Beta coefficient is a statistical concept, which reflects the performance of an investment object relative to the market. The greater its absolute value, the greater the change of its income relative to the broader market; The smaller the absolute value, the smaller the change range relative to the market. If it is negative, it means that the direction of change is opposite to the market; When the market rises, it will fall, and when the market falls, it will rise. Because the purpose of investing in investment funds is to obtain financial services from experts, so as to obtain better performance in the market than passive investment, this index can be used as an index to examine the ability of fund managers to reduce the risk of investment fluctuation. When calculating the beta coefficient, besides the performance data of the fund, it also needs to be used as an indicator to reflect the market performance.

Calculation of β coefficient

Beta coefficient is calculated by regression method. The beta coefficient is 1, that is, the securities price changes with the market. Beta coefficient is higher than 1, that is, the stock price fluctuates more than the whole market. Beta coefficient is lower than 1 (greater than 0), that is, the volatility of securities prices is lower than that of the market.

Calculation formula of β coefficient

The formula is: \ beta _ a = \ frac {\ mbox {cov} (r _ a, r _ m)} {\ sigma _ m 2}

Where Cov(ra, rm) is the covariance between the return of security A and the market return; {\ sigma _ m 2} is the variance of market return.

Because:

Cov(ra，rm) = ρamσaσm

So the formula can also be written as:

\ beta _ a = \ rho _ { am } \ cdot \ frac { \ sigma _ a } { \ sigma _ m }

Where ρam is the correlation coefficient between securities A and the market; σa is the standard deviation of security A; σm is the standard deviation of the market.

According to this formula, the beta coefficient does not represent the direct relationship between the fluctuation of securities prices and the fluctuation of the overall market.

It cannot be absolutely said that the greater β is, the greater the fluctuation of securities price (σa) relative to the overall fluctuation of the market (σm); Similarly, the smaller β is, it does not completely mean that σa is less than σ m.

β coefficient application

Beta coefficient reflects the sensitivity of individual stocks to market (or broader market) changes, that is, the correlation between individual stocks and broader market or "stock" in popular parlance. Securities with different beta coefficients can be selected according to the market trend forecast to obtain additional income, which is especially suitable for band operation. When predicting a big bull market or big market with confidence, you should choose those securities with high beta coefficient, which will multiply the market yield and bring you high returns; On the contrary, when a bear market comes or a certain decline stage of the market comes, you should adjust your investment structure and choose those securities with low beta coefficient to resist market risks and avoid losses.

In order to avoid unsystematic risks, we can choose those securities with the same or similar beta coefficient for portfolio under the corresponding market trend. For example, the beta coefficient of a stock is 1.3, which means that when the market rises 1%, it may rise 1.3%, and vice versa; But if the beta coefficient of a stock is-1.3%, it means that when the market rises 1%, it may fall 1.3%. Similarly, if the market falls by 1%, it may rise by 1.3%.

Beta coefficient is an important indicator reflecting the degree of systemic risk change of a single security or portfolio relative to the securities market. By calculating the beta coefficient, investors can get the market risk that a single security or portfolio will face in the future. Usually, the beta coefficient is calculated from historical data, and whether the beta coefficient calculated from historical data has certain stability will directly affect the application effect of the beta coefficient. CHOW test is used to test the listed companies that have fully circulated shares in China stock market. It is found that the beta coefficient of most listed companies has not changed significantly after full circulation, and the reliability of predicting system risk with beta coefficient is still quite high.