Covariance is used in portfolio theory to determine what assets to include in the portfolio. Covariance is a statistical measure of the directional relationship between two asset prices. Modern portfolio theory uses this statistical measurement to reduce the overall risk for a portfolio. A positive covariance means that assets generally move in the same direction. Negative covariance means assets generally move in opposite directions. Here we'll discuss how covariance is used to reduce investment risk and provide portfolio diversification.

### Key Takeaways

• Covariance is a statistical tool investors use to measure the relationship between the movement of two asset prices.
• A positive covariance means asset prices are moving in the same general direction.
• A negative covariance means asset prices are moving in opposite directions.
• Investors using modern portfolio theory (MPT) seek to optimize returns by including assets in their portfolio that have a negative covariance.
• Covariance helps investors create a portfolio that includes a mix of distinct asset types, thus employing a diversification strategy to reduce risk.

## Covariance and Modern Portfolio Theory (MPT)

Covariance is an important measurement used in modern portfolio theory (MPT). MPT attempts to determine an efficient frontier for a mix of assets in a portfolio. The efficient frontier seeks to optimize the maximum return versus the degree of risk for the overall combined assets in the portfolio.

The goal is to choose assets that have a lower standard deviation for the combined portfolio that is less than the standard deviation of the individual assets. This can reduce the volatility of the portfolio. Modern portfolio theory seeks to create an optimal mix of higher-volatility assets with lower-volatility assets. By diversifying the assets in a portfolio, investors can reduce risk and still allow for a positive return.

Dr. Harry Markowitz created the modern portfolio theory (MPT) in 1952 to help investors match their risk tolerance with their reward expectations in order to create their ideal portfolio.

## Negative Covariance and Portfolio Construction

In the construction of a portfolio, it is important to attempt to reduce overall risk by including assets that have a negative covariance with each other. Analysts use historical price data to determine the measure of covariance between different stocks. This assumes that the same statistical relationship between the asset prices will continue into the future, which is not always the case. By including assets that show a negative covariance, the risk of a portfolio is minimized.

## Covariance Formula

The covariance of two assets is calculated by a formula. The first step of the formula determines the average daily return for each individual asset. Then, the difference between daily return minus the average daily return is calculated for each asset, and these numbers are multiplied by each other. The final step is to divide that product by the number of trading periods, minus 1.

Covariance can be used to maximize diversification in a portfolio of assets. By adding assets with a negative covariance to a portfolio, the overall risk is quickly reduced. Covariance provides a statistical measurement of the risk for a mix of assets.

## Covariance Drawbacks

The use of covariance does have drawbacks. Covariance can only measure the directional relationship between two assets. It cannot show the strength of the relationship between assets.

The correlation coefficient is a better measure of that strength. An additional drawback to the use of covariance is that the calculation is sensitive to higher volatility returns. More volatile assets include returns that are farther from the mean. These outlying returns can have an undue influence on the resulting covariance calculation. Large single-day price moves can impact the covariance, which leads to an inaccurate estimate of the measurement.