An Empirical Analysis of Behavioral Finance in the Saudi Stock Market: Evidence of Overconfidence Behavior

Theoretically, investors are considered to be rational decision makers in regard to trading in stock markets, however, some empirical studies have statistically discredited this believe. Evidence shows that typically, investors act irrationally in the financial markets. Therefore, this research aims to empirically investigate investor’s irrational behavior, specifically, overconfidence behavior in the Saudi stock market, Tadawul. The data under investigation is from 2007 to 2018, monthly based. According to previous research, positive past market returns influence the level of investors’ overconfidence leading to higher trading turnover in stock markets. To test for overconfidence behavior, a market-wide Vector autoregression (VAR) model is designed to investigate the lead-lag relationship between market returns and market turnover. The results obtained in this research suggest that investors in the Saudi stock market are overconfident.


Background
"People in standard finance are rational. People in behavioral finance are normal."

-Meir Statman
Many of the theories in both finance and economics, such as in Sharpe (1964), Miller andModigliani (1958), and Malkiel and Fama (1970), share a common assumption that investors act rationally and analyze all available information before making investment decisions. However, more recent studies, such as Kahnemen (1979), Hirshleifer and Shumway (2003), and Statman et al. (2006) pointed out that investors are far from rational. These studies argue that investors cannot conform to the "rational" assumptions of the standard finance theories. Perhaps most notably, it has been pinpointed by Statman et al. (2006) that investors are not the "calculative utility maximizing machines" as assumed by the traditional theories in finance. More precisely, people are influenced by their sentiments or emotions and are more likely to make cognitive errors when making investment decisions. For instance, they may be overconfident about their abilities, overreact, or follow the crowd blindly.
Overconfidence bias is one of many examples of the cognitive errors affecting investor decision making. 1 This bias, among others, influences investors' stock 1 Other observable biases are herding behavior, disposition effect, self-attribution bias, anchoring bias, etc (Thaler, 2005). valuation and trading skills. Numerous empirical findings in the academic literature have shown a positive relationship between trading activity and past stock market returns. 2 Specifically, past stock gains influence investors to trade more. Researchers have pointed out that overconfidence bias cause this positive relationship. This cognitive error is a form of heuristics that develops from the brain's tendency to make mental shortcuts rather than engaging in longer analytical processing. There are various studies in the literature of economics and finance that provide evidence of overconfidence bias in stock markets. For example, this is best explained in both Daniel et al. (1998) theoretically, andStatman et al. (2006), empirically. They have concluded that subsequent to positive stock returns, there will be an increase in trading (volume) in the stock market. That is because gains from past returns have the effect of increasing the confidence of investors, by which it induces them to trade more. The ramification of such behavior could lead to a bubble in stock market, according to Shiller (2002), Scheinkman and Xiong (2003), Michailova (2010), and Gasteren (2016). Statmen et al. (2006) described overconfidence bias as an exaggerated estimation by an investor of his or her likelihood to experience positive events. This bias has a negative effect on investors' overall portfolio returns. According to Trinugroho and Sembel (2011), overconfidence increases the likelihood of making 2 See the literature review section. irrational investment decisions. For example, it is stated in their research that overconfidence can lead investors to buy a stock at a high price, overconfidently thinking its price might go up further, or sell at a low price, overconfidently thinking the stock is worth less now than it was at the purchase date. This is best described by , who has designed a behavioral model to understand overconfident investors. In his model, he assumes that overconfident investors believe they have above average accuracy in their security valuations, and as a result, trade too much and, thereby, lower their wealth or expected utility. Gevias and  have developed a theory on overconfidence behavior by which investors tend to exaggerate their trading skills and ignore the fact that they are in a bull market. For instance, they argue that during a bull market, stocks tend to perform well, and generate profits, but overconfident investors tend to attribute the realized profit to their own skills. They disregard the fact that the realized gains where most likely due to the current state of the market, which is bullish.
Several studies that investigated overconfidence bias in stock markets consider trading volumes as a proxy for investor overconfidence, such as in , Statman et al. (2006), Goetzmann and Massa (2003), and Ranguelova (2001). These studies took into account the influence of past stock market returns on investors' overconfidence. In an empirical study, Statman et al. (2006) investigated the impact of overconfidence bias on trading volume in the US 6 stock market. They used market returns to measure the degree of overconfidence, given that the level of overconfidence changes with market returns. Their results showed a significantly positive relationship between market turnover and past (lagged) market returns. This also indicates the presence of overconfidence bias in the US stock market. In another related study about the German stock market, Glaser and Weber (2007) found that investors tend to trade more when they are overconfident, which is consistent with the Statman et al. (2006) findings.

