Investor Sentiment and Option Prices: Evidence from Value and Growth Index Options

Transcription

1 Investor Sentiment and Option Prices: Evidence from Value and Growth Index Options Jerry Coakley, George Dotsis, Xiaoquan Liu, and Jia Zhai Essex Business School, Essex University 2 March, 2011 Abstract This paper examines the impact of investor sentiment on the valuation of value and growth index options. To this end, we investigate the empirical relationship between institutional and individual sentiment and time variation in the risk-neutral skewness derived from options written on S&P 500, Nasdaq 100, Russell 2000 Value and Growth indices. We find that the risk-neutral skewness of the S&P 500 and Russell 2000 Value index options is affected by institutional sentiment. Meanwhile, the skewness of the riskneutral density of Nasdaq 100 and Russell 2000 Growth index options is significantly positively related to individual sentiment. Our empirical results provide evidence that options on portfolios of growth stocks are more likely to be affected by the behavior of unsophisticated investors. Essex Business School, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK. 1

2 1. Introduction In the past decade, a rapidly growing number of studies have investigated empirical anomalies in financial markets that do not seem to conform to neo-classic economics theories and found that psychological biases and investor sentiment play an important role in the determination of asset prices (see Baker and Wurgler 2006 and 2007; Coval and Shumway, 2005; Grinblatt and Han, 2005; Kumar and Lee, 2006; Lemmon and Portniaguina, 2006; Mahani and Poteshman, 2008; and Tversky and Kahneman, 1992, among others). In this paper, we draw upon three strands of literature and examine the relationship between investor sentiment and risk-neutral skewness of value and stock index options. In the behavioral finance literature, Baker and Wurgler (2006) provide evidence that investor sentiment has significant effect on the cross section of stock returns. Adopting the principal component analysis, they extract common sentiment-related information from six macroeconomic variables to construct proxies for sentiment. Empirical evidence over a long sample period from 1961 to 2001 suggests that future stock returns vary significantly with beginning-of-period sentiment index. In addition, firm characteristics such as firm age, return volatility, and growth prospect that have little unconditional predictive power show strong conditional patterns when conditioned upon sentiment. The authors also show that these results cannot be explained by riskmotivated models. The link between asset valuation and investor sentiment is also the subject of examination in Brown and Cliff (2004, 2005), Kumar and Lee (2006), and 2

3 Lemmon and Portniaguina (2006). Schmeling (2009) provide international evidence on investor sentiment and stock returns for 18 industrial countries. In the option pricing literature, behavioral biases and sentiment are also reported to affect option prices. Poteshman (2001) find that in the S&P 500 index options market, investors underreact to information in the short term, overreact information over long horizons, and underreact (overreact) to current changes in risk that are preceded mostly by changes of the opposite (same) sign. These findings are consistent with a model of investor sentiment proposed by Barberis, Shleifer, and Vishny (1998) and are robust to model misspecification or estimation errors. More closely related to our work is Han (2008), who studies whether investor sentiment affects S&P 500 option prices via changing the risk-neutral skewness of these options. Adopting three sentiment proxies, he finds a positive relationship between investor sentiment and risk-neutral skewness. In particular, the risk-neutral skewness becomes significantly more negative when investor sentiment is bearish while the risk-neutral skewness becomes more positive when sentiment is bullish. The results are robust to alternative measures of skewness and the inclusion of control variables that are found to relate to risk-neutral skewness, such as implied volatilities (Bakshi, Kapadia, and Madan, 2003), relative demand for options (Bollen and Whaley, 2004, and Garleanu, Pederson and Poteshman, 2009), and stock market momentum (Brown and Cliff, 2004). 3

4 In our study, we test the relationship between proxies of investor sentiment and the riskneutral skewness from options written on two value indices, the S&P 500 index and the Russell 2000 Value index, and two growth indices, the NASDAQ index and the Russell 2000 Growth index. Hence we also contribute to the strand of literature that examines the clientele effect. The clientele effect is well-documented in the equity market, especially in the study of tax effect of dividend payment (see, for example, Graham, Michaely, and Roberts, 2003, Grinstein and Michaely, 2005, and Mori, 2010, among others). Kumar and Lee (2006) identify clienteles for growth and value stocks and suggest that the different clientele sentiment can explain the cross section of stock returns. Baker and Wurgler (2006) argue that low-cap stocks, younger, unprofitable, highly volatile, non-dividend paying, growth stocks, or stocks of firms in financial distress, are more likely to be affected by investor sentiment. Similar results are also reported in Lemmon and Portniaguina (2006). In the options market, Blackburn, Goetzmann, and Uhkov (2007) closely study the risk attitude embedded in traders of growth and value index options. They infer latent risk aversion coefficient as the difference between risk-neutral probability density function and subject price distribution from options written on five pairs of major US value and growth index options. They find that on average value investors exhibit a higher level of risk aversion than growth investors. Based on this result, they construct trading strategies in the value and growth index options market that in buying risk from one clientele and selling it to the other. The strategies generate modest positive returns of their sample 4

