Money & Capital Markets Fall 2011 Homework #1 Due: Friday, Sept. 9 th. Answer Key

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1 Money & Capital Markets Fall 011 Homework #1 Due: Friday, Sept. 9 th Answer Key 1. (6 points) A pension fund manager is considering two mutual funds. The first is a stock fund. The second is a long-term government and corporate bond fund. The information for each fund is the following: Fund Expected Return Standard Deviation Stock 0% 30% Bond 10% 0% The correlation between the funds is.0 (which happens to be a good historical approximation to the actual correlation between stocks and bonds by the way). What is the expected return and standard deviation of a portfolio composed of: a. 5% stock fund and 75% bond fund = (.5.0) + (.75.10) = % = (.5.30) + (.75.0) + (.5)(.75)(.30)(.0)(.0) =.0365 = = % b. 50% stock fund and 50% bond fund = (.5.0) + (.5.10) =.15 15% = (.5.30) + (.5.0) + (.5)(.5)(.30)(.0)(.0) =.0385 = = % c. 75% stock fund and 5% bond fund = (.75.0) + (.5.10) = % = (.75.30) + (.5.0) + (.75)(.5)(.30)(.0)(.0) =.0576 = =.4 4%

2 . ( points) An investor is considering the purchase of two assets. She has determined that Asset 1 has an expected rate of return of 0% with a standard deviation of 40%. Asset, on the other hand, has an expected rate of return of 5% with a standard deviation of 10%. The correlation coefficient for the two assets is Suppose the investor put 0% of her money in Asset 1 and 80% in Asset. Calculate the expected rate of return and risk (i.e., standard deviation) of the resulting portfolio. = (.0.0) + (.80.05) =.08 8% = (.0.40) + (.80.10) + (.0)(.80)(.40)(.10)( 0.50) =.0064 = =.08 8% 3. ( points) Draw the familiar efficiency frontier with many possible assets. Now, considering your personality, preferences, etc. demonstrate with an indifference curve the portfolio that you might choose. Explain your choice and the shape of your indifference curve. Something like the following would do. Your indifference curves might be flatter or steeper, but they should be upward sloping ---- unless you would really accept lower expected return for higher risk!!! Return Risk

3 4. ( points) Suppose a retired person is currently holding 100% of her wealth in the stock of a very safe and mature corporation. The stock of this company (call it Stock 1) has an expected rate of return of 10% with a standard deviation of 10%. An investment manager advises our retired person to hold 80% of her wealth in stock 1 and 0% in a stock. This stock has been issued by a new, high-tech corporation. Stock has an expected rate of return of 30% with a standard deviation 50%. The correlation coefficient between the two stocks is -.5. If the retired person follows the investment manager s advice (80% in stock 1 and 0% in stock ), what will be the expected rate of return and standard deviation of the resulting portfolio? = (.80.10) + (.0.30) =.14 14% = (.80.10) + (.0.50) + (.80)(.0)(.10)(.50)( 0.50) =.0084 = = % The point of the question was to show again that the initial holding was not very efficient. We were able to increase return while decreasing risk.

4 5. (6 points) An investment manager has formed the efficient frontier by using the meanvariance technique. The manager has two individuals in his office seeking advice on investing. The first individual, Ms. Betty, has recently taken her first job as a lawyer in a leading law firm and looks forward to many productive years in her career. The second individual, Mr. Alan, is a few years away from retirement after a long career as a partner in the law firm. a. Using mean-variance analysis demonstrate graphically and explain the reasoning behind the type of portfolio the investment manager would likely suggest to each individual. Return Ms. Betty Mr. Alan Risk

5 b. Later, after returning from a week long training session on the Separation Theorem, the investment manager realizes that he has given the wrong advice. Assuming a risk-free asset exists, what will be the likely new advice of the investment manager to the two individuals? Illustrate the advice with a new graph. The manager puts both clients in the optimum risky portfolio (Z in the graph). But, the investment manager will have Alan put some of his wealth in the risk-free asset, while having Betty borrow at the risk-free rate and purchase more than 100% of her wealth of Z. Return Ms. Betty Mr. Alan Z Risk

6 c. Even later, the risk-free rate declines. Demonstrate graphically the likely impact on the two individual s suggested portfolio s of the decline in the risk-free rate. Return Ms. Betty Mr. Alan Z New optimum risky portfolio Risk Not sure if you can see it in the graph, but it would be very possible for Betty to borrow even more at the risk-free rate (since it s lower now) in order to invest more in the new optimum risky portfolio. Alan, is likely going to take on some additional risk as he puts more of his wealth in the risky portfolio and less in the risk-free rate. We do know for sure that the new optimum risky portfolio is going to occur down and to the left along the efficient frontier.

7 6. ( 4 points) An investor is currently holding all of her wealth in a portfolio composed of risky assets. The risky portfolio, assumed to be the optimal risky portfolio, currently has an expected rate of return of 10% with a standard deviation of 0%. Her investment manager has advised her to keep 60% of her entire wealth in the risky portfolio, while investing 40% of her wealth in a risk-free asset paying a 4% rate of return. a. What will be the expected rate of return and risk of this complete portfolio? = (.60.10) + (.40.04) = % = (.60.0) + (.40 0) + (.60)(.40)(.0)(0)(0) =.0144 = =.1 1% b. What is the return-to-risk ratio (thus, the Sharpe ratio, slope of the capital allocation line) for this investor. 10% 4% Return to Risk Ratio = = %

8 See Excel File for the following problems. For the following problems, Excel will be very helpful 7. ( 4 points) For each of the following, construct the efficient frontier using historical data (i.e., returns). For each, present the efficient frontier in graphical form and in a table --- you can use 5% increments to develop both. Finally, I would like you to use data from 8/1/00 to 8/1/009. a. Starbucks (SBUX) and Peets (PEET) b. Starbucks (SBUX) and General Mills (GIS) 8. (4 points) The table describes all possible investment assets. Asset 1 Asset Risk-Free Expected Return (%) Variance Standard Deviation (%) Correlation Coefficient -0.3 a. What is the optimum risky portfolio? b. If you invested 80% of your wealth in the optimum risky portfolio and 0% in the risk-free asset, what would be the expected return and risk of this complete portfolio?