What Is Covariance and Its Uses

What is Covariance

Covariance in the most basic sense refers to a measure of the directional relationship that exists between the prices of two assets.It can also refer to the degree to which the returns of two assets of high risk move together.

Types of Covariance

There are two types of covariance:

Positive Covariance

This implies that the asset returns have moved together in the same direction. When one has a high return, the other is likely to have a high return as well.

Negative Covariance

This implies that the returns have moved inversely or in opposite directions. When one has a positive return, the other is likely to have a negative return.

How to calculate Covariance

To calculate covariance, the standard deviations of expected returns are analyzed, or simply one gets the product of the correlation of the two variables and each of their standard deviations. When calculating the covariance of two assets, a formula is used. The formula comprises of three steps:

• Determining the average daily returns of each asset
• Taking the determined daily returns and subtracting it from the average daily returns and thereafter getting the product of the numbers.
• Dividing the product by the number of trading periods and then subtracting 1.

Uses and Benefits of Covariance

Covariance is mostly used in the Modern Portfolio Theory (MPT). When assets are mixed up in a portfolio, the MPT is employed to get an efficient frontier which ultimately optimizes the maximum return against the degree of risk of all combined assets. MPT is used by investors to create an optimal mix of assets of higher and of lower volatilities. When a portfolio is highly volatile and there is great need to reduce it, one can simply analyze the underlying assets to identify those with a lower standard deviation. This should be done in comparison to the combined portfolio. Your ultimate pick should be those assets that not only have a lower standard deviation, but also one that’s lesser than the standard deviation of individual assets. It’s also a good practice in the construction of portfolios to include assets that have a negative covariance together in order to reduce the overall risk. The main item of analysis during the determination of covariance of stocks is the historical price data. Covariance is an important tool for investors as it gives them an idea of how stocks may move in tandem in the future. Since it involves analyzing historical price data, they can be able to predict price movements, especially of two stock portfolios since analyzing the prices enables one to tell whether prices will move in a similar direction or an opposite direction. It can also be used in the diversification of portfolios. This is achieved by adding assets that have a negative covariance. You can select stocks that complement each other thereby increasing your overall returns and reducing overall risk. Covariance is also widely used in the stock market and stock trading especially in the construction of portfolios to identify stocks that are better placed to work together.

The Downside of Covariance

As much as covariance has positive utility, it still has some drawbacks. They include:

• It can only be used to measure directional relationships between two assets. This, by itself, is not sufficient as an investor needs to see the strength of the relationship between various assets.
• When using covariance, the calculations are normally sensitive when dealing with higher volatility returns. This brings an undue influence especially on the calculation since assets that are more volatile tend to be farther from the mean.
• In the event of large price moves in a day, the calculation is negatively impacted leading incorrect values in the estimates.
• There is also the aspect of uncertainty. Since the calculation greatly uses historical prices and historical returns, absolute certainty is hampered. Thus, investors can never be too sure of what will happen in the future.

All in all, in order to increase the chances of having a better outcome with covariance, it’s best to use it together with other calculations and measures.