Question

You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 10 percent and 16 percent, respectively. The standard deviations of the assets are 27 percent and 35 percent, respectively. The correlation between the two assets is .37 and the risk-free rate is 5.4 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? What is the smallest expected loss for this portfolio over the coming year with a probability of 1 percent? (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your Sharpe ratio answer to 4 decimal places and Probability answer to 2 decimal places. Omit the "%" sign in your response.)

Answer 1

wA = [(0.1 - 0.054)(0.35^2) - (0.16 - 0.054)(0.27)(0.35)(0.37)] / {(0.1 - 0.054)(0.35^2)+ (0.16 - 0.054)(0.27^2) - (0.1 - 0.054 + 0.16 - 0.054)[(0.27)(0.35)(0.37)]}

wA = 0.2397

wB = 1 - 0.2397 = 0.7603

E(RP) = 0.2397(0.1) + 0.7603(0.16) = 0.1456

σ = [(0.2397^2)(0.27^2) + (0.7603^2)(0.35^2) + 2(0.2397)(0.7603)(0.27)(0.35)(0.37)]^1/2 = 0.2962

Sharpe ratio = (0.1456 - 0.054)/0.2962 = .0.3093

Prob(R ≤ 0.1456 - 2.326(0.2962)) = 1%

Prob(R ≤ -0.5435) = 1% = -54.35%