Beta coefficient is a statistical concept, which reflects the performance of an investment object relative to the broader market. The larger the absolute value, the greater the change in its earnings compared to the broader market; the smaller the absolute value, the smaller the change in earnings relative to the broader market. If it is a negative value, it means that its direction of change is opposite to that of the market; when the market goes up, it goes down, and when the market goes down, it goes up. Since our purpose of investing in investment funds is to obtain expert financial management services to achieve better performance than passive investment in the broader market, this indicator can be used to examine the fund manager's ability to reduce investment volatility risks. When calculating the beta coefficient, in addition to the fund's performance data, there are also indicators that reflect the performance of the market. Beta coefficient

According to investment theory, the beta coefficient of the entire market itself is 1. If the fluctuation of the net value of the fund's investment portfolio is greater than the fluctuation range of the entire market, the beta coefficient is greater than 1. On the contrary, if the fluctuation of the net value of the fund's investment portfolio is less than the fluctuation of the overall market, the beta coefficient will be less than 1. Securities with larger beta coefficients are usually more speculative securities. Taking the United States as an example, the stock market is usually represented by the Standard & Poor's 500 Index (S&P 500), with a beta coefficient of 1. If the beta coefficient of a mutual fund is 1.10, it means that its volatility is 1.10 times that of the stock market, that is, it is 10% better than the market when it rises, and 10% worse when it falls; if the beta coefficient is 0.5 , the fluctuation situation is only half. β= 0.5 indicates low-risk stocks, β= l. 0 indicates average-risk stocks, and β= 2. 0 → high-risk stocks. The β coefficient of most stocks ranges from 0.5 to l.5. [1] Beta coefficient measures the overall volatility of stock returns relative to performance evaluation benchmark returns and is a relative indicator. The higher the beta, the more volatile the stock is relative to the performance evaluation benchmark. If β is greater than 1, the volatility of the stock is greater than the volatility of the performance evaluation benchmark. vice versa. If β is 1, then if the market rises by 10%, the stock will rise by 10%; if the market falls by 10%, the stock will fall by 10%. If β is 1.1, when the market rises by 10%, the stock rises by 11%; when the market falls by 10%, the stock falls by 11%. If β is 0.9, when the market rises by 10%, the stock rises by 9%; when the market falls by 10%, the stock falls by 9%. Edit this paragraph calculation method β coefficient of a single asset

β coefficient

(Note: Leverage is mainly used to measure non-systematic risk) The systemic risk of a single asset is measured by the β coefficient. Taking the entire market as a reference, the risk-return rate of a single asset is compared with the average risk-return rate of the entire market, that is: β calculation formula where Cov(ra,rm) is the covariance of the return of security a and the market return; is The variance of market returns. Because: Cov(ra,rm) = ρamσaσmSo the formula can also be written as: ? β calculation formula

where ρam is the correlation coefficient between security a and the market; σa is the standard deviation of security a; σm is the market standard deviation. According to this formula, the beta coefficient does not represent a direct connection between security price fluctuations and overall market fluctuations. It cannot be said absolutely that the larger β is, the greater the security price fluctuation (σa) is relative to the overall market fluctuation (σm); similarly, the smaller β is, it does not completely mean that σa is smaller relative to σm. Even if β = 0, it does not mean that the security is risk-free. It is possible that the security price fluctuations have nothing to do with the market price fluctuations (ρam = 0). However, it is certain that if the security is risk-free (σa), β must be zero. Note: Understand the meaning of β value ◆ β=1, means that the risk return rate of this single asset changes in the same proportion as the average risk return rate of the market portfolio, and its risk profile is consistent with the risk profile of the market portfolio; ◆ β>1, indicating The risk-return rate of this single asset is higher than the average risk-return rate of the market portfolio, then the risk of this single asset is greater than the risk of the entire market portfolio; ◆ β<1, indicating that the risk-return rate of this single asset is less than the average risk-return rate of the market portfolio , then the risk of this single asset is less than the risk of the entire market portfolio. Summary: 1) β value is a measure of systemic risk, 2) there are two ways to calculate β coefficient.

