Question

Problem 3 - Optimal Risky Portfolios (10 marks] The correlation coefficients between different stocks are provided in the following table: HPQ MSFT KO DELL HPQ MSFT DELL 1 0.85 0.60 0.45 1 0.75 0.35 1 0.30 KO 1 Assume that investors are risk averse and that all stocks have an expected return of 5% and a standard deviation of 12%. Use this information to answer the following questions: a) Jane is one of your clients and she is fully invested in KO. 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 KO, 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]

Answer 1

a) The lower the correlation coefficient between two stocks, the lower is the value of the standard deviation of the portolio combining the two stocks. Since Jane is fully invested in KO and can only add one more stock to her portfolio , she would be better off by adding the stock with which KO has the least correlation. i.e. MSFT with which KO has a correlation coefficient of 0.30.

b) Joe is more risk averse than Jane, i.e. Joe has a higher risk taking capacity. However, here since all the stocks have expected return of 5%. a portfolio composed of one or more of the stocks would also have the same expected return of 5%. As the return is constant, it is better to reduce the risk, thereby choosing the stock with which KO has the least correlation coefficient. ie. MSFT . Hence the recommendation would not change

c) If there is a third option of investing in T-bills which are considered as risk free investments, also with a return of 5%, the recommendation would change from that in part a) as the T- bills' correlation coefficient with any other stock is 0. Hence, the T-bill is now the instrument with which KO has the least correlation. So, the recommendation would change from MSFT to T-Bills. It may please be noted that since we have a risk free asset giving 5% return and any combination of the stocks would also give 5% expected return, it can be suggested to switch from risky portfolio to T-bills and invest all the money in T-bills which is a risk free investment.