МАГИСТЕРСКАЯ ДИССЕРТАЦИЯ MASTER THESIS

Transcription

1 МАГИСТЕРСКАЯ ДИССЕРТАЦИЯ MASTER THESIS Title: Using modern search engines and social networks to predict stock returns and volatility Название: Новый подход в предсказании волатильности и доходности акций Студент/ Student: Дмитрий Митрофанов/Dmitry Mitrofanov Научный руководитель/ Supervisor: Олег Шибанов/Oleg Shibanov Оценка/ Grade: Подпись/ Signature: Москва 0/03

2 Content Abstract 3. INTRODUCTION.4. THEORETICAL MODEL DATA 9 4. DESCRIPTIVE STATISTICS 0 5. RESULTS CONCLUSION ACKNOWLEDGEMENTS REFERENCES APPENDIX 6

3 Abstract In my Master Thesis I analyzed the use of modern search engines and social networks to predict stock returns and volatility. In particular, I developed a model to predict a future return and volatility of a particular stock using Google Trends which can provide us with search frequencies for particular company in Google search engine and investor sentiments, measured in Twitter. Recent literature, Google Search Volume and its Influence on Liquidity and Returns of German Stocks by Matthias Bank, Martin Larch; Can Internet Search Queries Help to Predict Stock Market Volatility? by Thomas Dimpfl and Stephan Jank, shows that an increase in search queries is associated with a rise in trading activity and stock return. I try to improve the predictive power of stock return and volatility by taking into account not only Search Volume Index(SVI), search frequencies from Google Trends for a particular company (as a proxy of investor attention to a particular company), but also investor sentiments. It comes from behavioral finance: when investors are in a good mood, they tend to be confident and underestimate the risk of investing in the stock of a particular company. In turn, it will increase the volatility and return of this stock. So, adding investor sentiment can considerably improve the prediction of stock return and volatility. I will show it using out of sample prediction analysis. Analyzing our model, I discovered different peculiar effects. For example, the increase of stock volatility due to increase in SVI of this company is higher when investors are happier. Also, the higher the market value of the company the less sensitive its stock volatility to SVI of this company. To estimate the mood of the society I use Twitter content, the ratio of smiley emoticons :) to frown emoticons :(. This Master Thesis add the new dimension to the existent literature, as both SVI and emotions on Twitter are used to predict stock returns and volatility. It is worth noting that empirical results are in accordance with theoretical model that is developed in our article. 3

4 . Introduction In this Master Thesis we use Google search query of firm names as a proxy for investor attention and study the implications for trading activity and returns of American stocks. We find that search volume is a good measure of investor recognition. In particular, an increase in Internet search volume in Google is related to higher volatility and leads to higher future returns of particular stock. Merton (987) introduces the notion of investor recognition and establishes that investor attention maybe relevant for stock pricing and liquidity. In practice, however, measuring investor recognition is a difficult task. For example, Fangand Peress (009) believes that attention attracted by a companies approximated by the number of published newspaper articles. Unfortunately, there is no reliable information as to the extent to which readers of a newspaper pay attention to the mention of a company in its pages. Other measures of investor attention, such as analyst coverage or advertisement expenditures, suffer from similar shortcomings. As an alternative proxy for investor recognition, Daetal. (009) propose using of information conveyed by search volume on Google. The number of search queries as an indicator for public interest has great appeal. First, the importance of the World Wide Web has grown significantly; it is the largest pool of freely available information, accessible to almost everyone nearly everywhere. Second, search volume seems appropriate, since an Internet user will only actively google a specific key word if she is interested in the object underlying the search term. Our study contributes to the research that focuses on the relation between investor attention and stock liquidity and return. We try to improve the predictive power of stock return and volatility by taking into account not only Search Volume Index (SVI) search frequencies from Google Trends for particular company (as a proxy of investor attention to a particular company), but also investor sentiments. According to behavioral finance theory, when investors are in a good mood, they tend to be confident and underestimate the risk of investing in the stock of a particular company. In turn, it increases the volatility and return of this stock. So, the economic intuition upon adding investor sentiment is as follows: when economy is growing rapidly (investors are in a good mood) the increase in SVI for a particular company will result in higher volatility and return than when economy is growing slowly( investors are in a bad mood). All the recent studies in this field do not take this factor into account. Our hypothesis is proved by our empirical analyses. So, it seems logical to find a measure for investor sentiments. In my Master Thesis I use a measure of investor mood which allows to capture sentiments, the ratio of smiley emoticons and frown emoticons on Twitter. Using data for 4

