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##### "Instructions: For analytical questions make sure...

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"Instructions: For analytical questions make sure to show your work for full credit. Do not report only the final answer but show formulas and calculations when appropriate. If you would like, you may work in small groups of 2-4 people to discuss the problem set. However, you must write up answers individually. If you decide to work in a group, please list the names of the group members on your problem set. Also, please write your program of study on the problem set (it makes it much easier to return the problem sets to you). 1. Investing in the market portfolio (5 points): You are interested in investing funds in the market portfolio of US stocks and 1 year Treasury notes, which you view as the risk-free asset. In order to figure out the characteristics of returns on the overall US stock market, you decide to analyze historical data. You collect data on historical Treasury note rates as well as historical data on stock returns. I have placed the file PS2.xls on LATTE. It contains Treasury note interest rate data from 1954 to 2010 (downloaded from The Federal Reserve Bank of St. Louis; the link to the website is on LATTE under ?Useful Links?) and return data for the value-weighted US stock market from 1954 to 2009 (downloaded from CRSP from WRDS). a. What is the average interest rate (not including 2010)? b. What is the average stock return? What is the standard deviation of the stock returns? Before making your capital allocation decision you take a close look at the data and especially the recent experience. c. If you had invested 100 at the beginning of 2000 in 1-year Treasury notes what would your investment have been worth at the end of 2009? How about if you had invested 100 in the stock market instead? What do you conclude from this exercise? d. Your estimate of the US stock market return for 2010 is 12%. In this case what would be the value of your Treasury note and stock market investments at the end of 2010 (this is part c. plus one more year)? e. Over the period 1954 to 2009 what was the average excess return of the stock market over Treasury notes, i.e. what was the risk premium on the stock market? What was the Sharpe ratio of the stock market (Hint: use the average interest rate as your measure of the risk-free rate)? f. After an extended meeting with your investors, you determine that they would be indifferent investing all of their funds in a portfolio with a 12% expected return and 20% standard deviation and a portfolio with a 6% expected return and a 10% standard deviation. What is their level of risk aversion A? Currently the 1-year Treasury note interest rate is 0.3%. You decide to use the Sharpe ratio from part e. as your best guess of the slope of the CML when investing over the next year (remember, you are investing in the risk-free asset and the market portfolio). Fin201a, Prof. Jens Hilscher, Sep 24 2010 g. Draw the CML in risk return space. What is the expected return and standard deviation of the risky portfolio? (Hint: Add the current Treasury note rate to the historical risk premium from e.) h. Your client chooses to invest 75% of a portfolio in the stock market and 25% in Treasury notes. Using your inputs from part g. what is the expected return and standard deviation of her portfolio? Indicate the portfolio that corresponds to your client?s portfolio on the CML. i. Now suppose that instead your client decides to invest a proportion y of funds so that the complete portfolio has an expected rate of return of 4%. What is the proportion y? j. What is the optimal amount y that your client should invest in the risky portfolio? Use the degree of risk aversion A from part f. to calculate the optimal proportion y of the total investment your client should invest in the market portfolio. What is the expected value and standard deviation of the rate of return on your client?s portfolio? 2. Investing in 2 risky assets and the risk free asset (5 points): Assume that there are two risky funds that you consider investing in: a corporate bond fund (B) and a large cap stock fund (L). After careful analysis you determine that B has expected return 3.5% and standard deviation 10% while L has expected return 7.5% and standard deviation 20%. You determine that the correlation between the returns is 0.25. a. What is the expected return and standard deviation of the portfolio that invests 50% in the corporate bond fund B and 50% in the large cap stock fund L? b. Tabulate the portfolio opportunity set of investing in the two risky funds B and L: make a table with the weights, the expected returns, and the standard deviations of the portfolios. Use investment proportions for the funds from zero to 100% in increments of 20%. (Hint: Use Excel.) c. What are the investment proportions in the minimum-variance portfolio of the two risky funds, and what is the MVP?s expected return and standard deviation? Use the formula from class to calculate this (show your work). If you want, you can then check your answer using the Excel solver. d. Draw the investment opportunity set POS in mean-variance space assuming that you can invest any fraction (larger or equal to zero) in the two assets (and the rest in the other asset). Remember that you now have eight feasible risk-return combinations that you can plot. Indicate the minimum variance portfolio and the two investment opportunities that invest 100% in either B or L and zero in the other in the graph. Now assume that you are advising a client. The investor has standard mean variance utility with A=4. The investor decides to invest in the two funds B and L you have been researching and decides to also invest in Treasury notes which offer a risk-free rate of return of 0.5%. [Note: here you add the risk-free asset as another investment choice.] e. Of the eight portfolios (that you considered in parts a. to d. above) which one has the highest reward to variability ratio (Sharpe ratio)? What is Sharpe ratio of that portfolio? f. What fraction w of funds invested in the bond portfolio maximizes the slope of the CAL? To figure this out adapt the worksheet ?Optimal_CAL? in PS2.xls and use the Excel Solver. What is the optimal weight w* invested in the bond portfolio B and what is the maximized slope of the CAL? g. Assuming your client decides to invest $1,000,000, what are the optimal investments in B, L and T-bills? (Hint: first find the optimal fraction y your client should invest in the risky portfolio. You can then further break that down into investments in B and L.)",Hi, I found in Google that someone else asked the same questions as mine, so I guess you may already have the answers for the problem set. I am running out of time. Thank you

Paper#10154 | Written in 18-Jul-2015

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