Behavioral Beta and Asset Valuation Models

Transcription

1 International Research Journal of Finance and Economics ISSN Issue 16 (2008) EuroJournals Publishing, Inc Behavioral Beta and Asset Valuation Models Nizar Hachicha University of Economics and Management, SFAX-Tunisia Abdelfettah Bouri University of Economics and Management, SFAX-Tunisia Abstract The investigation of investor sentiment and its relation to stock returns, volatility and asset valuation is the subject of considerable debate in many empirical researches. Using indirect sentiment measures, we provide evidence that sentiment levels and changes have important predictive power for stock returns. In addition, we find that most of our sentiment measures cause volatility rather than vice versa. Finally, our evidence supports strongly the evidence that sentiment affects asset valuation. Market pricing errors implied by fundamental valuation models are strongly related to sentiment. These results are robust to the inclusion of investor sentiment as an explanatory variable in these pricing models and prove the improvement of the shares evaluation quality. 1. Introduction The efficiency theory has been the starting point of many asset valuation models that have incorporated different types of risk. Generally, theses risks present a micro-structural aspect, such as the case of the original version of the CAPM model which considers the systematic risk as the single risk factor. However, it is obvious that there are a myriad of risk factors facing companies today. Some of these factors are market risk, bankruptcy risk, currency risk, supplier risk, etc. As a result of the many hypotheses regarding various risk factors, and the abundance of data available regarding publicly traded stocks, a great deal of research has been performed with the goal of identifying additional risk factors that have robust predictive capability. In this area, Fama and French have done extensive research and found factors describing value and size to be the most significant factors, outside of market risk, for explaining the realized returns of publicly traded stocks. The researchers first published their findings on these factors in 1992 and have continued to refine their work since. Similarly, in order to develop an extension of the original CAPM, Acharya and Perderson have introduced a recent risk factor called systematic risk adjusted to liquidity risk Despite these extensions, abnormal returns still exist in most financial markets in the world. Thus, the recent studies have tended to explain more the origin of this problem by incorporating the psychological side of the investor. So, they assume that there is a relationship between the investor sentiment, return and volatility. The link between return, volatility and investor sentiment has been the subject of considerable researches. However, the precise form in which sentiment will affect returns or volatility is not clear ex ante. If noise traders are sensitive to sentiment changes, then sentiment changes should drive returns and volatility. Alternatively, if noise traders only trade if sentiment is extreme (either high or low) relative to previous levels, then it might be expected that it is sentiment levels that influence returns and volatility. Evidence of this was found by Solt and Statman (1988) and Brown and Cliff (2004) who document that returns cause sentiment rather than vice versa. Similarly, Wang, Keswani and Taylor

2 International Research Journal of Finance and Economics - Issue 16 (2008) 176 (2006) show that it is returns rather than sentiment that contains useful information for volatility forecasting purposes. These studies are limited to document the causality sense between volatility and sentiment without worrying about its implications on the assets valuation. This study makes two particular contributions. Firstly, it clarifies the relationship between returns, sentiment and realized volatility. In particular our results show that sentiment contain useful information for return and volatility forecasting purposes. Secondly, it discusses the implications of these relations on the assets valuation models. The analysis is conducted on monthly horizons by employing data of stocks included in the two indexes of the Tunisian stock exchange: BVMT and TUNINDEX over the period from 2/01/1999 to 31/12/2005. The remainder of this paper is organized as follows. In the second section we test the existence of the relationship between the investor sentiment and return at the aggregate level, as well as the stability of this relation according to the asset nature. The link between sentiment and volatility present the subject of the third section. In this section, we test the causality sense of this relationship, then, we document, in the fourth section, the explicative power of behavioral beta concerning the abnormal returns. Such validation contributes enormously to the improvement of the fundamentalist valuation models. Finally, the fifth section offers concluding remarks and discusses implications of our findings. 2. Literature Review, Sentiment Measures and Data Base Looking at the relation between market returns and sentiment is appealing for two reasons. First, it seems natural to view sentiment as a persistent variable. People become more optimistic as they are reinforced by others joining on the bandwagon. Thus, the importance of sentiment may build over time. Second, arbitrage forces are likely to eliminate short-run miss pricing but may break down at longer horizons. The predictive power of sentiment for returns has been explored in a number of papers. However, not all papers have come to the same conclusions. The results of earlier works show that sentiment helps to explain the time series of returns (Kothari and Shaken (1997), Neal and Wheatley (1998), Shiller (2000), Baker and Wurgler (2002)). Campbell and Cochrane (2000), Wachter (2000), Lettau and Ludvisgon (2001), and Menzly, Santos and Veronesi (2004) examine the effects of conditional systematic risks; here we condition on investor sentiment. Fisher and Statman (2000) find that the causality between equity returns and sentiment can be significant in both directions. Brown and Cliff (2004) use a large number of sentiment indicators to investigate the relationship between sentiment and equity returns and find much stronger evidence that sentiment is caused by returns. Solt and Statman (1988) also make similar findings. Our paper is also related to a growing literature in behavioral finance that examines the correlated trading behavior of retail investors and its impact on stock returns. Jackson (2003) provides additional evidence of systematic trading patterns among Australian investors. Also, Barber, Odean, and Zhu (BOZ; 2003) provide evidence of correlated trading among retail investors in the United States, and explore psychology-based explanations for these patterns. According to Brow and Cliff (2004), Kumar and Lee (2005) and Lee, Jiang and Intro (2000), the relationship between the investor sentiment and return depend on stocks sorts. Thus, we have to test the significance and the stability of this relationship not only at the aggregate level but also at the individual level and according to some financial variables such as activity sector, size, book to market and liquidity. Sentiment Measures Ever since the theoretical work of De Long, Shleifer, Summers, and Waldmann (1990) [DSSW] researchers have sought empirical evidence of a sentiment factor that reflects fluctuations in the opinions of traders regarding the future prospects for the stock market. It is potentially valuable to find