5 all tweeting activity from 008 till 00, we find that smiley usage on Twitter has a statistically and economically significant effect on the stock market returns and volatility. Our analysis shows that the SVI index, sentiment from Twitter and their cross term are statistically and economically significant. I chose Twitter to measure investor sentiments for several reasons. First, Twitter is able to react fast on every event. Second, it is able to transmit current activity and current mood tweets. Many users write tweets about what they like or dislike at this moment. Hence, Twitter collects information about the emotional state of its users. In this Master Thesis I use a mood proxy from this information. Smiley and frowny emoticons show people's emotions. One of the main advantages of measuring sentiments by emoticons is that smileys like ":)" corresponds to positive emotions almost in any language and any context. Hence, it is difficult to misinterpret the mood of tweets with a smiley icon. Using a ratio of positive to negative emotions has another important advantage: although the number of positive and negative emoticons rises gradually, their ratio remains stable. According to Nofsinger (005), the general level of optimism/pessimism in society influences the mood of financial decision makers. Thus, high level of optimism in the society leads to optimistic mood of decision makers in financial area. Hence, high ratio smiley emoticons to frown on Twitter corresponds to optimistic mood of traders. Optimistic investors tend to underestimate risks and thus they are more likely to buy stock of a particular company. So, it is very reasonable to include investor sentiment proxy in addition to SVI to predict stock volatility and return for a particular company.. Theoretical Model The model is based on price taking traders. A riskless asset and one risky asset are exchanged in two rounds of trading at times t=, t=. Consumption takes place only at t=3, when riskless asset pays unit per share and each share of risky asset pays, where Nvh (, v ). The riskless interest rate is assumed to be 0. There are M investors. Thus each investor correctly assumes that his own demand does not affect prices. At t=0 each trader has an endowment f 0i of the riskless asset and x 0i of the risky asset. In trading round t, trader i s demand for the riskless asset and risky asset are fti and x ti. x is the per capita supply of the risky asset; it is fixed, known to all, and unchanging. P t is the price of the risky asset in trading rounds,. Trader i s wealth is Wti fti Px t ti, for t=, and W3i f3i vx 3i. There is no signal prior to the first round of trading at t=. Prior to trading at t=, trader i receives one of M private signals, yti v tm, where (0, ) and,..., M are mutually independent. M Y y / M t i ti 5 tm N h is the average signal at time t.

6 Each trader believes that the precision of his signal h,. She believes the precision of other signals to be h,. All traders believe that the precision of is h v, ; that is, traders underestimate, or correctly estimate, the precision of their prior information. Let Ф {}, { P } T i Ф i y i. Thus, Ф i represents the information available to trader i (in addition to prior beliefs) at time t. Every trader when forming her believes pay attention not only on her idiosyncratic signal; also she takes into account the average signal among all the agents. yti v tm ( ) t, where describes the importance of her individual signal, based on her own knowledge, is extent to which trader rely on the average signal among traders. Trader i s utility function is exp( aw it ), thus traders have constant absolute risk aversion (CARA) with a risk aversion coefficient a. Traders are assumed to be myopic, that is, they look only one period ahead when solving their trading problem. Thus, at times t=, trader i solves: max E[-exp(-a(W ) Ф ] s.t. P x f P x f () x ti ti ti t ti ti t ti ti The traders in this model correctly conjecture that they do not affect prices. When solving their maximization problems, traders conjecture that prices are linear functions of the average signals: P Y The conjectures are identical for all traders and the coefficients determine an equilibrium in which the conjectures are fulfilled. Equilibrium is obtained because traders believe that they are behaving optimally even though, in fact, they are not. We first solve the equilibrium for the second round of trading. Trader i believes has a multivariate normal distribution. We calculate the mean and the covariate matrix of this distribution which are E( Ф ) [ v, v] i Var( y ) ( M ) ( ) ( M ) i hv M h M h ( M ) ( )( M ) Cov( y, P ) h M h M h i v Ф i 6

7 Var( P ) ( M ) h M h M h v ( M ) ( ) ( M ) ( M ) ( )( M ) hv M h M h hv M h M h ( M ) ( )( M ) ( M ) hv M h M h hv M h M h A T cov( v, Ф ) i hv hv E( Ф ) v A ( Ф E( Ф )) i i i T Var( Фi ) A A hv ( M ) ( M )( ) E( Фi ) v ( Y v) Var( Ф ) ( M ) ( M )( ) i hv h h M ( v he M he M hh e v hhm e v hh e v M ) hhm hhm e v e v We can solve maximization problem () following Grossman (976) and get demand function: x i E( Ф ) P avar( v Ф ) i i () x M xi M i (3) Then using () and (3) we can get: ax ( M ) ax ( M )( ) ax hv hv hv P v ( Y ) ( Y ) (4) 7

