to speculators than ITM options, and that OTM index puts are the main instruments used for portfolio hedging. The measures of PDS and PDI used here are a simple measure of the net demand for option positions that have positive-exposure to the underlying stocks and SPX index, 6 We use open volume but not close volume because investors might close existing option positions not solely based on their perceptions about the future. Other conditions, such as past performance of the position, time to expiration and margin requirements, can also cause investors to close a position. For example, when the option expiration day is approaching, many investors close their stock option positions to avoid physical delivery of the underlying. In addition, margin requirements might also force investors to close short positions, even though they would otherwise be unwilling to do so. 8

11 respectively. The PDS and PDI are different from the proxies for option demand examined in Bollen and Whaley (2004) and Gârleanu, Pedersen, and Poteshman (2009), where the option demand is measured as the difference between buy and sell option volume or open interest. The PDS and PDI have positive-exposure to the underlying, while the option demand measures in the studies referred to above have positive-exposure to volatility. We use PDS and PDI instead of option demand because our intent is to capture changes in the exposure of investors to the direction of underlying price movements, which is one of the main drivers of option market activity identified by Lakonishik, Lee, Pearson and Poteshman (2007). The primary measure we use to examine the relation between sentiment and option prices is the slope of the implied volatility function, i.e., the implied volatility difference between OTM calls and OTM puts. 7 For individual stock options, the slope measure is the average slope across all stocks in the sample in the month of interest. For index options, the slope measure is the slope of the implied volatility function for SPX options. Specifically, the slope measures for stock options (SlopeS t ) and SPX options (SlopeI t ) in month are given by: = 1 _,, _,, (2.1) =_,, _,, (2.2) where N t is the number of stocks having both OTM calls and OTM puts on the last trading day of month t, _,, and _,, are the implied volatilities (IVs) of OTM calls and OTM puts with strike price K and maturity T for underlying stock i. The above slope 7 We consider options with (or ) are OTM calls (or OTM puts). When computing the option delta, i.e., and, we estimate volatility using the previous 60 trading days stock or index returns. We obtain similar results by using the implied volatilities of the options to compute delta or by using K/S to classify moneyness. 9

12 measures are similar to the measure used by Bollen and Whaley (2004), and are essentially equivalent to the risk-neutral skewness embedded in option prices (Bakshi, Kapadia and Madan (2003)). We use the slope of the volatility smile instead of model-free risk-neutral skewness developed in Bakshi, Kapadia and 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. 1.3 Sentiment Measures We employ two main measures of investor sentiment. The first is the monthly index of Consumer Sentiment (CS) collected by University of Michigan. We view CS as a measure of the sentiment of individual investors 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 future returns on small stocks and those with low institutional ownership. The second measure is the Baker and Wurgler (2006) sentiment index (BW). This sentiment index is based on the first principal component of six sentiment proxies orthogonalized to a set of macroeconomic variables. The six sentiment proxies include NYSE turnover, the dividend premium, the closed-end fund discount, the number and first-day returns on IPOs, and the equity share in new issues. In contrast to the consumer confidence index, which is based on survey data, the Baker and Wurgler measure is generated from market data. We also use sentiment estimated by the bull-bear spread (BB) based on the Investor s Intelligence survey on investment newsletter writers. Han (2008) considers the bull-bear spread as a proxy for institutional investor sentiment because many of the writers are market professionals. Han (2008) finds that among three measures of institutional investor sentiment, 10

13 BB has the most power to explain the prices of index options. In this study, we use BB as a control variable to help isolate the sentiment of unsophisticated traders from that of more sophisticated market participants. In addition to the direct sentiment measures, we also use lagged market returns to capture the idea that changes in stock valuations are likely to be associated with both hedging demands and with the potential for overreaction by unsophisticated traders. 8 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, while Lakonishok, Lee, Pearson, and Poteshman (2007) show that the least sophisticated investors increased their exposure to growth stocks through the options market during the stock-market bubble of the late 1990 s and early Index and stock option trading 2.1 Summary statistics Table 1 presents summary statistics for the main variables. The level and monthly change of positive-exposure demand for stock options (PDS and 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 positiveexposure demand for SPX index options (PDI, PDI_C and PDI_P) are all negative, especially for puts (PDI_P), suggesting put purchases comprise the bulk of index option trading (Bollen 8 In addition, the measures of investor sentiment are also likely in part driven by past stock returns and we wish to separate the component on sentiment that is unrelated to market returns from sentiment associated with changes in stock market valuations. 11