Research Objective, Justification and Contribution
There are certain objectives that form the basis of this research. The aim is to meet these objectives using empirical models like those of previous studies. Earlier studies have confirmed the presence of overconfidence bias in many countries. This study investigates whether this bias is manifested in the Saudi stock market (Tadawul). In addition, we will evaluate, from the obtained results, how strong the level of overconfidence is and go further to investigate the reasons behind it. Considering data availability, we followed Statman et al. (2006) and used turnover of stocks as a proxy for the level of overconfidence. Trading volume (turnover) is affected because overconfident investors believe in their abilities and act based on the information they obtain. Therefore, if past market returns can explain the current changes in trading volume, it can be considered as evidence of overconfidence. Based on this lead-lag relationship, this study uses a market-wide Vector autoregression (VAR) model and Impulse Response Function analysis to examine the existence of overconfidence bias in Tadawul.
Several studies have found evidence of a relationship between current trading volume and lagged returns in the stock markets of developed countries (Statman et al., 2006;Chuang & Lee, 2006;Glaser & Weber, 2007). However, there have been hardly any such empirical studies on the Saudi stock market. This study aims to fill this void in the existing literature by investigating the Saudi stock market with recent data of Tadawul. By testing the lead-lag relationship between returns and turnover, our empirical results confirmed the existence of overconfidence bias in the Saudi stock market.