8 ax ( M )( ) ( M ) ax v ( )( ) h h v v ( M ) ( M )( ) x i EP ( ) P avar( P ) M x i M i x M P ax ( ) (5) hv h M Proposition When M is sufficiently high P P is an increasing function of M Proof : From 4 and 5 we can get that P P ( Y ) ax ( ) hv h M Since M is sufficiently high; than Y v is close to 0. Since is positively related to, the statement can be concluded. Proposition Var( P P) is an increasing function of M Proof : From Proposition we can get that Var( P P ) ( ). Since is positively related to, the statement can be concluded. Proposition 3 When M is sufficiently high of Proof : Since part of P which depends on is ( M )( ) ax M ax hv hv h M hm P P P P and var( ) are increasing functions P P P( ) ( ), P P which negatively depends on, and using Proposition we can conclude that is positively P related to. P P Since P is constant, and using the Proposition, it can be concluded that Var( ) is P positively related to. 8

9 Proposition 4 When M is sufficiently high of. P P P P and var( ) P P are increasing functions Proof P P P P P P : In the given parameter range, the derivative of and var( ) with respect to is positive, which is in accordance with the article "Volume, volatility, price, and profit when all traders are above average" by Terrance Odean. So, from our theoretical model we derived that the higher the degree of overconfidence of traders, measured by, the higher is the return and volatility of the stock. The higher is the extent to which a trader searches for the information of a particular stock to form her own believe of the stock, measured by the higher would be the return and volatility of a particular stock. Next we will see if the data will support this theoretical model. The proxy for will be SVI. If SVI is high, it means that investors investigate the firm to invest and mostly form their own believes, based on information provided by search engine. In this case will be high. On the contrary, when SVI is low, it means that people rely on common knowledge of society to take investment decisions. In this case will be low. The proxy for is Twitter Mood Index. When investors are in the good mood, they tend to be more overconfident. 3. Data To quantify public interest in a particular stock, we use the number of Internet search queries of firm names as provided by Google Insights. The search volume for a specific key word provided by Google Insights is not given in absolute terms, but as a value relative to the total number of searches on Google in the corresponding time interval. For each search term, this relative value is then normalized so that the search volume always varies between 00 ( period in which the highest relative volume was observed) and 0 (a period in which search volume does not meet a designated threshold ). The data transformation done by Google eliminates a general trend in search volume due to a higher popularity of the Internet, but also inhibits us from making use of information about the absolute number of search queries. Consequently, variation in the level of search volume among different companies does not convey any analyzable information for our investigation and we are thus restricted to analyzing variation in search volume within each firm. Firms that 9

10 have only very few search records on Google Insights usually have the largest within variation due to normalization of the data. To ensure that stocks with few observations of Internet search volume do not drive our results, we include only those firms for which more than five monthly or more than 0 weekly search volumes are provided. Of the remaining observations, we drop all values if the search volume in two or more consecutive months equals zero because Google Insights has designated a threshold for search volume below which the variable is set to zero. As a result, search terms with very low overall traffic may have long periods with zero searches. We discard these observations because they do not provide any analyzable within variation for our investigation. In the analysis, we use the variable AbSVI (Abnormal SVI) which is the difference between SVI and the average SVI during a special time period for a given firm. As to the proxy for investor sentiment from Twitter, I collect data about Twitter emoticons usage from the Infochimps website. The Infochimps database include smiley and frowny timestamp from the launch of Twitter (March 006) till April 00. Twitter was not popular at the beginning. As I want my mood index to reflect general mood of society, I excluded early observations (where smiley to frowny ratio reflect only mood of several thousand people). Thus I restrict data to the interval from nd of June 008 through the st of April 00. This time period includes 467 working days. The data includes a timestamp about every emoticon on Twitter for this period. Financial data for returns and volatility of the stocks was downloaded from Google Finance. 4. Descriptive statistics In the Master Thesis we use 40 companies. We examine the influence of company s size on the relationship between search volume and volatility by means of analyzing the effect of increase in SVI for stock volatility for companies with different market capitalization. The market to book value, on the other hand, does not seem to be significantly related to changes in Google search volume. To convince skeptics that SVI really measures people s interest in particular word the frequency for word New year is depicted on the picture. As anyone can predict, the interest for New Year is higher close to the st January which is in accordance with Google Trend. 0

