You consider $4$ stocks with the following correlations

Corr$(1,2)=0\mathrm{.}25$;Corr$(1,3)=0\mathrm{.}60$;Corr$(1,4)=0\mathrm{.}45.$ Each stock has the same expected return of

$10\%$ and standard deviation of $20\%.$

Assume your portfolio currently has only $$100,000$ of stock $1.$ You would like to invest another

$$100,000$ in only one stock $(2,3,$ or $4).$ Which stock $($you choose only one stock among $2,3,$ and

would be the best to add to your current portfolio. Justify your answers. Calculate the

expected return and standard deviation of your new portfolio after adding that stock.