14 and Whaley (2004)). The slope of the volatility smile for stock options (SlopeS) is -204 basis points (-2.04%), 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 implied volatility function for index options (SlopeI) is -415 basis points, which is much more negative than SlopeS, and is consistent with the high demand for index puts as portfolio insurance. Insert Table 1 around here The Michigan consumer sentiment index (CS) has a mean value and strong auto correlation (0.93), while its monthly change dcs has a mean close to zero and near zero autocorrelation. The other two sentiment measures, stock market sentiment from Baker and Wurgler (2006) (BW) and institutional investor sentiment measured by the Bull-Bear Spread (BB), also exhibit high auto-correlation in levels. Table 1 also reports summary statistics for the realized volatility for stocks and the S&P500 index over the remaining life of the option contracts ( or ), and the monthly excess return on the value-weighted CRSP index (Rm). Table 2 reports the correlation coefficients for the main variables used in the tests. The positive-exposure demand for stock calls and puts, PDS_C and PDS_P, are positively correlated with each other, and the positive-exposure demand for index calls, PDI_C, is positively correlated with PDS and PDS_P. In contrast, the positive-exposure demand for index puts, PDI_P, is uncorrelated with PDS, PDS_C or PDS_P. These correlations suggest PDI_P is driven by different forces from those that influence PDS_C, PDS_P and PDI_C. The positiveexposure demand for stock options (PDS) is positively correlated with the slope of the stock option implied volatility smile (SlopeS) and with the measures of investor sentiment and lagged market returns (Rm -1 ). In contrast, the positive-exposure demand for index puts (PDI_P) has 12

15 either negative or near zero correlations with the sentiment and past market returns. The slope of stock option smile, SlopeS, is positively correlated with both the levels and changes of the consumer sentiment and Baker Wurgler sentiment variables and lagged market returns. In contrast, the slope of the SPX index option smile, SlopeI, is negatively associated with CS and BW, and exhibits a small positive correlation with dcs and Rm -1. These correlation coefficients provide preliminary evidence consistent with the view that our sentiment measures are positively associated with the demand for options that increase 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 options. Insert Table 2 here 2.2 Option trading, sentiment, and stock returns Figure 1 plots the time series of PDS and PDI, the level of the S&P 500 index, and of the two sentiment measures. 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 of PDS with 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 1 around here 2.3 Option trading behavior of different investor types 13

16 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 open buy and open sell option volume obtained from the CBOE for the time period from 1990 to 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 be an employee of Goldman Sachs trading for the bank s own account. From 1990 to 2001, the CBOE further subdivided the public customer data into orders that originated from customers of discount brokerages, customers of full-service brokerages, and other public customers. Clients of brokerage firms such as E-Trade are an example of discount brokerage 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 subdivided 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 customers/small trade sizes as most likely to be associated with unsophisticated investors, and full service customers/large trade sizes and the other customers/medium size trades as more likely to be associated with relatively more sophisticated investors (for example, most 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 14

17 new purchased call (put) positions before stock price increases (decreases). Also Mahani and Poteshman (2005) show that discount brokerage customers have a greater propensity for entering option positions that load up on growth stocks relative to value stocks in the days leading up to earning announcements, despite the fact that at earnings announcements value stocks tend to outperform growth stocks by a wide margin (LaPorta et al. (1997)). Figure 2 depicts the monthly percentage of total non-market maker volume attributable to each class of investors. The percentage volume is computed as the sum of buy and sell option volume for a particular type of investor divided by the sum of long and short volume of all nonmarket maker investors. Figure 2 shows that discount/small public customers trade stock options much more actively than index options, while sophisticated public customers are active traders of both stock and index options. Trading generated from discount brokerage customers and small trades constitutes 18% of total non-market maker trading volume of stock options, but only 3% of total trading volume of SPX index options for the period 1990 through Full service customers and large trades make up the majority of both stock and index option trading volume, representing 58% of non-market maker volume in stock options and 55% of non-market maker volume in index options. Trading by other public/medium customers represents about 20% of trading volume in both stock and index options. Insert Figure 2 around here 3. Results In this section we present our main results. We first examine how the measures of investor sentiment and lagged market returns are related to option demand. We then investigate the associations of sentiment and past returns with the pricing of stock and index options and the 15

