4. (40 points) Suppose that investors base their decisions on mean-variance analysis and there exists two assets: A risk-free asset with return rf = 8%. A risky asset with an expected return E[r] = 0.20, and standard deviation of o = 0.30. Let y be the proportion of your wealth invested in the risky asset, so that (1 y) is the proportion invested in the risk-free asset. (a) Let E[rp] be the expected return of a portfolio that invests y in the risky asset. Let op be the standard deviation of that portfolio. Find the equations that relate both E[rp) and op to y. (b) For what ranges of y is your portfolio short in the risky asset? For what ranges of y are you lending? For what ranges of y are you borrowing? (c) Choose different portfolios (change y from -1 to 2 in steps of 0.1 say) and find their mean and variance. Plot the mean-standard deviation combinations that you get from these portfolios. What is the relationship between Erp] and op? (d) Describe the set of portfolios that are mean variance efficient. Will a portfolio that is short in the risky asset be efficient? 4. (40 points) Suppose that investors base their decisions on mean-variance analysis and there exists two assets: A risk-free asset with return rf = 8%. A risky asset with an expected return E[r] = 0.20, and standard deviation of o = 0.30. Let y be the proportion of your wealth invested in the risky asset, so that (1 y) is the proportion invested in the risk-free asset. (a) Let E[rp] be the expected return of a portfolio that invests y in the risky asset. Let op be the standard deviation of that portfolio. Find the equations that relate both E[rp) and op to y. (b) For what ranges of y is your portfolio short in the risky asset? For what ranges of y are you lending? For what ranges of y are you borrowing? (c) Choose different portfolios (change y from -1 to 2 in steps of 0.1 say) and find their mean and variance. Plot the mean-standard deviation combinations that you get from these portfolios. What is the relationship between Erp] and op? (d) Describe the set of portfolios that are mean variance efficient. Will a portfolio that is short in the risky asset be efficient