Herd behaviour in stock markets: an international perspective

In this paper, we study the behavioral finance as a theory that seeks to combine cognitive and psychological components with economic and financial aspects to explain irrationality of financial decisions. It is a paradigm where financial markets are studied using models that are less tight than those based on expected utility theory of Neumann Morgenstern and on arbitrage assumptions. Behavioral finance has two main parts: cognitive psychology and the limits to arbitrage. Cognitive refers to how people think. There is a large literature in psychology that claims people make asymmetric errors in thinking. Limits to arbitration refer to prediction data where forces of arbitrage circumstances will be effective or not. Our empirical validation focused on one of the cognitive components: herding. Indeed, we examined herd behaviour in an international context (the United States (DJU), Argentina (MERV), and France (CAC20)) using the model of Chang et al (2000). Our results led us to conclude that there is no herd behaviour. Indexing terms/


INTRODUCTION
Researchers have long focused on understanding investment behaviour of market actors and its impact on stock prices. Such behaviour was linked to factors like investment opportunities, tools used to measure performance, behaviour of other market participants, market volatility and presence of speculative trading in financial markets. Chang et al (2000) examined investment behaviour of market participants in different international markets, in particular the tendency to herd others (herd behaviour). Herding may be interpreted as a rational or irrational form of investment behaviour. According to Devenow and Welch (1996), irrationality relates to the psychology of investors where these latter neglect their prior beliefs and follow blindly other investors. Still, rationality relates to the "principal-agent" problem where managers herd others ignoring completely private information to maintain their reputation in the market (Scharfstein and Stein (1990) and Rajan (1994)). Bikhchandani et al (1992) and Welch (1992) have pointed to this behaviour as an informational descent.
In a recent empirical study, Christie and Huang (1995) examined investment behaviour of market participants in the U.S. stock market. Using cross-sectioned standard deviations of returns (CSSD) as a measure of the average proximity of individual assets returns of the average obtained market, they developed a herd behaviour index. In particular, they examined behaviour of CSSD under different market conditions. They argue that if market participants remove their own predictions about stock prices during periods of significant market movement and they base their investment decisions solely on the aggregate market behaviour, individual stocks returns do not substantially differ from the aggregate market performance, which results in a CSSD smaller than normal.
In this section, we will extend the work of Christie and Huang (1995) in three ways. First, we propose a new and powerful approach to detect herding based on the behaviour of stocks returns. Using a nonlinear regression, we examine the relationship between degree of dispersion of stocks returns (as measured by the absolute crosssectioned standard deviation of returns), and aggregate market returns. In the presence of a moderate herding, we expect that dispersion of returns will drop (or increase at a decreasing rate) with an increase in market returns.
Second, we examine the presence of herding across developed and developing financial markets. Studying herd behaviour is interesting in an international context given the presence of different factors such as the relative importance of institutional investors than individual investors, quality and degree of information disclosure, degree of sophistication of derivatives markets, etc. These may affect investors' behaviour in these markets. ISSN:2321-1098 332 | P a g e This dispersion measure quantifies the average proximity of individual returns to achieved average. Christie and Huang (1995) claim that rational asset pricing models predict that dispersion increases with the absolute market return value as individual equities differ in their sensitivity to market return. However, in case of a herd behaviour (where individuals cancel their own beliefs and base their investment decisions uniquely on market's collective behaviour), asset returns would not deviate far from aggregate market return. Such behaviour will lead to an increase in dispersion and if herding is noticeable it might lead to a decrease in dispersion. Consequently, herd behaviour and rational asset pricing models provide for contrasting predictions of dispersion of market returns. Christie and Huang (1995) suggest that individuals are more likely to cancel their own beliefs in favour of a market consensus during periods of extreme market movements. Accordingly, Christie and Huang (1995) examine whether asset returns dispersion are significantly lower than average during extreme market movements. They estimate the following estimation: , if market return on day t is at the extreme lower distribution tail, and it is 0 otherwise, and D t U = 1, if market return on day t is at the extreme upper distribution tail, and it is 0 otherwise.