Research Structure
In this study, there will be five sections organized as follows. Section 1 introduces and covers a concise background of the study. To give more context to the study, the objectives, justifications and the contribution are also included in Section 1. Section 2 delivers a theory review, as well as summarizes related research findings. Section 3 presents the data and provides a discussion on the empirical model. It also covers details on the dependent and independent variables, for instance, the formulas used in calculating the variables. Section 4 is the empirical section of the study. It discusses and analyzes the findings. The last section, Section 5, lays out a summary of the main findings and discusses whether the objectives are met.
One of the basic assumptions in classical Finance, and perhaps the most controversial, is that of rational agents and efficient markets. The Efficient Market Hypothesis, developed by Eugene Fama in the 1960s, has become one of the fundamental theories of market behavior 3 . Fama defined an efficient market as "a market where there are large numbers of rational profit-maximizers actively competing, with each trying to predict future market values of individual securities, and where important current information is almost freely available to all participants" (Malkiel & Fama, 1970, p. 56). According to their research paper, an efficient financial market should have no speculation because all traders would have the same information as one another and could not therefore rationally expect to profit from speculative trading. However, this fundamental concept of market efficiency is highly unlikely to occur in the real world.
In the late 1980s, several empirical papers found that investors in financial markets exhibited irrational behavior that could not be explained by classic economic theory. Therefore, the assumptions of the Efficient Market Hypothesis were questioned, especially its assumption of agents rationality. Several prominent studies in psychology showed that people are not always rational when they make decisions. In a Nobel Prize winning research on prospect theory, Kahneman and Tversky (1979) argued that people value gains and losses differently and base decisions more on the prospect of gains than on the possibility of losses. 4 Applying cognitive psychology to evaluate the effect of investors' behavior in financial markets led to the development of behavioral finance. Unlike classical finance, behavioral finance assumes that people exhibit subjective reasoning, which leads to more realistic empirical models. Overconfidence bias is one of many cognitive errors or biases discussed in behavioral finance.
In the behavioral psychology literature, such as in Yates (1990) andCampbell et al. (2004), people who presume themselves to have more abilities than they actually retain, and who make decisions based on that presumption, are described as being overconfident. Glaser and Waber (2007) presented three manifestations of overconfidence: miscalibration, underestimation of volatility, and the 'above average' effect. The following is a concise elaboration on these forms of overconfidence.
According to Glaser and Waber (2007), miscalibration is the difference between the accuracy and the probability assigned in any decision making process.
For instance, when asked to make a forecast without being precise but estimating within a certain confidence interval, people usually are less accurate. In a similar study by Alpert and Raiffa (1982), participants were presented with a sequence of ten difficult questions, such as "What is the length of the Nile river?". They were, then, asked to provide a low guess and a high guess that they thought would be the correct answer with a probability of 90%. If participants were well calibrated, nine out of ten of them would provide upper and lower guesses that actually contained the correct answer. As expected, participants were, in general, not well calibrated since they provided guesses that contained fewer correct answers than nine out of ten. In a related study, DeBondt (1998) asked 46 stock market investors to predict stock prices and forecast risks in US stock market. The results confirmed that there was a miscalibration in the stock market since investors were asked to place 90 percent confidence intervals on their predictions. In another word, DeBondt have found that the majority of investors failed to specify a range of expected future stock prices. Glaser et al. (2010) obtained similar findings for student and professional stock traders.
Some studies have focused on the volatility estimates of investors. For example, Hilton (2001) and Andersen et al. (2004) asked investors to provide confidence intervals for the return or price of a stock in the future. These studies concluded that investors tend to provide intervals that are too tight and therefore deviate from the possibilities of a correct guesses; such studies underestimated historical volatilities. In addition, Graham and Harvey (2015) found similar findings.
They asked Chief Financial Officers of US firms to provide quarterly confidence intervals for the market risk premium. In their research, Graham and Harvey (2015) tended to underestimate historical volatilities.
A third form of overconfidence is the belief that one is better than the average person is. This is called the 'above average' effect. Numerous studies have confirmed the existence of this effect, such as Dunning (2005), Beer and Hughes (2010), Sharot (2011) andChamorro-Premuzic andFurnham (2014). Many researchers have concluded that the above average effect is nearly universal. For instance, when a sample of U.S. students (22 years of age) were asked to evaluate their own driving safety, 93% judged themselves to be in the top 30% of the group (Svenson, 1981). Glaser and Weber (2007) found that more than half of stock market traders think their investment skills are above average, which leads them to trade more. Investors who attribute past success to their skills and past failure to bad luck are likely to be overconfident. An investor who is overconfident will want to utilize his/her perceived superior ability to obtain large returns. Furthermore, overconfident investors underestimate the risks of their active investment, and so, on average, trade more than other investors do (Kyle & Wang, 1997;Odean, 1998b).

Stock Market Returns and Overconfidence Bias
The correlation between stock market returns and overconfidence has been under the scope for many years. Miller and Ross (1975)  They also showed that greater overconfidence leads to higher trading volume. The authors also argue that their model could apply to the changing stock market states.
For instance, investors during a bull market have more opportunities to make successful investments and gain profits. Accordingly, investors with self-attribution bias will become overconfident and trade more in a bull market, ignoring the fact that their success is more likely to have resulted from the bull market than from their own ability. Based on that, it could be expected that overconfidence bias among investors is higher and trading volume is greater, when there is an overall stock market gain. Glaser and Weber (2007) investigated the effect of stock returns on individual investors in the German stock market from 1997 to 2001. More specifically, they considered which type of stock returns had a stronger effect on investors' overconfidence level: past market returns or past portfolio returns. They found that both past market returns and past portfolio returns affect investors' overconfidence, leading them to trade more. In their study, Glaser and Weber (2007) showed that higher past portfolio returns make investors trade more, leading to higher risk taking.
However, high past market returns are not associated with higher risk taking.
According to them, high past portfolio returns make investors overconfident because of self-attribution bias. Investors feel overconfident in the sense that they think themselves to be better investors than others. On the other hand, high past market returns could potentially make investors overconfident in the sense that they underestimate the volatility of stock returns. As a result, prediction intervals would be too tight that ultimately may result in misevaluation of the stocks.

