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 = 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 p be the standard deviation of that portfolio. Find the equations that relate both E[rp] and 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[rp] and p? (d) Describe the set of portfolios that are mean variance efficient. Will a portfolio that is short in the risky asset be efficient?