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Minimum Variance Frontier, Efficient Portfolios and Optimal Portfolio Selection) (10 points) The Triad family of mutual funds allows investors to split their money between three portfolios managed by Triad. Portfolio C has an expected return of E[Rc] 10% and a standard deviation of returns of o(Rc) 15%. Portfolio B has an expected return of E[Ry] = 19% and a standard deviation of return of o(Ri) = 25%. The correlation coefficient between the returns of portfolios B 0.2. Portfolio A consists entirely of riskfree securities, and has a certain return of 4%. Your client is leaning towards investing her money entirely in portfolio C, since she is unwilling to take the higher risk associated with portfolio B, but wants a higher return than offered by portfolio A. and C is Pb,c (a) As a Triad investment advisor, you suggest to her an alternative portfolio P (consisting of a combination of only portfolios A and B) that has the same expected return as portfolio C but a lower standard deviation. If she has $200,000 to invest, how much should she invest in B and how much in A? What is the standard deviation of the return on her investment in this case? Sketch a mean standard deviation diagram that you would use to explain why the portfolio you suggest is better. (b) However, after your convincing presentation of the alternative portfolio P, your client now says that she is really comfortable with the level of risk in portfolio C. So, you suggest to her another portfolio P1 (also consisting of a combination of only portfolios A and B) that has the same standard deviation as portfolio C, but higher expected return. If she has $200,000 to invest, how much should she invest in B and how much in A? What is the expected return on her investment in this case? Sketch a mean standard deviation diagram that you would use to explain why the portfolio you suggest is better. (c) Your client also recalls reading a while ago in the 1st edition of ”Investments” by Sharpe and Alexander (Jeff Bailey at the time she went to school was not a coauthor of this book), that people should hold efficient portfolios, but she is unsure how to do it. She asks you for advice on how to optimally combine portfolios C and B in order to take advantage of diversification. You suggest her to invest in a mix of the portfolio A and a so called mean-variance efficient portfolio (MVEP) which is made up of portfolios B and C. Find this MVEP portfolio (i.e. find the weights on portfolio B and C that generate the MVEP). Use Excel’s solver function to do this (feel free to use the Example Optimal CAL.xls that is posted on the course webpage). What is the expected return, standard deviation and Sharpe ratio of the MVEP portfolio that you found? (d) Your client wants to keep the level of risk of her portfolio at the same level of portfolio C (i.e. standard deviation of 15%) but take advantage of diversification. If she invests $200,000 in A and MVEP, how much should she invest in portfolio A and how much in the MVEP ? How much in each of the portfolios B and C? What is the expected return on her portfolio in this case ? Compare it to the expected return on P1 obtained in part (B) and explain the difference, if any. (e) Suppose that now portfolio C has a standard deviation of 25% (the same as portfolio B, this is not a mistake), but the expected return on fund C is the same as before, only 10%. Would you still advise your client to hold portfolio C? If no, explain why. If yes, also explain why. Hint: find the new MVEP using Excel’s solver and explain the result.