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What is the difference between variance and covariance?

A:

Variance and covariance are mathematical terms frequently used in statistics, and despite the similar-sounding names they actually have quite different meanings. A covariance refers to the measure of how two random variables will change together and is used to calculate the correlation between variables. The variance refers to the spread of the data set—how far apart the numbers are in relation to the mean, for instance. Variance is particularly useful when calculating the probability of future events or performance.

In addition to their general use in statistics, both these terms have specific meanings for investors as well, referring to measurements taken in the stock market. In a finance context, covariance is the term used to describe how two stocks will move together. A positive covariance indicates both tend to move upward or downward in value at the same time, while an inverse, or negative, covariance means they will move counter to each other; when one rises, the other falls. Purchasing stocks with a negative covariance is a great way to minimize risk in a portfolio. The extreme peaks and valleys of the stocks’ performance can be expected to cancel each other out, leaving a steadier rate of return over the years.

Similarly, many stock experts and financial advisors use variance to measure a stock’s volatility. Being able to express in a single number just how far a given stock’s value can travel away from the mean is a very useful indicator of how much risk a particular stock comes with. (For related reading, see: Calculating Covariance for Stocks.)

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Cobi Jones writes about the blockchain community in the US. He is an entrepreneur and private investor in blockchain projects