You are interested in creating a portfolio of two stocks$-$Coca$-$Cola and Texas Utilities. Over the last decade, an investment in Coca$-$Cola stock would have earned and average annual return of $25\%,$ with a standar deviation in returns of $36\%.$ An investment in Texas Utilities stock would have earned and averdage annual return of $12\%,$ with a standar deviation of $22\%.$ The correlation in returns across the two stocks is $0\mathrm{.}28.$

a$.$ Assuming that the average and standard deviation, estimated using past returns, will continue to hold in the future, estimate the average returns and standard deviation of a portfolio composed $60\%$ of Coca$-$Cola and $40\%$ of Texas utilities stock.

b$.$Estimate the minimum variance portfolio.

c$.$Now assume that Coca$-$Col's international diversification will reduce the correlation to $0\mathrm{.}20$ while increasing Coca$-$Cola's standard deviation in returns to $45\%.$ Assuming all of the other numbers reamin unchanged, answer $($a$)$ and $($b$).$