Correlation

Correlation is the measurement of how two different securities move in relation to one another.
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Correlation measures the strength of the relationship between the two assets.

The correlation coefficient is a formula that assigns a value between -1 and 1 to assess the degree to which two securities move together. The correlation coefficient does not explain why securities are or are not related; the correlation coefficient only quantifies the relationship.

Two securities that have a correlation of 1 are said to have perfect correlation and theoretically move identically. Two securities that have a correlation of -1 are said to be perfectly negatively correlated and theoretically move in complete opposition. A correlation of zero implies that two securities move completely random from each other with no measurable relationship.

Zero correlation is considered a strength of a balanced, diversified portfolio to ensure that all assets under management do not move in conjunction. Zero correlation suggests that while some stocks in a portfolio may decline in price, others will move independently of those declines.

Negatively correlated assets may be combined to serve as a hedge. Positively correlated assets may be combined to express a directional bias.

Research has shown that when volatility increases, securities auto correlate, and assets with little or no previous correlation suddenly move in sync with one another, thus rendering diversification less effective when markets crash. Relative correlation can change as time progresses and securities demonstrate different characteristics.

Volatility Clustering image example

R-Squared

R-squared measures the amount that a portfolio’s performance can be explained by the movement of a benchmark, like an index.

R-squared is the squared correlation of the portfolio or fund to the market. R-squared is measured on a scale of 0-100 percent.

The higher the value, the more the portfolio’s performance will be linked to the benchmark index’s performance, with a value of 1 indicating that the portfolio will behave exactly like the index. Values above .70 are said to be high.

R-squared helps interpret a portfolio’s performance. For example, an R-squared of .80 implies the benchmark explains 80% of the portfolio’s return, and 20% of the portfolio’s return is driven by the specific portfolio holdings.

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FAQs

How do you find the correlation coefficient?

The correlation coefficient for two securities is calculated by finding the covariance and standard deviation of each security and dividing the covariance by the sum of the two standard deviations.

The correlation coefficient assigns a value between -1 and 1 to assess the degree at which two securities move together. The correlation coefficient does not explain why securities are or are not related; the correlation coefficient only quantifies the relationship.

Two securities that have a correlation of 1 are said to have perfect correlation and theoretically move identically. Two securities that have a correlation of -1 are said to be perfectly negatively correlated and theoretically move in complete opposition. A correlation of zero implies that two securities move completely random from each other with no measurable relationship.

How is R-squared calculated?

R-squared measures the amount that a portfolio’s performance can be explained by the movement of a benchmark, like an index. R-squared is the squared correlation of the portfolio or fund to the market.

For example, if a portfolio’s correlation to the S&P 500 is 0.80, then the R-squared is 0.64. An R-squared of 0.64 means the market’s return can explain 64% of the portfolio’s performance. 

What is a good R-squared value?

R-squared is measured on a scale of 0-100 percent. The higher the value, the more the portfolio’s performance will be linked to the benchmark index’s performance, with a value of 1 indicating that the portfolio will behave exactly like the index. Values above .70 are said to be high.

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