Problem 1 – Risk and Return [15 marks]

The following table presents the expected performance of Intel and Apple stock over the next year.

Use the information presented in the table to answer the following questions:

a)   What is the expected return of INTL and AAPL? [4 marks]

b)   What is the standard deviation of the returns of INTL and AAPL? [4 marks]

c)    Assume that you have decided to invest 25% of your wealth in INTL and the rest of it in AAPL. What is the expected return of your portfolio? [2 marks]

d)   If the risk-free rate is 1%, what is the expected risk premium in each stock? [2 marks]

e)    If you could only invest in one security, which one would you select? Why? (Hint: Calculate the Sharpe ratios) [3 marks]

Problem 2 – Risk Aversion and Capital Allocation [60 marks]

You are the manager of a technology fund that has an expected rate of return of 11% and a standard deviation of 17%. Your fund is currently invested in the following stocks:

The T-bill rate is 2%. In addition, you have a client who is currently investing 40% of her wealth in your fund and the rest in a T-bill money market fund.

a)   What are the expected return and the standard deviation of your client’s portfolio? [4 marks]

b)   What are the weights of your client’s overall portfolio in each of the stocks included in your fund and in T-bills? [4 marks]

c)    What is the reward-to-variability ratio (i.e., the Sharpe Ratio) of your fund? What is the reward- to-variability ratio of your client’s portfolio? [2 marks]

d)   Draw the CAL of your fund on an expected return-standard deviation diagram and show your client’s position. What is the equation that defines the CAL of your fund? What is the slope of this CAL? [10 marks]

e)    Now, suppose that your client is considering rebalancing her portfolio by investing a proportion y1 of her total wealth in your fund, such that her overall portfolio has an expected return of 7%.

i.       What is the value of y1 ? [2 marks]

ii.       As a share of her overall portfolio, what would be your client’s investment proportions in the T-bill fund and in each of the three stocks included in your fund? [4 marks]

iii.       What would be the expected return and the standard deviation of your client’s new portfolio? [4 marks]

f)    Now, suppose that your client would prefer to invest in your fund a proportion y2 that  maximizes the expected return of her overall portfolio subject to the constraint that the portfolio’s standard deviation does not exceed 12%.

i.       What would be the investment proportion y2 ? [2 marks]

ii.       What would be the expected return of the overall portfolio? [2 marks]

g)    Now, suppose that your client’s degree of risk aversion is A = 4.

i.       What proportion y ∗ of her total wealth should she invest in your fund? [2 marks]

ii.       What would be the expected return and standard deviation of your client’s portfolio in this case? [4 marks]

h)   You estimate that a passive investment strategy (i.e. one that mimics the S&P/TSX composite index) yields an expected return of 5% and a standard deviation of 7%.

i.       Draw the CML and your fund’s CAL on an expected return-standard deviation diagram.

[4 marks]

ii.       What is the equation that defines the CML? What is the slope of the CML? [6 marks]

i)    Your client is considering switching the 40% of her wealth currently invested in your fund to the passive portfolio.

i.       Explain to your client the disadvantages of the switch. [5 marks]

ii.       What is the maximum fee that you could charge (as a percentage of the investment in  your fund deducted at the end of the year) such that your client will be at least as well- off investing in your fund as in the passive strategy? (Hint: The fee will lower the slope  of your client’s CAL by reducing your fund’s expected return by the amount of the fee).

[3 marks]

iii.       Is the fee that you can charge to make your client indifferent between your fund and the passive strategy affected by her capital allocation decision? Why? [2 marks]

Problem 3 – Optimal Risky Portfolios [10 marks]

The correlation coefficients between different stocks are provided in the following table:

Assume that investors are risk averse and that all stocks have an expected return of 5% and a standard deviation of 15%. Use this information to answer the following questions:

a)   Jane is one of your clients and she is fully invested in MSFT. She can only add one more stock to her portfolio. Which stock would you recommend her to add to her portfolio? Why? [4 marks]

b)   Joe is also one of your clients and he is in the same situation as Jane. He is fully invested in   MSFT, he can only add one more stock to his portfolio, but he is more risk averse than Jane. Would you advise Joe to invest in a different stock than Jane? That is, would your                    recommendation in part (a) change in this case? Why? [4 marks]

c)    Consider once again the situation in part (a). Suppose that in addition to investing in one more  stock, Jane can invest in T-bills with a return of 5%. Would you change your answer to part (a)? Why? [2 mark]