# Your client wants to construct

1. Your client wants to construct a portfolio from two stocks(Stocks Y and Z) and has asked you to determine the portfolioweights for each stock that will generate the portfolio with thesmallest standard deviation. Use the relevant information in thetable below to calculate the standard deviation for each portfolioweighting scenario and indicate the scenario that you shouldrecommend to your client.
 Stock Y Stock Z Portfolio Weighting Scenario1 60% 40% Portfolio Weighting Scenario2 70% 30% Portfolio Weighting Scenario3 80% 20% Standard Deviation 9% 6% Covariance Between Stocks Y andZ -0.003

Portfolio Weighting Scenario 1

Portfolio Variance = w1212 +w2222 +2w1w2Cov(Y,Z)

w1 = weight of stock Y; w2 = weight of stock Z; 1 =standard deviation of stock Y; 2 =standard deviation of stock Z; Cov(Y,Z) = covariance between stockY and Z

Portfolio Variance = 0.62*0.092 + 0.42*0.062 + 2*0.6*0.4*-0.003= 0.36*0.0081‬ + 0.16*0.0036 – 0.00144 = 0.002916‬ + 0.000576‬ -0.00144 = 0.002052‬

Portfolio Standard deviation = (Portfolio Variance)1/2 =(0.002052‬)1/2 = 0.002052‬0.5 = 0.0453 or 4.53%

Portfolio Weighting Scenario 2

Portfolio Variance = 0.72*0.092 + 0.32*0.062 + 2*0.7*0.3*-0.003= 0.49*0.0081‬ + 0.09*0.0036 – 0.00126 = 0.003969‬ + 0.000324‬‬ -0.00126 = 0.003033

Portfolio standard deviation = (0.003033‬)1/2 =0.003033​​​​​​​​​​​​​​0.5 = 0.0551 or 5.51%

Portfolio Weighting Scenario 3

Portfolio Variance = 0.82*0.092 + 0.22*0.062 + 2*0.8*0.2*-0.003= 0.64*0.0081‬ + 0.04*0.0036 – 0.00096‬ = 0.005184‬‬ + 0.000144‬‬ -0.00096‬ = 0.004368‬

Portfolio standard deviation = (0.004368‬‬)1/2 =0.004368‬​​​​​​​​​​​​​​0.5 = 0.0661 or 6.61%

Portfolio Weighting Scenario 1 is recommended because portfolioweight of stock Y’s 60% and stock Z’s 40% will generate theportfolio with the smallest standard deviation of 4.53%.

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