Price Weighted Stock Index Calculation and Biases

Equity index weighting methods

Stock indices perform important functions in the global investing universe. They serve as benchmarks of equity markets and therefore as good indicators of economic situation and investor sentiment. Stock indices are widely used in analyses and investment decision making.

There are three common methods of stock index construction: there are price weighted stock indices, value (or market cap) weighted indices, and equally weighted stock indices. Of these three methods, the price weighted index method is the simplest and the oldest.

Price weighted index construction

A price weighted stock index is in fact the simple arithmetic average of prices of all stocks included in the index. For example, consider a price weighted index containing 3 stocks:

• Stock A priced 10 dollars,
• Stock B priced 40 dollars, and
• Stock C priced 100 dollars per share.

The value of this price weighted index would be 10 + 40 + 100 divided by the number of stocks in the index, which gives us an index value of 50.

Over time, price weighted stock indices are adjusted for stock splits and other changes in the index constitution (the divisor of the index changes accordingly).

Price weighted stock index biases

The most serious bias of price weighted indices and the reason why most stock indices don’t use the price weighting method today is the fact that in price weighted indices the stocks which nominally have higher share price have the greatest impact. Let’s use the example above again.

If stock C increases by 10% to 110 dollars and the other two stocks remain unchanged, the index will increase to (10+40+110)/3 = 53.3, which is an increase by 6.7%.

On the other hand, if stocks A and B rise by 10% each, the new index value will be (11+44+100)/3 = 51.7, which is an increase by 3.3%. Although two out of three stocks in the index have grown by 10%, the index as a whole has changed much less than when only one stock (but the one with the highest price) rose.

If you had Google, priced 525, and Citigroup, with a share price of 4.37, in a price weighted index, the impact of Google’s share price move on the index value would be more than 100x greater than the impact of Citi. Is Google more than hundred times more important to the economy and to the stock market than Citi is? I doubt.

Examples of widely used price weighted stock indices

The best known example of price weighted stock indices is the good old Dow Jones Industrial Average, which is calculated as the average of share prices of 30 big companies. The index was started in 1896 and originally contained 12 stocks. Of these 12 stocks only one – General Electric – is still part of the DJIA index today (2010).

Because of the long history and adjustments to stock splits, spin-offs, and other events, the divisor of the Dow Jones index (known as Dow Divisor) is not 30 – it is about 0.13 (as in 2010). This means that one dollar move in any one of the stocks included in the index results in 1/0.13 = approximately 7.5 point move in the DJIA.

Another example of price weighted equity indices is the Japanese Nikkei 225.