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 $3\mathrm{.}49\%,$ Gas Co$.$ has a standard deviation of return of $3\mathrm{.}43\%,$ and they have a correlation of $0\mathrm{.}2376,$ calculate the volatility $($standard deviation$)$ of a portfolio that is $65\%$ invested in Cola Co$.$ stock and $35\%$ 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?

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$(R_{\text{C}\text{o}\text{l}\text{a}},R_{\text{G}\text{a}\text{s}})SD(R_{\text{C}\text{o}\text{l}\text{a}})SD(R_{\text{G}\text{a}\text{s}})$

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

$\backslash$table$[[$Date$,$Cola Co$.,$Gas Co$.],[$Jan$,5\mathrm{.}60\%,-2\mathrm{.}00\%$