Three risky assets have the following expected returns, variances, and covariances: Variance-Covariance Matrix Asset Expected Return X Y Z X 0.20 0.040 0.015 0.008 Y 0.30 0.015 0.090 0.018 Z 0.40 0.008 0.018 0.160 Suppose the market portfolio, M is made of 20% of X, 30% of Y, and 50% of Z. The risk-free rate of return is 4%. Assume the Capital Asset pricing Model (CAPM) holds. (a) Calculate the expected return and standard deviation of the market portfolio. (10 points) (b) An investor is looking to invest a proportion of her wealth in the market portfolio and the remaining in the risk-free asset. Calculate her optimal allocation to the risky portfolio if she requires an expected return of 6%. What is the level of risk she has to bear? (10 points) (c) Assuming the investor can borrow and lend at the risk-free rate of return, what is her optimal allocation if she require an expected return of 15%? Explain your answer. What is the level of risk she has to bear? (10 points) (d) Calculate the Sharpe ratio of the market portfolio. Suppose there exists another portfolio, P*, composed up of 60% of X, 10% of Y, and 30%% of Z. Calculate the Sharpe ratio of this portfolio and compare it with the Sharpe ratio of the market portfolio. Explain the difference in Sharpe ratios. (10 points) (e) Calculate the beta of each asset. (10 points)