# Index

 Definition: A statistic reflecting the composite value of some collection of instruments.

An index is used as a tool to represent the characteristics of its component parts, all of which bear some commonality. The most common type of index is stock market related, but there are also those for fixed income, commodities, and other things as well. Most indices are calculated by news or financial services organizations, such as the Financial Times.

Indices are designed to pull together the disparate movements of the instruments it comprises of to find out whether the market it represents is moving up or down, in a bullish or bearish direction.

Most fund managers will attempt to outperform the major indices, though some will aim to merely track them.

Also they are often used as a benchmark so that companies can seek to ensure their share price is not underperforming the overall market.

## Contents

Indices can usually be traded via:

## Calculation of Indices

There are various ways to calculate indices, including:

### Arithmetic

An arithmetic index is one in which the price of the components averaged (arithmetic mean). For example, if we have the following 5 stocks:

AAA - 100 BBB - 130 CCC - 50 DDD - 70 EEE - 10

The index in this case is 72 (100+130+50+70+10=360/5=72).

The short-coming of the arithmetic index is that the moves of large priced components will (given equal percentage moves) overweight those of lower priced ones. Using our example, were AAA to rise 10% and all others remain the same, the index would rise to 74 (370/5). If EEE rose 10% instead (again, all others the same), the index would only move up to 72.2 (361/5)

It should be noted, however, that in order to maintain a consistent index in the face of things like stock splits, the multiplier for each component in this index must be adjusted. By definition this multiplier starts off as 1. If, for example, a component of a stock index is split 2 for 1, the multiplier for that stock must go up to 2. If not, the index would look as if that stock's price dropped by 50%.

### Equal-Weighted

An index which is equal-weight is one created by assuming that an equal "investment" were made in each component. Using the above set of stocks as an example, if one were to assume an initial "investment" of 1000, then it would mean the "purchase" of:

AAA - 10 "shares" BBB - 7.69 shares CCC - 20 shares DDD - 14.29 shares EEE - 100 shares

The advantage to an equal-weight index is that no one component can influence the market any more than another, the opposite of the cast of the arithmetic index. Like the latter, however, adjustments to the "shares" of equal-weight indices must be adjusted to reflect stock splits, dividends, etc.

### Value-Weighted

A common type of index is the value-weighted indices in the stock market which use market capitalisation as the weight. These sorts of indices are popular because they tend to reflect well the broad market, as high market capitalization stocks tend to have the highest volumes (in monetary terms). The other advantage to this calculation method is that they weightings never need adjustment based on things like stock splits.