# Correlation Increase Between Returns on Stock & Returns on Index

by Vicki A. Benge

A stock index may be used as a benchmark to keep abreast of and review stock trading throughout the day or over time. Index funds are mutual funds that own the stocks a particular index tracks. Exchange-traded funds mirror a particular stock index by purchasing and holding shares of stocks that make up the index. An increase in returns on the stocks tracked by the index has a direct reciprocal relation to the returns on an index fund as a whole.

## Index Methodologies

The correlation between an increase in returns on stocks within an index and the index value as a whole depends on the methodology used to calculate the index — particularly how the values within the index are weighted. For example, two of the three major U.S. stock indexes, the Nasdaq Composite and the S&P 500, are weighted by market capitalization of the component companies. The third, the Dow Jones Industrial Average is a price-weighted index.

## Price-Weighted Results

To understand how a price-weighted index works, consider an index that tracks only 10 stocks. Suppose when the index tracking is initiated, each of the 10 stocks is worth \$10 each. Fluctuations in share prices of each of the 10 stocks would have a similar effect on the index and on returns on a fund that tracked the index. Conversely, if one stock holds a current market value of \$100 and the remaining nine are selling at \$10 per share, a \$2 change in the price of the \$100 stock would have much less of an impact on the correlation of the index returns than would a 20 percent, or \$2 change of value in a \$10 stock.

## Market Cap Index

In an index such as the Nasdaq Composite or S&P 500, where the values of each stock in the index are based on market capitalization, the resulting correlation between the returns on individual stocks and returns on the index fund as a whole will depend on which stocks carry the most weight. Weight refers to the value a stock is given relative to the value of all others in the index. For example, as of late December 2011, in the S&P 500, Exxon Mobil Corp. made up slightly more than 3.5 percent of the index value. Therefore, a significant change in returns on Exxon Mobil stock would result in a noticeable correlative increase in a fund tracking the index as a whole.

## Weighted Values

Comparatively, the top 10 holdings in the S&P make up more than 20 percent of the total market capitalization. Thus, an increase in the returns of these 10 stocks will cause a reciprocal or correlated increase in returns on the index, resulting in a more noticeable change than returns on stocks holding less weight in the index.

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