What is a weighted index and what is a weighted composite index?

Weighted and unweighted: if it is calculated differently. Simple average and weighted average.

Specifically, an unweighted index simply sums the stock prices of the index stocks and divides them by the total number. The weighted stock price should be calculated to calculate the number of shares in good faith for each **, which is the circulating market value of each **. Sue for peace.

It is divided by the total market capitalization of the index shares.

For example: the first purchase of products**10 yuan, quantity 10 pieces; The second purchase is 15 yuan, and the quantity is 20 pieces; The third purchase is 20 yuan, and the quantity is 30 pieces. The weighted average hair method is used to calculate the average ** of the product.

Then the weighting number is (10 + 20 + 30) pieces 60 pieces.

The weight of the first purchase is 10 60, the weight of the second purchase is 20 60, and the weight of the third purchase is 30 60

The weighted average** is 10 10 60+15*20 60+20*30 60

Weighted average method: It is a method that uses the opening balance quantity of a certain material and the income quantity of the current month as weights at the end of the month to calculate the average unit cost of the material. Specifically, this method is to divide the sum of the inventory amount at the beginning of the month and the amount purchased in this month by the sum of the inventory quantity at the beginning of the month and the quantity purchased in this month, and the average unit price of the material at the end of the month is obtained as the unit price of the material cost issued this month, and its calculation formula is as follows:

The average unit price at the end of the month (the amount of materials in stock at the beginning of the month, the amount of materials purchased in each batch this month) (the number of materials in stock in the month, the quantity of materials purchased in each batch this month).

Cost of materials issued = Number of materials issued Average unit price at the end of the month.

The advantage of the weighted average method is that it is easy to calculate. The disadvantages are: first, using this method, the weighted average unit price of the whole month can only be calculated at the end of the month, which is obviously not conducive to the timeliness of accounting; Second, the value of materials in stock at the end of the period, calculated based on the weighted average unit price at the end of the month, is quite different from the current cost.

When prices show an upward trend, the weighted average unit price at the end of the month will be lower than the current cost; Conversely, when prices show a downward trend, then the weighted average unit price at the end of the month will be higher than the current one.

The weighted index refers to the trend of all ** stocks, and there are two yellow and white lines in the ** time-sharing chart, where the white line refers to the trend of the weighted index, that is, the trend of ** stocks.

The weighted ** index is weighted according to the relative importance of the sample ** in each period, and its weight can be the number of shares traded, ** issuance, etc. By time, the weights can be either base options or reported options. An index weighted by the number of traded shares (or issued volume) in the base period is called the Rasbyr index; An index weighted by the number of traded shares (or issued volume) in the reporting period is called the Payout Index.

The Rasbyr Index focuses on the number of shares traded (or issued) during the base period, while the Payout Index focuses on the number of shares traded (or issued) during the reporting period. At present, most of the world's ** indices are Paixo indices.

Weighted composite index is a concept in statistics, which specifically refers to the use of the same metric factor to transition the quantity that cannot be added to the quantity that can be added directly: the quality index should use the quantitative index as the same measurement factor; Quantitative indices should use qualitative indicators as co-measure factors.

The weighted composite index is based on the method of "synthesis first, then comparison", and the comprehensive changes of various phenomena are measured by weighting. Due to the different contents reflected by the quantitative index and the quality index index, the selection method of their weights is different, so there are different calculation formulas. The composite index consists of a quantitative index and a qualitative index and is designed to measure the aggregate dynamics of complex phenomena composed of many commodities or products in different units of measurement, as opposed to a weighted average index.

However, in the actual application of sales, the base period weighted composite index has a wide range of applications and is also more practical, which can be divided into the following aspects:

1. Comprehensive concept: the weighted composite index of the base period, also known as the Lassell index, is an index calculation method proposed by the German scholar Laspeyres in 1864, which is to calculate the comprehensive index of a group of items, and fix the values of each variable as a weight in the base period;

2. Inherent defects: such as ** index.

It is the level of change in the reporting period under the assumption that the sales volume remains unchanged, although this index can simply reflect the change level of **, but cannot reflect the change in the consumption cluster;

3. Application in life: From the perspective of actual life, people are more concerned about the impact of sales volume on actual life due to changes in the reporting period. Therefore, the Lascrois index is rarely used in practical applications, and the Lascrois quantity index is a comprehensive change in the sales volume of the reporting period under the assumption that the ** is unchanged, which can not only simply reflect the comprehensive change level of the sales volume, but also meet the actual requirements of calculating the sales volume index, therefore, the Lascrois quantity index is more used in practice.