5 period, which is limited by data availability. Their results suggest the existence of significant clientele effect in the options market. From the perspective of investors, evidence of clientele effect between unsophisticated individual investors who are more prone to sentiment and more sophisticated or institutional investors who are rational and efficient at decision making is growing. This segmentation of investors has an impact on the valuation of value and growth stocks and their derivatives. Mahani and Poteshman (2008) classify three categories of sophistication among investors and find that the least sophisticated group increases their long position on growth stock options relative to value stock options shortly before earnings announcement dates while the most sophisticated investors do not. This finding is made more significant as value stocks outperform growth stocks by a big margin on earnings announcement dates. In a similar vein, Lemmon and Ni (2010) study the trading pattern of options written on S&P 500 index and their composite stock options. They show that stock options are actively traded by unsophisticated investors for speculation while index options trades are motivated by sophisticated investors for the purpose of hedging. In this paper, we contribute to the literature by making a careful distinction between individual and institutional investors and study the empirical relationship of their respective sentiment and time-varying risk-neutral skewness of value and growth index options. We examine traded options written on four indices, the S&P 500 index, the 5

6 Nasdaq 100 index, and the Russell 2000 Value and Growth indices 1. Among the four indices, the S&P 500 index and Russell 2000 Value index mainly consist of blue-chip value stocks; while the Nasdaq 100 and Russell 2000 Growth index are mainly made up of younger and smaller stocks with higher expected growth rate. Our sample period is from June 2001 to January We first extract model-free risk-neutral skewness following Bakshi, Kapadia and Madan (2003). This is a popular choice for inferring risk-neutral moments from option prices and free from potential model misspecification (Han, 2008, and Taylor, Yadav and Zhang, 2009, among others). In the empirical analysis we rely on four popular measures of investor sentiment in order to disentangle institutional sentiment from individual sentiment. We use (1) the index of consumer sentiment based on the survey conducted by University of Michigan; (2) the net position of large speculators in S&P 500 Index Futures provided by the Commodity Futures Trading Commission (CFTC); (3) the bull-bear spread computed by Investors Intelligence; and (4) the market sentiment proxy from Baker and Wurgler (2007). The index of consumer sentiment compiled by the University of Michigan is used as a measure of individual sentiment, which reflects the behavior of unsophisticated investors. 1 The Russell 2000 indices measure the performance of US small-cap equity segment and have a liquid options market. The Russell 2000 growth index includes those companies with higher price-to-book ratios (3.49) and forecasted growth values (16.18%). The Russell 2000 value index includes those with lower price-to-market ratios (1.39) and lower forecasted growth values (9.48%). Both indices are reconstituted annually to ensure that larger stocks do not distort the performance and characteristics of small-cap stocks ( 6

7 In Lemmon and Portniaguina (2006), the authors find that the returns of small capitalization stocks and those with low institutional ownership can be predicted by this measure of consumer sentiment. The net position of large speculators and the bull-bear spread are considered institutional sentiment. Han (2008) shows that both measures can help explain time variation in the risk-neutral skewness of S&P 500 options. Finally, the sentiment measure of Baker and Wurgler (2007) is derived from market data and based on the first principal component of various sentiment proxies. The authors consider this measure as a proxy for broad waves of market sentiment. Using monthly data from June 2001 to January 2010, our regression analysis shows that there is a consistent pattern that the risk-neutral skewness of options written on both growth indices are significantly positively related to individual sentiment. This relationship is robust to the inclusion additional control variables such as relative demand for index options, capitalization of composite stocks, and future return jumps. We consider this finding as evidence that option prices on growth indices are more likely to be affected by the behavior of unsophisticated individual investors. We also find some evidence that only institutional sentiment affects the risk-neutral skewness of options written on value indices. Different from Han (2008) but consistent with Birru and Figlewski (2010), we find the relationship to be negative, implying that the risk-neutral skewness becomes more negative (positive) when investors are more optimistic (pessimistic) towards economic prospects. This difference could be a result from different sample periods under investigation. 7

8 The reminder of this paper is organized as follows. In Section 2, we introduce the sentiment measures used in the analysis. In Section 3, we outline the methods for constructing model-free risk-neutral skewness from option prices, describe data, and analyze empirical results. In Section 4, we perform a number of robustness tests. Finally, we conclude in Section Sentiment Measures In the empirical analysis we use four alternative sentiment measures mainly to distinguish between institutional and individual sentiment. For individual sentiment we use the Michigan Consumer Confidence Index (CS), which is compiled from consumer confidence surveys. The Michigan Consumer Research Centre has been conducting the survey since 1947, accessing consumer confidence regarding personal finances, business conditions and purchasing power based on 500 surveys. Answers to each question are translated into a relative score to compile the index. The index is available on a monthly basis since 1978 and considered one of the leading indicators of perceived health of the US economy. The Consumer Confidence Index is viewed as a measure of individual investor sentiment since it is based on householder surveys. Han (2008) employs the net position of large speculators in the S&P 500 index futures market and the bull-bear spread as indications of bullish (bearish) market sentiment. He finds that the net position of large investors and the bull-bear spread capture the sentiment of institutional investors and help explain the time variation in risk-neutral 8