Overconfidence Bias and Trading Volume
When analyzing investors' behavior using stock brokerage data, trading frequency is commonly used as a proxy for overconfidence. Odean (2000, 2001) and Odean (1999) found that U.S. individual investors trade excessively, expose themselves to a high level of risk, and make poor investment decisions. Investors with superior information and better trading skills will utilize this ability by trading often to capture high returns. Therefore, people with actual high ability and those who believe they have high ability will both trade excessively. It is generally assumed that there are few truly highly investors compared to the number of overconfident ones. Therefore, the trading frequency proxy is often believed to represent the behavior of overconfident investors on average. Similarly, Gervais and Odean (2001) examined an overconfidence hypothesis that proposes if investors are overconfident, they will trade more aggressively after experiencing stock gains.
They pointed out that successful past trading experience creates overconfidence in investors' original price trend predictions. Such trading gains would then induce investors to buy or sell more in the following periods, and to do so more aggressively.
In a related study, Chuang and Lee (2006) reported several comprehensive results such as, past stock market gains lead investors to be overconfident and thus trade more actively. 6 Furthermore, a positive relationship between investor's overconfidence and stock market volatility was confirmed in their model.
Additionally, overconfidence leads investors to underreact to risks associated with investments, causing them to trade more in riskier stocks and as a result, lower their returns. These results are parallel to an experiment conducted by Yeoh and Wood (2011) in which participants were engaged in an eight weeks trading competition using London Stock Exchange share prices. Simulating a real-life investment experience, participants were given freedom to trade at any time. Using miscalibration as a measure of overconfidence, Yeoh and Wood (2011) revealed that overconfident participants tended to trade more and, as a result, underperformed in the experiment.
In a prominent empirical study, Statman et al. (2006) examined the New York Stock Exchange from 1962 to 2002. The focal point in their research was to test the trading volume predictions of formal overconfidence models. They pointed out that when examining long-term stock market trading activity, one must account for the fact that the number of shares for a typical stock has increased noticeably over the last four decades. Therefore, to offset the secular increase in number of shares, they measured trading activity with turnover (shares traded divided by outstanding shares). 7 Using Vector Autoregression and Impulse Response Functions, they were able to show that there is a statistically significant tendency for market trading activity to increase in the months following positive market returns after accounting for volatility associations. 7 See also, Lo and Wang (2000).

Overconfidence Bias and Stock Market Bubble
Ultimately, stock market bubbles are infamous for its destructive impact on investments and the economy as a whole. In financial economics, a bubble is referred to as the systematic deviation from the asset's fundamental value (Kindleberger, 1978). Even more specifically, a stock market bubble occurs when the asset's trading price exceeds the discount value of the expected future cash flows (Gasteren, 2016). Perhaps, this is best explained by the Daniel, Hirshleifer and Subrahmanyam (DHS) model as it demonstrates the relationship between overconfidence, volatility and bubbles. It starts when investor X receives some private information at time t, he/she tends to overreact to this piece of information and value stocks much higher than its actual price. At time t+1, this private information reaches the public, consequently other investors will eventually correct the initial overreaction until the stock reaches its rational expected value at t+k. This is what is considered a short run (harmless) bubble according to Daniel et al. (1998). However, in the long run when more investors are involved, the bubble could do a lot of damage in the stock market where instead of stocks prices going back to its rational expected value, it plummets sharply.
The role of overconfidence in creating bubbles begins when investors overvalue stocks prices, overconfidently thinking that other investors would pay higher in the future and thus generating profits, for instance similar to investor X. Michailova and Schmidt (2011) designed an experiment on 60 subjects (German participants) who were asked to participate in a simulated stock market with virtual money. At the end of the experiment, each participant was paid the exact amount earned in the simulation in cash. The purpose of their experiment was to closely test if overconfidence contributes to the creation of bubbles in stock markets. Their findings demonstrated that the majority of participants were overconfident which led to the formation of a bubble in the simulated stock market, and the ramification of participants' overconfidence led to overall lower returns. This experiment, however, was on a smaller scale as in any given real stock market, this potentially means that many people could lose substantial amount of money and as a result, the general confidence becomes weak in the stock market and the economy as a whole. that Saudi investors tended to be overconfident when they made their investment decisions, which means Saudi investors have a tendency to overestimate their own knowledge, abilities, and judgements. In an attempt to examine investors' stock portfolios in the Saudi stock market, Alsedrah and Ahmed (2018) found that investors in the Saudi stock market appeared to participate in a speculative behavior when making investment decisions. They concluded that overconfidence bias was one of the behaviors that persisted in the Saudi stock market.

