Determinethis stockstodowellatthesametimeandtodopoorlyatthesametime isnegative duringdifferentyears connectionbetweenthereturnstothetwostocks stockxandstocky percent averagereturntostockyis percent samplecovarianceformulaiscomputedasfollows years differentyearsandpoorlyindifferentyears percent whilestockyhadalossof percent sameyear stockyhadareturnof percent percent thatthisisthesamplecovariance ton variables asameasureofassociationfortwomainreasons unlikecovariance and soits valuecanbemoreeasilyinterpreted

determine�this.

If�the�covariance�between�the�stocks�is�positive,�then�there’s�a�tendency�for�the�two stocks�to�do�well�at�the�same�time�and�to�do�poorly�at�the�same�time.�If�the�covariance is�negative,�then�the�two�stocks�tend�to�do�well�during�different�years�and�do�poorly during�different�years.�If�the�covariance�is�zero�(or�very�close�to�it),�then�there�is�no connection�between�the�returns�to�the�two�stocks.

Substitute�these�results�into�the�sample�covariance�formula.�The�numerator�of�the sample�covariance�formula�is�computed�as�follows:

You�compute�the�covariance�between�two�samples�like�this:

n�is�the�number�of�elements�common�to�both�samples.

i�is�an�index�that�is�used�to�assign�a�number�to�each�sample�element,�ranging�from�1 to�n.

The�correlation�measure�is�closely�related�to�covariance.�Correlation�is�often�preferred as�a�measure�of�association�for�two�main�reasons:

Unlike�covariance,�correlation�can�only�assume�values�between�–1�and�1,�so�its value�can�be�more�easily�interpreted.

This�equation�shows�that�the�variance�of�the�returns�to�Stock�X�is�0.0014.�The�standard deviation�is�the�square�root�of�the�variance: