Inter Relationship Between High Returns, Over Confidence and Trading Volume

1. INTRODUCTION

Some puzzles found on the financial markets, which previously could not be solved using the standard economic theory, we accounted for once overconfidence of investors was assumed. These issues include excessive trading volume. Several studies consider the proposition that investor overconfidence generate the high trading volume observed in financial markets (De Bondt and Thaler, 1995), Odean (1998a, 1998b, 1999), Gervais and Odean (2001), Barberies and Thaler (2003) and Statman, Thorley and Vorkink (2006). These models predict that overconfident investors trade more than rational investors. De Bondt and Thaler (1995) ague that “the key behavioural factor needed to understand the trading puzzle is overconfidence”. Overconfident investors overestimate the precision of their own valuation abilities, in the sense that they overestimate the precision of their private information signals (Daniel, Hiershleifer and Subrahmanyam (1998, 2004), Gervais and Odean

(2001)).

Researches develop theory and testable implications under two assumptions. First, that investors are overly overconfident about the precision of their private information, and second, that biased self attribution causes the degree of overconfidence to vary with realised market outcomes. There is no obvious ideal way to measure overconfidence (Deaves, Luders and Luo, 2008). According to Glaser and Weber (2007), overconfidence can manifest in four facets: miscalibration (Lichtenstein and al., 1982; Yate (1990), Keren (1991), and Mcclelland and Bolger (1994), better than average (Svenson (1981) and Taylor and Brown (1988)), illusion of control (Langer (1975) and Presson and Benassi (1998) and unrealistic optimism (Weinstein, 1980). The calibration technique is the one that most closely conforms to the new overconfidence models (Deaves, Luders and Luo, 2008). Statman, Thorley and Vorkink (2006) reports that there is a little difference in the trading patterns implications between the miscalibration version of overconfidence and the better than average one (the idea that most investors simply believe their investment skills are better than average). In our study, the tests we conduct do not distinguish between them and we refer to previews voluminous studies that model overconfidence as the idea that investors often overestimate their private information. Statman, Thorley and Vorkink (2006) argue that investor overconfidence is a driver of the disposition effect (the tendency to sell winners too early and ride losers too long), because overconfidence encourages investors to trade asymmetrically between gains and losses. Overconfidence differs from the disposition effect in two ways. First, the disposition effect refers to an investor’s attitude towards a specific stock in the portfolio (Odean (1998b), Ranguelova (2001) and Dhar and Zhu (2002). However, overconfidence affects the stock market in general. Second, the disposition effect explains the motivation for only one side of a trade. In contrast, overconfidence can explain both sides of a given transaction. Many studies predict a link between current volume and lagged returns in the developed markets (Statman, Thorley and Vorkink (2006), Chuang and Lee (2006), Glaser and Weber (2007)), but, we find a little evidence in emergent market (Griffin, Nardi and Stulz (2007). Furthermore, compared to developed markets, emerging markets are considerably smaller and less liquid. This death of liquidity can play an important role in determining the relationship between stock returns and trading volume; it can potentially alter the previous findings of the developed markets (Pisedtasalasai and Gunasekarage, 2006). The goal of our paper is to study to what extend overconfidence correlate with trading volume in the Tunisian market. Empirically, we use monthly data in order to correlate past market returns with market trading activity. Through the use of a threshold VAR, we find little evidence indicating that past market returns affect trading activity of individual investors (as measured by volume ). Thus, overconfident investors trade more than the others. The rest of the paper is organised as follows. Section 2 describes our data set and the methodology we employ. Section 3 reports the results. Section 4 discusses the results and concludes. 2. DATA AND METHODOLOGY Our database consists of monthly observations of Tunisian common stocks4 from January 2000 to December 2006. We focus on monthly observations under the perspective that changes in investor overconfidence occur over monthly or annual horizons (Odean, 1998; Gervais and Odean, 2001; Statman, Thorley and Vorkink, 2006). Following Lo and Wang (2000) and Statman, Thorley and Vorkink (2006), we use a value-weighted rather than equal-weighted basis. Figure 1 and 2 present trading

volume approximated respectively by volume (sharestraded) from January 2000 to December 2006.