Model Specification
In this study, overconfidence bias is tested in the Saudi stock market (Tadawul) by closely examining the interactions between market returns and market turnover (i.e. trading volume) using empirical model designed specifically to investigate overconfidence bias. This model, the market-wide security model which is based on Statman et al. (2006) 8

is formulated by estimating vector autoregression (VAR) and
Impulse Response Functions (IRF) analysis using aggregate stock market data.
Ultimately, empirical tests based on these estimates are critical in studying the interactions between lagged market returns and trading volume, which are used to test for overconfidence.
: The current trading volume of transactions is not positively related to lagged market returns.
: The current trading volume of transactions is positively related to lagged market returns. This hypothesis is justified by the fact that following a bull market, the overconfidence of investors leads them to trade more aggressively due to selfattribution bias. Of this fact, this study assumes an increase in transaction volume following gains achieved by the market. 9 The Vector autoregression (VARX) model is applied to examine whether investors will trade more aggressively after market gains, as predicted by the overconfidence hypothesis.
Where,  Y t: a (n*1) vector of endogenous variables 11 with t observations each.
 A k: the matrix that measures how trading proxy and returns react to their lags.
9 This hypothesis is also mentioned by  and Gervais and Odean (2001). 10 The VARX model is different from VAR in that it allows the use of control variables (exogenous variables in which their values are calculated outside the model). 11 Returns and trading proxy (turnover and volume).   The market turnover series is required to be stationary to ensure the model estimation is non-biased and valid. The variables are stationary at their level according to the Augmented Dickey Fuller and Phillips Perron tests that have been applied to the data.

Definition of Variables
 Mturn: The monthly market turnover (shares traded) According to previous research, trading volume (in shares) and the turnover ratio are both commonly used indicators to measure trading activities. This paper takes into account the historically growing trend of trading volume in the sample period.
Following Statman et al. (2006), the turnover ratio is used because it is a relative measure that eliminates the influence of growth. The turnover ratio has to be estimated for each stock, using the data of trading volume (in shares) for each individual stock. Lo and Wang (2000) provided thorough calculation formulas for both share turnover and value-weighted turnover. Suppose V i represents the number of shares traded monthly for individual stock i, and S i is the outstanding shares of the stock i. Hence, the individual turnover is calculated by, T = . The weight w i for each stock is different with its own market value divided by the total market capitalization. By applying different weights to the turnover ratio for each stock, the market turnover is expressed as follows: The calculation of each stock during the whole sample period was repeated to obtain a market turnover time series. Figure 1 is the plotted graph of monthly market turnover. Perhaps, it is noticeable that Figure 1 indicates that the series may be accompanied with a trend. Therefore, the Augmented Dickey-Fuller (ADF) unit root 15 Where, w = Thecapitalizationofthesecurity Sumofcapitalizationforallsecuritiesinthemarket and = * (Pi, is initial price per share, and Si, is shares outstanding for each security).
test was applied, and the test rejected the null hypothesis of existence of a unit root at 1% confidence level. The results revealed market turnover is stationary at its level.
A stationary turnover time-series is desired as it eliminates bias in coefficient estimates of the VAR model. The results of the unit root tests will be presented in details in section 4.