11 Picture To convince skeptics that Twitter index really captures people s emotional state the mood of people during the working days and weekends based on Twitter index is depicted on the picture. As anyone can predict, the mood of people gets better during working days from Monday to Friday. During weekends the mood gets worse from Saturday to Sunday, the closer working days are. Our Twitter index proves this intuition. Picture Mood dynamics during working week

12 Picture 3 Mood dynamics during weekend Picture 4

13 Picture 5 Smiley to frowny ratio Picture 6 From the pictures below it can be concluded that SVI and Volume of trade of a company are related to each other because they have patterns, which are similar to some extent. The rest of the descriptive statistics is in Appendix. 3

14 Picture 7 4

15 5. Results Volatility prediction Time series for different stocks Tables 3 present results of regression of Volatility of the stocks to the mood index, volatility lags, Search Volume Index (SVI) and cross term of first lag of SVI and mood index. We estimated different models including and omitting different variables. The full regression model: Vol t SQ Vol t 3 t SQ t3 Vol t Return Vol 3 t t3 Sense Return t t 3 5 Sense Return t3 t Sense 3 t3 Sense_ SQ SQ Where Return return of the stock for a particular company, Vol volatility of the stock for a particular company, Sense mood index from Twitter, SQ SVI index for a particular company, Sense_SQ multiplication of mood index and SVI index. In all models (coefficient of the mood index of investors) is positive and significant at 5 % level. So, the increase of investor s mood will increase stock volatility. Coefficient (coefficient of the Search Volume Index) is positive and significant at % level. So, the increase of Search Volume Index for particular company will increase the stock volatility of this company. The most interesting coefficient is (coefficient of the cross term Sense_SVI) which is positive and significant. It means that including investor s mood substantially changes the influence of SVI increase on the stock volatility. So, the effect of increase of stock volatility due to increase in SVI of the company is higher when investors are happier. Comparing coefficient for big (Apple), medium (OBAS) and small (Tlab) firms in tables 3, we can conclude that the higher the market value of the company the smaller is the coefficient, and the less sensitive its stock volatility to SVI increase for this company. In all models we use HAC errors (Newey and West (987) and Andrews (99)) in order to avoid problems with autocorrelation or heteroskedastisity of errors. An important feature of the regression in this Master Thesis is that a stock return and volatility depends on values which are known by the exchange opening. Panel data analysis In the previous section we analyzed time series data for a particular stock. Here we will investigate relation between Volatility, SVI, TMI and market capitalization using panel regression with FE. The results are provided in the Table 0. From Table 0 it follows that SVI (Search Volume Index) positively and significantly influence Volatility. Since the coefficient of cross term svi_cap is significant and negative; it is again supports the fact that the higher the market value of the company the less sensitive its stock volatility to SVI increase for this company. Coefficient on Sense is positive and significant which indicates that Twitter Mood Index is positively related to Volatility of stocks. Cross term sense_svi is also positive and t ()

16 significant. All in all, the results from panel data analysis are in accordance with previous section. APT model to predict stock returns: Arbitrage pricing theory (APT) holds that the expected return of a financial asset can be modeled as a linear function of various factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient. We make a three factor model: the first factor is AbSVI Abnormal Search Volume Index, the second factor is Twitter Mood Index, the third one is market excess return. Also we make a factor model where the first factor is Twitter Mood Index and the second factor is market excess return. We will compare these factor models to find out if inclusion of Abnormal Search Volume index will improve the factor model. For testing the three factor model with AbSVI we use Fama MacBeth Procedure. The parameters in this procedure are estimated in two steps. First step: We regress each stock on the proposed risk factors to determine that asset's beta for that risk factor. In the pictures below betta coefficients are provided. With red color are marked risk factors at % significance level, with yellow at 5 % level, with green at 0% level. We can see that market_rf excess market return is almost always very significant, but other factors also stand out very often. We will see the final results on the second step, but even now we can see from tables below that our factor AbSVI is quite reasonable; so, it can significantly improve our prediction power. 6