The dummy variables (binary) are there to capture the lower or upper tendency of investment behaviour in relation to the relatively normal markets. Obtaining negative and significant β L and β U coefficients indicates herd behavior. Christie and Huang (1995) use 1 or 5% of observations at the lower or upper tail of market returns distribution to define extreme price volatility days.
Using cross-sectioned absolute deviation of returns (CSAD) as a measure of dispersion, Eric C. Chang, Joseph W. Cheng, Ajay Khorana (2000) show that rational asset pricing models predict not only that dispersions of asset returns are an increasing function of market performance but also that the relationship between these two is linear. If market participants tend to follow aggregate market behaviour and ignore their own prior beliefs during periods of strong variations in average prices, then the linear and growing relationship between dispersion and the market return will no longer hold. Rather, the relationship may become non-linearly increasing or even decreasing.
As a starting point of their analysis, Eric C. Chang, Joseph W. Cheng, Ajay Khorana (2000) posit the relationship between CSSAD and market return. Ri indicates return on equities i, Rm is return on market portfolio and Et (.) indicates expectation in period t. A conditional version of the CAPM (Black (1972)) can be expressed as-follows: Where γ denotes the return on zero-beta portfolio, β i is a measure of time-unvarying systematic risk of asset i = 1, ..., N and t = 1, ..., T. Moreover, β m is systematic risk of the equally weighted market portfolio.
The absolute value of the deviation of asset i (DSA) is the expected return in period t from the tth period of expected portfolio return and may be expressed as: Thus, we can define the cross-sectioned absolute deviation of expected stock returns (ECSAD) in period t as follows: Et(R m − γ 0 ) (1-5) The increasing and linear relationship between dispersion and expected time-varying market returns can be easily shown as follows: Against the above results, Eric C. Chang To allow for the possibility that herding degree may be asymmetric, we test the following empirical specification: Where CSADt is the AVD t means for each asset relative to the equally weighted market portfolio return, R m,t in results. Nonlinearity will be captured by a negative and statistically significant γ 2 coefficient.
To compare the two methods, in Figure 1, Eric C. Chang, Joseph W. Cheng, Ajay Khorana (2000) trace CSAD measure for each day and use for the equally weighted market return of Hong Kong using assets return over the period between January 1981 and December 1995. The relationship of market return CSAD seems to be linearly positive. By focusing on the right side where achieved average daily returns were all positive, the estimated coefficients and t-statistics for their model is: The results point to the presence of a positive and statistically significant linear term. However, since the nonlinear term is not significantly negative CSAD t has not increased at a decreasing rate nor decreased like the average price movement. Hence rational assets prediction models (as suggested above) have not been violated.
The same conclusion may be true using the methodology suggested by Christie and Huang (1995). Using the 1% criterion, the estimated coefficients for their model are: The two estimates of the coefficients of the dummy variable are positive and statistically significant. Thus, the method of Christie and Huang (1995) gives no evidence of a herd behaviour in Hong Kong.
However, both methods may give conflicting results on the presence of herd behaviour. As an illustration, for all positive values R m,t , they take a general quadratic relationship between CSAD t and R m,t of the following form: Where the presence of a negative parameter γ 2 indicates a herd behaviour in their model. The quadratic relationship suggests that CSAD t reaches its maximum value when R m,t * = − ( γ 1 γ 2 ). Differently put, as R m,t increases, where the achieved average daily returns are less (greater) than R m,t * CSAD t is an upward trend (downward). At least some, if not all, of the R m,t values during periods of market stress fall in a region where CSAD t is a downward trend, in the model of Christie and Huang (1995 ) β U will never be negative. For example, using 3% of average market return as a threshold of market stress, with γ 1 = 0.3562, the estimated value of the γ 2 parameter needs to be -5.937 or smaller before it is possible that the β U parameter is negative. Thus, Christie and Huang's (1995) approach needs a much larger magnitude of nonlinearity in return dispersion suggesting a relationship of a herding evidence suggested by rational asset pricing models.

