How do you interpret the magnitude of the covariance between two variables?

Covariance indicates the relationship of two variables whenever one variable changes. If an increase in one variable results in an increase in the other variable, both variables are said to have a positive covariance. Decreases in one variable also cause a decrease in the other. Both variables move together in the same direction when they change. Decreases in one variable resulting in the opposite change in the other variable are referred to as negative covariance. These variables are inversely related and always move in different directions. When a positive number is used to indicate the magnitude of covariance, the covariance is positive. A negative number represents an inverse relationship. The concept of covariance is commonly used when discussing relationships between two economic indicators or terms. For example, market values of publicly traded companies typically have a positive covariance with reported earnings. Similarly, the value of one security may rise when another rises. Covariance calculations are also used in modern portfolio theory (MPT).

If two stocks have share prices with a positive covariance, they are both likely to move in the same direction when responding to market conditions. Both stocks may be tracked over a period of time with the rate of return for each time period recorded. Determining the covariance of two variables is called covariance analysis. For example, conducting a covariance analysis of Stocks A and B records rates of return for three days. Stock A has returns of 1.8%, 2.2% and 0.8% on days one, two and three respectively. Stock B returns 1.25%, 1.9% and 0.5%. Both stocks increased and decreased on the same days, so they have a positive covariance. When graphed on a X/Y axis, covariance between two variables displays visually as both variables mirror similar changes at the same time. Covariance calculations provide information on whether variables have a positive or negative relationship but cannot reveal the strength of the connection. The magnitude of covariance may be skewed whenever the data set contains too many significantly different values. A single outlier in the data can dramatically change the calculation and overstate or understate the relationship. Covariance helps economists predict how variables react when changes occur but cannot predict as effectively how much each variable changes.

Covariance is used frequently in MPT. When building efficient financial portfolios, financial managers seek investment mixes that provide optimal returns and minimize risks. The risk/return tradeoff concept demonstrates that increasing risks in investment often requires increases in returns. This is a result of investors' desire to minimize risks and maximize returns. When high-risk loans are offered, the lender must protect the investment by charging higher rates. Different asset classes, different companies and different borrower credit histories all prompt different rates. Covariance is used in portfolio management theory to identify efficient investments with the best rates of return and risk levels to create the best possible portfolios. On a regular basis, the calculation may be modified by the portfolio manager to improve results or track a particular rate of return.

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