The following table contains monthly returns for Cola Co$.$ and Gas Co$.$ for $2013($the returns are shown in decimal form, i$.$e$.,0\mathrm{.}035$ is $3\mathrm{.}5\%).$ Using this table and the fact that Cola Co$.$ and Gas Co$.$ have a correlation of $-0\mathrm{.}0969$ calculate the volatility $($standard deviation$)$ of a porffolio that is $60\%$ invested in Cola Co$.$ stock and $40\%$ invested in Gas Co$.$ stock. Calculate the volatility by: a$.$ Using the formula:

Var$(R_p)=w_1^{2}SD(R_1{)}^2+w_2^{2}SD(R_2{)}^2+2w_1{w}_2$Corr$(R_1,R_2)SD(R_1)SD(R_2)$

b$.$ Calculating the monthly returns of the portfolio and computing its volatility directly.

c$.$ How do your results compare?

a$.$ Using the formula:

Var$(R_p)=w_1^{2}SD(R_1{)}^2+w_2^{2}SD(R_2{)}^2+2w_1{w}_2$Corr$(R_1,R_2)SD(R_1)SD(R_2)$

The volatility $($standard deviation$)$ of the portfolio is $\%.($Round to two decimal places.$)$

Data table

$($Click on the following icon in order to copy its contents into a spreadsheet.$)$

$\backslash$table$[[$Month$,$Cola Co$.,$Gas Co$.],[$January$,-0\mathrm{.}0210,0\mathrm{.}0280],[$February$,0\mathrm{.}0000,-0\mathrm{.}0050],[$March$,-0\mathrm{.}0200,-0\mathrm{.}0180],[$April$,0\mathrm{.}0090,0\mathrm{.}0280],[$May$,-0\mathrm{.}0310,0\mathrm{.}0840],[$June$,-0\mathrm{.}0840,-0\mathrm{.}0460],[$July$,-0\mathrm{.}1190,0\mathrm{.}0820],[$August$,-0\mathrm{.}0160,0\mathrm{.}0460],[$September$,0\mathrm{.}0550,0\mathrm{.}0300],[$October$,-0\mathrm{.}0110,0\mathrm{.}0140],[$November$,-0\mathrm{.}0380,0\mathrm{.}0290],[$December$,-0\mathrm{.}0220,0\mathrm{.}0740]]$