 Mret: The monthly stock market return
One way of calculating market returns is directly through raw data on TASI. For monthly market returns, the process involves calculating returns for all stocks within the index for each month.
The market return series, mret is therefore generated by repeating the process for all months during the sample period. Furthermore, market return passes the stationary test (ADF unit root test) at 1% significance level. Figure   In addition to Mturn and Mret, market volatility (Msig) is employed as the first control variable.
Following the Statman et al. (2006) specification of the monthly volatility, using the formula provided by French et al. (1987), which is computed by adding squared daily returns with twice the sum of the products of adjacent returns.
Assuming that is day t's return and T is the number of trading days in month t. The second control variable dispersion (Disp) is introduced, following Campbell and Lettau (1999). In order to capture the individual risk for individual firms, dispersion variable is employed, which is the cross-sectional volatility of individual firms within TASI on monthly basis. The reason the return dispersion is used as a control variable is to account for any potential trading activity associated with portfolio rebalancing. For instance, large deviations between the individual stock returns within an investment portfolio might lead investors to initiate a trading activity in 28 order to maintain their incepted portfolio weights associated with an investment strategy.
First, squared deviation from mean return for each stock is computed and following is the multiplication of market-capitalization weights to generate disp series.

Data
The data of the Saudi stock market in this paper were collected from Bloomberg's database. The TASI is a free float market capitalization-weighted index of more than

Descriptive Statistics and Unit Root Tests
There is a fairly large number of observations in this study at which N = 143. We believe, in this study that it is important to have an adequate number of observations as it provides an estimation that is more precise. By looking at  Intuitively stationarity implies that the statistical properties of a time series variables do not change over time. In a time series model, it is essential for the variables to be stationary in order to have a valid assumption. As can be seen in Table 3, we ran the Augmented Dickey Fuller (ADF) test on all the variables. 20 The results show that at 1% confidence level, all variables are stationary at its level. This 20 After processing the data, the following ADF test (1981) is used: The theory of unit root test underlies consideration of the serial correlation problem. The null hypothesis of the ADF test is γ = 0 versus the alternative hypothesis γ ≠ 0. Failing to reject the null hypothesis means that the series under investigation is not stationary, and a unit root exists.  Table 4 summarizes the estimation results of the market VARX system that contains endogenous variables: market turnover, Mturn, and market return, Mret.

Market VAR Estimation
Furthermore, the control variables are market volatility, Misg 2 , and dispersion, Disp.
The following paragraphs discuss the main results obtained from VARX model that was designed to test overconfidence behavior in the Saudi stock according to Statman et al. (2006), the overconfidence hypothesis is verified when lagged market returns are associated with increased market turnover (trading volume). 21 The PP unit root (1988) statistics are computed as: ) 1/2 , and 2 = −1 ∑ 2 =1 and ̂2 are estimators of the short and long run variances of . The null hypothesis of the PP test proposes that there is a unit root. Failing to reject the null hypothesis means that the series under investigation is not stationary. Table 4 shows the results of testing this study's hypothesis using VAR estimation by incorporating the full sample (2007 to 2018). This study is interested in the in the interactions between lagged market returns and market turnover.
Looking at market turnover (Mturn) with market return (Mret) at lag 1, the result shows a statistically significant coefficient, with the estimated parameter of 0.067. However, we noticed the existence of serial correlation at lag 1. To solve this problem, we proceeded to use lag 2 for all endogenous variables as the selection of lag 2 seemed to remove serial correlation problem as proposed by Foscolo (2012). 22 This suggests that current market turnover depends on the first lagged market return.
From this observation, the overconfidence hypothesis of our model is verified and confirmed in the Saudi stock market, Tadawul. In other words, positive past market returns make investors overconfident leading them to trade more. Besides, the results 22 Foscolo suggested that serial autocorrelation rapidly declines at higher lags. The serial correlation test results will be displayed in the Appendix. indicate that market volatility at lag 1 has a positive and statistically significant coefficient of 0.042 in explaining market turnover. That is, when volatility is high, Saudi investors tend to trade more in the subsequent period. We believe the reason behind it is that when there is volatility in TASI, Saudi investors might anticipate that the market is reacting to positive news while in reality that is not the case as in many cases, volatility is caused by noisy traders. These results are consistent with Statman et al. (2006).
The results in table 4 are similar to the results that have been observed in the US stock market (Statman et al., 2006;Odean, 1998a;Gervais and Odean, 2001), Hong Kong stock market Zhang, 2011), andFrench stock market (Siwar, 2011). However, the degree of overconfidence understandably varies between countries. 23 For instance, the coefficient of the market return lag 1 with current market turnover in the United States (Statman et al., 2006), is 0.816, in Hong Kong the coefficient is 0.3330, and in France, the coefficient is significant at 0.540, compared with this study's equivalent results, in which Saudi Arabia has a significant coefficient of 0.082. 23 It could be a result of different time series or different estimation models. Nevertheles, this relationship does not hold in the opposite way. The p-value is greater than 10% when the dependent variable is market return. Thus, the null hypothesis cannot be rejected. As a result, the influence of past trading volume on the current market return is not realized in the Granger causality test. To sum up, this study found a unidirectional granger causality running from lagged market returns and current market turnover.

