# 7. Covariance and Correlation

## k. calculate and interpret covariance and correlation;

What is covariance and correlation a measure of?

These are a measure of the degree to which two random variables are related to each other.

What is the formula for the covariance between two variables `R_i`

and `R_j`

?

- $$Cov(R_i, R_j) = E[(R_i - E(R_i)) \times (R_j - E(R_j))]$$

What does it mean when a covariance is a negative number?

It means that, on average, there is an inverse relationship between the two numbers. When one is high, the other is lower.

What does a covariance of zero mean?

Covariance = zero means two variables are unrelated to each other

What does a covariance > 0 mean?

Covariance > 0 means that the two variables are related to each other. When one goes up the other one goes up, and vice versa.

What is the covariance of a variable to itself?

The same as it's variance.

What is the formula for correlation between two variables `R_i`

and `R_j`

?

- $$\rho(R_i, R_j) = \frac{Cov(R_i, R_j)}{\sigma(R_i) \times \sigma(R_j)}$$

- Could also be `corr(R_i, R_j)`

or `\rho_i_j`

What are the numerical boundaries of correlation?

Correlation will always be between -1 and 1

What does a correlation of zero mean?

Correlation equals zero means there is no linear (straight line) relationship between the variables

What does a correlation closer to one or closer to negative one mean?

The closer correlation gets to one or negative one indicates a stronger positive or inverse correlation.

##### Source:

- CFA