You are constructing a portfolio of two assets, Asset A and Asset B. The expecte

Question

You are constructing a portfolio of two assets, Asset A and Asset B. The expected returns of the assets are 13 percent and 29 percent, respectively. The standard deviations of the assets are 16 percent and 32 percent, respectively. The correlation between the two assets is 0.1 and the risk-free rate is 3 percent. What is the optimal Sharpe ratio in a portfolio of the two assets? (A negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your Sharpe ratio answer to 4 decimal places when calculating your answer. )

Explanation / Answer

Sharpe Ratio = (Rp - Rf) / SDp

here, Rp - Portfolio Returns, Rf - Risk-free rate, SDp - Standard Deviation of portfolio

Here, Rp = w1 x R1 + w2 x R2, where w1 + w2 = 1

and SDp = [(w1 x SD1)^2 + (w2 x SD2)^2 + (2 x w1 x w2 x SD1 x SD2 x corr12)]^(1/2)

R1 = 13%, R2 = 29%, SD1 = 16%, SD2 = 32%, corr12 = 0.1

We need to find w1 and w2 such that, Sharpe Ratio is maximized. Using excel solver, we get optimal Sharpe Ratio = 0.9792

Asset E(R) SD weights Corr A 13% 16% 59% 10% B 29% 32% 41% Portfolio 19.53% 16.88% Sharpe Ratio 0.9792

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