3 177 International Research Journal of Finance and Economics - Issue 16 (2008) an empirical measure of sentiment because of the suggestion that it may be priced. Empirical studies usually differ in the way they measure investor sentiment. This might be one reason why the evidence concerning the forecasting ability of sentiment is mixed and sentiment measures based on different data sources (e.g. questionnaires, stock transactions) yield different results The literature review has distinguished two types of measures. The first is relative to the direct measure which include measures compiled from survey and questionnaire carried out by the American Association for Individual Investors (AAII) and Investor Intelligence (II). The American Association for Individual Investors (AAII) has conducted a sentiment survey by polling a random sample of its members each week since The respondents are asked whether they are bullish, bearish, or neutral about the future condition of the stock market in six months. Only subscribers to AAII are eligible to vote and they can only vote once during the survey period. As the respondents to this survey are individuals, this can be interpreted as a measure of individual sentiment. Investor Intelligence (II) has compiled its sentiment data weekly by categorizing approximately 150 market newsletters since Newsletters are read and marked starting on Friday each week. The results are reported as percent bullish, bearish, or neutral on the following Wednesday. Since many of the writers of these newsletters are current or past market professionals, the ratio of bullish to bearish responses compiled by II can be considered as a proxy of institutional investors sentiment (Wanga, Aneel Keswanib and Stephen J. Taylorc; 2006). The second type of measure called indirect measure is based on financial indicators which are interpreted in terms of bullish or bearish trend. Such measure is used by many empirical studies such as those of Brown and Cliff (2004). The list of the indirect measure is quite long, but we limit our analysis to two principle indicators as the Tunisian stock exchange data is not compiled. One of the most common technical indicators is the ratio of the number of advancing issues (ADVt) to declining issues (DECt). We calculate this measure by using the following expression: ADV sent = t ( 1 DECt (1) The second indirect indicator can be expressed as: HI sent = 2 LO (2) Where HI represents the number of the new highs and LO represents the number of the new lows. This sentiment measure is designed to capture the relative strength of the market (Brown and Cliff (2004)). The extension of the first measure leads to the ARMS index is a modification of ADV/DEC, which incorporates volumes. This measure is the ratio of the number of advances to declines scaled by their respective volumes: ADVt ADV volt ARMSt = DECt DEC volt (3) The ARMS measure can be interpreted as the ratio of volume per declining issue to the volume in each advancing issue. If the index is greater than one, more trading is taking place in declining issues whilst if it is less than one more volume in advancing stocks outpaces the volume in each declining stock. The trading volume can be assessed either by the number of traded issues or by the trading volume in dinars, consequently, we can deduce from the ARMS the two following sub- indicators: ADV t ADV LOGVt sent = ARMSv = 3 t DEC t DEC LOGVt (4)

4 International Research Journal of Finance and Economics - Issue 16 (2008) 178 ADVt ADV LOGTt sent 4 = ARMSt = DECt DEC LOGTt (5) Where: V and T denote respectively the number of traded issues and the trading volume in the Tunisian dinars. The results of the four sentiment measures are illustrated in the following figures. Figure 1: Sentiments investor 20 Sent 1 16 Sent 2 Measure sentiment Measure sentiment Date PANELA PANELB Date PANELA PANELB 10 Sent 3 14 Sent 4 Measure sentiment Measuresentiment Date Date PANELA PANELB PANELA PANELB This figure shows the four measurements of sentiment investor from 1999 through Database The analysis includes monthly data for two indexes of the Tunisian stock exchange: BVMT and TUNINDEX, as well as for theirs constituent stocks. The sample covers 20 firms, where 10 are belonging to the banking sector. The data is obtained from the Website of the Tunisian stock market from 2/01/1999 to 31/12/2005. So we have 1680 observations for each stock. For some firms, there is loss of significance of the relationship between investor sentiment and return at the individual level. So, we separate individual stocks into four groups according to activity sector, size, book to market and liquidity criteria. We also aim to see if there are different relation between investor sentiment and returns on these classes. According to these criteria, we subdivide our sample into two sub samples. Hence, we obtain sub samples of small and big size companies, great and small value book to market companies or liquid and illiquid companies. The size effect is calculated from the stock exchange capitalization. A company which has a lower capitalisation than the average capitalisation of the total sample is considered as a small size company and vice versa. For the book to market effect, we use a ratio that compares the book value of a firm to its market value. Book value is calculated from the firm's historical costs, or an accounting value. Market value is determined in the stock market through its market capitalization. For liquidity we apply a measure of Amihud (2002). According to this author, the illiquidity of an action I for one month T is measured by the following formula: i 1 N i t i R d, t ILLIQ t = i d 1 i N t = V d, t

