The following table contains monthly returns for Cola Co$.$ and Gas Co$.$ for $2022$: The following table contains monthly returns for Cola Co$.$ and Gas Co$.$ for $2022$: $.$ Using this table and the facts that

Cola Co$.$ has a standard deviation of return of $4\mathrm{.}45\%,$ Gas Co$.$ has a standard deviation of return of $5\mathrm{.}56\%,$ and they

have a correlation of $-0\mathrm{.}0028,$ calculate the volatility $($standard deviation$)$ of a portfolio that is $70\%$ invested in Cola Co$.$

stock and $30\%$ invested in Gas Co$.$ stock.

a$.$ Calculate the volatility using the formula:

Var$(R_p)=w_{\text{C}\text{o}\text{l}\text{a}}^{2}SD(R_{\text{C}\text{o}\text{l}\text{a}}{)}^2+w_{\text{G}\text{a}\text{s}}^{2}SD(R_{\text{G}\text{a}\text{s}}{)}^2+2w_{\text{C}\text{o}\text{l}\text{a}}{w}_{\text{G}\text{a}\text{s}}$Corr$(R_{\text{C}\text{o}\text{l}\text{a}},R_{\text{G}\text{a}\text{s}})SD(R_{\text{C}\text{o}\text{l}\text{a}})SD(R_{\text{G}\text{a}\text{s}})$

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

c$.$ How do your results compare?

Data table

$($Click on the following icon $$ in order to copy its contents into a spreadsheet.$)$Using this table and the facts that Cola Co$.$ has a standard deviation of return of $4\mathrm{.}45\%,$ Gas Co$.$ has a standard deviation of return of $5\mathrm{.}56\%,$ and they have a correlation of negative $0\mathrm{.}0028,$ calculate the volatility$($standard deviation$)$ of a portfolio that is $70\%$ invested in Cola Co$.$ stock and $30\%$ invested in Gas Co$.$ stock.

a$.$ Calculate the volatility using the$$ formula:

Var left parenthesis Upper R Subscript p right parenthesis equals w Subscript Cola Superscript $2$ Baseline SD left parenthesis Upper R Subscript Cola Baseline right parenthesis squared plus w Subscript Gas Superscript $2$ Baseline SD left parenthesis Upper R Subscript Gas Baseline right parenthesis squared plus $2$ w Subscript Cola Baseline w Subscript Gas Baseline Corr left parenthesis Upper R Subscript Cola Baseline comma Upper R Subscript Gas Baseline right parenthesis SD left parenthesis Upper R Subscript Cola Baseline right parenthesis SD left parenthesis Upper R Subscript Gas Baseline right parenthesis

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

c$.$ How do your results$$ compare?