The calculation formula of beta coefficient used in the securities market

The summary formula of beta coefficient is: Where Cov(ra,rm) is the covariance of the return of security a and the market return; is the market return Variance of returns. Because: Cov(ra,rm) = ρamσaσmSo the formula can also be written as: Where ρam is the correlation coefficient between security a and the market; σa is the standard deviation of security a; σm is the standard deviation of the market. The beta coefficient is calculated using the regression method: When the beta coefficient is equal to 1, the price of the security moves with the market. A beta coefficient greater than 1 means that the security's price is more volatile than the overall market. A beta coefficient below 1 means that the security's price is less volatile than the market.

If β = 0 means there is no risk, β = 0.5 means the risk is only half that of the market, β = 1 means the risk is the same as the market risk, and β = 2 means the risk is twice as high as the market. Edit the meaning of this paragraph: The Beta coefficient originates from the capital asset pricing model (CAPM model), and its true meaning is the systematic risk measurement of a specific asset (or asset portfolio). How to calculate the β coefficient

The so-called systemic risk refers to the price fluctuation of assets affected by overall factors such as macroeconomics and market sentiment. In other words, it is the linkage between stocks and the market. The higher the system risk ratio, the stronger the linkage. The opposite of systemic risk is individual risk, that is, price fluctuations caused by the company's own factors. Total risk = systematic risk + individual risk and Beta reflects the sensitivity of a specific asset's price to overall economic fluctuations, that is, if the market portfolio value changes by 1 percentage point, the asset's value changes by several percentage points - or in more popular terms Saying: When the market rises by 1 percentage point, the stock's price changes by several percentage points. Expressed as a formula: In practice, the historical return rate of a single stock asset is generally used to regress the index (market) return rate in the same period, and the regression coefficient is the Beta coefficient. Edit this paragraph General purposes Generally speaking, the purposes of Beta are as follows: 1) Calculate capital costs and make investment decisions (only projects with a return rate higher than the capital cost should be invested); 2) Calculate capital costs and formulate performance Assessment and incentive standards; 3) Calculate capital cost and conduct asset valuation (Beta is the basis of cash flow discount model); 4) Determine the systematic risk of a single asset or portfolio for investment management of asset portfolios, especially stock index futures or Hedging (or speculation) in other financial derivatives. Portfolio Beta Coefficient

The discussion of the fourth use of Beta will be the focus of this article. Portfolio Beta The Beta coefficient has a very good linear property, that is, the Beta of an asset portfolio is equal to the weighted sum of the Beta coefficients of a single asset according to its weight in the portfolio. 5) Application of beta coefficient in the securities market Beta coefficient reflects the sensitivity of individual stocks to changes in the market (or the broader market), that is, the correlation between individual stocks and the broader market or the "stock nature" in popular terms. Securities with different beta coefficients can be selected based on market trend predictions to obtain additional income, which is especially suitable for swing operations. When you are very confident about predicting the arrival of a big bull market or a certain phase of the market not rising, you should choose securities with high beta coefficients, which will exponentially amplify market returns and bring you high returns; on the contrary When a bear market arrives or a certain period of decline in the market arrives, you should adjust your investment structure to resist market risks and avoid losses by choosing securities with low beta coefficients. To avoid non-systematic risks, you can choose securities with the same or similar beta coefficients for investment portfolios under corresponding market trends. For example: a stock's beta coefficient is 1.3, which means that when the market rises by 1%, it may rise by 1.3%, and vice versa; but if a stock's beta coefficient is -1.3%, it means that when the market rises by 1%, it may rise by 1.3%. It may fall by 1.3%. Similarly, if the market falls by 1%, it may rise by 1.3%. Edit this paragraph influencing factors: β coefficient is an indicator that measures the extent to which changes in the price of a certain (type of) asset are affected by the average changes in the prices of all assets in the market. It is a key enterprise system risk coefficient when using the income method to evaluate the value of an enterprise. It is necessary for evaluators to analyze various factors that affect the beta coefficient to properly determine the system risk of the evaluation object.