5 179 International Research Journal of Finance and Economics - Issue 16 (2008) i i Where: R dt, : return on stock i in the day d of the month t, V dt, : Trading volume of stock i in i the day d of the month t, N t : A number of days of transaction of stock i in the month t The subdivisions of our total samples to sub samples according to these criterions can be presented by the following table: Table 1: Data statistics Name in English Sector Size Book to market Liquidity Banking Non banking Big Little Big Little Liquid Illiquid AB Amen Ban X X X X ATB Arabic Tunisian Bank X X X X BH habitat Banks X X X X BIAT international Arabic Tunisian Bank X X X X BNA agricultural national Bank X X X X BS south Bank X X X X BT Tunisian Bank X X X X UBCI Union trade industrial banks X X X X UIB International union banks X X X X STB Tunisian company banks X X X X AMS Metal workshop Sahel X X X X ASTR Reinsurance and insurance company X X X X ICF Chemical Industries of Florine X X X X ATL Arab Tunisian Lease X X X X CIL International Company of Leasing X X X X MONOPRIX Company New House of the Town Tunis X X X X SFBT Refrigerating company and Brewery Tunis X X X X SOTETEL Tunisian company of telecommunication X X X X TAIR Tunis airlines X X X X SOTUVER Tunisian company of glass makings X X X X Total This table summarizes constituent firms of our sample and its divisions according to activity sector, size, book to market and liquidity criteria. 3. Behavioral Beta and Returns Relationship between Sentiment and Return at the Aggregate Level To further investigate the existence of a link between investor sentiment and market return, we propose a simple specification without identifying the nature or the sense of this relationship. However, it is important to signal the contemporaneous characteristic of such relation. Rm, t= α + β sentt+ ε t R mt, = α + β sentt+ ε t Where Rm,t represents the market return at time t, sent t is the investor sentiment measure at sentt denotes the change level of the investor sentiment. Coefficient on sentiment level time t and and change represents the behavioral beta or sentiment beta. The theoretical idea of behavioral beta is inspired by the research of Shefrin and Statman (1994). They have developed a behavioral asset-pricing theory as an analogue to the standard CAPM. In the behavioral asset-pricing model (BAPM), the expected returns of securities are determined by their behavioral betas, betas relative to the tangent mean variance-efficient portfolio. However, our behavioral beta is different from the BAPM s beta, since it evaluates simply the impact of the investor (6) (7)

6 International Research Journal of Finance and Economics - Issue 16 (2008) 180 sentiment measures on asset return. The market return is assessed on the basis of the two stock exchange indexes (BVMT and TUNINDEX) and we use the four indicators, as specified above, to measure sentiment. The results of these regressions are summarized in the following table. Table 2: Relationship between Sentiment and Return Coefficients Stability of the Normality of the standard Student-test estimates relationship deviation R2 TEST SHOW Skewne Jarque Alpha Beta t* alpha t* beta Kurtosis P1 P2 ss -Bera Panel A: BVMT index sent ** 1.205*** ,.393 0, sent ** , sent ** sent ** sent ** sent sent ** sent * * Panel B: Tunindex index sent ** 1.394*** sent ** 0.871*** sent ** ** sent ** ** sent *** sent ** sent ** sent ** ***, **, * denote statistical significance at the 1%, 5% and 10% levels respectively This table shows the resultants of the estimate linear relation between four measures of sentiment investor and the market return These findings show the significance of behavioral Beta for all the sentiment measures and especially beta on the ratio of the number of advancing issues to declining issues (sent1) which represents the highest t-statistic for the two panels A and B. However, such significance is drawing in with the sentiment change and it even disappears in the second and forth sentiment change measures applied to the BVMT index. Theses results confirm the existence of a strong relationship between the investor sentiment and the market return at the aggregate level. But, we cannot conclude about the sign of this relationship given the fact that the behavioral beta takes now positive sign now negative one. The most previous empirical studies are based on a single sentiment measure and they have not encountered such sign contradiction. Generally, the findings of these studies support the positive impact of the investor sentiment on market return (Neal et Wheatley (1998), Wang (2001), Simon et Wiggins (2001) and Jones (2002)). Thus, we can put forward that the sign of this relation depend on the choice of the sentiment proxy. In order to test the authenticity of this relationship, we undertake two types of statistical tests. The first deals with the stability of this relationship by using SHOW test over two periods. The results show that only 37 % (12 tests) of these tests reveal the stability of this relationship and the 63 % provide support for instability. In term of panels this stability is stronger for the BVMT index (50 %) than for the Tunindex (only 25 %). But, in terms of sentiment measures, the stability is the same for all proxies (50%). The second test treats the normality of the standard deviation through the Skewness, Kurtosis and JB coefficients. The results show a positive Skewness coefficient, a Kurtosis one > 3 and the value of the JB reaches for the ARMS T measure. Such findings allow us to confirm the non normality of the standard deviations.

