c$.$ Based on the estimated correlation values do you think diversification will reduce risk with these assets? $(5$p$)$

$5.$ Convert the monthly sample means into annual estimates by multiplying by $12.$ Monthly variances and covariances can be annualized by multiplying by $12.$ Standard deviations are annualized by multiplying monthly standard deviations by the square root of $12.(5$p$)$

$6.$ Using the annualized estimated means, variances and covariances computed earlier. Suppose, an investor currently owns a portfolio consisting of two stocks, COST and WFC$,$ with $60\%$ invested in COST. $(5$p$)$

a$.$ Calculate the expected value of the portfolio returns. $(5$p$)$

b$.$ Calculate the risk $($standard deviation$)$ of the portfolio returns. $(5$p$)$

$7.$ Suppose the previous investor wants to keep her stake in Costco Wholesale Corporation $($COST$)$ and would like other asset to substitute for WFC$.$ Which of the remaining three stocks will give her the maximum benefit of diversification, assuming she still keeps $60\%$ invested in COST? $(5$p$)$

a$.$ Calculate the expected value of returns of this new portfolio. $(5$p$)$

b$.$ Calculate the risk $($standard deviation$)$ of this new portfolio. $(5$p$)$