Two discount rate models involving beta coefficients

There are two forms of models for determining beta coefficients. One is the CAPM model (capital asset pricing model, also called security market line model, security market line): E (Ri) = Rf + βi (Rm-Rf) where: E (Ri) = expected return rate Rf of asset i = Risk-free rate of return Rm = Market average rate of return The other is the market model: E (Ri) = αi + βiRm. Both models are single-variable linear models, and the parameters in the model can be determined by the least squares method. In both models, the beta coefficient is the slope of the model. When αi = Rf (1-βi), these two models can be converted to each other. However, the assumptions, data used for variables, and application conditions of the two models are different. Theoretically, the CAPM model is an equilibrium model based on a series of strict assumptions. The assumptions are a complete market, no cost of information, divisible assets, investors are risk-averse, investors have the same expectations for returns, and investors are free to borrow and lend money according to the risk-free asset rate of return, etc. That is, the CAPM model describes the relationship between asset expected return E (Ri) and 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 market return. The market model reflects the relationship between the expected rate of return of an asset and the expected rate of return of the market, regardless of whether the market is in equilibrium. The beta coefficient reflects the extent to which changes in the market's expected return rate affect changes in the asset's expected return rate. Using the CAPM model to determine the β coefficient inevitably involves the risk-free rate of return, which has caused controversy over the model.

Black (1972) pointed out in the article "Capital Market Equilibrium under Restricted Lending Conditions": Due to the existence of inflation, the true risk-free interest rate does not exist. Therefore, Black believes that the foundation of the CAPM model itself has problems. However, the CAPM model is still widely used. In the United States, the risk-free rate of return in the CAPM model is the long-term Treasury bond rate.

The impact of the choice of security index on the β coefficient

The market average rate of return Rm usually uses the rate of return of a certain index in the securities market. At present, there are many kinds of securities market indexes in my country, including Shanghai Composite Index, Shenzhen Composite Index, CSI 300 Index, Shenzhen Component Index, SSE A-Share Index and B-Share Index, SSE 180 Index, SZSE A-Share Index and B-share index and new Shanghai Composite Index, etc. The securities represented by each index and the method of compilation are different. Evaluators should master the basic information and compilation methods of various indexes, and analyze whether the compilation methods of securities indexes have an impact on the rate of return of the enterprises being evaluated. The following uses two stocks: Baosteel Co., Ltd. (600019) and Guilin Tourism (000978) to illustrate the impact of different market index conditions on the determination of β coefficients. First, the changes in the month-end closing price of Baosteel Co., Ltd. from April 29, 2005 to June 30, 2007 were regressed on the changes in the month-end closing price corresponding to the Shanghai Composite Index and the CSI 300. It was concluded that Baosteel Co., Ltd. The β coefficients under the two index conditions during this period: Using two exponential regressions respectively, the β coefficients are 0.9789 and 0.9439 respectively, which are relatively close. The following is based on the changes in the month-end closing price of Guilin Tourism's stock from April 29, 2005 to December 28, 2007, respectively, and compares the month-end closing prices corresponding to the Shanghai Composite Index, CSI 300, Shenzhen Stock Exchange Component Index, and Shenzhen Stock Exchange Composite Index. Regression of changes. According to the obtained regression equation, it can be seen (the regression analysis diagram and regression equation are omitted based on the change rate of the Shenzhen Stock Exchange Component Index and the Shenzhen Stock Exchange Composite Index). When the rate of change of the Stock Exchange Composite Index is used as the market rate of return, the β coefficients of Guilin Tourism are 0.7466, 0.7511, 0.6259 and 0.7988 respectively. Guilin Tourism is a stock listed on the Shenzhen Stock Exchange. It is not included in the samples of the Shanghai Composite Index, the CSI 300 Index and the Shenzhen Stock Exchange Component Index. It is only a sample of the Shenzhen Stock Exchange Composite Index. When the change rate of the Shenzhen Stock Exchange Composite Index is taken as the market return rate, the beta coefficient differs by 17.29 percentage points. Therefore, when selecting the return rates of different security indexes to represent the market return rate, it will have a great impact on the calculated β coefficient.