7 181 International Research Journal of Finance and Economics - Issue 16 (2008) 4. Behavioral Beta Investor Sentiment and Return at the Individual Level In order to investigate the link between investor sentiment and return of individual asset we present each panel as a sample of 20 quoted stocks. This relationship is expressed by the following equation: Ri, t= α + β sentt + ε t (8) Where Ri,t represents the asset return at time t and sentt is the investor sentiment measure at time t. Table 3: Relationship between Return and Investor Sentiment at the Individual Level Panel A: BVMT index Sent1 Sent2 Sent3 Sent4 ALPHA BETA R2 ALPHA BETA R2 ALPHA BETA R2 ALPHA BETA R2 AB ** ** 0, ** 0, , ATB * 0.012** ** * * 0.03 BH ** 0.014*** ** ** ** ** ** 0.1 BIAT *** ** ** -0.01** ** * 0.03 BNA -0.02*** 0.009*** ** 0.004** BS ** ** * BT ** ** ** ** UBCI ** 0.02*** ** ** ** ** ** 0.05 UIB ** 0.012*** * STB -0.02*** 0.014*** ** 0.006** ** * 0.02 AMS * 0.024** * * 0.1 ASTR ** -0.2* * ** ** * 0.12 ICF -0.02** 0.008** * * ** * * ATL ** 0.019*** ** 0.009** * ** * ** 0.09 CIL ** 0.014*** ** * 0.1 MONOPRIX * 0.01*** ** ** * * 0.09 SFBT ** * ** ** ** ** 0.13 SOTETEL ** ** ** ** ** ** 0.18 TAIR ** 0.021** * 0.011** * ** ** 0.08 SOTUVER ** * Panel B: TUNINDEX Sent1 Sent2 Sent3 Sent4 ALPHA BETA R2 ALPHA BETA R2 ALPHA BETA R2 ALPHA BETA R2 AB ** 0.024*** ** ** *** * 0.1 ATB ** 0.018** ** 0.01*** ** 0.09 BH *** 0.019*** ** 0.009*** ** ** 0.13 BIAT ** 0.014*** ** ** ** 0.05 BNA *** 0.013*** ** 0.006** ** * 0.09 BS ** ** * 0.09 BT *** ** ** UBCI ** 0.027*** ** 0.018*** * ** * 0.08 UIB ** 0.014*** ** 0.011** * 0.08 STB ** 0.012*** ** 0.009** * 0.07 AMS * * ASTR 0.013** 0.001* ** * ** * * 0.12 ICF * 0.005* * 0.003* * 0.08 ATL ** 0.022*** * 0.012** ** ** 0.18 CIL ** 0.017*** * 0.008** ** 0.07 MONOPRIX ** ** * * SFBT ** ** ** ** 0.23 SOTETEL ** ** * ** ** 0.26 TAIR ** * ** 0.11 SOTUVER ** ** ***, **, * denote statistical significance at the 1%, 5% and 10% levels respectively This table shows the resultants of the estimate linear relation between four measures of sentiment investor and the return at the individual level These results show that 120 betas among 160 estimated are significant. Such finding implies that the significance degree remains still important (75 %) but it has decreased by 25 % in passing from the aggregate level (100 %) to the individual one (75 %). The two panels A and B represent nearly the same significance percentages which achieve respectively % and %. However this percentage presents remarkable differences between sentiment measures. The highest percentage is noted down by the first measure with a significance percentage of 90 %. This percentage is in the order of 75 %, 45 % and 40 % respectively for the second, the third and the forth measures. Thus, the stability of the relationship between sentiment and returns as well as the significance percentage at the aggregate and individual one depend appreciably on the choice of the sentiment proxies (Nicolosi, Peng and Zhu (2006), Statman, Thorley and Vorkink (2006)).

