**#Index introduction (index)**

An index is a number compiled from the prices of a series of assets using statistical methods to reflect the overall price performance of these assets.

In macroeconomic analysis, economists often need to use indexes to judge the overall situation of the economy.

For example, the price index is calculated by counting the price and demand of a series of commodities. Another example is the U.S. dollar index, which is calculated based on the exchange rate of the U.S. dollar against a series of currencies.

Another example is the gross domestic product—GDP, which is also a statistical index.

In the financial industry, investment and analysis institutions compile a series of financial indexes to reflect the overall asset price changes in the capital market.

For example, the S&P 500 Index is an index compiled by Standard & Poor’s, which contains 500 constituent stocks and is used to evaluate the trend of the US stock market.

**# index compilation**

The index is mainly compiled using two statistical methods. Here we take the stock index as an example. Assume that the stock prices of the four companies are 10, 16, 24, and 30 respectively, and the number of issued shares (or tradable shares) is 5, 10, and 15 respectively. , 20. but:

Arithmetic Mean Compilation: (10+16+24+30)/4=20

Weighted Comprehensive Method Preparation

For an index like the price index that evaluates the price level and cost of living in different periods, generally use:

Pap Index Compilation

pull indexing

**# Arithmetic mean compilation**

This method is of course simple and rude, but it is unreasonable in many cases. For example, the fourth company splits 1 stock and splits 3, the stock price changes from 30 to 10, and the number of shares changes from 20 to 20*3=60. There is no change in the overall price of , but at this time the index has fallen (10+16+24+10)/4=15.

The defects of the arithmetic mean calculation should consider its background. In the early financial market, computers were not yet very powerful, and sometimes there were no computer conditions, so it could only be calculated by humans. In order to quickly calculate the results, a simple arithmetic mean had to be used.

**#Weighted comprehensive method preparation**

According to the above introduction, the calculation of the arithmetic mean value is unreasonable, so can some improvements be made? The answer is yes.

You can use the average value method of the total market value: (10*5+16*10+24*15+30*20)/4=292.5, so that even after the stock split becomes (10*5+16*10+24* 15+10*60)/4=292.5, the index will not change.

Of course, this improvement solves some problems, but there is still a problem that has not been solved, that is, the data calculated in this way is too large, because once the number of shares is introduced, it will be much larger than the average price alone, such as Apple The number of outstanding shares of the company is as high as 4 billion shares, and it participates in the index calculation. How many zeros must be followed by this index calculation?

Therefore, the denominator can be adjusted. The denominator is no longer the number of stocks, but a set divisor. This divisor can be very large, so that the value of the index is within a reasonable range.

This divisor actually needs to be adjusted. For example, if an index includes or excludes a company, the total market value of the molecule will occur. At this time, the divisor can be adjusted to keep the index unchanged.

**# Paasche index and La index**

The Paascher index is also called the Pasch index. Sometimes, the index is designed to reflect changes in a period. For example, take the price index as an example. Suppose there are only two commodities, apples and watermelons. a and b, and the current prices are 3 yuan and 5 yuan respectively, and the quantities of goods are c and d respectively.

We call one year ago the base period (base date) and now the reporting period.

Then there are two ways to calculate the change in the price index:

(3*a+5*b)/(1*a+2*b), the weight here is the number of the base period, and this kind of calculation is called the pull index.

(3*c+5*d)/(1*c+2*d), the weight used here is the number of reporting periods, and this kind of calculation is called Paasche’s index.

In fact, it is: the cost of living today/the cost of living in the past, there are two questions here:

Why introduce quantity as weight? Because the quantity of commodity consumption will cause price changes, if a commodity is too troublesome to produce or not sold well, then the manufacturer may produce less in the second year, so that the market supply will decrease, and the price may even rise slightly. Rising prices are not inflation caused by printing money, so this is taken into consideration when designing the price index. Using the above two indexes to calculate it can eliminate the impact of price changes caused by manufacturers adjusting supply.

Why not use (3*c+5*d)/(1*a+2*b)? Because productivity is improving, c and d may be significantly higher than a and b, and the price index calculated in this way will exaggerate the increase in prices.

Both indexes reflect price changes to a certain extent, but each has its own shortcomings:

Pull index: The weight of the pull index uses the consumption quantity in the base period, but the demand for the consumption quantity of various commodities has changed (from a and b to c and d), so the pull index ignores A situation where a price increase causes consumers to choose to buy other substitutes (the substitution effect), overestimating the increase in the cost of living.

Paasche index: The weight of the Paasche index is the consumption quantity in the reporting period. The assumption is that people will have the consumption demand of existing commodities in the base period, but in fact, people may not have that in the base period. consumption quantity demand (c and d), and lower cost consumption quantity demand (a and b), so the cost of living before the denominator calculated by Paasche’s index may be too high, resulting in the calculated index being too small and underestimated increased cost of living.

Note that the above theories all assume that people always pursue lower-cost consumption demand.