18 profitability of a contrarian trading strategy based on sentiment and past returns. We also present several robustness tests and conclude with an examination of the cross-sectional effects of sentiment on positive-exposure demand for stock options and stock option prices Determinants of Speculation and Hedge 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 positiveexposure demand for index options (PDI) is more likely to be driven by hedging needs. In contrast, we argue that the positive-exposure demand for stock options (PDS) is more likely to be driven by the desire to speculate on the future direction of stock prices. To investigate how the demand for options is influenced by sentiment, we estimate the following time-series regression specifications: = (3.1) = , (3.2) where PDS t and PDI t are computed from Eq.( ). In the analysis, we also break down PDS t and PDI t into the components associated with call and put options separately. Sent t is sentiment measured either by the Michgan index of Consumer Sentiment (CS) or the Baker and Wurgler (2006) sentiment index (BW). Because PDS, PDI, CS and BW have high autocorrelations, we also use their monthly changes in some model specifications. 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. 9 The results are presented in Table 3. In the left hand side of Panel A, when the dependent variable is the level of positive-exposure demand for stock options (PDS), the coefficient 9 We also try the specifications that include underlying volatilities and bull-bear sentiment, the coefficient estimates on these variables are not statistically different from zero. 16

19 estimates on the raw measure of consumer sentiment (CS) and its monthly change (dcs) are positive and statistically significant. The coefficient estimates on the sentiment measures BW and dbw are also positive, but are not statistically significant. This finding is consistent with Lemmon and Portniaguina (2006), who also find that the Michigan index is a better predictor of the small stock return premium than the Baker Wurgler measure after The coefficient estimates on both lagged and contemporaneous market returns are positive and statistically significant. In addition, the coefficient estimates on lagged market returns are approximately twice as large as those on contemporaneous market returns. In Panel B, when the dependent variable is the monthly change of positive-exposure demand for stock options (dpds), the coefficient estimates on dcs and lagged market returns remain positive and statistically significant. In economic terms, a one standard deviation change in dcs is associated with a five unit change in dpds, amounting to 23% of the unconditional standard deviation of dpds. A one standard deviation change in the lagged market return is associated with a 8.32 change in dpds, amounting to 38% of the unconditional standard deviation of dpds. 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_p than to dpds_c. For put demand, the coefficient estimate on dcs is 0.51 with a t-statistic of 2.28, while for call demand, the coefficient estimate is 0.24 with a t-statistic of This result is consistent with the findings in Lakonishok et al.(2007), who document that hedging does not appear to motivate trading of 17

20 stock options except for the writing of covered calls 10, and that the trading of stock puts, in particular, tend to be naked positions motivated by directional bets on stock prices. Panel C and D also show that dpds_p and dpds_c are 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 various sentiment measures and past market returns are insignificant when PDI or dpdi is the dependent variable. Breaking down dpdi into the demands for puts and calls separately shows that the monthly change of positive-exposure demand for puts (dpdi_p) is negatively related to contemporaneous market returns (although the coefficient estimates are not statistically significant). The negative coefficient on the contemporaneous market return is however consistent with the view that the hedging demand for SPX puts increases when the market is going up. The results presented in Table 3 confirm the visual observations in Figure 1. The timeseries variation in the positive-exposure demands for stock options and index options do not follow the same patterns. When consumer sentiment and past returns are high, investors increase their exposures to individual stocks through the options market by purchasing calls and selling 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, but there is some evidence that relatively more index puts are purchased when contemporaneous market returns are high. 10 Writing a covered call refers to writing a call and purchasing the underlying stock. One of the reasons for the popularity of covered calls is that the only option transactions permitted in an Individual Retirement Account(IRA) is the writing of covered calls. Purchasing a call or put within an IRA requires certain qualifications to be met (Ameritrade Handbook for Margins). 18

21 Referring back to Figure 2, 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 coefficient estimates on the change in consumer sentiment (dcs) and lagged market returns from regressions (3.1) and (3.2), where the dependent variables are the monthly change of positive-exposure demand for stock options (dpds) or index options (dpdi) of different types of investors. Panel A reports the results for the period and panel B reports results 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 magnitude of the coefficient estimate on dcs is largest for discount/small investors and turns negative for firm proprietary traders. In the first time period, the coefficient estimate on dcs is statistically significant for discount brokerage customers, while in the latter period, the coefficient estimates are statistically significant for both small and medium trades. When the dependent variable is dpdi, none of the coefficient estimates on dcs are statistically significant. Insert Table 4 around here The coefficient estimates on lagged market returns are positive and statistically significant for discount brokerage customers and small trades, while the coefficient estimates on 19

22 lagged returns are negative for firm proprietary traders/large trades when the dependent variable is dpds. When the dependent variable is dpdi, the coefficient estimates on lagged returns are not significant for discount brokerage customers or small trades, but remain negative and statistically significant for firm proprietary traders/large trades. Overall, the results suggest that less sophisticated investors (proxied by discount 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 market returns. In contrast, firm proprietary traders trades appear to act more like market makers and take the opposite side of these trades Sentiment and Option Prices The previous section documents that the measures of 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 our sentiment and return measures 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 option prices. Specifically, our prior results show that investors increase their exposures to underlying stocks through the options market when sentiment and past market returns are high. Given the fact that the volume of OTM options is far greater than that of ITM options, the results suggest that demand for high strike options will be larger than demand for low strike options following 20