8 International Research Journal of Finance and Economics - Issue 16 (2008) 182 Similarly, like at the aggregate level, the sign of the relationship between investor sentiment and returns is sensitive to the sentiment measure. It is, generally, positive for the first and the second measure and negative for the third and the forth ones. But, these signs are not constant for all assets especially in the case of the third and the forth sentiment proxies. 5. Behavioral Beta and Return According to Asset Sorts The loss of significance of the relationship between investor sentiment and return at the individual level for some firms leads us to separate individual stocks into four groups according to activity sector, size, book to market and liquidity criteria and to see if there are different relation between investor sentiment and returns on these classes. We explore this issue by estimating the following regressions: R si, t = α + β sentsi, t + ε t (9) R gr cap, t = α + βsent gr capt, + ε t (10) R pt cap, t = α + βsent pt cap, t + ε t (11) Rgr Book, t = α + β sent gr Book, t + εt (12) R pt Book, t = α + β sent pt Book, t + ε t (13) R liquid, t = α + β sent liquid, t + ε t (14) Rilliquid, t = α + β sentilliquid, t + εt (15) Where R si,t : Return on activity sector at time t; i = 1 for the banking sector (BS) and = 2 for the non banking (NBS) one; sentsi, t : Sentiment measure for the sector i at time t R pt cap,t: Return on small stocks capitalization at time t, Rgr cap,t: Return on large stocks capitalization at time t; sent pt cap, t : Sentiment measure for return on small capitalization at time t; sent gr cap, t : Sentiment measure for return on large capitalization at time t; R gr book,t : Return on high book to market firms at time t; R pt book,t : Return on low book to market firms at time t; sent gr, book, t : Sentiment measure for return on high book to market firms at time t; sent pt book,t : Sentiment measure for return on low book to market firms at time t; R liquid : Return on liquid at time t; R illiquid, t : Return on illiquid firms at time t; sent liquid, t : Sentiment measure for return on liquid firms at time t; sent illiquid, t : Sentiment measure for return on illiquid firms at time t; The results from these regressions are reported on the table 4:

9 183 International Research Journal of Finance and Economics - Issue 16 (2008) Table 4: Relationship between Return and Sentiment According to the Asset Sorts Panel A: BVMT index Sent1 Sent2 Sent3 Sent4 Coef α Coef β R2 Coef α Coef β R2 Coef α Coef β R2 Coef α Coef β R2 Sector Banking ** *** * ** ** ** ** ** 0.18 sector Non banking sector ** *** * ** ** ** ** ** 0.21 Size G cap *** *** * ** ** ** ** ** 0.24 P cap ** *** ** ** * ** ** 0.17 Book to market G BOOK *** * ** ** ** ** 0.21 P BOOK *** *** ** *** ** ** * ** 0.18 Liquidity liquid ** ** ** ** * ** * ** 0.22 illiquid ** ** ** ** * ** * ** 0.24 Panel B: TUNINDEX Sector Banking sector *** 0.014*** ** *** * ** ** ** 0.21 Non banking sector ** *** * ** ** ** 0.23 Size G cap *** 0.015*** ** *** ** ** 0.22 P cap *** ** ** ** 0.17 Book to market G BOOK *** ** ** ** 0.2 P Book *** *** ** *** * ** 0.28 Liquidity liquid ** ** * ** * ** 0.24 illiquid ** ** ** ** ** ** 0.26 ***, **, * denote statistical significance at the 1%, 5% and 10% levels respectively This table shows the resultants of the estimate linear relation between four measures of sentiment investor and stoks return according to criteria size, book to market and liquidity From Table 4 we find that sentiment does consistently affect returns in a statistically significant manner for all different classes of assets. Regressions with returns as the dependent variable consistently reveal statistically and economically significant coefficients on all sentiment measures (89 % of estimated coefficients) with the exception of ARMS V t measure in panel B which represents 90 % of non significant coefficients.for activity sector criterion, we consider two sectors activity the banking sector and the non banking one. Results show evidence of significant relationship between sentiment and returns on activity sector but there is no sensitivity to the sector change.concerning the size criterion, we have considered two groups according to their capitalization stocks value compared with the market average. If the capitalization stocks value of the firm is above (below) the average, the firm is considered large (small). The results from estimating the regressions (6) and (7) suggest a significant relationship between sentiment and returns for the two groups. But coefficient on sentiment is lightly more important for large capitalization stocks firms than for small capitalization stocks ones (Neal and Weatley (1998), Barberis, Shleifer et Wurgler (2005)). Unlike the previous criteria, we find a significant difference on the impact of sentiment on returns according to book to market criterion. In fact results show that the significance of the coefficient on sentiment is more remarkable for low book to market firms (87.5 %) than high book to market ones (only 62%). Thus, such findings allow us to conclude that relationship between sentiment and returns is stronger for low book to market firms than high book to market ones (Fama and French (1993), Kothari et Shaken (1997)). Finally, with regard to liquidity criterion, we refer to the classification given by the Tunisian stock exchange authorities. These later consider two groups: group 11 including the more liquid firms and group 12 which represents the less liquid ones. This classification does not result in difference in terms of relationship between sentiment and returns. Indeed, the behavioral beta is significant and it takes the same sign for the two groups. It is positive for the first and the second measures and negative for both ARMS indexes (Vayanos (1998), D avolio (2002), Jones and Lamont (2002)). In summary, we have found that for both the aggregate and individual level the behavioral beta is positive in the case of the first and the second sentiment measures and negative for the third and the