17 7 Second step: We regress all asset returns for a fixed time period against the estimated betas in the first step without a constant to determine the risk premium for each factor, for every time (T=467). Than we take residuals from these cross section regressions. We have 467 residual vectors. Than these residuals are used to form a statistic that is distributed as chi square. Than we will see if our hypothesis that we explained returns variation substantially with our 3 factors is rejected or accepted. This statistics equal to 34.3, with p value over 0.4. It means that the null hypothesis that we explained almost all variation with our factor is not rejected. So, 3 factor model with AbSVI is in accordance with our stock returns. it t i ei t R ', i=,,.n for each t ; ˆ ˆ T t t T ; ˆ ˆ T t it i T ; ˆ) ˆ ( ˆ) ( T t t T ; ˆ) ˆ ( ) ˆ ( T t it i T ; ˆ ˆ T t t T ; ˆ) ˆ ˆ)( ˆ ( ˆ) cov( T t t t T

18 ˆ ' cov( ˆ) ˆ N. Relevance of SVI to predict stock returns in APT models: We will compare models based on their R square adjusted from following regressions. In factor model R square adjusted is taken from linear regression of stock excess returns on market excess return and Twitter mood index; in 3 factor model in addition to two factors we include Abnormal SVI. In the table below we provide these R square adjusted values for both models (for every company) and compare them. We depicted the model with higher R square with red color. So, we can see that 3 factor APT model posses more red colors, so Abnormal SVI has an important role in predicting stock returns. Relevance of Twitter Mood Index and SVI with macroeconomic data We showed that SVI and Twitter Mood Index are of big importance in explaining stock returns. However, one may think that macroeconomic variables may substitute these indexes, because people can have bad mood in Twitter network or increase they search volume for a given firm only because of macroeconomic situation. So, we should test if macroeconomic variables such as unemployment and average hourly earnings can explain 8

19 variation that is explained by Twitter Mood Index and SVI. Here we will show that the variables in question, Twitter Mood Index( TMI) and SVI will be still significant almost for all firms, even if we include macroeconomic variables in the model. Firstly, we regress stock market returns of different firms on market return, TMI and SVI. Than we add macroeconomic variables in addition such as unemployment and average hourly earnings into our model. From the table below we can see even with macroeconomic components, TMI and SVI are still significant. So, SVI s and TMI s role in explaining stock returns can not be substituted by macroeconomic variables. From the table below it follows that significance of TMI and SVI almost remains the same after inclusion of macroeconomic variables. However, it is not honest enough to use this comparison, since available for us macroeconomic data frequency is only monthly. I am going to return to this problem in my further research. 9

20 0

21 Out of sample prediction analysis From the recent literature, it follows that Twitter Mood Index and market return can explain a significant variation of stock return of a given company. In this section we will show that out of sample predictive power of the stock return will increase if we include SVI in addition to Twitter Mood Index and market return explanatory variables. We divide our sample into parts: the first part for N=..300 in sample model selection; the second part for N= out of sample checking for predictive ability. We use MSPE (Mean Square Predictive error) measure to compare model with SVI as an explanatory variable and the model without SVI. The model with the lowest MSPE is better in stock return prediction. From the table below we can find out that the model with SVI is better almost for all companies; in this case the cell is filled with red color. Moreover the difference between MSPE is significant in 5% significance level. Endogeneity problems The regressions in our study might bear an endogeneity concerns. There is a probability that stock market activity determines Twitter mood. But only a negligible percent of tweets are financial oriented. In order to prove this we collected most popular financial words. Interest rate, inflation, unemployment are examples of these words. Then we calculated the frequency of these words. Sum of these frequencies was less than 0.%. Thus only small percent of Twitter accounts is financial related. Hence, stock market does not determine Twitter mood. Also, there is a probability of reverse causality problem with SVI, because it is possible that stock market volatility is not influenced by SVI increase; on the contrary, an increase in stock market volatility influences SVI. To investigate this problem we use Granger causality test. The results showed in appendix suggest that based on the test we do not have such kind of problem. However, it is very important to understand Granger causality cannot

22 establish causality in theoretical sense, also Granger causality is not test for strict exogeneity. Relation between theoretical model and data The theoretical model developed above posits that the higher the degree of overconfidence of traders, measured by, the higher is the return and volatility of the stock. It is in accordance with the data, since from the regression analysis the higher is Twitter Mood Index, the higher is the return and volatility. The proxy for is Twitter Mood Index. When investors are in the good mood, they tend to be more overconfident. The higher is the extent to which a trader searches for the information of a particular stock to form her own believe of the stock, measured by,the higher would be the return and volatility of a particular stock. The proxy for will be SVI. If SVI is high, it means that investors investigate the firm to invest and mostly form their own believes, based on information provided by search engine. In this case will be high. On the contrary, when SVI is low, it means that people rely on common knowledge of society to choose investment decisions. In this case will be low. From our empirical analysis we obtained that SVI is positively related to return and volatility of a particular stock. So, data supports our theoretical model.

