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# How can the value of a stock market index be calculated?

When assessing the health of any given economy or industry, the recent performance of a major stock index can be a good place to start. But how is the value of a stock market index calculated, and what factors determine which stocks belong to which? Learn more.

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### How can the value of a stock market index be calculated?

When selecting an index to trade, the amount of choice can feel overwhelming, especially to those who are new to the markets. By classifying the different types of stock indexes, you can better identify which is best suited for your individual investment needs.

In general, there are two classification methods: capitalization-weighted and price-weighted.

The capitalization-weighted index is calculated as follows:

Capitalization-weighted index = \ \ cdot \ sum (d \ limits_ {k = 1} ^ m {N_i \ cdot P_i} \]

$$P_i$$ represents a company's share price in the stock index.

$$N_i$$ represents the total number of shares in the company; and the multiplication of both equals the company's capitalization.

$$\sum\limits_{k = 1}^m {N_i\cdot P_i}$$ adds up the capitalization of all the companies in the index (in total $$m$$).

$$d$$ is a divisor, which aims to avoid unnecessary fluctuations in the stock index when the company's ownership structure changes (or replaces constituent shares).

The stock index management agency will adjust $$d$$ regularly to ensure there is no default in the stock index. For example, the adjusted value of the S&P 500 index (in the first quarter of 2020) is approximately 1/8289270000.

The alternative is a price-weighted index:

Price-weighted index =$$a\cdot\sum\limits_{k = 1}^m {P_i}$$

As above, $$P_i$$ represents the share price of a company in the stock index.

$$m$$ represents the number of companies included in the index.

$$\sum\limits_{k = 1}^m {P_i}$$ adds up the unit price per share of all the companies in the index.

$$a$$ is an adjustment, similar to that of $$d$$ in the capitalization-weighted index, to ensure no default in the stock index.

For example, the adjusted value of the Dow Jones Industrial Average is (in April 2020) about 6.7822.

Here $$a$$ can be read as taking the average of the stock price and multiplying it by an adjustment $$c$$, i.e., $$a=\dfrac{1}{m}\cdot c$$.

It is important to remember that depending on the chosen calculation method, it is either the capitalization or the price of the stock that will affect the index value. Owing to the functionality of averages, the larger a constituent stock is, either in price or capitalization, it will have more influence in determining the overall index value.

Capitalization-weighted index: The larger the capitalization, the greater the influence

Price-weighted index: The higher the share price, the greater the influence

### By which attributes are stocks typically organized into indexes?

Usually, a stock can be organized into an index on the basis of two attributes.

The first is by country. For example, the three major US indexes are the Dow Jones Industrial Average (DJIA), the Nasdaq-100 (NAS100), and the Standard & Poor's 500 (S&P 500). To be a constituent stock in any of these, the stock, among other criteria, must be traded on a U.S. stock exchange. Therefore, those looking to focus on US stocks may choose to invest in these indexes as part of a broader strategy.

The same applies for other nations too; if you would like to invest in Chinese equity, options such as FTSE China A50 are also available.

The second method is by industry. For example, the aforementioned Nasdaq-100 is made up of the 101 largest 'non-financial' stocks in the United States. Although relatively ambiguous, this 'non-financial' component means that the index is overwhelmingly representative of the U.S. tech sector, including stocks such as Amazon, Electronic Arts, and Google.

When categorized by industry, global macroeconomic events, such as the COVID-19 pandemic, affect individual indexes differently. During the market sell-off in early 2020, some indexes, particularly those concerning pharmaceutical companies, gained in value, while others fell sharply.

The following table shows both the calculation method and associated industry for the sixteen most common stock market indexes: