The Triad family of mutual funds allows investors to split their money between several portfolios managed by Triad. Portfolio C has an ex- pected return of 10% and a standard deviation of return of 15%. Port- folio B has an expected return of 19% and a standard deviation of return of 25%. Portfolio A consists entirely of risk-free securities, and has a certain return of 4%. Your client is leaning towards investing his money entirely in portfolio C, since he is unwilling to take the higher risk associated with portfolio B, but wants a higher return than offered by portfolio A.

(a) In your role as a Triad investment advisor, you suggest to him an alternative portfolio (consisting of a combination of A and B) that has the same standard deviation as portfolio C but a higher expected return. If he has $200,000 to invest, how much should he invest in B and how much in A? What is his expected return in this case? (Note that since you work for Triad you cannot recommend investing in a market index fund, since this is not sold by Triad!)

(b) Sketch a risk/return diagram to help explain to him why his com- bination of risk and return is improved by this option, and why his risk has not increased. Show all four portfolios on the diagram (the original three plus your suggestion).

(c) Now assume that the correlation between portfolios B and C is 0. Find the combination of B and C that is mean-variance efficient.

That is find the "MVE" portfolio that combines these two portfolios. Calculate and report the portfolio weights in the MVE portfolio. Also calculate the expected return and standard deviation of the MVE portfolio. What is the Sharpe ratio of the MVE portfolio? How does this compare to the Sharpe ratio for portfolios B and C?

(d) Using the "MVE" portfolio and portfolio A nd a portfolio that has the same standard deviation as portfolio C but has higher expected return. What amount of money would be invested in each of the securities A, B and C to achieve this return? How does the expected return of this portfolio compare with the expected return of the portfolio you constructed in part ??? Why is it different?

(e) Draw a diagram that shows how considering all possible combi- nations of investments in the available portfolios improves the set of risk and return choices. Indicate the set of combinations that investors should prefer (e.g., those which minimize risk for a given level of return).