Investing Report

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1. Introduction

With the development of modern security markets, stock price reflects the entire financial system and the overall macroeconomic operation system more and more significantly. As the financial system matures, problems such as inadequate regulation and asymmetric information cause stock market anomalies. The classic Capital Asset Pricing Model (CAPM) cannot accurately predict the volatility of stock price.

There are many opinions on stock volatility. Osberne (1959) proposed "random walk theory", asserting that the changes of stock price are similar to the Brownian movement, whose path is unpredictable. Similarly, Fama (1965) argued that stock returns do not have "memory": Investors cannot predict the future movements based on historical stock prices. Both theories assume that stock price volatility is a random process. However, the theories of Osborne and Fama on stock price are based on a few ideal assumptions and they need to be further examined before we apply them in the real situation.

Meanwhile, some scholars believe that the stock price can be forecasted to some degree. DeBondt and Thaler (1985) argued that asset returns have a long-term reversal effect, and then Jegadeesh and Titman (1993) found a short-term momentum effect of asset prices. Long-term reversal effect states that Investors can buy past winners and sell the losers to gain excess return on investment decisions. The momentum effect refers that the rate of return of a stock will maintain its trend for a short period. These two effects have proved the abnormal fluctuations in asset prices, but they do not explain the deep-seated reasons behind.

Therefore, behavioral finance was founded to further study the mechanism of stock anomalies by taking investors' psychological factors into account. Herding is very common in such stock anomalies. The herding effect originally means that the pack will always follow the “king” and ignore the underlying threats ahead or better opportunities. Introduced in stock market, herding effect refers to the tendency of investors to follow others.(Eric C Chang, 2002) It can also be explained as the common irrationality of the investors, which has been proved to have a great negative impact on the overall market trend and stability.(Peiyuan Sun, 2002)

    There have been some researches relating to the herding effect and the typical methods including LSV model, CH model, and CCK model. Among them, the LSV model conducts inspection based on the fund managers’ buying and selling behaviors, but it does not consider most individual investors in the market. CH model tests the changing path of the stock price deviation. However, in the absence of a rational assumption, the model deviates from irrational factors of investors. CCK model is suitable for our study because it is constructed on the basis of individual investors’ behaviors. The test of CCK model is based on the rational CAPM model and it has a more explicit theoretical explanation for its test results.

Although the herding effect in China has been studied by scholars (Jun song, 2001; Wermers R. 1999), we notice that some results and conclusions are obtained through small and old data. It is still worth going deeper in each industry and trying to explain the underlying reasons. It is also important to consider the herding effect when we forecast the expected rate of stock return, which has rarely been studied before. In this paper we use Arch model to study whether the herding effect exists in each industry of China and we introduce the herding effect into the CAMP model to study how it may impact the rate of return of individual stock in China’s stock market.

2. Model & Methodology

2.1 The CCK Model

        ①[pic 6]

Where,  is the cross-sectional absolute deviation of individual stock from the average rate [pic 7]

of return of the market portfolio at time t

n is the number of stocks in the market

        is the rate of return of stock I at time t[pic 8]

       is the rate of return of market portfolio at time t[pic 9]

From the Capital Asset Pricing Model (CAPM), we can derive the expected rate of return of market portfolio.

    ②[pic 10]

          ③[pic 11]

Substitute equation ③ in equation ①,we can derive

     ④[pic 12]

According to the first order deviation and the second order deviation of equation ④ with

respect to , we can analyze the relationship between the deviation and the rate of return of the market portfolio.[pic 13]

      ⑤[pic 14]

     ⑥[pic 15]

The above two equations indicate that the deviation is linear with the rate of return of market portfolio, and the slope is positive. If the investors are rational, the rates of return of individual stocks should be determined by the CAPM model (i.e. With the increase of the rate of return of market portfolio, the cross-sectional deviation of the rate of return of individual stock from the  market portfolio will increase proportionally. )

Therefore, if herding effect exists,  will be non-linear with   [pic 16][pic 17]

2.2 The Arch Model

Given the above analysis, we conduct an Arch regression model:

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[pic 19]

[pic 20]

()[pic 21]

Where,  is the rate of return of market portfolio at time t[pic 22]

        is a sequence of randomly distributed variables.[pic 23]

        is the 3-month SHIBOR(Shanghai Interbank Offered Rate) [pic 24]

When there exists herding effect in the stock market, decision-making behaviors of investors tend to be the same as a result of herding behavior. Then the positive linear correlation between the cross-sectional absolute deviation (CSAD) and the market rate of return (Rm) will not exist and may be expressed as a negative linear correlation or non-linear diminishing growth. In fact, when there exists a negative linear correlation, it means that the herding effect is very significant. Hence, as long as the coefficient of quadratic term in the polynomial regression is significantly negative, we can say that the herding effect exists. A positive or negative coefficient of linear term has no direct explanation on the conclusion, and the specific degree of herding effect requires a further exploration of the significance level and the value of coefficient.