10 International Research Journal of Finance and Economics - Issue 16 (2008) 184 forth ones. This result remains valid even when we have examined assets sorts in terms of activity sector, size and book to market variables. However for the liquidity criterion, the results is reversed that s mean that the coefficient on sentiment takes negative sign on the first and the second measures and positive one on the two ARMS measures. So, it is evident that sentiment impact on returns is an unstable phenomenon. At this step, main question that arises is what causes this instability. 6. Behavioral Beta and Return According to the Asymmetric Effect Majority of papers assumes that an extreme return occurs if market movements exceed some predetermined threshold value (for example 1 or 5%) on either side of a probability distribution of equity return. This threshold is arbitrary and can t be generalizing on all the stock markets. In our case, we have divided our sample into two equal sub samples in order to empirically test if instability is caused by an asymmetric effect. The first is composed of normal returns on average and the second includes returns having extreme values. We therefore estimated two regressions that used sentiments measures, one forecasts normal return on average and another forecasts extreme return: R average mt, = α + β sentit, + ε t (16) extrem e R m,t = α + β senti, t + ε t (17) average Where: R mt, represents the more close observations to the average of the series and extreme R m,t represents the more far observations to the average of the series. The results of this decomposition are shown in table 5. Table 5: Relationship between Return and Sentiment According to the Asymmetric Effect Normal returns Extreme returns Alpha Beta t* alpha t* beta R2 Alpha Beta t* alpha t* beta R2 Panel A: BVMT index sent *** sent ** sent ** ** sent ** ** Panel B: TUNINDEX index sent ** ** *** sent ** ** sent ** sent ** ** ** ***, **, * denote statistical significance at the 1%, 5% and 10% levels respectively This table shows the resultants of the estimate linear relation between four measures of sentiment investor, extreme return and normal returns According to these findings, the predictive power of sentiment proxies becomes very limited when returns are near the average (non significant beta) and it is still statistically significant for extreme returns. Thus, the asymmetric effect explains properly the instability of the relationship between sentiment and returns We can therefore conclude that investor sentiment affect returns only when these later take extreme values, that s mean that sentiment has impact on prices dynamic only during periods of market inefficiency; when asset prices will deviate from their intrinsic value. Such conclusion leads us to consider a fuzzy relationship between behavioral and fundamentalist data. 7. Behavioral Beta and Risk In this section, we examine the ability of sentiment measures to predict volatility. Specifically, we explore the bi-directional relation between investor sentiment and asset volatility in a vector autoregression (VAR) framework using sentiment measures discussed above and a GARCH (1, 1) specification to measure realized volatility. The VAR model allows us to examine the interactions

11 185 International Research Journal of Finance and Economics - Issue 16 (2008) between sentiment and asset volatility and to identify the Granger causality sense by calculating the T- statistic. Risq r t α rent, t β rent, t Risq t i = + + ε t sentt α sent, t i = 1 β sent, t sentt i (18) To identify the causality senses, we estimate for each sense two models, one restricted and the other unrestricted. For example, to decide whether or not sentiment causes volatility, the restricted model consists in regressing volatility on lagged values of volatility alone, but the unrestricted model regresses volatility on lagged values of volatility and lagged values of sentiment. A standard likelihood ratio is used to see whether we have significant evidence to reject the restricted form of the model, i.e. whether we have evidence to reject the null hypothesis that sentiment does not cause volatility. We use an identical methodology to decide if volatility do or do not cause sentiment. The degrees-of-freedom depend on the number of lags used in the vector autoregressions. To determine the appropriate number of lags, we optimize the Akaike Information Criterion. We estimate the models using both levels and changes in sentiment measures since it is not easily determined which specification should reveal the primary effects of sentiment. The results of the Granger causality tests using sentiment measures and volatility are presented in Table 6. Table 6: Granger Causality Tests between Sentiment and Volatility Granger causality tests between sentiment measures and volatility Granger causality tests between changes in sentiment and volatility Lag 1 Lag 2 Lag 1 Lag 2 TEST 1 TEST 2 TEST 1 TEST 2 TEST 1 TEST 2 TEST 1 TEST 2 Panel A Panel A Sent Sent Sent Sent Sent Sent Sent Sent Panel B Panel B Sent Sent Sent Sent Sent Sent Sent Sent Test 1: volatility causes sentiment Test 1: volatility causes changes in sentiment Test 2: sentiment causes volatility Test 2: changes in sentiment cause volatility p-value < 0.05: significant causality sense p-value < 0.05: significant causality sense This table shows the resultants of the Granger Causality Tests between Sentiment and Volatility There is significant evidence that the levels of the first and the second sentiment measures Granger-cause realized volatility for both panels A and B at 1 % level (lee and al. (2002)). Such result contradicts the finding of Wang, Keswani and Taylor (2006) which suggests that volatility causes sentiment. This suggestion is only supported by changes in the ARMS V measure (sent 3). For the forth sentiment indicator, the Granger causality tests provides no evidence of relation in the two senses between volatility and the ARMS T measure (sent 3) in both levels and changes. After identifying the causality sense between volatility and sentiment, we test whether past volatility and sentiment is useful for volatility forecasting purposes in the restricted and unrestricted models. Results of past volatility and sentiment forecasting power are reported respectively in the table 7 and 8.

12 International Research Journal of Finance and Economics - Issue 16 (2008) 186 Table 7: Past Volatility Forecasting Power in Restricted Model Risk (panel B) Risk (panel A) Risk (-1) ** *** Risk (-2) C * ** Adjusted- R ***, **, * denote statistical significance at the 1%, 5% and 10% levels respectively This table shows the AR(2) modelling of volatility Table 8: Var (Volatility; Sentiment) Panel A: BVMT index Sentiment measure Var Sent1 Var Sent2 Var Sent3 Var Sent4 var(-1) 0.502** var(-1) 0.489** var(-1) 0.493*** var(-1) 0.493** var(-2) - - var(-2) - - var(-2) - - var(-2) - - Sent1(-1) ** * Sent2(-1) 4.078** ** Sent3(-1) * Sent4(-1) Sent1(-2) - - Sent2(-2) - - Sent3(-2) - - Sent4(-2) - - C C * 2.869** C ** 0.938* C * 1.014*** R-adjust R-adjust R-adjust R-adjust Change in sentiment Var Sent1 Var Sent2 Var Sent3 Var Sent4 var(-1) 0.547** * var(-1) 0.38*** var(-1) 0.477*** var(-1) 0.47*** var(-2) var(-2) var(-2) var(-2) Sent1(-1) 10.52** -0.71** Sent2(-1) *** Sent3(-1) ** Sent4(-1) *** Sent1(-2) 6.503** -0.42** Sent2(-2) *** Sent3(-2) ** Sent4(-2) *** C ** C 20.83** C ** C 20.86** R-adjust R-adjust R-adjust R-adjust Panel B: Tunindex sentiment measure Var Sent1 Var Sent2 Var Sent3 Var Sent4 var(-1) 0.379** var(-1) 0.324** 0.009* var(-1) var(-1) 0.327** var(-2) 0.004** var(-2) * var(-2) * var(-2) Sent1(-1) ** ** Sent2(-1) ** ** Sent3(-1) * 0.15** Sent4(-1) Sent1(-2) * * Sent2(-2) * Sent3(-2) 0.077* Sent4(-2) C 7.169* C 7.604** 1.964* C 7.15** 0.111* C 7.040** R-adjust R-adjust R-adjust R-adjust Change in sentiment Var Sent1 Var Sent2 Var Sent3 Var Sent4 var(-1) 0.468** 0.163** var(-1) 0.36** var(-1) 0.335* 0.165* var(-1) 0.325** var(-2) * var(-2) var(-2) -0.01** var(-2) * Sent1(-1) ** ** Sent2(-1) Sent3(-1) ** Sent4(-1) -0.06** ** Sent1(-2) * Sent2(-2) ** Sent3(-2) * ** Sent4(-2) ** C 6.282* * C 6.83** C 7.124* ** C ** R-adjust R-adjust R-adjust R-adjust **, * denote statistical significance at the 5% and 10% levels respectively This table shows the results of the VAR modelling between sentiment and volatility The results provide evidence that all sentiment measures present an incremental contribution for forecasting volatility even those that do not have any causal relation with volatility (Fisher and Statman (2000)). For example, the adjusted R 2 of the unrestricted models that contain lagged sentiment in Sent 1 are significantly higher ( ) than those of the restricted models ( ). Similarly, for the forth sentiment measure, volatility forecasting power of panel B is increased from in the restricted model to in the unrestricted one. 8. Behavioral Beta and Asset Valuation We have seen how sentiment and returns interact. We are asking now about possible effect of investor sentiment on assets prices and its ability to explain asset values from their theoretical prices. We tend to respond to a simple question can sentiment explain the pricing errors? we start by testing whether abnormal returns can be explained by the behavioral risk. Then, we include the behavioral risk in fundamentalist models to test its explicative power comparatively to other types of risks.

13 187 International Research Journal of Finance and Economics - Issue 16 (2008) Abnormal Returns and Behavioral Risk We determine the abnormal returns from Security Market Line as expressed by the following equation: Rit, = α + β Rmt + ε t (19) Given the fact, that asset pricing model includes only the systematic risk; we suppose that the behavioral risk explains partially the pricing errors ε t. We therefore regress abnormal returns first on a constant and investor sentiment then on a constant and change in investor sentiment: RAt = α + β sent t (20) RAt = α + β sent t (21) Where RA t denotes abnormal return coming from the CAPM at time t, sent t and sent t represent respectively the level of sentiment measure and change in sentiment level at time t. The results from the two regressions are collected in table 9. Table 9: Relationship between Abnormal Return and Behavioral Risk Sentiment Measure Sent1 Sent2 Sent3 Sent4 ALPHA BETA R2 ALPHA BETA R2 ALPHA BETA R2 ALPHA BETA R2 RA BVMT ** ** ** ** 0.21 RA TUNINDEX ** ** ** ** ** 0.15 Change in Sentiment Sent1 Sent2 Sent3 Sent4 ALPHA BETA R2 ALPHA BETA R2 ALPHA BETA R2 ALPHA BETA R2 RA BVMT * ** ** ** ** 0.11 RA TUNINDEX * ** ** ** ** 0.21 **, * denote statistical significance at the 5% and 10% levels respectively This table shows the resultants of the estimate linear relation between four measures of sentiment investor and abnormal returns For both regressions, tests provide statistically significant coefficients on sentiment. That s mean that sentiments of investors do in fact explain stock price deviations from fundamental value. This finding is consistent with the predictions of behavioral models that that some portion of stock price movements can be attributed to investor psychology. We next explore if the inclusion of behavioral risk improve the valuation ability of the fundamentalist asset pricing models. CAPM and Behavioral Risk To examine the implications of the behavioral beta in the CAPM, we resort to the following mathematic equations: RAt = rit, ˆ α ˆ 1 β1( rmt, rf ) = α2 + β2sentt (22) So equation (24) becomes: ( rmt ) Rit, = α + β1, rf + β 2sentt + µ t Estimation results are reported in table 10. (23)