The impact of the length of the data period used in the calculation on the β coefficient

The β coefficient in the income method should be a β coefficient that can represent the future. However, we can usually only use historical data to calculate the beta coefficient. But is it better to use a longer or shorter period of historical data? The longer the period of using data, the variance of the β coefficient will be improved, and its stability may be improved. However, if the period is too long, due to changes in business operations, market changes, technological updates, changes in competitiveness, and inter-enterprise differences, Mergers and acquisitions and changes in securities market characteristics may affect the calculation results of the β coefficient. It is generally believed that the best calculation period is 4-6 years. Below, the return rate of the Shanghai Stock Exchange Composite Index is used as the market average return rate, and the β coefficient of Guilin Tourism in different periods is as follows: It can be seen that the β coefficient of Guilin Tourism is calculated in different periods, and the difference is very large.

The impact of the length of the calculation period on the β coefficient

The unit period of security return rate can be calculated on a daily, weekly, or monthly basis. Different calculation unit period lengths may have an impact on the β coefficient. The return rates of Guilin Tourism and the Shanghai Composite Index from 2002 to 2007 were calculated on a weekly and monthly basis respectively, and different β coefficients of Guilin Tourism under different unit time periods of return were obtained. The β coefficient calculated on a weekly basis is smaller than the β coefficient calculated on a monthly basis. Most foreign researchers believe that the monthly rate of return should be used to calculate the β coefficient. If daily returns are used, although many observations will be added, it will cause problems such as asynchronous trading. Research by Hawawini, Corrado and Schatzberg (1991) pointed out that if daily return data are used to calculate β, since the return distribution is wide-tailed relative to the normal distribution, the least square The multiplicative estimation method may not be valid. Chinese scholar Wu Shinong tested the statistical distribution of the daily returns of 20 stocks on the Shanghai and Shenzhen exchanges from June 1992 to December 1994. The results showed that the frequency distribution of the daily returns of the 12 stocks on the Shanghai Stock Exchange was significantly different. It does not belong to the normal distribution, but the frequency distribution of the daily returns of 6 of the 8 stocks on the Shenzhen Stock Exchange is close to the normal distribution. Xu Di and Wu Shinong (2001) applied the Hurst index test and the results showed that the current daily returns in China's securities market tend to be non-normally distributed. Therefore, different unit calculation periods of returns may lead to different frequency distributions of returns, resulting in different β coefficient calculation results.

The impact of dividend distribution on the β coefficient

Since the β coefficient is determined based on the relationship between the changes in the market average rate of return and the change in the rate of return of a certain asset, so , during the period of calculating the β coefficient, when the securities index that is the average market return rate in the sample of securities that issue dividends account for a large proportion, then the calculated results of the β coefficient of the assets that issue dividends are affected by the dividend issuance. Small; on the contrary, for asset securities that do not pay dividends for a long time, the impact will be great.

Other factors that may affect the β coefficient

Chinese scholar Wu Shinong et al. studied the company size, financial leverage, operating leverage, dividend payout ratio, and profitability of listed companies in my country from 1996 to 2001 Correlation between 11 accounting variables such as variability, current ratio, total assets growth rate, main business income growth rate, main business profit rate, capital return rate, capital gains growth rate and β coefficient. The conclusion is that the β 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, inflation rates, etc. on the β coefficient requires in-depth study.

[2] More pictures of entries in the album (7 pictures)

Reference materials

1. What is beta coefficient and beta coefficient? ．

2. Analysis of factors affecting β coefficient.

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