9 skewness of S&P 500 options. Following Han (2008), we first access the Commitments of Traders Reports from the Commodity Futures Trading Commission (CFTC). The CFTC requires large traders to report their positions on a daily basis. These data are used to aggregate a report that contains the breakdown of each Tuesday s open interest. The report contains the number of long positions and the number of short positions for both commercial traders and non-commercial traders. The non-commercials are large speculators. From non-commercials traders we compute the number of long-position contracts minus the number of short-position contracts, scaled by the total open interest in the S&P 500 index futures. The net-position (LS) is used as a proxy for institutional sentiment. The bull-bear spread (BB) computed by Investors Intelligence is based on a survey of over 120 market newsletters and measures the difference between the percentage of bullish advisors and the percentage of bearish advisors. This measure is based on the opinions of professional advisors and we use it as another proxy for institutional sentiment. The fourth proxy for investor sentiment (BW) is proposed in Baker and Wurgler (2007). The data are obtained from the official website of Wurgler and available from June 2001 to December 2007 on a monthly basis. This sentiment measure is based on principal component analysis and captures the common variation of six underlying sentiment proxies, i.e. trading volume as measured by NYSE turnover; the dividend premium; the 9

10 closed-end fund discount; the number and first-day returns on IPOs; and the equity share in new issues. 3. Data and Empirical Analysis 3.1 Risk-neutral Skewness Although a number of methods have been proposed to estimate the moments of the riskneutral density from option prices, in this paper we use the widely adopted model-free method developed by Bakshi, Kapadia and Madan (2003) 2. They express the risk-neutral skewness as a function of three contracts: the volatility contract, the cubic contract and the quadratic contract, respectively, as follows, q r Vt (, τ ) E{ e τ R t } 2, τ q r Wt (, τ ) E{ e τ R t } 3, τ q rτ 4 X ( t, τ ) E { e R }. At date t, they show that the three contracts have the following form: t,τ St 2(1 ln[ K / St ]) Vt (, τ) = Ct (, τ; KdK ) 0 2 K St 2(1 + ln[ S t / K ]) + Pt (, τ; KdK ), 0 2 K 2 6ln[ K / St] 3(ln[ K / St]) Wt (, τ) = Ct (, τ; KdK ) S 2 t K 2 St 6ln[ St / K] 3(ln[ St / K]) Pt (, τ; KdK ) 0 2 K (1) (2) 2 Other methods include the mixture of lognormal distributions of Melick and Thomas (1997), the implied binomial tree of Jackwerth and Rubinstein (1996), and the cublic spline of Bliss and Panigirtzoglou (2002). 10

11 2 3 12(ln[ K / St]) 4(ln[ K / St]) X (, t τ) = C(, t τ; K) dk S 2 t K 2 3 St 12(ln[ St / K]) + 4(ln[ St / K]) + Pt (, τ; KdK ), 0 2 K (3) The risk-neutral variance and skewness can be expressed as: VAR(, t τ ) E {( R E [ R ])} = e V (, t τ) μ(, t τ) (4) q q 2 rτ 2 t, τ t, τ E {( R E [ R ]) } e W( t, ) 3 e ( t, ) V( t, ) + 2 ( t, ) SKEW (, t τ ) = = E R E R e V t t q q 3 rτ rτ 3 t, τ t, τ τ μ τ τ μ τ q q 2 3/2 rτ 2 3/2 {( t, τ [ t, τ]) } [ (, τ) μ(, τ) ] (5) 3.2 Data and summary statistics Option prices are collected by Ivy Database of OptionMetrics, which provides historical prices of options based on closing quotes at the Chicago Board of Option Exchange (CBOE). The sample period in our analysis is from June, 2001 to January, We use end of month observations to construct the risk-neutral moments and we obtain a total of 104 monthly observations. We extract the security ID, trading date, expiration date, call or put flag, strike price, best bid, best offer and implied volatility from the option price file for S&P 500 (SPX), Nasdaq 100 (NDAQ), Russell 2000 Growth (RSG) and Russell 2000 Value (RSV). Underlying security prices and interest rates are taken separately from the security price file and the zero curve file. The following conventional selection criteria are applied to our data. First, we require the trading volume to be non-zero in order to avoid stale quotes. To reduce noise caused by bid-ask bounce we use the mid-point of best bid and best offer price as the observed option price. Second, we only make use of out-of-money (OTM) call and put options, 11