2-1 Presentation of data:
To

2-2 The research hypotheses:
We aim at validating the following two hypotheses: • Hypothesis 1: There is herd behaviour among investors in financial markets, • Hypothesis 2: Each investor behaves according to their own conceptions and beliefs about the financial market.

-EMPIRICAL RESULTS AND THEIR INTERPRETATION: 3-1 Time series Descriptive statistics:
A.

Descriptive statistics of DJU index and its components:
The table below summarizes the statistical characteristics of the time series DJU index and its components: The descriptive statistics of the DJU lead us to conclude that index return shows a high variability as the standard deviation is relatively high (0.0136529). Indeed, this index

B. Descriptive statistics of the MERV index and its components:
The table below shows the descriptive statistics of the MERV index's time series and its components:

C. Descriptive statistics of the CAC20 index and its components:
The table below shows the descriptive statistics of the CAC20 index's time series and its components:

Table 3. Descriptive statistics of the CAC20 index and its components
The

3-2 The results ad their interpretation:
A.

Results of the regression of the diatomic variables
Results of the regression of the diatomic variables are reported in the following We start our study of the presence of herd behaviour in the three financial markets using regression tests of the diatomic variables that are similar to CH. The first change relates to replacing CSSD by CSAD as a measure of dispersion. The coefficients of the diatomic variables capture the differences between CSAD and highlight the presence of herd behaviour over trading days with upward and downward extreme price movements. Equation 2 is estimated using 1%, 2% and 5% of price movement days as a definition of extreme price movements (Chang et al. (2000)). In the table below, we report the estimation of the parameters in terms of t-statistics consistent with heteroscedasticity.
In the first model (the 1% criterion), we noticed positive and statistically significant β L and β U (exception is β L of CAC20 and MERV). Consequently, stocks returns dispersion tends to increase rather decrease during periods of price extreme movements. The two other models show positive and significant β U yet non-significant and null β L .
Consequently, stocks returns dispersion tends to increase rather decrease during periods of price upward extreme movements.
This is inconsistent with the operational definition of CH which stipulates a decrease in dispersion levels. Given the similarity between degree of economic development for these countries and degree of their financial markets' integration, these results are not surprising. As a proof of market capitals integration, Campbell and Hamao (1992) found a co-movement in expected excess returns across different developed countries.

A. The results of the regression of the general model
The table below reports the results of the regressions of absolute standard deviation in daily frequencies on the squared term of market portfolio returns:

A. Non-linearity between CSAD and market return
scenarios: upward market and downward market. In model B, we studied the relationship between CSAD and market return during downward market price movements. We found insignificant γ 2 DOWN coefficients for CAC 20 and MERV and significantly positive for DJU (at the 1% level). However, global significance of model B is validated at the 1% level and R ² is average for the three markets. Consequently, we may conclude that there is no herd behaviour on CAC20 and MERV during downward market price movements, whereas the result for the DJU indicates the presence of an additional dispersion due to stocks' slow response to good news.
In this section, we tried to examine investment behaviour of markets participants in three different international markets (DJU, CAC20 and MERV), in particular their tendency to imitate aggregate market behaviour.
To that end, we used a variety of empirical tests taken after Christie and Huang (1995). The main aim of our approach is to show that stocks return dispersion is measured by cross-sectioned standard deviation of returns (CSAD) and that rational asset pricing models can predict not only that dispersion is an increasing function of market return but also that the relationship is linear. In addition, a growing tendency of market participants to herd around market consensus during periods of large price movements is sufficient to convert the linear relationship into a nonlinear relationship.
To capture this effect, we used a non-linear regression that is similar to market timing measurement of Mazuy and Treynor (1966).
Our empirical tests indicate that during periods of extreme price movements, dispersion of equity returns of the DJU, CAC20 and MERV markets tends to increase rather than decrease. Then, we were able to conclude on the absence of herd behaviour. These results are consistent with those of Christie and Huang (1995) and Jurkatis, Kremer and Nautz Following conventional financial theory, rational investors are those who seek to maximize their wealth. However, there are several cases where psychology and emotions influence our decisions. Therefore, our behaviour will be unpredictable and irrational.