Market Impulse Response Function
Impulse response function uses all the VAR coefficient estimates to check the impact of one standard deviation shock from the residual. Figure 5 shows the four 36 possible impulse-response function graphs using the VAR estimation results in Table 4. respectively. For instance, Figure 5.1 shows that a one standard deviation shock to market turnover results in a positive response of 1.8% in the next month's turnover.
This verifies the serial dependence of market turnover, by which the positive effect of a one standard deviation shock to market turnover persists at period one (the effect starts to slowly decline after period one). In Figure 5.2, the first and second period impulse-responses imply that a one standard deviation shock to market return is followed by 0.4% increases in the market turnover of the second month. The accumulated response over the first 10 months is a 1.0% increase in market turnover compared to average levels. This is a key finding, as it is an evidence that market return impacts investors' overconfidence, leading them to trade more. Figure 5  deviation shock to market turnover is weak, and is present only from 1 month to 3 months. In the third month and afterwards, the impact of the shock starts to move to the negative range. That means that a one-unit shock of market turnover will negatively affect returns by -0.2% in the third month. In other words, positive lagged market returns lead Saudi investors to trade more, resulting in negative overall current market returns. Figure 5.4 indicates that the first period impulse-response with a one standard deviation shock to market return results in a 6.4% increase in the next month's return. However, the impact of the shock declines after 2 months and starts to disappear after 3 months. This behavior of market returns can be explained by the Momentum Theory (Rouwenhorst, 1998), which suggests that positive returns tend to follow gains in a short time horizon.
This section summarizes the main empirical findings obtained in Section 4.
Furthermore, there will be a brief discussion whether the objectives of this research are achieved as well as addressing the limitations of this research. In addition, suggestions and recommendations for future research will be highlighted in this chapter. i.e., they exhibited overconfidence bias. This study aimed to test for overconfidence bias in the Saudi stock market. This objective has been met using appropriate estimation model (VAR model) and the brilliant example of Statman et al. (2006) as the primary foundation to build up the hypothesis and model of this study.

Limitations and Recommendations of the Study
The results confirm that investors in the Saudi stock market (Tadawul) exhibit overconfidence behavior in their decision-making. The most substantial limitation of this study is being unable to collect stock market data before 2007. This would have been beneficial in terms of studying the Saudi investor's behavior before and after the global financial crisis of 2008 and the local market crash of 2006. Moreover, a longer sample size would allow for more insights into past stock market behavior and comparison of changes in behavior with recent data.
This study investigated the lead-lag relationship between market returns and market turnover, using Statman et al. (2006) estimation models on a monthly basis.
However, there are more ways to test for overconfidence behavior. Most obvious and most difficult is by conducting experiments 26 . Another limitation, it is time consuming but effective to collect data using a questionnaire, such as in Zaiane and Abaoud (2010) and Huisman et al. (2012). Also, as mentioned earlier, the data were collected and then calculated on a monthly basis. As Statman et al. (2006) suggested, a daily-based data might introduce more insight into investor's behavior. Given the fact that there is no research on the Saudi stock market (at the time of conducting this research) that contains daily observations, it would be interesting for future studies to take that into consideration. One concern of using daily observations is that it will produce an extremely large dataset. Therefore, shortening the sample period is ideal in this case.