The correlation coefficient has limited ability in predicting returns in the stock market for individual stocks. Still, the statistical measurement may have value in predicting the extent to which two stocks move in relation to each other because the correlation coefficient is a measure of the relationship between how two stocks move in tandem with each other, as well as the strength of that relationship.

## Modern Portfolio Theory

Although the correlation coefficient may not be able to predict future stock returns, the tool is helpful for the understanding (and mitigation) of risk because it is a central component of modern portfolio theory (MPT), which seeks to determine an efficient frontier. The efficient frontier, in turn, 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.

### Key Takeaways

- Correlation measures the amount of co-movement between two investment securities.
- A criticism of modern portfolio theory is the assumption that the correlation between assets is fixed over time, when in reality, it is dynamic and changing.
- Correlation coefficients are on a scale from -1 to 1, with 1 indicating perfect correlation, -1 suggesting inverse correlation, and 0 indicating no correlation.
- Understanding correlations can help investors build diversified portfolios, but correlation coefficients have no real predictive power beyond that.

## 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 the prices of 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 two variables in question and each variable's standard deviation.

While standard deviation is a measure of the dispersion of data from its average, covariance is a measure of how two variables change together. By dividing covariance by the product of the two standard deviations, one can calculate the correlation coefficient and determine to what extent assets in a portfolio are likely to move in tandem.

## Predictive Power

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 as well.

However, the correlation between two investments is dynamic and subject to change. The correlation may shift, especially during times of higher volatility, just 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. The limitations of MPT also limit the predictive power of the correlation coefficient.

## The Bottom Line

Correlation is used in modern portfolio theory to include diversified assets that can help reduce the overall risk of a portfolio. One of the main criticisms of MPT, however, is that it assumes the correlation between assets is static over time. In reality, correlations often shift, especially during periods of higher volatility. In short, while correlation has some predictive value, the measure has limitations in its use.

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