# Unweighted Index

## DEFINITION of 'Unweighted Index'

A simple arithmetic or geometric average used to calculate stock indexes. Equal weight is invested in each of the stocks in an index with equal dollar amounts invested in each underlying stock. Because the stocks are equally weighted, one stock's performance will not have a dramatic effect on the performance of the index as a whole. This differs from weighted indexes, where some stocks are given more weight than others, usually based on their market capitalizations.

## BREAKING DOWN 'Unweighted Index'

As an example of how to calculate an arithmetic average, suppose that there are three stocks in an index with returns of 10%, 11% and 15%. The arithmetic return would be calculated as follows:

(0.10+0.11+0.15)/3 = 0.1200 =12%

In other words, you add the returns of each of the stocks in the index and divide this figure by the total number of stocks in that index.

To calculated a geometric average, suppose again that there are three stocks in an index with returns of 10%, 11% and 15%. The geometric return would be calculated as follows:

[(1+0.1)*(1+0.11)*(1+0.15)]^(1/3) = 1.1198 = 11.98%

In this case, you multiply the returns and take the 'n'th (where 'n' equals the number of stocks in the index) root of the product. The geometric average will either be equal to or lower than the arithmetic average.