You manage an investment fund (risky portfolio) with an expected return of 18% and a standard deviation of 28%. The risk free rate is 8%. Based on...

You manage an investment fund (risky portfolio) with an expected return of 18% and a standard deviation of 28%.  The risk free rate is 8%. Based on this information, answer the following:

a)     Your client, Joe, chooses to invest 65% in your fund and the rest in a money market fund. What are the expected return and standard deviation of Joe's portfolio? (2 marks)

b)     Suppose that your fund (risky portfolio) includes the following investments in the given proportions:

Stock A: 40%; Stock B: 33%; Stock C: 27%.

What are the investment proportions of Joe's overall portfolio, including his position in the money market fund? (3 marks)

c)      What is the reward-to-variability ratio of your fund (risky portfolio)? Joe's portfolio? Explain. (3 marks)

d)     Now suppose that Joe decides to invest in your fund (risky portfolio) a proportion, y, of his total investment budget, so that the overall portfolio will have an expected return of 16.5%. 

                    i.           What is the value of y? (3 marks)

                  ii.           What are Joe's investment proportions in each of the 3 stocks in the fund (risky portfolio): A, B and C and the money market fund? (4 marks)

                iii.           What is the standard deviation of Joe's portfolio? (2 marks)

e)     If Joe invests the amount calculated in (d) into your fund (risky portfolio), calculate his degree of risk aversion.(2 marks)

f)       What if Joe wants to invest a proportion in your fund (risky portfolio) that maximizes the expected return on his overall portfolio but does not exceed a standard deviation of 18%. What is the proportion? (2 marks)

g)     What if Joe becomes more cautious about his investment decision and his degree of risk aversion is now 3. (5 marks)

                    i.           What is the optimal amount he should invest in your fund (risky portfolio)? (2 marks)

                  ii.           What is the expected return of the optimal complete portfolio? (2 marks)

                iii.           What is the standard deviation of the complete portfolio? (1 mark)