How Do We Calculate a Stock Index? – Part I
As retail investors, have you ever wondered how an index is constructed and calculated in order to measure the index performance? This 3-part series would aim to explain the various kinds of equity index weighting schemes used.
A stock index is constructed for several purposes such as providing a useful benchmark for an investment manager or investor’ to measure his/her performance; to give a representative market return; to be able to create an index fund and also be able to measure a stock’s technical indicators.
There are 4 different types of stock index weighting scheme, namely:
- Price-weighted Index
- Value-weighted Index (Market Capitalization Index)
- Free-float Adjusted Market Capitalization Index
- Equal-weighted Index
We will first show how a price-weighted index is being calculated…
A price-weighted index is the summation of all the stocks’ prices divided by the total number of stocks in a particular index. The denominator is adjusted for stock splits and changes in the composition of the index, that is when a stock is are being added or subtracted from the index itself. This would prevent any changes made to the index’s total value. Below is a simple calculation of 3 stocks in a price-weighted index:
|Price-weighted Index||Stock Price|
|Stock A||$ 100.0||$ 120.0||20.0%|
|Stock B||$ 50.0||$ 40.0||-20.0%|
|Stock C||$ 10.0||$ 15.0||50.0%|
|Total||$ 160.0||$ 175.0|
|Index||$ 53.3||$ 58.3||9.4%|
Examples of a Price-weighted Index
1. Dow Jones Industrial Average – representing the 30 US blue chip companies as chosen by the Wall Street Journal
It is also the oldest and most widely followed US equity index
2. Nikkei Stock Average – representing 225 Japanese blue chip companies
It is originally formulated by the Dow Jones & Company, utilizing almost the same method as the DJIA. However, the Index has systematically reduced its weighting of extremely high-priced stocks in order to minimize the bias toward the highly-priced stocks.
What sort of biases should investors look out for when looking at price-weighted indices?
A price-weighted index tend to be biased toward the highest-priced share. For example, a stock with at $50 a piece will have 2x their weight as compared to a stock with a price of $25. Hence, a 10% increase in the higher-priced stock will have a similar effect as a 20% increase in the lower-priced stock.
The index is easy to construct whereby share prices are simply added up and then divided by the total number of shares being represented in the index as shown in the table above.
Stock price data are easier to obtain as opposed to a market value series.
Value in Action
A price-weighted index is one of the stock index weighting scheme in order to measure an index’s performance. Although it is the easiest to construct, one must be aware of the biases it entails in its performance calculations.
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All views and opinions articulated in the article were expressed in Willie’s personal capacity and do not in any way represent those of his employer and other related entities. Willie does not own any shares in the companies mentioned above.
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