What Is a Beta Coefficient?

The beta coefficient, also known as the beta coefficient , is a risk index used to measure the price fluctuations of individual stocks or stock funds relative to the entire stock market. The beta coefficient is a tool for assessing the systematic risk of securities. It is used to measure the volatility of a security or an investment portfolio relative to the overall market. It is common in investment terms such as stocks and funds.

beta coefficient

At present, according to the characteristics and perspectives of research paradigms, there are three main methods of stock investment analysis:

Beta is

Generally speaking, there are several uses for Beta:

1) Calculation

The beta coefficient is a measure of the degree to which the change in the price of a certain type of asset is affected by the average change in the price of all assets in the market. It is a key corporate system risk factor when using the income method to assess the value of an enterprise. It is necessary for the evaluator to analyze various factors that affect the coefficient in order to properly determine the system risk of the evaluation target.

Involving beta coefficient

There are two forms of the model for determining the beta coefficient. One is the CAPM model (capital asset pricing model, also known as the security market line model, security market line): E (Ri) = Rf + i (Rm-Rf) where: E (Ri) = expected return on asset i

Rf = risk-free rate of return

Rm = market average yield

The other is the market model: E (Ri) = i + iRm

Both models are univariate linear models, and the parameters in the models can be determined using the least squares method. In both models, the coefficient is the slope of the model. When i = Rf (1-i), these two models can be converted to each other.

However, the assumptions of the two models, the data used in the variables, and the application conditions are different. In theory, the CAPM model is an equilibrium model based on a series of strict assumptions. The assumptions are a complete market, no cost of information, separable assets, investors' aversion to risk, investors' common expectations of income, and investors' free borrowing at risk-free asset returns. That is, the CAPM model describes the relationship between the expected asset return E (Ri) and the asset risk compensation (Rm-Rf) when the market is in equilibrium. The market model describes the relationship between the expected return on assets and the average return on the market. The market model reflects the relationship between the expected return on assets and the expected return on the market, regardless of whether the market is in equilibrium. The coefficient reflects the degree to which changes in the market's expected rate of return affect the changes in the expected rate of return on assets.

Using the CAPM model to determine the coefficient necessarily involves a risk-free rate of return, which has caused controversy over the model. Black (1972) pointed out in the article "Capital Market Equilibrium under Restricted Borrowing Conditions" that due to the existence of inflation, true risk-free interest rates do not exist. Therefore, Black believes that the foundation of the CAPM model is inherently problematic. However, the CAPM model is still widely used. In the US, the risk-free rate of return in the CAPM model uses long-term Treasury rates.

Impact of securities on the beta coefficient

The average market rate of return Rm is usually the rate of return of an index in the securities market. At present, there are many types of securities market indexes in China, including the Shanghai Composite Index, the Shenzhen Composite Index, the CSI 300 Index, the Shenzhen Component Index, the Shanghai A-Share Index and the B-Share Index, the Shanghai 180 Index, and the Shenzhen A-Share Index. B-share index and new Shanghai Composite Index. The securities represented by each index and the method of compilation are different. Assessors should have basic information and compilation methods for various indexes, and analyze whether the compilation method of securities indexes has an impact on the returns of the assessed enterprises.

In the following, two stocks of Baosteel (600019) and Guilin Tourism (000978) are used to illustrate the impact of different market index conditions on the determination of the coefficient. First of all, based on the changes in the closing prices of Baosteel's stocks at the end of the month from April 29, 2005 to June 30, 2007, the changes in the closing prices at the end of the month corresponding to the Shanghai Composite Index and Shanghai and Shenzhen 300 were regressed. Beta coefficients for two exponential cases during this time:

Using two kinds of exponential regression, the coefficients are 0.9789 and 0.9439, which are relatively close.

The following are the changes in the closing prices of the stocks at the end of the month of Guilin Tourism from April 29, 2005 to December 28, 2007 for the Shanghai Stock Exchange Composite Index, Shanghai and Shenzhen 300 Index, Shenzhen Stock Exchange Composite Index, and Shenzhen Stock Exchange Composite Index. Changes in the situation.

