Financial Market Anomalies And Behavioral Biases: Implications Of Overconfidence Bias

Literature Review and Theoretical Framework

The theory of finance has been the subject of many recent renovations to demystify the market and seize the wheels. A panoply of theoretical research combined with a wide range of empirical work led to the genesis of the theory of financial market efficiency (EMH).

The EMH that we owe to Bachelier's work (1900) was a great success from the 1960s. The triumph of this theory lies in the definition of the fundamental principles of the functioning of markets and the behaviour of investors.

The first definition of market efficiency gives by Fama (1965). He predicts “a financial market is said to be efficient if and only if all available information about each financial asset quoted on that market is immediately included in the price of that asset”. From this perspective, the observed price must be at the same level as its fundamental value. As a result, the EMH stipulates that investors operating on the financial markets are rational with a normative behaviour aiming at increasing their earnings and the hypertrophy of their wealth.

EMH, a component inherent in the economies of the countries and the functioning of the financial markets, has been questioned in recent years because of its inability to prevent the events that are shaking the biggest financial like the famous Krash of 1987 or the crisis of the 2000s. That is why the economic and financial literature has renounced the hypothesis of the rationality of investors.

Based on the rationality of investors as definite by Mangot, (2008), behavioral finance favors the social psychology underlying investors who are permeable to irrational beliefs and preferences).

Indeed, the proponents of the behavioral approach show that investors subject to psychological bias systematically make mistakes during their perception and processing of information. This explains the widening of prices of financial assets to their fundamental values (predicted by the theory), creating certain anomalies on the markets.

Among these anomalies we will focus, in our research work, on the enigma of excessive transaction volumes, the enigma of the excessive volatility of share prices as well as the phenomena of over and under-reactions to information. Since these are the most visible on the financial markets during the last decades.

As such, Daniel, Hirshleifer and Subrahmanyam (1998), Chuang and Lee (2006) and Glaser and Weber (2009) integrate through overconfidence in explaining these phenomena.

In this frame of idea is our work whose objective is to highlight the contribution of the bias of confidence to the explanation of certain anomalies of the financial market namely the excessive volume of transactions, the excessive volatility share prices as well as the phenomena of over and under-reaction to information.

To carry out this study, we will plan it so as to find an answer to our problem:

Can we explain the enigma of excessive transaction volumes, the enigma of the excessive volatility of stock prices and the phenomena of over and under-reaction to information through overconfidence?

However, this study aims to provide information that answers the following questions:

• Try to explain the volume of transactions due to gains in the market.

• Try to understand the effect of the transaction volume component of overconfidence on volatility in its conditional and implicit measure.

• Trying to analyze the asymmetric reaction of over-confident investors to information.

In addition to the introductory in the section I; the rest of papier is organized as follows: section II present the literature review on the subject; section III: an explanation of the Enigma of Excessive volumes by overconfidence; section IV explanation of excessive volatility through overconfidence; section V attempt to explain the asymmetric reaction to information through overconfidence and conclusion.

Data

The data used in this study were collected from the website of the Paris Stock Exchange and Yahoo finance. These are the monthly closing prices and the average volumes exchanged.

Operation of models will be shown from the data of the CAC40 index of the French financial market for the period extending from March 2000 until December 2012: with 154 comments.

The use of monthly variables used by Gervais and Odean (2001), Statman, Thorley, & Vorkink ( 2004), Barber, Lee, Liu, and Odean (2009).

is justified by the fact that the change in the level of overconfidence investors will be held on monthly data

In this section, we will analyze the CAC40 series of returns, the CAC40 trading volume series and the CAC40 index implied volatility series to study their statistical characteristics.

Specification of variables

The variables we will use are:

• The return of the CAC 40 index noted R _t . It is measured by the following equation:

Where R _t is the return on the CAC40 index at time t.

P _t and P _t-1 respectively represent the CAC40 closing price at t and t-1 .

• The trading volume of the CAC40 index noted V _t : This variable defined as the average number of traded CAC40 index in a given month and is calculated in logarithm

• The implied volatility index of CAC40 denoted VCAC_t : this variable measures the implied volatility of option prices in a given month.

• The absolute value of the returns of the CAC40 index at time t noted│R_t│.