Fig. no. 1 - Monthly volume for index market Figure 1 presents index volume from January 2000 toDecember 2006. An examination of long-term Tunisiantrading volume indicates that the volume has increasedover the last two years. The increase of transactions canbe explained by the existence of noise traders. In fact,Black (1986) first argued that noise traders offer an exitfrom no-trading equilibrium of perfectly rational modelsof security markets. Odean (1998) and Gervais andOdean (2001) explained that overconfidence of noise traders increases trading volume as theyattribute high returns in bull markets to their tradingskills. 2.1 DEFINITION OF VARIABLES - mret : the monthly stock market return - mtrading : the monthly volume (shares traded). - msig : the monthly temporal volatility of marketreturn based on daily market returns within the month,correcting for realized autocorrelation, as specified inFrench, Schwert and Stambaugh (1987). This volatility control variable is based on Karpoff’s(1987) survey of research on contemporaneousvolume-volatility relationship, as is similar to the meanabsolute deviation (MAD) measure in the trading volumestudy of Bessembinder, Chan and Seguin (1996). According to French, Schwert and Stambaugh (1987),non synchronous trading of securities causes dailyportfolio returns to be autocorrelated, particularly atlag one7. However, the negative sign of variance inthe case of some individual securities leads us touse the approximation of Duffe (1995)8. In fact, French,Schwert and Stambaugh (1987) approximation results ina negative variance estimate if the first-orderautocorrelation of daily returns in a given month is lessthan -0.5. - Disp: cross-sectional standard deviation ofreturns for all stocks in month t. We note: wi : the weight of stock i in the market portfolio month t. 20 Disp =  wi it i 1 2.2 SUMMARY STATISTICS The table 1 provides summary statistics on monthly market return and market trading as well as two market-wide based control variables: volatility and dispersion, during the period 2000- 2006.

(mtrading)

ity (msig)

on (Disp) 0.0004 2.81 E+08 3.84 E-14 0.0235 0.0042 v 0.0016 1.08 E+09 0.4032 0.0139 0.0029

-0.0034 8682751 -0.9077 0.0051 0.0014 0.0060 6150000000 0.9808 0.0714 0.0171

ess 0.7717 4.3837 -0.0799 1.2744 2.1866 is 4.8985 20.6944 2.7361 4.3859 8.0665 Bera 20.9536 1364.869 0.3332 29.4627 156.7879

0.00002 0.0000 0.8465 0.0000 0.0000

This table gives descriptive statistics on market-wide variables, where Return is defined as the monthly value-weighted market return, , Volume is the monthly volume (shares traded), Detrended log volume is the Hodrick-Prescott (1997) detrended natural log of market volume, Market volatility (Msig) is the French, Schwert and Stambaugh (1987) monthly volatility measure based on daily return standard deviation and Dispersion (Disp) is the monthly cross-sectional standard deviation of security returns. To test for unit root, we employ the ADF and Phillips- Peron (PP test) for all variables. The test results indicate that the null hypothesis that the variables are non stationary is strongly rejected except for the variable volume. We employ the Hodrick-Prescott (1997) algorithm (HP) for detrending the trading variable. In fact, the use of non stationary series can lead to bias in the coefficient standard errors of vector autoregressive we employ in this study. Hodrick-Prescott (HP) algorithm is a two sided linear filter that computes the smoothed series S of y by minimizing the variance of y around S, subject to a penalty that constrains the second difference of S. Specifically, The HP filter chooses St to minimize: The penalty parameter , controls the smoothness of the series St. The larger the , the smoother the St. As 12 → ∞ , St approaches a linear trend. Our motivation for detrending is to extract a stationary time- series, not to predict the trend13. To test the normality of returns, we refer to Skewness and Kurtosis statistics. For market return, the Skewness is ≠ 0 (0.77) and the Kurtosis is ≠ 3 (4.89). This implies the non-normality of the distribution of returns.

2.3 EMPIRICAL METHODOLOGY

Following Statman and al. (2006), we use a vectorautoregressive (VAR) and impulse response functionsin order to study the interaction between marketreturns and trading proxies (volume). We use thefollowing form of the VAR model: Where, - Yt : a (nx1) vector of endogenous variables (return and trading proxy : turnover and volume). - Xt : a (nx1) vector of exogenous variables : dispersion and volatility. - et : a (nx1) residual vector. It captures the contemporaneous correlation between endogenous variables. - Ak : the matrix that measures how trading proxy and returns react to their lags. - Bl : the matrix that measure how trading proxy and returns react to month (t-1) realizations of exogenous variables. - K et L: numbers of endogenous and exogenous observations. K and L are chosen based on the Akaike (1974) (AIC) and Schwartz (SC) information criteria14. In our case, the SIC leads to k = 515 and L = 2. Glaser and Weber (2007) note that overconfidence models are not very precise on how we should specify the lag length in empirical studies. Statman, Thorley and Vorkink (2006) find that returns that are lagged more than 6 months do not significantly affect trading activity anymore. In order to provide more insight into the finding of the VAR model, we employ impulse response functions to aggregate over coefficient estimates and illustrate how the endogenous variables relate to each other over time (Hamilton, 1994). Impulse response functions trace the effect of a one standard deviation shock in one residual to current and future values of the endogenous variables through the

dynamic structure of the VAR. 15 Chuang and Lee (2006) chose also 5 lags for their model.