According to the regression equations obtained (the regression analysis chart and regression equations are based on the market rate of return of the Shenzhen Stock Exchange and Shenzhen Stock Exchange), the Shanghai Composite Index, Shanghai and Shenzhen 300 Index, Shenzhen Stock Exchange and Shenzhen Stock Exchange When the rate of change of the Shenzhen Stock Exchange Composite Index is used as the market rate of return, the coefficients of Guilin Tourism are 0.7466, 0.7511, 0.6259, and 0.7988, respectively.

Guilin Travel is a Shenzhen-listed stock, which is not included in the Shanghai Composite Index, Shanghai-Shenzhen 300 Index and Shenzhen Component Index. It is only a sample of the Shenzhen Composite Index. The beta coefficient when the rate of change of the Shenzhen Stock Exchange Composite Index is used as the market rate of return is a difference of 17.29 percentage points when the rate of change of the Shenzhen Stock Exchange Component Index is used as the market rate of return. Therefore, when choosing the return rate of different securities indexes to represent the market return rate, it will have a great impact on the calculated coefficient.

Impact in calculation

The beta coefficient in the income method should be a beta coefficient that can represent the future. But we can usually only use historical data to calculate the coefficient. But is the period of historical data longer or shorter? The longer the period for which the data is used, the variance of the coefficient will be improved, and its stability may be improved, but the period is too long. Due to changes in business operations, changes in the market, technological updates, changes in competitiveness, and inter-enterprise Mergers and acquisitions and changes in the characteristics of the securities market may affect the calculation of coefficients. It is generally believed that the best calculation period is 4-6 years . The yield of the Shanghai Composite Index below is taken as the average market yield, and the coefficient of Guilin Tourism at different periods is as follows:

It can be seen that the calculation period of Guilin's tourism coefficient is different and varies greatly.

Impact of calculation period

The unit time period of securities yield can be calculated daily, weekly, and monthly. The calculation unit length is different, which may affect the coefficient. The Guilin Tourism and Shanghai Stock Exchange Composite Index from 2002 to 2007 were calculated weekly and monthly, respectively, to obtain the different coefficients of Guilin Tourism under different unit time periods.

The weekly rate of return is smaller than the beta coefficient calculated from the monthly rate of return. Most foreign researchers think that the calculation of the beta coefficient should use the monthly rate of return. If the daily rate of return is used, although many observations will be added, it will cause problems such as asynchronous transactions. Research by Hawawini, Corrado, and Schatzberg (1991) states that if the daily yield data is used to calculate , the yield distribution is broad-tailed relative to the normal distribution. Multiplication estimates may not be valid. Chinese scholar Wu Shinong examined the statistical distribution of the daily returns of the 20 stocks on the Shanghai and Shenzhen exchanges from June 1992 to December 1994. The results show that the frequency distribution of the daily returns of the 12 stocks on the Shanghai Stock Exchange are significantly different. It does not belong to the normal distribution, but the frequency distribution of the daily rate of return of 6 of the 8 stocks of the Shenzhen Stock Exchange is close to the normal distribution. Xu Di and Wu Shinong (2001) applied the Hirst index test, and the results showed that the current daily return rate of China's securities market tends to be non-normally distributed. Therefore, the difference in the unit calculation period of the rate of return may result in different frequency distributions of the rate of return, which may result in different calculation results due to the coefficient.

Effect of bonus distribution on coefficient

Since the coefficient is determined based on the relationship between the change in the average market rate of return and the change in the rate of return of a certain asset, during the period in which the coefficient is calculated, it is regarded as the sample of the securities index that is the average market rate of return. When the proportion of securities that issue dividends is large, the calculation of the coefficient of the assets that issue dividends is less affected by the issue of dividends; on the contrary, for asset securities that do not issue dividends for a long time, the impact will be large.

Other may affect beta coefficient

Chinese scholar Wu Shinong and others studied the company size, financial leverage, operating leverage, dividend payout ratio, profit variability, current ratio, total asset growth rate, main income growth rate, and main business profit of listed companies in China from 1996 to 2001. Correlation between 11 accounting variables such as rate, return on capital, and growth rate of capital return and coefficient. The conclusion is that the coefficient is generally not highly correlated with these accounting variables, and the significance of the correlation test is not strong.

In addition, the impact of macroeconomic factors such as business cycles, interest rates, and inflation rates on the beta coefficient requires further study. ^[2]