How Does Covariance Affect Portfolio Risk and Return?

Covariance is a statistical measure of how two assets move in relation to each other. It provides diversification and reduces the overall volatility of a portfolio. A positive covariance indicates that two assets move in tandem. A negative covariance indicates that two assets move in opposite directions.

It’s important to attempt to reduce the overall risk and volatility in the construction of a portfolio while striving for a positive rate of return. Analysts use historical price data to determine which assets to include in a portfolio. The overall volatility of a portfolio can be reduced by including assets that show a negative covariance.

Key Takeaways

• Covariance measures how two assets move in relation to each other.
• Covariance can be positive or negative.
• The formula for calculating covariance takes the daily return minus the mean return for each asset multiplied by each other.
• Covariance can maximize diversification in a portfolio.
• The goal is to create a group of assets with an overall standard deviation that’s less than that of the individual securities.

How to Calculate Covariance

The covariance of two particular assets is calculated by a formula that includes the historical asset returns as independent and dependent variables as well as the historical mean of each asset price over a similar number of trading periods for each asset.

The formula takes the daily return minus the mean return for each asset multiplied by each other. It’s then divided by the number of trading periods for the respective time frames that are being measured. The covariance formula is:

Covariance=Sample Size −1∑(ReturnABC​−AverageABC​) × (ReturnXYZ​−AverageXYZ​)​

Covariance as a Diversification Tool

Covariance can maximize diversification in a portfolio of assets.

Adding assets with a negative covariance to a portfolio reduces the overall risk. This risk drops off quickly at first as additional assets are added then it drops off slowly. Diversifiable risk can’t be significantly reduced beyond including 25 different stocks in a portfolio but including more assets with negative covariance means that the risk drops more quickly.

Covariance has some limitations. It can show the direction between two assets but it can’t be used to calculate the strength of the relationship between the prices. Determining the correlation coefficient between the assets is a better way to measure the strength of the relationship.

An additional drawback to the use of covariance is that the measurement is subject to being skewed by the presence of outliers in the underlying data.

Important

Large single-period price movements may affect the overall volatility of the price series and provide an unreliable statistical measurement of the nature of the direction between the assets.

Modern Portfolio Theory’s Use of Covariance

Modern portfolio theory (MPT) uses covariance as an important element in the construction of portfolios.

MPT assumes that investors are risk-averse but still seek the best return possible. It therefore attempts to determine an efficient frontier for a mix of assets in a portfolio or an optimal point at which the relationship between risk and return is most beneficial. The efficient frontier calculates the maximum return for a portfolio versus the amount of risk for the combination of the underlying assets.

The goal is to create a group of assets with an overall standard deviation that’s less than that of the individual securities. The graph of the efficient frontier is curved, demonstrating how higher-volatility assets might be mixed with lower-volatility assets to maximize return but reduce the impact of large price fluctuations. Investors can reduce risk while obtaining returns on their investments by diversifying the assets in a portfolio.

What Is Volatility in a Portfolio?

Volatility is a statistical measure of the difference between a portfolio asset’s price around the mean price. It can gauge the totality of a portfolio or it can be applied to just one of its stocks. Volatility calculates risk. High volatility translates into more significant price swings.

What Is a Correlation Coefficient?

The correlation coefficient is a measurement of the strength of the relationship between two variables. It ranges from -1 to 1. A coefficient of 0 indicates no relationship. There are different types of correlation coefficients. Choosing the right tool depends on your goals and needs.

Who Created the Modern Portfolio Theory (MPT)?

Harry Markowitz is credited with developing the modern portfolio theory. He introduced it in his 1952 article, “Portfolio Selection” in The Journal of Finance. He was awarded a Nobel Prize for his work in 1990.

The Bottom Line

Covariance measures how two assets move in relation to each other and it can be positive or negative. Adding assets with a negative covariance to a portfolio tends to minimize risk. A negative covariance indicates that the two assets are moving in opposite directions. A formula can help you calculate it but it’s wise to check the result with an advisor before acting on the result.

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