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You have the following information about the returns on three risky assets over the next year:
Asset Expected return Standard deviation Correlation coefficient X Y Z
X - 20% - 40% 1 - 0.4 - 0Y - 24% - 50% 0.4 - 1 - 0.1Z - 4% - 12% 0 - 0.1 - 1
a. Determine the minimum-variance portfolio of the three assets. Do the portfolio weights seem reasonable given the inputs? Compute the expected return and the standard deviation of the return on the minimum-variance portfolio.
In addition to the three risky assets, you can also invest in a risk-free asset with a return of rf = 3%.
b. Compute the Sharpe ratios of the three assets.
c. Construct a (standard deviation, expected return)-diagram in which you plot the minimum-variance portfolio, the three assets, and the risk-free asset.
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