12 which are the most frequently traded options and effectively cover the whole moneyness spectrum. Third, we only focus on the trading days that have at least two OTM call prices and two OTM put prices. We use the trapezoidal rule to estimate the integrals with discrete data in equations (1) to (3). It is important to note that since we do not have a continuum of option prices, there are two possible sources of biases: discreteness and asymmetry of integration. We follow Carr and Wu (2004) and Jiang and Tian (2005), for each maturity we interpolate implied volatilities across moneyness levels (K/S) to obtain a continuum of implied volatilities. For moneyness below the lowest available moneyness level in the market, we use the implied volatility at the lowest strike price. For moneyness above the highest available moneyness, we use the implied volatility at the highest strike. After this interpolation and extrapolation procedure, we are able to generate a fine grid of 1000 implied volatilities for moneyness levels between 0.01% and 300% from current spot price. Given this fine grid of implied volatilities, we obtain OTM call and put prices using the Black-Scholes formula (Black and Scholes, 1973). We calculate model-free skewness using options with two months to expiration (60 days), as this is one of the most actively traded maturities for the Russell 2000 Growth and Value index options. To construct a constant two-month to maturity risk-neutral skewness, we first compute mode-free moments using options that expire within the two nearest maturities (less than 60 days and greater than 60 days). Then we linearly interpolate between the two maturities to synthesize the risk-neutral skewness with 12

13 constant 60 days to maturity. The final sample for the four index options contains 104 observations of monthly risk-neutral skewness. Table 1 reports the summary statistics for risk-neutral skewness inferring from option prices. For all indices, the average skewness of the risk-neutral density is negative indicating higher changes of downward movement for the index than predicted by the lognormal distribution. The SPX index has the most negative skewness (-1.768) while the NDAQ is the least skewed (-0.771). The RSV index appears to be more negatively skewed than the RSG index ( and , respectively). The skewness of all indices is positively autocorrelated. SPX skewness has the highest autocorrelation (0.755) and RSV the lowest (0.306). Figure 1 shows the evolution of the risk-neutral skewness of these four indices from June 2001 to January 2010.The risk-neutral skewness of SPX fluctuates substantially over time, consistent with the high sample standard deviation reported in Table 1. Note that during the market turmoil that started in September 2008, the risk-neutral skewness of SPX increased substantially (became less negative). This is also noticed in Birru and Figlewski (2010). During that period, the implied volatility increased to 75%. This is consistent with parametric stochastic volatility models such as Heston (1993), in which the riskneutral skewness is an increasing function of the volatility state variable. The risk neutral skewness of the other three indices also varies over time but to a less extent. The riskneutral skewness of NDAQ increased after the events of September 2008 but not as much 13

14 as that for the SPX. The skewness of Russell 2000 Value and Growth indices seems more stable over time and does not substantially change during the period of the credit crunch. In Table 2, we present descriptive statistics of sentiment proxies and control variables. The mean value of Michigan Consumer Confidence Index (CS) is with a standard deviation and strong autocorrelation (0.9546). Lemmon and Ni (2010) report similar results. The average level of the monthly LS series is and its standard deviation is , which is consistent with the findings of Han (2008). The average value of the BB variable is with a standard deviation of Figure 2 plots the three sentiment proxies (CS, LS, and BB) from June 2001 to January 2010 and BW from June 2001 to December Large speculators in the S&P 500 index futures were substantially short after August 2007 (the hedge funds crisis) and reverted back to long positions in Note that after the events of September 2008, large speculators continued to be net-long in the S&P 500 index futures. The Consumer Confidence Index (CS) shows little variation over the time-period After September 2008 consumer confidence reached historical lows and started to increase again after the middle of Similarly, the bull-bear spread declined sharply after September The BW sentiment index of Baker and Wurgler (2006) decreased substantially during the period between 2001 and 2003 after the dot-com bubble and had a small upward trend between 2003 and In Table 3, we report the correlation coefficients of the variables used in the empirical analysis. We first notice that the sentiment proxies are not highly correlated among 14

