How to Calculate Correlation Coefficients $-$ a step$-$by$-$step example

O Click to start. Then click on each step below to calculate the correlation coefficient

The following columns show the return on IBM and GE in a recent $12-$month period:

$\backslash$table$[[,1,2],[,$IBM,GE$],[$Month$,$Return, $\%,$Return, $\%],[1,2\mathrm{.}79,-9\mathrm{.}40],[2,-1\mathrm{.}57,-3\mathrm{.}89],[3,6\mathrm{.}47,5\mathrm{.}31],[4,-2\mathrm{.}02,-4\mathrm{.}84],[5,8\mathrm{.}85,-0\mathrm{.}22],[6,-3\mathrm{.}09,-4\mathrm{.}44],[7,5\mathrm{.}31,3\mathrm{.}74],[8,-5\mathrm{.}84,0\mathrm{.}44],[9,0\mathrm{.}69,-4\mathrm{.}81],[10,-5\mathrm{.}67,-5\mathrm{.}79],[11,-0\mathrm{.}77,-0\mathrm{.}24],[12,1\mathrm{.}90,-0\mathrm{.}34],[$Total$,7\mathrm{.}05,-24\mathrm{.}49],[$Average$,0\mathrm{.}59,-2\mathrm{.}04]]$

OStep $1$

Ostep $2$

OStep $3$

OStep $4$

Ostep $5$

Ostep $6$

Ostep $7$

Step $7$

Calculate the average monthly return of each stock

For each stock calculate the deviations from the average return

Square these deviations

Calculate the average squared deviation $($the variance$).$

Take the square root of the variance. This is the standard deviation of returns $().$

Multiply together the deviations from the average return in columns $3$ and $4.$

Average these products. This is the covariance $($cov$)$ between IBM and GE returns $(|)$ GE$)$

Divide the covariance by each of the two standard deviations. This is the correlation between IBM and GM returns.

The formula for the correlation coefficient between IBM and GE is ${}_{\text{I}\text{B}\text{M}}.G\frac{E}{{}_{\text{I}\text{B}\text{M}}{}_{GE}}$