• The average of the absolute values of the deviations, in cross section, of the yields at the instant t denoted MAD_t. It is measured by the following equation:

• $$\begin{array}{}\text{(1.2)}& \mathit{M}\mathit{A}\mathit{D}\mathit{t}={\underset{\mathit{i}=\mathit{1}\mathit{}}{\overset{\mathit{N}}{\sum }}〖{\mathit{w}}_{\mathit{i}\mathit{t}}|{\mathit{R}}_{\mathit{i}\mathit{t}}-{\mathit{R}}_{\mathit{t}}|〗}_{}\end{array}$$

Chuang and Lee (2006) use R_t and MAD_t as control variables. Indeed, in order to control the relationship between the volume of transactions and the volatility of securities returns, these authors use the absolute value of returns. In addition, Ross (1989) shows that in a frictionless market, characterized by the lack of arbitrage opportunity, the rate of diffusion of information is revealed from the degree of price volatility. On the basis of this intuition, Bessembinder and al. (1996) use the absolute value of returns as a proxy for the diffusion of common information and MAD_t as a proxy for the diffusion of firm-specific information.

Normality test

The series are normally distributed if Skewness = 0, Kurtosis = 3 and the probability associated with the Jarque-Bera statistic is greater than 5%.

Where the test hypotheses Jarque-Bera are written as follows:

H₀: Normal Distribution / H₁: Non Normal Distribution

Stationarity study

A time series follows a stationary process when its structure remains constant over time, that is, when the series fluctuates around its mean with a constant variance.

To check the stationarity of series observations, we proceed by unit root tests.

With the Augmented Dickey Fuller test, we will be able to test the stationarity of our series by taking into account the autocorrelation of perturbations Ɛ_t.

“Dickey-Fuller Augmented” tests are performed on the following three autoregressive models:

Model 1: model without constant or deterministic trend:

Δx_t= ϕx_t-1 + $\underset{j=1}{\overset{p}{\sum }}{\gamma }_{j{∆X}_{t-j}+{\epsilon }_t}$

Model 2: model with constant without deterministic trend:

ΔX_t = ϕxt-1 + μ + ${\sum }_{j=1}^p{\gamma }_{j{∆X}_{t-j+}{\epsilon }_t}$

Model 3: model with constant and deterministic trend:

ΔX_t = ϕxt-1 + μ +σ_t + ${\sum }_{j=1}^p{\gamma }_{j{∆X}_{t-j+}{\epsilon }_t}$

Excess confidence and conditional volatility

Excess confidence and implicit market volatility

In order to study the relationship between overconfidence and implied volatility, we will examine the effect of the trading volume component of the over-confident investor exchange rate on the implied volatility of the CAC40 index. The proposed model is as follows:

VCAC _t = ɑ ₀ + ɑ ₁ EC _t + ɑ ₂ NEC _t +Ɛ _t

The proposed estimation method is the ordinary least squares method.

Excess of confidence and conditional volatility

Excess confidence and conditional volatility of market returns

The estimated MA (1) -EGARCH (1,1) model is written as follows:

R= -0,004948-0,076606Ɛ_t-1 +Ɛ_t

η_t / ( ΔV_t ,η_t-1, η_{t-2 ,.....,} R_t-1, R_t-2 ,...) →GED(0,h_t )

$\ln {\mathrm{h}}_t$= - 1,073576 + 0,048311([η_t-1]-0,362378η_t-1 / $\sqrt{{\eta }_{t-1}}$ ) + 0,0826359 $\ln {\mathrm{h}}_{t-1}$+ 3,063452 EC_t +1, 052301 NEC_{t .}

In view of the results set out in Table 9 , it appears that the effect of the bias of overconfidence is indeed present on the French market. Indeed, the positive sign of the coefficient f 3 and its statistical significance at the 5% threshold implies that the conditional volatility increases synchronously with the volume of transactions linked to the excessive trust of the players in the market.

Finally, the positive sign of f2 and its statistical significance implies that volatility has a long memory.

These results confirm our initial hypothesis that excess investor confidence contributes to the excessive volatility of returns observed on the French market. And they are consistent with those found by Chuang and Lee (2006).

Excess confidence and implicit market volatility

In view of the results presented in the table above, it can be seen that the excess confidence bias has no effect on the excessive volatility of stock market returns.

Indeed, the sensitivity coefficient associated with excess confidence is negative and is significantly different from zero. Implying that implied volatility decreases synchronously with the volume of transactions associated with the behaviour of over-confident investors.

Regarding the effect of the non-overconfident variable on the implied volatility of the CAC40 index, the non-significance of the coefficient reinforces the absence of a relationship between excessive volatility and the volume of transactions.