15 themselves. The correlation coefficient between consumer confidence (CS) and net position of large speculators (LS) is , and the coefficient between CS and bullbear spread (BB) is The correlation between two institutional sentiment indices is The CS variable has a high positive correlation with the risk-neutral skewness of Nasdaq and Russell 2000 Growth index options ( and , respectively). The correlation between CS and RSV is small and negative ( ). The LS variable has a negative correlation with the risk-neutral skewness of all indices. The BB variable is positively correlated with risk-neutral skewness from growth index options while negatively correlated with that from value index options. Overall, these correlation coefficients provide some preliminary evidence that the risk-neutral skewness of growth index option prices may be affected more by consumer sentiment. 3.3 Empirical Analysis In this section, we report our regression results on how intuitional and individual sentiment affects the skewness of the risk-neutral density of SPX, NDAQ, RSG and RSV index options. We use the following baseline regression, Skew = a + b Sent + b Vol + b Skew + ε (6) t 1 t 1 2 t 3 t 1 t where Skew t is the risk-neutral skewness calculated according to equation (5) at time t, Sent is a sentiment variable at time t-1 and measured either by institutional sentiment t 1 (LS or BB), individual sentiment (CS) or the market based sentiment index of Baker and Wurgler (2007) (BW). We include a lagged skewness Skewt 1 as a control variable to take 15

16 into account the positive autocorrelation in skewness dynamics. We also include the implied volatility Vol t as an independent variable because in many stochastic volatility models (Heston, 1993) volatility is an important determinant of skewness (Han, 2008). The implied volatility is constructed according to equation (4) and has a constant 60-day to maturity. In Table 4, we report the regression results when sentiment is measured either by LS or CS. We use the Newey-West method to account for heteroscedasticity and serial correlation of the standard errors of the coefficients (Newey and West, 1987). For the value index options, risk-neutral skewness is negatively related to institutional sentiment as measured by net position of large speculators (LS) and the relation is statistically significant. This is the case whether LS is the sole sentiment measure (model 1) with coefficient of (t-stat -1.57) or one of the sentiment measures (model 3) with coefficient (t-stat -2.70) for SPX. The same pattern is found for Russell 2000 Value index options. LS is negative and significant when it is the sole sentiment measure with coefficient at (t-stat -2.79) or when it is one of two sentiment proxies with coefficient (t-stat -2.75). Han (2008) also finds low t-statistics but he obtains a positive coefficient for LS for the period from January 1988 to June This inconsistency may be attributed to the different sampling period used in our study. For the growth index options, we find that individual consumer sentiment measure CS is consistently positive and statistically significant whether it is the only sentiment measure in the regression model 1 (0.94 with t-stat of 2.80 for NDAQ and 0.50 with t-stat of

17 for RLG) and when both sentiment measures are adopted in model 3 (1.04 with t-stat of 3.10 for NDAQ and 0.41 with t-stat of 2.59 for RLG). For RLG, institutional sentiment LS is significant (model 2) but the coefficient is negative (-1.06 with t-stat at -2.09). In Table 5, we re-examine the regression analysis using CS coupled with bull-bear spread (BB) and in Table 6 we use CS coupled with the sentiment measure of Baker and Wurgler (2007) (BW). The results hardly change. The CS variable remains significantly positively related to the skewness of Russell 2000 Growth and Nasdaq 100 index options even after the inclusion of the BW or BB variable. The BW measure is statistically significant for the skewness of NDAQ and RSV options. However, contrary to Han (2008) we do not find a significant relationship between the risk-neutral skewness of the value index options and the bull-bear spread. Our empirical results can be summarized as follows. First, the risk-neutral skewness of value indices, i.e. the S&P 500 index and the Russell 2000 Value index, seems to be related mainly to institutional sentiment (LS) or market based sentiment (WB). However, different from previous studies (Han, 2008) we obtain a negative sign for the coefficient and this is not consistent with behavioral explanations although the same result is obtained in Birru and Figlewski (2010). The negative sign implies that when large speculators increase their long positions in the S&P 500 index futures, the skewness becomes more negative. 17

18 Second, the risk-neutral skewness of growth index options, i.e. the Russell 2000 Growth index and Nasdaq 100 index, is significantly related to individual consumer sentiment. In economic terms, when consumer confidence becomes more (less) confident the riskneutral density of Russell 2000 Growth and Nasdaq 100 indices is less (more) negatively skewed. The results provide further support for behavioral explanations of the value premium. Previous studies have shown that the returns of growth stocks are driven by sentiment and investors overreaction. Here we provide evidence that investor sentiment has also an impact on the option prices of growth indices. 4. Robustness Tests Additional Control Variables In this section, we undertake robustness tests by including additional control variables in the regression analysis. The first control variable is a proxy for the relative demand of index options (Relative Demand). Bollen and Whaley (2004) and Garleanu, Pedersen and Poteshman (2009) have shown that net buying pressure is an important determinant of the slope of the implied volatility smile. Following Han (2008) and Bollen and Whaley (2004), the pressure is defined as the ratio of the open interest for out-of-money index put options to the open interest for near- and at-the-money index options. The out-of-themoney puts are classified as those options whose delta falls between 38 Δp 18, where delta is the Black and Scholes (1973) option delta. The near and at-the-money options include calls with delta between 12 Δc 58 and puts with delta between 12 Δp

