In this post, I am going to share how a market index can be created. The two commonly ways in which an index can be represented are by capitalization weighted and price weighted calculation of the index stocks. Let us use a fictitious index consisting of just three stocks.
| Company | Price | Outstanding Shares | Market Capitalization | Weightage of stock in cap weighted index | Weightage of stock in price weighted index |
| ABC | $2 | 2,000,000 | $4,000,000 | 25.0% | 20.0% |
| DEF | $4 | 1,000,000 | $4,000,000 | 25.0% | 40.0% |
| XYZ | $4 | 2,000,000 | $8,000,000 | 50.0% | 40.0% |
Calculating price weighted index
The summation of price for all the stocks is obtained and then divided by a divisor to obtain the final index value. The divisor is just an arbitrary number that is first defined when the index was created.
Summation of price = $2 + $4 + $4 = $10
Assuming the index is to begin from 1000, a divisor of $0.01 is to be selected in this case.
Calculating capitalization weighted index
The summation of market capitalization for all the stocks is obtained and then divided by a divisor to obtain the final index value. The market capitalization of each stock can be calculated by multiplying the price of each stock with the total number of outstanding shares. The divisor is just an arbitrary number that is first defined when the index was created.
Summation of market capitalization = $4,000,000 + $4,000,000 + $8,000,000 = $16,000,000
Assuming the index is to begin from 1000, a divisor of $16,000 is to be selected in this case.
Effect of price on indices
Now assuming that the price of company DEF increases by 50% to $6, the weightage in the index will be adjusted as follows:
| Company | Price | Outstanding Shares | Market Capitalization | Weightage of stock in cap weighted index | Weightage of stock in price weighted index |
| ABC | $2 | 2,000,000 | $4,000,000 | 22.2% | 16.7% |
| DEF | $6 | 1,000,000 | $6,000,000 | 33.3% | 50.0% |
| XYZ | $4 | 2,000,000 | $8,000,000 | 44.4% | 33.3% |
New price weighted index = ($2 + $6 + $4) / $0.01 = 1,200
New capitalization weighted index = ($4,000,000 + $6,000,000 + $8,000,000) / $16,000 = 1,125
From the table you can see that in a price weighted index, price has a big effect on the outcome of the new index. Even though company DEF is smaller than company XYZ in terms of capitalization, it has the highest weightage in the index when computed based on price.
I hope now you have some idea on how the market indices are computed. Just to name some, the Dow Jones and Nikkei 225 are examples of price weighted indices while S&P 500, FTSE 100 and Nasdaq are examples of market capitalization weighted indices.
1 comment:
In a price weighted index, the divisor is adjusted when a component stock issues a dividend or undergoes a stock split.
The divisor of a price weighted index does not change when a component stock issues new shares.
In a capitalization weighted index, the divisor is adjusted when a component stock issues new shares.
The divisor of a capitalization weighted index does change when a component stock issues dividend or undergoes a stock split.
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