14 International Research Journal of Finance and Economics - Issue 16 (2008) 188 Table 10: CAPM Adjusted To Behavioral Risk Sentiment Coefficient Panel A: BVMT index Panel B: Tunindex Sentiment Coefficient BS NBS BS NBS Alpha ** * Alpha ** Sent1 Beta * ** Sent1 Beta ** ** Beta ** ** Beta * ** Alpha ** Alpha * Sent2 Beta ** ** Sent2 Beta ** ** Beta * ** Beta ** * Alpha * Alpha * Sent3 Beta ** ** Sent3 Beta ** ** Beta * ** Beta * * Alpha ** ** Alpha 0.006** Sent4 Beta ** ** Sent4 Beta ** ** Beta * ** Beta ** ** **, * denote statistical significance at the 5% and 10% levels respectively This table shows the resultants of the estimate CAPM Adjusted To Behavioural Risk Together these four sentiment measures provide strong and consistent support for the hypothesis that asset values are affected by investor sentiment. Each of the measure provides statistically significant behavioral beta. To attribute more robustness to this finding, we tend to validate it in the context of Fama-French model (1992) as expressed by the following specification: ( It ft ) r r = r r SMB HML it ft α + i β + 1i β + 2i t β + 3i t ε it (24) Analogous to the CAPM, Fama French Three Factor Model describes the expected return on an asset as a result of its relationship to three risk factors: market risk, size risk, and value risk. They create three return measures as proxies for these risks. Their market risk measure is the value-weighted average return the market return in excess of the risk-free rate). Their size- risk is measured by SMB, which stands for Small minus Big, representing the difference between the returns on small-firm portfolios and large-firm portfolios. Similarly, their value risk measure is HML which is short for High minus Low, it represents the difference between the value-weighted return of firms with the highest book-to-market ratios and the value-weighted returns of firms with the lowest book-to market ratios. To examine the incremental ability of sentiment to explain stock returns, our investigation follows procedures that have become standard in recent asset pricing studies. We employ a five-factor model in which the first three factors are those of Fama and French (1992, 1993) and the fourth is the sentiment measure. That is, we estimate the following factor model: ( ) r it r ft = αi + β1 i r It r ft + β 2i SMB t + β 3i HML t + β4 i sentt + µ t (25)

15 189 International Research Journal of Finance and Economics - Issue 16 (2008) Table 11: Fama-French Model Adjusted to Behavioral Risk Sent Coefficient Panel A Panel B Sent Coefficient BS NBS BS NBS Coef t* Coef t* Coef t* Coef t* Alpha *** *** Alpha *** ** Sent1 Beta ** *** Beta *** *** Sent1 Beta *** ** Beta ** *** Beta Beta Beta *** *** Beta *** Alpha ** ** Alpha ** ** Beta *** *** Beta *** *** Sent2 Beta ** ** Sent2 Beta ** *** Beta Beta ** Beta ** Beta ** Alpha Alpha *** ** Beta *** *** Beta *** *** Sent3 Beta ** ** Sent3 Beta ** *** Beta Beta ** * Beta Beta ** Alpha Alpha ** ** Beta ** *** Beta *** *** Sent4 Beta ** ** Sent4 Beta ** *** Beta Beta ** ** Beta Beta * ***, **, * denote statistical significance at the 1%, 5% and 10% levels respectively This table shows the resultants of the estimate Fama-French Model Adjusted To Behavioral Risk The results suggest statistically significant sentiment beta for the first and the second measures, but this is not the case for the others. Even if betas for the all three Fama-French factors are significant, sentiment preserve its explanatory power in asset valuation model. We conduct additional tests to check whether the inclusion of sentiment does improve both valuation model CAPM and Fama-French model. For this reason, we resort to R-adjusted, AIC, SC and F-statistic. Results show an increase of R-adjusted for the fundamentalist models adjusted to sentiment and a decrease of AIC and SC information criteria. As regard to F-statistic, it is calculated by the following expression: * ( SCRR SCRU ) F = SCRU ( n k 1) Where SCRR denotes the sum of squared errors generated by initial asset valuation model and SCRU represents the sum of squared errors generated asset valuation model adjusted to sentiment risk, n is the sample size and k is the number of variables in the initial asset pricing model. We have found * that F > 0.05 F for both models. Such results provide consistent and strong support for the 1, n k 1 conclusion that investor sentiment improves asset pricing models.