"Weighting" refers to the multiplication of different measurements by their corresponding weights or coefficients.

The weight is the weight taken by the accuracy of the measured value, and the higher the accuracy of the measured value, the greater the weight.

The purpose of weighting: mainly to make the sample better reflect the characteristics of the population. Because the general survey data is randomly sampled with stratified equal probabilities, the population represented by each layer is different, so it needs to be weighted.

"Weighting" is a mathematical concept, let's explain this word separately first, "plus" means "multiplication"; The popular understanding of "weight" is the meaning of "coefficient", and this coefficient is called "weight". So "weighted" means "multiplied by weight", that is, "multiplied by coefficient". In mathematics there is".Weighted average"And".Additive averageWhen the "weight" is the same, the additive average and the weighted average calculation value are the same, because the "weight" is different in some cases, the additive average calculation cannot reflect the real and reasonable average value, so we generally use it at this timeWeighted average

For example: 1. Calculation when the weight is known:

Your exam results for the academic year are: 30% for midterms, 50% for final exams, and 20% for assignments. (These percentages are the known weights, the proportions of each period) to find the average grade of the three semesters.

Suppose you scored 84 points in the midterm exam, 92 points in the final semester, and 91 points in the assignment, if pressAdditive averagecalculation, then it is (84 + 92 + 91) 3 = 89 points.

SoWeighted average methodThe calculation is: 84*30%+92*50%+91*20%=, which is in the case of known weights, where the weights are % and 20%.

Second, what about the unknown weight?

If you calculate the average score of your participation in the competition: a group of 50 people, you will be given 80 points; The second group of 60 people will give you 82 points, pressAdditive averageCalculate, your score is (80 + 82) 2 = 81 pointsWeighted averageAfter calculation, it is (50 * 80 + 60 * 82) (50 + 60) = points, so that the weighting is more reasonable.

Weighting means multiplying by weight.

The weights are different in the adjustment calculation due to the difference in the accuracy of the measured values. The higher the accuracy, the greater the weight. "Weighted" means "multiplied by weight", i.e. "multiplied by coefficient".

Given a set of data, where 3 occurs 6 times, 4 appears 3 times, and 2 occurs 1 time is called the weight. This method is called the weighting method. Generally speaking, the average number is to add up all the numbers and divide them by the total number of these numbers.

It is expressed as: (p1+p2+p3+....pn)/n。

A market capitalization-weighted index is an index that is determined based on the number of constituents in circulation multiplied by the number of each stock.

1. Statistics of the number of days when the weighted index is lower than the monthly line When the weighted index falls below the monthly line, the probability of the index being lower than the monthly line for less than 10 trading days is the highest.

2. When the weighted index falls below the monthly line, the probability that the index will be lower than the monthly line for more than 20 trading days is about 45%.

3. Statistics of the number of days when the weighted index is higher than the monthly line When the weighted index exceeds the monthly line, the probability that the index is higher than the monthly line for less than 10 trading days is the highest.

4. When the weighted index exceeds the monthly line, the probability that the index will be higher than the monthly line for more than 20 trading days is about 52%.

Further information: 1. Market capitalization weighting is the most common weighting method for A-share indexes, that is, the proportion of the sample ** value in the total market value of the index is used as the weight. The larger the sample value, the more weight it has in the index. The common ones are SSE 50 and CSI 300

And the group which CSI 500 and so on.

2. Add two concepts: equal-weighted index and style factor weighting.

Equal-weighted exponents. 1. The weight of each sample stock of the equal weight index is the same, and the purchase of the equal weight index is equivalent to averaging each sample stock in the index. In practice, the index does not keep the sample weights the same every day, but only adjusts the weights regularly.

This is equivalent to "selling high and buying low" on a regular basis, and at the same time avoiding the problem of over-concentration of some index weights. or groups such as CSI Pension, CSI Environmental Protection, etc.

Style factor weighting.

2. In the study, some excess returns are attributed to the role of style factors, such as value factors, growth factors, trend factors, etc. In order to allow indices to enjoy alpha, some indices have added a style factor to their compilation schemes. For example, CSI Bonus uses dividend yield.

As a basis for weight allocation, it is hoped to obtain excess returns with high dividend yields**; CSI 500 has low volatility and volatility.

Countdown-weighted, hoping to capture excess returns with low volatility**.