# How Is the Value of the Stock Index Calculated?

Recap – What is a stock index?

A stock index is a statistical indicator that measures the combined value of a number of underlying stock prices. As stock indices are usually formed by a group of leading stocks in a market, they represent the overall health of an economy as well as the value of the stocks.

Although a stock index is not a tradeable product, but the rise and fall of its value can be traded on.

Methods for determining stock index prices

The price of each stock represented in a stock index affects the overall value of the index. However, there are different methods for determining how much weight each stock should be allocated. These include:

• Price-weighting
• Capitalisation weighting/ market-value weighting
• Market-share weighting
• Fundamental weighting
• Float-adjusted weighting
• Equal weighting

Price-weighted stock indices

A price-weighted stock index is an index where the fraction that a stock makes up of an index is proportionate to the price of that stock. This means that a stock trading at \$500 will make up 10 times more of the total index when compared to a stock trading at \$50.

Price-weighted stock indices do not accurately reflect underlying market values, as the stock trading at \$500 could be that of a small company, whereas the stock trading at \$50 could be that of a large company. As the stock of the smaller company makes up 10 times more of the total value of the index than the larger company, a change in its price will have a larger impact on the value of the stock index than a change in the price of the larger company. Meanwhile, the combined market values will not change to the same degree as the price of the larger company has not changed.

Also, price-weighted indices need to be constantly adjusted, as the changing prices of stocks will affect their appropriate weight in the index.

Examples of price-weighted indices include the Amex Major Market Index, the Dow Jones Industrial Average and the NYSE ARCA Tech 100 Index.

Capitalisation-weighted stock indices

In contrast to price-weighted stock indices, a capitalisation-weighted/market-value weighted index factors in the size of the company as well as the share price. This means the impact of a company’s price change is proportional to its overall market value, or the share price multiplied by the number of shares outstanding.

Consequently, small changes in large companies will have a greater influence on the value of the stock index than larger changes in small companies.

Some examples of capitalisation-weighted indices include the Hang Seng Index, Kuala Lumpur Composite Index, NASDAQ Composite, NASDAQ-100, NYSE Composite and the Taiwan Capitalization Weighted Stock Index.

Market-share weighted indices

A stock index that is market-share weighted is similar to a capitalisation-weighted index, but a market-share weighted index measures the price of shares relative to the number of shares, as opposed to their total value.

Fundamentally-weighted stock indices

Fundamentally-weighted stock indices weight stock indices by one of many economic fundamental factors, or by a composite of several fundamental factors.

This method of weighting argues that fundamental factors, such as sales, earnings, book value, cash flow and dividends, are a more accurate measure of its value than the share price, which can fluctuate with investor sentiment. One of the benefits of trading on these indices is that they might average out sector-specific biases.

Fundamentally-weighted stock indices are often contrasted to capitalisation-weighted indices. As the method of capitalisation-weighted stock indices focuses on company size and share prices, capitalisation-weighted indices could overweight overvalued stocks while underweighting undervalued stocks, meaning investors can’t see the true value of a company, and that the index doesn’t provide a true representation of an economy. As fundamental weighting weights industries by fundamental factors, an over- or undervalued share value will not have as large an impact.

That being said, although there isn’t a perfect correlation between fundamentals and share prices, there is some correlation, as large changes in fundamentals can result in large share-price movements. This was evidenced in the global financial crisis, when both fundamentally-weighted and capitalisation-weighted indices plummeted.

Float-adjusted weighted stock indices

Traditionally, capitalisation-weighted stock indices have had full-weighting. Full-weighting means that all shares outstanding for each company are included. Recently, many capitalisation-weighted indices have shifted to float-adjusted weighting, which takes into account the proportion of shares a company has free floated.

Both the S&P 500 and S&P 100 indices are now float-weighted.

Equal-weighted stock indices

Equal-weighted stock indices assign each stock in an index the same weight, so a movement in the share price of all companies have the same impact on the index, regardless on the size or market-share of that company.