Problem 5 (40 marks)

SPY and XIU are ETFs tracking the S&P 500 and S&P/TSX 60 index, which are often used as proxies for the US and Canadian stock markets, respectively. From a set of their historical data, the annual expected returns and standard deviations of those two ETFs and their covariance are estimated as follows:

SPY:

E(r) = 0.36

0.26

XIU:

E(r) = 0.44

0.28

Covariance between= 0.0568

Suppose that you have $5 million to invest for one year and you want to invest this money into SPY, XIU and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-Bill is 6% per annum.

Suppose that you have the following utility function:

(r) ? ?²

Answer following questions using EXCEL:

Draw the opportunity set offered by these two securities (with an increment of 0.01 in weight).

What is the optimal portfolio of SPY and XIU?

Determine your optimal asset allocation among SPY, XIU, and T-Bill, in percentage and in dollar amounts.

Assignment 1 Instructions Assignment 1 should be submitted after you have completed Unit 2. This assignment is worth 15 percent of your final grade. Assignment 1 contains five problems. The maximum mark for each problem is noted at the beginning of the problem. This assignment has a total of 100 marks. Read the requirements for each problem and plan your responses carefully. Although your responses should be concise, ensure that you answer each of the required components as completely as possible. If supporting calculations are required, present them in good form. When you receive your graded assignment, carefully review the comments the marker has made. This review component is an important step in your learning process. If you have any questions or concerns about the evaluation, please contact the Student Support Centre. Problem 1 (15 marks) You have $30,000 in your margin account, and you want to invest in BMO stock. The minimum margin requirement for BMO is 30%. You just got a quote on BMO as follows: Bid: 55.25 Ask: 55.26 The interest rate on the margin loan is 6% per annum. 1) If you want to buy BMO in margin, what is the maximum number of shares can you buy? 2) Suppose you want to buy 1200 shares of BMO in margin. Answer the following questions: a. What is the initial margin ratio? b. Suppose you are going to hold the shares for one year. At what price at the end of next year will your investment break even? (assuming no margin calls in the year) c. How far could the stock price fall before getting a margin call? d. If the stock price falls to $40, you would get a margin call. If this happens, how much new fund would you need to add to your account to respond the margin call? FNCE 401v6 Assignment 1 Oct 9/2013 Problem 2 (15 marks) Assume you sell short 100 shares of common stock at $70 per share, with initial margin at 55%. The minimum margin requirement is 30%. The stock will pay no dividends during the period, and you will not remove any money from the account before making the offsetting transaction. 1) At what price would you face a margin call? 2) If the price is $86 at the end of the period, what is your margin at that point? 3) What would be your profit if you repurchase the stock at $63/share? Problem 3 (15 marks) Use the following expectations on stocks X and Y to answer the questions below: Probability Stock X Stock Y Bear Market 0.2 -20% -15% Normal Market 0.5 18% 20% Bull Market 0.3 50% 10% The correlation between stock X and Y is 0.4. 1) What is the expected return for each stock? 2) What is the standard deviation for each stock? 3) Assume you invest your $100,000 in a portfolio with $90,000 in stock X and $10,000 in stock Y. What are the expected return and standard deviation of your portfolio? Problem 4 (15 marks) You have $800,000 invested in a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills. The information below refers to these assets. E(rp)=12.00% FNCE 401v6 Assignment 1 Oct 9/2013 p =7.00% T-Bill rate=3.6% Proportion of T-Bill in the complete portfolio: 20% Proportion of risky portfolio P in the complete portfolio: 80% Composition of P: Stock A Stock B Stock C Total 40% 25% 35% 100% 1) What is the expected return on your complete portfolio? 2) What is the standard deviation of your complete portfolio? 3) What are the dollar amounts of Stocks A, B, and C, respectively, in your complete portfolio? 4) If your degree of risk aversion is A=4, is your complete portfolio optimal? (assuming P is the optimal risky portfolio) FNCE 401v6 Assignment 1 Oct 9/2013 Problem 5 (40 marks) SPY and XIU are ETFs tracking the S&P 500 and S&P/TSX 60 index, which are often used as proxies for the US and Canadian stock markets, respectively. From a set of their historical data, the annual expected returns and standard deviations of those two ETFs and their covariance are estimated as follows: SPY: E(r) = 0.36 0.26 XIU: E(r) = 0.44 0.28 Covariance between= 0.0568 Suppose that you have $5 million to invest for one year and you want to invest this money into SPY, XIU and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-Bill is 6% per annum. Suppose that you have the following utility function: U=E(r) - 2 Answer following questions using EXCEL: 1) Draw the opportunity set offered by these two securities (with an increment of 0.01 in weight). 2) What is the optimal portfolio of SPY and XIU? 3) Determine your optimal asset allocation among SPY, XIU, and T-Bill, in percentage and in dollar amounts. FNCE 401v6 Assignment 1 Oct 9/2013