23 6. Conclusion In this Master Thesis we improved the predictive power of stock return and volatility by taking into account not only SVI (Search Volume Index), search frequencies from Google Trends for a particular company, but also investor sentiments, measured on Twitter. We showed that our models have higher predictive power than recent models, based only on investor emotional state, measured on Twitter, using out of sample analyses. So, using SVI and Twitter Mood Index can considerably improve the prediction power of stock returns and volatility. Also, we showed that the significance of Search Volume Index and Twitter Mood Index persist even if we add some macroeconomic variables. Analyzing my model, I discovered interesting effects, such as: the higher TMI of society and SVI, the higher would be stock return and volatility; the increase of stock volatility due to increase in SVI of a given company is higher when investors are happier; the higher the market value of the company the less sensitive its stock volatility to SVI of this company. Also, it is worth noting that it is easy to use SVI and TMI for investment decision since these data are open and the frequency of these data is very high. So, investors can considerably improve their positions in the stock market analyzing Twitter Mood Index and Search Volume Index. Since the theoretical model developed in this article is in accordance with the data; it adds additional strength to the results of this paper. 3

24 7. Acknowledgments The author is deeply grateful to his research advisors Oleg Shibanov and Dmitry Makarov for responsive guidance and useful comments. It has been a great honor to work with them. Oleg Shibanov and Dmitry Makarov created special collaborative atmosphere in the research seminars; thank you for your support. 4

25 8. References. Baker, Malcolm, and Jefrey Wurgler, 006, Investor sentiment and the cross section of stock returns, Journal of Finance 6, Baker, Malcolm, and Jefrey Wurgler, 007, Investor Sentiment in the Stock Market, Journal ofeconomic Perspectives, Barberis, N. and R. Thaler (003): A survey of behavioral finance", Handbookof the Economics of Finance,, Bollen, J., H. Mao, and X. Zeng (0): Twitter mood predicts the stock market", Journal of Computational Science. 5. Cochrane, John, Asset Pricing, Princeton University Press, Glaser, M. and M. Weber (007): Overcondence and trading volume", The Geneva Risk and Insurance Review, 3, Hirshleifer, D. (00): Investor psychology and asset pricing," The Journal of Finance, 56, Matthias Bank, Martin Larch, and Georg Peter, Google Search Volume and its Influence on Liquidity and Returns of German Stocks, working paper. 9. Terrance Odean, Volume, Volatility, Price, and Profit When All Traders Are Above Average. 0. Tetlock, P. (007): Giving content to investor sentiment: The role of media in the stock market", The Journal of Finance, 6, Thomas Dimpfl and Stephan Jank, Can internet search queries help to predict stock market volatility?. Volkova E., Twitter Emoticons and Stock Market Returns 3. Zhi Da, Joseph Engelberg and Pengjie Gao In Search of Attention. 5

26 9. Appendix () () (3) (4) (5) (6) VARIABLES volatility volatility volatility volatility volatility volatility volatility_ 0.67*** 0.673*** 0.673*** 0.673*** ( ) ( ) (0.0089) (0.0085) sense 0.006** ** 0.006** ** *** ** ( ) ( ) ( ) ( ) ( ) ( ) sense_ ( ) ( ) ( ) svi *** *** *** *** *** *** (5.3e-05) (4.4e-05) (4.40e-05) (4.4e-05) (5.84e-05) (5.7e-05) svi_ 3.7e-05 (3.03e-05) return *** *** *** *** -0.00** -0.0** ( ) ( ) ( ) ( ) ( ) ( ) sense_svi.0e-05*.0e-05*.5e-05.e-05* 3.6e e-06 (5.60e-06) (5.96e-06) (8.95e-06) (5.06e-06) (.0e-05) (.04e-05) svi_cap -6.35e-06* -7.e-06* -6.40e e-06* -.04e e-06* (3.73e-06) (4.8e-06) (7.e-06) (3.9e-06) (9.30e-06) (4.07e-06) return_ *** ( ) volatility_ 0.56*** ( ) Constant -0.05*** -0.05*** -0.04*** -0.04*** *** *** (0.0067) (0.0067) (0.0067) (0.0064) (0.0035) ( ) Observations 8,44 8,44 8,44 8,44 8,406 8,08 Number of id Adjusted R-squared Table 0 Panel regression with FE 6

