How to calculate covariance? (Definition and guide)

By Indeed Editorial Team

Updated 24 November 2022

Published 9 May 2022

The Indeed Editorial Team comprises a diverse and talented team of writers, researchers and subject matter experts equipped with Indeed's data and insights to deliver useful tips to help guide your career journey.

Choosing which stocks to add to your portfolio so that you're financially secure while still making money remains a difficult task. One metric you're able to use to assess the risk of adding new stocks to your account refers to covariance. Understanding how to calculate covariance helps you understand the link between two shares, whether you own them or are considering buying them in the future. In this article, we go through what covariance is, how it relates to variance, how to calculate it in five stages, how to use it and an example of the calculation.

What is covariance?

Covariance refers to a statistical metric that determines whether two variables move in the same direction. It's the difference between two or more variables, where the variables used to calculate this metric remain unrelated. The metric contrasts the positive and negative aspects of the two variables.

The two or more variables move in opposing directions if the covariance value remains negative. When the covariance value remains positive, the two variables move in the same direction. This indicates that, even if two variables drop in the same direction, the covariance remains positive. If two corporations' stocks are both getting cheaper over time, for instance, their covariance becomes positive.

Related: How To Become a Stock Trader (With Job and Salary Info)

How to calculate covariance?

Knowing how to calculate covariance can help when comparing two data sets. Assume an anthropologist is researching the weights and heights of a portion of people in a certain culture. Use a data pair of X and Y to indicate the weight and height of each participant in the research. Calculate the covariance connection using these numbers and a conventional formula. Calculate covariance using the steps below:

1. Use the standard formula

Understanding the formula for covariance and how to use it is essential when computing two variables. The standard formula to calculate covariance is:

Cov (X, Y) = Σ (Xi - µ) (Yj - v) / n

Whereas, each portion of the formula has its own purpose, like:

  • Cov (X, Y) represents the covariance of x and y is represented by Cov (X, Y)

  • Σ indicates the total of the formula's other elements

  • (Xi) represents all the values of the x-variable

  • µ represents the mean values of the X-variable

  • Yj represents the variables of the Y-variable

  • v represents the average value of the Y-variable

  • n represents the total number of points for both variables

2. Obtain the data

Gathering data for both groups is the first stage in determining the covariance of two or more variables. For example, if comparing company stocks, create a table of data with stock information from different years. This ensures you have the data you need easily accessible to you.

3. Find the average value for the variables

Next, find the average value of each variable. Total all the X-values together again and divide it by the total quantity of X-values to obtain the overall average. Repeat this calculation again for the Y-values.

4. Establish the difference between each value

Minus the mean of each group of variables from the number of each variable in that group. Next, multiply the values for both variables together. You may only complete this step after you have confirmed the values for the variables.

5. Combine the values

You may add the numbers to get the second to last section of the equation once you've computed the product of two variables together. For example, you may add product values to establish the addition of all values. After you've computed the portions of the equation, fill in the blanks with your values.

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Benefits of covariance

Some of the advantages of covariance in trade and investing include:

  • Diversification: When opposed to having investments that are most similar in scope and hazard, utilise covariance to broaden your investment strategy, which can result in improved risk management or profits.

  • Historical outlook: Covariance is a measurement that allows investors to compare the previous price and return data from two stock holdings to better forecast stock market behaviour and occurrences.

  • Volatility comparison: When investments or assets are extremely volatile, minimise unpredictability by comparing merged portfolios or even other investment option groups using covariance.

Related: What is strategy diversification? A comprehensive guide

What is variance?

The measure of the breadth of the distribution refers to variance, which is a statistical measure of the spread among a data set and its average score. It is possible to estimate the difference between the predicted value and the average of the squared difference. The greater the difference between the specified numbers and the mean, the greater the variance. When the values in a set appear close to the average, the variance is less. Typically, the classification of these variations is nature, price, stability and impact.

A stock variance is used to determine possible investment risk by demonstrating how much a stock value might deviate from the average in a financial setting. Stocks with a larger variance frequently have a greater risk, whether for greater or worse returns. A smaller variation stock might be less risky while still producing average profits. Variance in accountancy demonstrates how much a company's or development's actual costs differ from the budgeted or expected amount.

Related: What is variance analysis? (Definition and examples)

Covariance vs variance

Variance measures the range between a variable and the average value of a data set, unlike in covariance, where one data is the median, and the other is a point of interest that you choose to assess. In covariance, one data point remains the average, and the other is the point that you choose to measure. For example, if the first company's stock is increasing in value over time, but the overall stock market is declining, the difference between the median and the business' stock widens.

The correlation remains positive if the second organisation's stock increased at a comparable rate to the first. In the finance sector, investors and managers use variance to assess an investment's volatility and risk, ensuring that you know and comprehend what might transpire with your money. To develop equitable portfolios for the correct risk assessment metric, they use covariance to estimate how stock classifications or portfolios move together.

Related: How to calculate variance step-by-step (with examples)

Covariance vs correlation

Both the correlation and covariance evaluate the connection between two variables. The link between them is most closely analogous to the relationship between standard deviation and variance. You can measure the entire variation of random variables from their anticipated values by covariance. You're only able to determine the direction of the link using covariance. It does not reflect the strength of the link or the interdependence of the variables. Correlation assesses the strength of the link between variables. The scalable measure of covariance refers to correlation.

Related: What is correlation? Plus how to calculate and examples

Applications of covariance

You may use this application in specific areas of finance, such as assessing the risk of individual stocks by analysing whether they move in synch or against each other. For instance, if the value of two stocks rises and falls in opposing directions, they are complementary, posing little risk since one grows while the other drops, minimising financial loss.

By using both covariance and correlation to identify how and if factors move simultaneously, you can decide whether to add companies to your portfolio. While covariance reveals how two or more sets of statistics flow, correlation reveals what other factors impact that movement and whether the two variables relate to one another.

Example: Peter is a business executive who wants to add the shares of ABC Corp to his investment portfolio, which currently monitors the performance of the S&P500. He evaluates the directional link between the company and the S&P500 before incorporating it into his portfolios. Peter figures out the correlation between ABC Corp's stock and other stocks. The positive correlation in this situation shows that the stock price and the S&P500 500 generally move in one direction. Peter doesn't wish to raise his portfolio's potential losses, so, as a result, he doesn't buy stocks.

Related: What is risk aversion? (with definition and examples)

What is sample covariance?

Sample covariance analyses the connection between two explanatory variables from a smaller population sample. When working with big populations, such as stock investing instruments or long-term medical investigations, this statistic comes in handy. Assessing the sample covariance in these cases provides statisticians and researchers with a better understanding of how their findings appear in the wider population. Since sample covariance allows you to work with lesser sample sizes, it also gives more data for predictive modelling.

Example: An investment analyst studies the price changes of two distinct stock instruments. The analyst generates a sample covariance number for both stock Y and stock X using the sample covariance method. For the last three months, the analyst collects price data for stocks X and Y. The analyst then uses the value to compute the correlation between the two stocks and establish if one acts as a reliant variable regarding the other. This allows the financial analyst to use the sample covariance to compute correlation and see if the changes in stock prices between instruments appear causal.

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