when the calculated covariance is less than negative this indicates that the two variables have an inverse relationship in other words a stock one value lower than average tends to be paired with a stock two value greater than average and vice versa 
applications of covariancecovariances have significant applications in finance and modern portfolio theory mpt for example in the capital asset pricing model capm which is used to calculate the expected return of an asset the covariance between a security and the market is used in the formula for one of the model s key variables beta in the capm beta measures the volatility or systematic risk of a security compared to the market as a whole it s a practical measure that draws from the covariance to gauge an investor s risk exposure specific to one security meanwhile portfolio theory uses covariances to statistically reduce the overall risk of a portfolio by protecting against volatility through covariance informed diversification possessing financial assets with returns that have similar covariances does not provide very much diversification therefore a diversified portfolio would likely contain a mix of financial assets that have varying covariances covariance vs variancecovariance is related to variance a statistical measure for the spread of points in a data set both variance and covariance measure how data points are distributed around a calculated mean however variance measures the spread of data along a single axis while covariance examines the directional relationship between two variables in a financial context covariance is used to examine how different investments perform in relation to one another a positive covariance indicates that two assets tend to perform well at the same time while a negative covariance indicates that they tend to move in opposite directions investors might seek investments with a negative covariance to help them diversify their holdings covariance vs correlationcovariance is also distinct from correlation another statistical metric often used to measure the relationship between two variables while covariance measures the direction of a relationship between two variables correlation measures the strength of that relationship this is usually expressed through a correlation coefficient which can range from 1 to 1 while the covariance does measure the directional relationship between two assets it does not show the strength of the relationship between the two assets the coefficient of correlation is a more appropriate indicator of this strength a correlation is considered strong if the correlation coefficient has a value close to 1 positive correlation or 1 negative correlation a coefficient that is close to zero indicates that there is only a weak relationship between the two variables example of covariance calculationthe capital sigma symbol signifies the summation of all of the calculations so you need to calculate for each day and add the results for example to calculate the covariance between two stocks assume you have the stock prices for a period of four days and use the formula covariance ret a b c avg a b c ret x y z avg x y z sample size 1 begin aligned text covariance sum frac text ret abc text avg abc times text ret xyz text avg xyz text sample size 1 end aligned covariance sample size 1 retabc avgabc retxyz avgxyz you would find the day 1 average return for abc 1 675 and xyz 4 125 subtract them from the corresponding term and multiply them do this for each day day 1 1 2 1 675 3 1 4 125 0 487 begin aligned text day 1 1 2 1 675 times 3 1 4 125 0 487 end aligned day 1 1 2 1 675 3 1 4 125 0 487 day 2 1 8 1 675 4 2 4 125 0 009 begin aligned text day 2 1 8 1 675 4 2 4 125 0 009 end aligned day 2 1 8 1 675 4 2 4 125 0 009 day 3 2 2 1 675 5 0 4 125 0 459 begin aligned text day 3 2 2 1 675 5 0 4 125 0 459 end aligned day 3 2 2 1 675 5 0 4 125 0 459 day 4 1 5 1 675 4 2 4 125 0 013 begin aligned text day 4 1 5 1 675 4 2 4 125 0 013 end aligned day 4 1 5 1 675 4 2 4 125 0 013 add each day s result to the previous result 0 487 0 009 0 459 0 013 0 943 begin aligned 0 487 0 009 0 459 0 013 0 943 end aligned 0 487 0 009 0 459 0 013 0 943 your sample size is four so subtract one from four and divide the previous result by it 0 943 3 314 begin aligned frac 0 943 3 314 end aligned 30 943 314 this sample has a covariance of 0 314 a positive number suggesting that the two stocks are similar in returns 