19 The second control variable is the most recent six-month index return of the underlying indices (Index Ret). Brown and Cliff (2004, 2005) find that sentiment changes are strongly correlated with contemporaneous market returns. In Table 7, we report the parameter estimates and the corresponding t-statistics. The riskneutral skewness of RSG and RSV is not significantly related to demand pressure or index returns. After including these two control variables, the CS remains significantly related to the risk- neutral skewness of Russell 2000 Growth index options. Demand pressure is a significant variable only in the case of NDAQ. Consistent with theory (Garleanu, Pedersen, and Poteshman, 2009), the coefficient of demand pressure is negative. When there is high demand for out-of-money put options, the risk-neutral skewness becomes more negative. After controlling for demand pressure, the CS remains a highly significant determinant of the NDAQ skewness. Large-capitalization Index (Russell 1000 Growth and Value indices) The Russell 2000 Value and Growth indices measure the performance of small capitalization firms. We also employ the Russell 1000 Value (RSVL) and Russell 1000 Growth (RSGL) to investigate whether our empirical results hold in large capitalization growth and value indices. The regression results are reported in Table 8. The coefficient of individual sentiment (CS) is not significantly related to the risk-neutral skewness of RSGL or RSGL. This finding is consistent with the results of Lemmon and Portniaguina (2006), who show that the Michigan index is a good predictor mainly for the returns of small capitalization stocks. Similarly, Lemmon and Ni (2010) find that impact of CS on 19

20 the implied volatility smile of individual stock options is more pronounced in the case of small capitalization stocks. Note also that mainly the returns of small growth portfolios are very difficult to be explained by standard rational asset pricing models (see, for example, Hodrick and Zhang, 2001). Future Return Jumps Similar to Lemmon and Ni (2010), we also test if individual sentiment is correlated with investors assessment of future return jumps. If investors assess rationally the probability of futures jumps this information could be reflected in the risk-neutral skewness. They would buy more put options relative to call options if they expect a negative jump and more calls relative to puts if they expect a positive jump. To examine if jump expectations subsume the information contained in CS we use one-month future realized skewness (Future Realized Skewness) as a proxy for future return jumps. Realized skewness is calculated using daily returns within every month in our sample and is used as an additional control variable with one-lag ahead in time in regression (6). The results are reported in Table 9. Individual sentiment (CS) remains a highly significant determinant of the risk-neutral skewness of both RSG and NDAQ. Consistent with the previous results, CS does not seem to be related to the risk-neutral skewness of RSV. 5. Concluding remarks In this paper, we test if investor sentiment affects the risk-neutral skewness of value and growth index options. We take the Russell 2000 Growth and Nasdaq 100 indices as growth portfolios and the S&P 500 index and Russell 2000 Value index as value 20

21 portfolios. We find that the risk-neutral-skewness of S&P 500 and Russell 2000 Value index options is affected by institutional sentiment. However, the skewness of the riskneutral density of Nasdaq 100 and Russell 2000 Growth index options is significantly positively related to individual sentiment. Our empirical results provide evidence that option prices on growth portfolios are more likely to be affected by the behavior of unsophisticated investors. These results are also consistent with behavioral theories of mispricing in growth stocks (e.g., Lakonishok, Shleifer, and Vishny 1994, and Baker and Wurgler, 2006). Growth stocks are found to be always overpriced relative to value stocks due to investors overreaction and more likely to be affected by investor sentiment. Our empirical results are also robust to a number of control variables. After controlling for demand pressure, which is shown to be an important determinant of the slope of implied volatility smile in Garleanu, Pedersen, and Poteshman (2009), the individual sentiment remains a highly significant determinant of the skewness of growth index options. Within the employment of large capitalization index options, our results show that individual sentiment is not significantly related to the skewness of large capitalization stocks, which is consistent with the findings of Lemmon and Portniaguina (2006). Finally, we test whether the investors assessment of future return jumps affects the impact of individual sentiment. Consistent with previous empirical results, the individual sentiment remains a significant determinant of the skewness of growth index options. 21

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26 Table 1: Summary Statistics for Risk-Neutral Skewness Summary statistics for the risk-neutral skewness of S&P500 (SPX), Russell 2000 Value (RSV), Nasdaq 100 (NDAQ) and Russell 2000 Growth (RSG). The risk-neutral skewness is derived according to Bakshi, Kapadia and Madan (2003). The data series cover the period from June, 2001 to January, 2010, a total of 104 monthly observations. Mean Median Stdev Serial Correlation S&P500 Index (SPX) Russell 2000 Value (RSV) Nasdaq 100 (NDAQ) Russell 2000 Growth (RSG)

