What is the index of the stock market?

When calculating the stock index, the stock index and the average price of the stock are often calculated separately. By definition, the stock index is the average share price. However, as far as their actual impact on the stock market is concerned, the average share price is an overall level reflecting the changes of various stock prices, which is usually expressed as an arithmetic average. By comparing the average stock prices in different periods, people can know the changes of various stock prices. Stock index is a relative index that reflects the changes of stock prices in different periods, that is, the percentage of the average stock price in the first period as the benchmark of the average stock price in another period. Through the stock index, people can know the percentage of stock price rising or falling relative to the base stock price during the calculation period. Because the stock index is a relative index, it can measure the change of stock price more accurately than the average stock price in a long period of time.

1. Calculation of average stock price The average stock price reflects the absolute level of listed stock prices at a certain moment, which can be divided into three categories: simple arithmetic average stock price, revised average stock price and weighted average stock price. People can see the changes and trends of stock prices by comparing the average stock prices at different times.

(1) simple arithmetic stock price average The simple arithmetic stock price average is obtained by dividing the sum of the daily closing prices of sample stocks by the number of samples, namely: simple arithmetic stock price average = (p1+P2+P3+…+PN)/nThe world's first average stock price-the average share price of Dow Jones is1928/kloc-0.

Now suppose that four stocks, A, B, C and D, are sampled from a stock market, and the closing prices on a certain trading day are 10 yuan, 16 yuan, 24 yuan and 30 yuan, respectively, to calculate the average stock price of this market. Substitute the above figures into the formula, that is, the average stock price = (p1+p2+P3+P4)/n = (10+16+24+30)/4 = 20 (yuan).

Although the simple arithmetic of stock price average is simple, it has two shortcomings: First, the weight of various sample stocks is not considered, so it is impossible to distinguish the different effects of sample stocks with different importance on stock price average. Second, when the sample shares distribute bonus shares and increase capital in share split, the average share price will break and lose continuity, which makes it difficult to compare the time series before and after. For example, if the above-mentioned D shares are split into three shares with 1 share, the share price will inevitably be lowered from 30 yuan to 10 yuan. The average value at this time is (10+16+24+10)/4 =15. That is to say, due to the technical changes in the division of D shares, the average share price has dropped from 20 yuan to 15 yuan (this has not taken into account other factors that affect the stock price changes), which obviously does not meet the requirements of taking the average value as an indicator to reflect the stock price changes.

(2) There are two ways to correct the average number of shares: one is the divisor correction method, also called Tao correction method. This is a method for calculating the average stock price created by Dow Jones in the United States at 1928. The core of this method is to find a constant divisor, so as to correct the changes of the average share price caused by stock split, capital increase, bonus and other factors, and maintain the continuity and comparability of the average share price.

The specific method is to divide the new total share price by the old average share price to find a new divisor, and then divide the total share price in the calculation period by the new divisor to get the revised average share price. Namely: new divisor = new stock price after change/average value of old stock price = total stock price during the reporting period/new divisor. In the above example, the divisor is 4, and the adjusted new divisor should be: new divisor = (10+16+24+10)/20 = 3. Then: the average value of the revised stock price = (10+16+24+10)/3 = 20 (yuan) is the same as that calculated when it is not divided, and the stock price level will not change due to stock split. The second is the stock price correction method. The stock price correction method is to restore the stock price after stock breakdown and other changes to the stock price before the change, so that the average stock price remains unchanged. The average value of 500 stock prices compiled by The New York Times, USA, is calculated by the stock price correction method.

(3) Weighted stock price average Weighted stock price average is the average stock price calculated by weighted average according to the relative importance of various sample stocks, and its weight (q) can be the number of trading stocks, the total market value of stocks, the stock circulation, etc.

2. Calculation of stock index The stock index is a relative index reflecting the changes of stock prices at different times. Usually, the stock price in the reporting period is compared with the fixed base period price, and the ratio of the two is multiplied by the index value of the base period, which is the stock index in the reporting period.

There are three methods to calculate stock index: one is relative method, the other is comprehensive method, and the third is weighting method.

(1) The relative method, also known as the average method, first calculates the stock index of each sample. Add up and get the arithmetic average of the total. Its calculation formula is: stock index = sum of n sample stock indexes /n The Economist common stock index in Britain adopts this calculation method.

(2) Comprehensive method The comprehensive method is to add the prices of sample stocks in the base period and the reporting period respectively, and then compare them to get the stock index. That is, stock index = sum of stock prices in the reporting period/sum of stock prices in the base period. If numbers are substituted, the stock index = (8+12+14+18)/(5+8+10+15) = 52/38. Judging from the calculation of stock index by average method and comprehensive method, the factors such as the different circulation and trading volume of various sample stocks and the different influence on the stock price of the whole stock market are not taken into account, so the calculated index is not accurate enough. In order to accurately calculate the stock index, it is necessary to add weight, which can be either volume or circulation.

(3) The weighted stock index is weighted according to the relative importance of sample stocks in each period, and its weight can be the number of shares traded, stock circulation, etc. According to the time division, the weight can be the number of basic options or the number of reported options. The index weighted by the number of shares traded in the base period (or circulation disk) is called Rasbel index; An index weighted by the number of stocks traded (or circulated) during the reporting period is called the quotation index. Rasbell index focuses on the number of shares traded in the base period (or circulation), while Paixu index focuses on the number of shares traded in the reporting period (or circulation). At present, most stock indexes in the world are Pais indexes.