27 () () (3) (4) (5) (6) (7) (8) (9) (0) Apple (Big firm) Vol Vol Vol Vol Vol Vol Vol Vol Vol Vol Vol_ 0.56*** 0.55*** 0.530*** 0.54*** 0.544*** 0.54*** 0.530*** 0.549*** 0.57*** (0.0500) (0.049) (0.0493) (0.049) (0.043) (0.0490) (0.0493) (0.043) (0.0488) Vol_ (0.0556) (0.0545) (0.0546) (0.0543) (0.0473) (0.0475) (0.0473) Vol_ (0.0508) (0.0466) (0.0466) (0.0463) Sense_ 0.06** 0.064** 0.066** 0.065** 0.078*** 0.073*** 0.073*** 0.078*** 0.07*** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Sense_ -9.53e e e e e e e e-06 (.0e-06) (.0e-06) (.07e-06) (.0e-06) (.08e-06) (.08e-06) (.06e-06) (.05e-06) Sense_3-3.7e e e e e-08 (.0e-06) (.00e-06) (.00e-06) (.99e-06) (.00e-06) SQ_ *** 0.000*** 0.005*** 0.000*** 0.007*** 0.007*** 0.000*** *** 0.008*** ( ) ( ) ( ) ( ) (0.0003) ( ) ( ) (0.0003) ( ) SQ_ ( ) SQ_ ( ) Return_ ** -0.3** -0.89** -0.33** -0.3** -0.38** -0.95** -0.89** -0.88** (0.33) (0.33) (0.33) (0.3) (0.3) (0.3) (0.3) (0.3) (0.3) Return_ (0.37) (0.37) (0.36) (0.36) (0.36) (0.36) (0.36) (0.35) (0.3) Return_3-0.68** -0.59* -0.57* -0.5* -0.5* (0.35) (0.34) (0.34) (0.34) (0.33) Sense_SQ_ ** * ** * (0.0007) (8.50e-05) (8.54e-05) (8.5e-05) (8.08e-05) (7.97e-05) (8.09e-05) (8.e-05) (7.99e-05) (8.09e-05) Constant * * * * (0.066) (0.065) (0.066) (0.065) (0.063) (0.06) (0.063) (0.064) (0.06) (0.063) Observations Adjusted R-squared Standard errors in parentheses *** p<0.0, ** p<0.05, * p<0. Table Big firm 7

28 () () (3) (4) (5) (6) (7) (8) (9) (0) OBAS (Medium firm) Vol Vol Vol Vol Vol Vol Vol Vol Vol Vol Vol_ 0.** 0.7** 0.7** 0.7** 0.34*** 0.9** 0.7** 0.3*** 0.7** (0.0470) (0.0468) (0.0468) (0.0468) (0.0463) (0.0464) (0.0465) (0.0463) (0.0464) Vol_ 0.3** 0.4** 0.5** 0.4** 0.6** 0.6** 0.6** (0.047) (0.0469) (0.0469) (0.0469) (0.0466) (0.0466) (0.0465) Vol_ (0.0474) (0.0473) (0.0470) (0.0473) Sense_ *** *** *** *** *** *** *** *** *** (3.83e-05) (3.8e-05) (3.8e-05) (3.8e-05) (3.79e-05) (3.77e-05) (3.78e-05) (3.78e-05) (3.76e-05) Sense_ -6.65e e e e e e-09-5.e e-09 (.9e-08) (.9e-08) (.8e-08) (.9e-08) (.9e-08) (.9e-08) (.8e-08) (.8e-08) Sense_3-3.67e e e-09-4.e e-09 (.6e-08) (.6e-08) (.6e-08) (.6e-08) (.5e-08) SQ_ *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) (0.0003) ( ) ( ) (0.0003) ( ) SQ_ ( ) SQ_ (3.05e-06) Return_ -0.83** -0.9** -0.64** ** -0.30** -0.94** -0.35** -0.74** -0.8** -0.88** (0.33) (0.33) (0.33) (0.33) (0.33) (0.33) (0.33) (0.33) (0.33) (0.3) Return_ -5.79e e e-05-4.e e e e e-05 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) Return_ ( ) ( ) ( ) ( ) ( ) Sense_SQ_ ** * ** * (0.0007) (8.50e-05) (8.54e-05) (8.5e-05) (8.08e-05) (7.97e-05) (8.09e-05) (8.e-05) (7.99e-05) (8.09e-05) Constant (0.000) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) (0.0000) Observations Adjusted R-squared Standard errors in parentheses *** p<0.0, ** p<0.05, * p<0. Table Medium firm 8