27 Table 2: Summary Statistics for Sentiment Measures and Control Variables This table reports summary statistics for sentiment proxies and control variables. LS is the net positions of large speculators in the S&P 500 Futures market. CS comes from the consumer sentiment survey conducted by University of Michigan. BB is the bull-bear spread computed by Investors Intelligence. BW is based on Baker and Wurgler (2006). Implied Volatility is derived according to Bakshi, Kapadia and Madan (2003) and has a constant 60-day maturity. Relative demand is defined as the ratio of the open interest for the out-of-the-money index put options to the open interest for the near and at-the-money index options. The out-of-the-money puts are classified as those options whose delta satisfy 38 Δp 18.The near and at-the-money options include calls with 12 Δc 58 and puts with 12 Δp 38. All the data series, apart from BW cover the period from July, 2001 to January, 2010 with a total of 104 monthly observations. The BW data consists of 79 monthly observations from July, 2001 to December, Variable Mean Median Standard Deviation Serial Correlation The Net Position in SPX Index Futures (LS) Consumer Confidence Index (CS) Bull-Bear Spread (BB) Baker and Wurgler (2007) Sentiment Index (BW) Implied Volatility of S&P Implied Volatility - Russell 2000 Value Implied Volatility - Nasdaq Implied Volatility - Russell 2000 Growth Relative Demand - Russell 2000 Value Relative Demand - Russell 2000 Growth Relative Demand - NDAQ Nasdaq

28 Table 3: Correlation Coefficients of Variables This table reports correlation coefficient of the variables used in the empirical analysis. Riskneutral skewness of S&P 500 (SPX), Russell 2000 Growth (RSG), Nasdaq 100 (NDAQ) and Russell 2000 Value (RSV). BB is the bull-bear spread computed by Investors Intelligence. LS is the net positions of large speculators in the S&P 500 Futures market. CS comes from the consumer sentiment survey conducted by University of Michigan. The data series cover the period from June, 2001 to January, 2010 with a total of 104 monthly observations. BB LS CS NDAQ RSV RSG SPX BB LS CS NDAQ RSV RSG SPX

29 Table 4: Investor Sentiment and Risk-Neutral Skewness: Net Position of Large Speculators This table presents the regression results for S&P500 (SPX), Russell 2000 Growth (RSG), Nasdaq 100 (NDAQ) and Russell 2000 Value (RSV). The dependent variable is the risk-neutral skewness derived according to Bakshi, Kapadia and Madan (2003). The data consists of 104 monthly observations from July, 2001 to January, The explanatory variables are: LS measures the net position of large speculators in S&P500 (SPX), using the number of long position contracts minus the number of short position contracts. CS is the Consumer Confidence Index of University of Michigan. Below the coefficient estimated the parentheses contain t-statistics. Standard errors are adjusted for heteroscedasticity and series correlation according to Newey-West (1987). S&P500 (SPX) Russell 2000 Value (RSV) Variable (1) (2) (3) (1) (2) (3) LS ( ) ( ) ( ) ( ) CS ( ) ( ) (0.0203) ( ) Implied Volatility (2.7538) (1.5566) (1.5214) (1.7226) (0.7000) ( ) Lagged Dependent (5.7572) (6.5727) (6.0926) (4.7253) (5.0292) (4.7465) Adjusted R-square Nasdaq 100 (NDAQ) Russell 2000 Growth (RSG) Variables (1) (2) (3) (1) (2) (3) LS ( ) (1.1070) ( ) ( ) CS (2.7999) (3.1035) (3.3461) (2.5850) Implied Volatility ( ) (2.1681) (2.0351) ( ) (0.5614) (0.3900) Lagged Dependent (8.6019) (4.6857) (4.8613) (2.6958) (2.3401) (2.2327) Adjusted R-square

30 Table 5: Investor Sentiment and Risk-Neutral Skewness: Bull-Bear Spread This table presents the regression results for S&P500 (SPX), Russell 2000 Growth (RSG), Nasdaq 100 (NDAQ) and Russell 2000 Value (RSV). The dependent variable is the risk-neutral skewness derived according to Bakshi, Kapadia and Madan (2003). The data consists of 104 monthly observations from July, 2001 to January, The explanatory variables are: BB is the bull-bear spread computed by Investors Intelligence. CS is the Consumer Confidence Index of University of Michigan. Below the coefficient estimated the parentheses contain t-statistics. Standard errors are adjusted for heteroscedasticity and series correlation according to Newey-West (1987). S&P500 (SPX) Russell 2000 Value (RSV) Variable (1) (2) (3) (1) (2) (3) BB ( ) ( ) ( ) ( ) CS ( ) ( ) (0.0203) (0.4285) Implied Volatility (1.4431) (1.5566) (1.2699) (0.4059) (0.7000) (0.4878) Lagged Dependent (6.4100) (6.5727) (6.4926) (5.1942) (5.0292) (5.1113) Adjusted R-square Nasdaq 100 (NDAQ) Russell 2000 Growth (RSG) Variables (1) (2) (3) (1) (2) (3) BB (1.8427) ( ) ( ) ( ) CS (2.7999) (2.4494) (3.3461) (3.8925) Implied Volatility (1.1945) (2.1681) (1.4109) ( ) (0.5614) ( ) Lagged Dependent (7.7361) (4.6857) (4.3530) (3.3173) (2.3401) (2.3792) Adjusted R-square