23 increases in sentiment or high market returns. Based on this argument, we expect the slope of the implied volatility function 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. as follows: The empirical specification used to investigate the impact of sentiment on option prices is = + +h (4.1) = + +h ,(4.2) where SlopeS t and SlopeI t are slope of implied volatility smile for stock and SPX index options and are calculated based on Eqs. (2.1) and (2.2), Sent t is sentiment measured either by Michgan index of Consumer Sentiment (CS) or the Baker and Wurgler (2006) sentiment index (BW). In some specifications, we instead use the monthly changes in the sentiment measures to estimate the coefficients and. and are previous and contemporaneous monthly market returns. If sentiment affects option prices through changes in demand, then the coefficient will be positive and significant, and the coefficient will be less than. Similarly, the coefficients on past market returns will be positive only for stock options. Alternatively, if sentiment and past returns instead influence option prices because they proxies for changes in risk preferences or fundamentals, we expect that the coefficients and, and h and h will be in same sign, as innovations in risk or fundamentals should affect prices of both index and stock options in similar ways. 11 Note that to the extent that the sentiment related demands for purchasing calls and selling puts are roughly equal, there will be no effect of sentiment on the prices of at-the-money options. In unreported results this is indeed what we find. 21

24 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) find that volatility is negatively related to the slope of the volatility smile for index options, and Dennis and Mayhew (2002), and Han (2008) find that volatility is related to the risk neutral skewness of both stock and index options, respectively. 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 for contemporaneous market returns because Amin, Coval and Seyhun (2004) document that S&P 100 index call (put) prices are overvalued following large upside (downside) market movements. Finally, we include the past month s 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 and dcs are positive and significant. In economic terms, a one standard deviation increase of dcs is associated with an 42 basis point increase in the slope of the implied volatility function for stock options (SlopeS), a magnitude equivalent to 15% of the unconditional standard deviation of SlopeS. The coefficient estimates for BW and dbw are also positive, but exhibit smaller t-statistics. This finding is consistent with the evidence in Section 3.1 that the Baker and Wurgler sentiment measure (BW) has a weaker relationship with the positive-exposure demand for stock options than does the index of consumer sentiment (CS). Also consistent with the results from the demand regressions, the coefficient estimates on lagged market returns are positive and statistically significant. In economic terms, in the regression that controls for dcs, 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 function. 12 For individual stock options, we average the realized volatility across options in the sample. 22

25 The results for index options (Panel B) exhibit a different pattern. None of the coefficient estimates on the various sentiment measures 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 estimates on BB (a measure of institutional investor sentiment) are not significantly related to the slope of the implied volatility function for stock options. For index options, however, the coefficient estimate on the level of BB is positive and statistically significant, which is consistent with the empirical findings of Han (2008). The coefficient estimates on realized volatility ( or ) are negative in most specifications. The negative relation between volatility and 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. Insert Table 5 around Here 3.3. Trading Strategy The results in the 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 contrarian trading strategy that sells calls and buys puts or buys calls and sells puts conditional on sentiment and lagged returns. In particular, we sell OTM calls and buy 23

26 OTM puts in the last three trading days of the month if the change in consumer confidence (dcs) in that month is larger than 1 or 2 points and the previous months market risk premium minus 0.5% (Rm %) is larger than 1% or 2%. And we buy OTM calls and sell OTM puts when dcs is less than -1 or -2 and Rm % is less than -1% or -2%. We subtract 0.5% because the average market premium in our sample is around 0.5% per month. In selecting the OTM call and put pairs for each underlying stock, we require each pair to have: (i) same maturity of less than 60 trading days; (ii) non-zero trading volume; (iii) larger than $0.125 bid price, and 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 price. The return with delta hedging is the proceeds from the delta hedged position divided by the average call and put price. To estimate delta, we use both historical volatility based on daily returns of the underlying stock in the previous 60 trading days and realized volatility based on the daily returns during the remaining life of the option contracts. The results are reported in Table 6. As seen in the table, 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 >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 >2%. Even after accounting for transactions costs, the returns for all of the unhedged strategies and those of the hedged strategies conditioned on Rm >2% yield positive and statistically significant returns. For example, the strategy that conditions on dcs >2, and Rm >2% yields returns after transactions costs of 32.08% 24