29 () () (3) (4) (5) (6) (7) (8) (9) (0) TLAB (Small firm) Vol Vol Vol Vol Vol Vol Vol Vol Vol Vol Vol_ 0.499*** 0.530*** 0.535*** 0.54*** 0.530*** 0.55*** 0.54*** 0.535*** 0.548*** 0.59*** (0.0504) (0.049) (0.0493) (0.0493) (0.049) (0.043) (0.0493) (0.049) (0.043) (0.049) Vol_ (0.055) (0.0543) (0.0545) (0.0545) (0.0484) (0.0486) (0.0487) (0.0486) Vol_ (0.0497) (0.0480) (0.048) (0.0483) Sense_ *** 0.059** 0.035** 0.059** 0.054** 0.035** (0.035) (0.036) (0.036) (0.006) (0.035) (0.035) (0.005) (0.035) (0.006) (0.0066) Sense_ (0.004) (0.004) (0.004) (0.004) (0.003) (0.003) (0.004) (0.004) (0.004) (0.00) (0.003) (0.003) (0.003) (0.00) (0.00) SQ_ *** *** *** *** *** *** *** *** *** *** ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) SQ_ ( ) SQ_ ( ) Return_ ** ** -0.75** -0.30** -0.30** -0.68** (0.33) (0.33) (0.33) (0.3) (0.3) (0.3) Return_ (0.3) (0.33) (0.33) (0.33) (0.3) (0.3) (0.33) (0.33) (0.3) (0.3) Sense_SQ_ ** * ** * (0.0007) (8.50e-05) (8.54e-05) (8.5e-05) (8.08e-05) (7.97e-05) (8.09e-05) (8.e-05) (7.99e-05) (8.09e-05) Constant ** (0.08) (0.069) (0.070) (0.069) (0.069) (0.068) (0.069) (0.069) (0.068) (0.056) Observations Adjusted R-squared Standard errors in parentheses *** p<0.0, ** p<0.05, * p<0. Table 3 Small firm 9

30 Granger causality test Equation Excluded chi df Prob > chi return_rf svi_ return_rf ALL svi_ return_rf svi_ ALL Equation Excluded chi df Prob > chi return_rf svi_ return_rf ALL svi_ return_rf svi_ ALL Equation Excluded chi df Prob > chi return_rf3 svi_ return_rf3 ALL svi_3 return_rf svi_3 ALL Equation Excluded chi df Prob > chi return_rf33 svi_ return_rf33 ALL svi_33 return_rf svi_33 ALL Equation Excluded chi df Prob > chi return_rf5 svi_ return_rf5 ALL svi_5 return_rf svi_5 ALL Equation Excluded chi df Prob > chi return_rf35 svi_ return_rf35 ALL svi_35 return_rf svi_35 ALL

31 Equation Excluded chi df Prob > chi return_rf7 svi_ return_rf7 ALL svi_7 return_rf svi_7 ALL Equation Excluded chi df Prob > chi return_rf svi_ return_rf ALL svi_ return_rf svi_ ALL Equation Excluded chi df Prob > chi return_rf9 svi_ return_rf9 ALL svi_9 return_rf svi_9 ALL Equation Excluded chi df Prob > chi return_rf38 svi_ return_rf38 ALL svi_38 return_rf svi_38 ALL

32 Unit root tests Smile_ratio: DF-GLS for total_smile_ra~o Number of obs = 449 Maxlag = 7 chosen by Schwert criterion DF-GLS tau % Critical 5% Critical 0% Critical [lags] Test Statistic Value Value Value Phillips-Perron test for unit root Number of obs = 466 Newey-West lags = 5 Interpolated Dickey-Fuller Test % Critical 5% Critical 0% Critical Statistic Value Value Value Z(rho) Z(t) MacKinnon approximate p-value for Z(t) =

33 Abnormal_SVI: DF-GLS for abnormal_svi Number of obs = 449 Maxlag = 7 chosen by Schwert criterion DF-GLS tau % Critical 5% Critical 0% Critical [lags] Test Statistic Value Value Value Phillips-Perron test for unit root Number of obs = 466 Newey-West lags = 5 Interpolated Dickey-Fuller Test % Critical 5% Critical 0% Critical Statistic Value Value Value Z(rho) Z(t) MacKinnon approximate p-value for Z(t) =

34 Descriptive statistics. Variable Obs Mean Std. Dev. Min Max svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ svi_ Variable Obs Mean Std. Dev. Min Max total_smil~o Variable Obs Mean Std. Dev. Min Max abnormal_svi

35 . Variable Obs Mean Std. Dev. Min Max return_rf return_rf return_rf return_rf return_rf e return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf return_rf