31 Table 6: Investor Sentiment and Risk-Neutral Skewness: Baker and Wurgler (2007) Index This table presents the regression results for S&P500 (SPX), Russell 2000 Growth (RLG), Nasdaq 100 (NDAQ) and Russell 2000 Value (RSV). The dependent variable is the risk-neutral skewness derived according to Bakshi, Kapadia and Madan (2003). The data consists of 79 monthly observations from July, 2001 to December, The explanatory variables are: BW is based on Baker and Wurgler (2006). This sentiment measure is derived from market data and is based on the first principal component of six sentiment proxies where each of the proxies is first orthogonalized with respect to a set of macroeconomic conditions. CS is the Consumer Confidence Index of University of Michigan. Below the coefficient estimates the parentheses contain t-statistics. Standard errors are adjusted for heteroscedasticity and series correlation according to Newey-West (1987). S&P500 (SPX) Russell 2000 Value (RSV) Variable (1) (2) (3) (1) (2) (3) BW ( ) ( ) ( ) ( ) CS (0.0622) ( ) (0.1958) ( ) Implied Volatility (3.8729) (3.3911) (3.7350) (3.1296) (2.8554) (2.4333) Lagged Dependent (3.4645) (3.6281) (3.4910) (2.4795) (3.4015) (2.4357) Adjusted R-square Nasdaq 100 (NDAQ) Russell 2000 Growth (RSG) Variables (1) (2) (3) (1) (2) (3) BW ( ) ( ) (0.0262) (0.1622) CS (2.9027) (3.0163) (2.2543) (2.2939) Implied Volatility (2.1256) (2.5107) (2.8413) (0.4775) (0.8835) (0.7986) Lagged Dependent (2.9921) (2.9877) (2.8146) (2.4541) (2.2211) (2.2120) Adjusted R-square

32 Table 7: Investor Sentiment and Risk-Neutral Skewness: Robust to Demand Pressure This table presents regression results for Russell 2000 Growth (RLG), Nasdaq 100 (NDAQ) and Russell 2000 Value (RSV). The dependent variable is the risk-neutral skewness derived according to Bakshi, Kapadia and Madan (2003). The data consists of 104 monthly observations from July, 2001 to January, The explanatory variables are: LS measures the net position of large speculators in S&P500 (SPX), using the number of long position contracts minus the number of short position contracts. CS is the Consumer Confidence Index of University of Michigan. Relative demand is defined as the ratio of the open interest for the out-of-the-money index put options to the open interest for the near and at-themoney index options. The out-of-the-money puts are classified as those options whose Delta satisfy 38 Δp 18.The near and at-the-money options include calls and with 12 Δc 58 and puts with 12 Δp 38. Index Return is the six-month return of the index. Below the coefficient estimated the parentheses contain t-statistics. Standard errors are adjusted for heteroscedasticity and series correlation according to Newey-West (1987). Variable RSV RSG NDAQ LS (1.3403) (0.4335) ( ) CS ( ) (3.0939) (2.6964) Implied Volatility (1.3982) (0.6814) ( ) (0.7003) ( ) (0.0571) Relative Demand (0.9246) (0.9080) (0.6130) (0.6969) ( ) ( ) Index Return (0.4068) (0.3808) (0.0779) ( ) (0.0616) ( ) Lagged Dependent (4.8649) (5.3558) (3.1558) (2.3981) (6.8419) (4.7212) Adjusted R-square

33 Table 8: Investor Sentiment and Risk-Neutral Skewness: Robust to Capitalization This table presents the regression results for Russell 1000 Growth (RSGL) and Russell 2000 Value (RSVL). The dependent variable is the risk-neutral skewness derived according to Bakshi, Kapadia and Madan (2003). The data consists of 98 monthly observations from December, 2001 to January, The explanatory variables are: LS measures the net position of large speculators in S&P500 (SPX), using the number of long position contracts minus the number of short position contracts. CS is the Consumer Confidence Index of University of Michigan. Below the coefficient estimates the parentheses contain t-statistics. Standard errors are adjusted for heteroscedasticity and series correlation according to Newey-West (1987). Russell 1000 Value (RSVL) Russell 1000 Growth (RSGL) Variable (1) (2) (3) (1) (2) (3) LS ( ) ( ) (0.6015) (0.7135) CS ( ) ( ) (0.1435) (0.4124) Implied Volatility (3.0979) (1.0317) (0.9075) (4.2000) (3.3061) (3.3796) Lagged Dependent (1.1661) (1.0233) (1.0394) (2.2403) (2.2275) (2.1558) Adjusted R-square