Financial markets are complex systems. A small incident halfway across the globe may be sufficient to affect hundreds of stocks in India. Successful investing is based on a consistent effort of anticipating the risks and analysing the performance of stocks. A variety of financial tools, charts and ratios are used to analyse stocks. Charts and ratios generally help in analysing the business of a company. Investors use certain mathematical and statistical concepts to analyse the price of a stock.

Variance and covariance are two terms used commonly in statistics and probability theory. However, both the concepts are also used in stock market investing primarily to analyse price movement and assess risk. Let us understand variance and covariance to know the difference between variance and covariance.

Variance

When one reads the word ‘variance’, the first idea that strikes the mind is the divergence of something from a level that is considered normal. The actual meaning of variance is not very different. In statistics, the variance is the spread of a data set from its mean value. Larger variance means that the numbers in the data set are farther from the mean, while smaller variance means the numbers are closer to the mean.

For instance, suppose a person has been walking 5 km every morning for the last year. Due to some reason, his walking pattern was disturbed and on some days he started walking 6 km while on others he would walk for 4.5 km. What is the variance in the distance from the mean? For understanding’s sake, the mean would be 5 km as he had walked the distance every day for a year. The maximum variance for the man would be 1 km as he never walked more than 1 km or less than 1 km from the mean.

The concept of variance is used in the financial markets to gauge the volatility of a stock. The variance indicates how far a stock can move from its mean. A stock with higher variance is riskier but may generate higher returns and vice versa.

Covariance

Like variance, covariance is also a common concept in statistics. Covariance is a measure of how two random variables will change when compared to each other. In financial markets, covariance is used to analyse the returns of two different assets over a period of time when compared to different variables. If two investment options have a positive covariance, then their returns will increase and decrease together. If one increases, the other will increase too. A negative covariance means the returns will move away from each other. When one rises, the other will fall. For instance, income and working hours have positive covariance. Income rises when the working hours increase.

Variance vs Covariance

With the concept of variance and covariance fairy clear, let us take a look at the differences between variance and covariance. With either the terms used for investing or more precisely, for portfolio allocation, what is the difference between variance and covariance? The basic difference between variance and covariance is the information that each provides. Variance is a value. It is expressed as a number, hence variance is a measure of magnitude. On the other hand, covariance tells about the directional relationship between two variables. It is not expressed as a number, but as positive or negative.

If you dive deeper into variance vs covariance, you will understand both serve different purposes. The value of variance is interpreted to gauge the risk associated with an investment. It is a rough measure of the volatility of a security’s price. On the flipside, covariance is interpreted as the relation of the returns of an asset to those of others. Covariance can be used to diversify your portfolio. Add assets with negative covariance in your portfolio. When the returns from one will turn negative, the returns from the other will be positive, balancing the portfolio.

Conclusion

While both variance and covariance are important, at a standalone basis each one shows only one aspect of an investment. Both should be used in conjunction with other statistical concepts to get a clear picture. One should also take into consideration the correlation between investments as it shows both the magnitude and the direction of the returns.