Equation (3) contains two endogenous variables (market turnover or market volume) and two exogenous variables (volatility and dispersion): Changes in one residual, say emtrading , t , will immediately change the current value of mtrading, but will also affect the coefficient matrix of future values of mtrading and mret since lagged values of mtrading appear in both equations through the coefficient matrix Ak To test the overconfidence, we shock the market return by one sample standard deviation and we track how market trading activity responds over timeto the market return residual.

3. MARKET VAR ESTIMATION AND TEST RESULTS 3.1 MARKET VECTOR AUTOREGRESSION

Table (2) provides the results of equation (3). The variable mtrading in table (2) represent volume. The table is organised by rows for each endogenous variable (mret and mtrading) and by columns for lagged endogenous variables and exogenous variables. For each coefficient, we report the estimated value, t statistic and the standard errors.

ngt

0.162807 (0.12369) [1.31628] 0.035738 (0.12347) [0.28945] 0.028013 (0.12169) [0.23020] -0.074074 (0.12971) [-0.57106]

0.0027(0.12940) [0.02146] mrett -0.000313 (0.00049) [-0.64031]

-8.85 E -05 (0.00049) [-0.18123] -0.000106 (0.00048) [-0.22060] 0.000163 (0.00051) [0.31777]

2.03 E(0.000) [0.03961] ( ): Standard errors; [ ]: t stat; *: coefficient significant at the level of 5 % ( ): Standard errors; [ ]: t stat; *: coefficient significant at the level of 5 %

( ): Standard errors; [ ]: t stat; *: coefficient significant at the level of 5 % From the first part of table (2), we document thatmarket trading is not autocorrelated, with non significant5 lag coefficients. Lagged observations of tradingvolume are also not correlated to market return. The second part of table (2) present the associationbetween market trading and lagged market returns. Weremark that market trading is positively related to lagmarket returns with only one significant coefficient (thefifth lag). This result is consistent with previous empiricalstudies of overconfidence hypothesis (Statman and al.(2006), Griffin, Nardi and Stulz (2007), Chuang and Lee(2006) and Glaser and Weber (2007)). According toGlaser and Weber (2007) and Deaves, Luders andSchroders (2007), high market returns make theinvestors overconfident in the sense that theyunderestimate the variance of stock returns. However,Hilary and Menzelt (2006) attribute this finding to the self

mrett-1 mrett-2 mrett-3 mrett-4 mrett-5 mtradingt 15.67898 (31.8742) [0.49190]

2.703257 (31.8685) [0.08483] 14.81631 (32.1965) [0.46018] -33.12995 (32.3617) [-1.02374] 68.58366 (32.2488) [2.12671]*

mrett 0.122507 (0.12613) [0.97129]

0.069077 (0.12611) [0.5477] 0.028561 (0.12740) [0.22418] 0.142152 (0.12806) [1.11007] 0.131071 (0.12761) [1.02712]

constante msigt msigt-1 msigt-2 dispt dispt-1 dispt-2 di0.040303 (0.17226) [0.23396]

7.999411 (3.97861) [2.01060]* -4.665465 (4.10699) [-1.13598] -1.667678 (3.83590) [-0.43476] -27.58485 (18.0826) [-1.52549] 0.352951 (18.6282) [0.01895] 3.417001 (17.7277) [0.19275]

t -0.000568 (0.00068) [-0.83371]

0.026479 (0.01574) [1.68191] -0.006500 (0.01625) [-0.39994] -0.007345 (0.01518) [-0.48392] -0.000514 (0.07155) [-0.00718] -0.007350 (0.07371) [-0.09971]

0.124796 (0.07015) [0.54777]

attribution bias. In fact, investors think that their predictions are better than the others. The third part of table (2) presents the relation between endogenous and exogenous variables (msig and disp). Results show a positive and significant contemporaneous association between volume and volatility. Our finding is consistent with Karpoff (1987) and Statman and al. (2006). Dispersion does not affect market trading. In fact, the association between disp and trading volume is non significant. This result is inconsistent with the result of Statman and al. (2006) who find a high positive contemporaneous association between market turnover (proxy of trading volume) and dispersion. 4. CONCLUSION In this study, we analyse the overconfidence hypothesis in the Stock market using vector autoregressive (VAR) and associated impulse response functions. We find a little evidence for this hypothesis. 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