2) Suppose that investors base their decisions on mean-variance analysis and there exists two assets:

- A risk-free asset with return R_f = 8%

- A risky asset with an expected return E[r] = 0.20 and standard deviation of 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[r_p] be the expected return of the portfolio that invests y in the risky asset. Let _p be the standard deviation of that portfolio. Find the equations that relate both E[r_p] & _p 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 E[r_p] & _p ?

d) Describe the set of portfolios that are mean variance efficient. Will a portfolio that is short in the risky asset be efficient?

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