The correlation coefficient has limited ability in predicting returns in the stock market for individual stocks, but it may have value in predicting the extent to which two stocks move in relation to each other. The correlation coefficient is a statistical measurement of the relationship between how two stocks move in tandem with each other, as well as of the strength of that relationship. Investors often use the correlation coefficient to diversify assets in the construction of portfolios.

## Modern Portfolio Theory

Although the correlation coefficient may not be able to predict future stock returns, it is helpful as a tool for the mitigation of risk. It is a main component of modern portfolio theory (MPT), which seeks to determine an efficient frontier. The efficient frontier provides a curved relationship between a possible return for a mix of assets in a portfolio versus a given amount of risk for that mix of assets. Correlation is used in MPT to include diversified assets that can help reduce the overall risk of a portfolio. One of the main criticisms of MPT is that it assumes the correlation between assets is static over time; in reality, correlations often shift, especially during periods of higher volatility. While correlation has some predictive value, it has limitations in its use.

## The Correlation Coefficient

The correlation coefficient is measured on a scale from -1 to 1. A correlation coefficient of 1 indicates a perfect positive correlation between two stocks, meaning the stocks always move the same direction by the same amount. A coefficient of -1 indicates a perfect negative correlation, meaning that the stocks have historically always moved in the opposite direction. If two stocks have a correlation coefficient of 0, it means there is no correlation and therefore no relationship between the stocks. It is unusual to have either a perfect positive or negative correlation. Investors can use the correlation coefficient to select assets with negative correlations for inclusion in their portfolios. The calculation of the correlation coefficient takes the covariance of the stocks against the mean returns for each stock divided by the product of the standard deviation of the returns of each stock.

The correlation coefficient is basically a linear regression performed on each stock's returns against the other. If mapped graphically, a positive correlation would show an upward-sloping line. A negative correlation would show a downward-sloping line. While the correlation coefficient is a measure of the historical relationship between two stocks, it may provide a guide to the future relationship between the assets. However, the correlation between two stocks is subject to change. The correlation may shift, especially during times of higher volatility. Periods of higher volatility occur when risk increases for portfolios. As such, MPT may have limitations in its ability to protect against risk during periods of high volatility due to the assumption that correlations remain constant. This fact also limits the predictive power of the correlation coefficient.