Assume that you recently graduated and landed a job as a financial planner with Cicero Services, an investment advisory company. The Client presently owns a bond portfolio with $1 million invested in zero coupon Treasury bonds that mature in 10 years. (The total par value at maturity is $1.79 million and yield to maturity is about 6%, but that information is not necessary for the mini case.) You have calculated the rate of return on 10-year zero coupon for each scenario.
Scenario Probability Return on a 10-year Zero
of Scenario Coupon During the next year
Worst Case 0.10 -14%
Poor Case 0.20 -4%
Most Likely 0.40 6%
Good Case 0.20 16%
Best Case 0.10 26%
Historical Stock Returns
Year Market Blandy Gourmange
1 30% 26% 47%
2 7 15 -54
3 18 -14 15
4 -22 -15 7
5 -14 2 -28
6 10 -18 40
7 26 42 17
8 -10 30 -23
9 -3 -32 -4
10 38 28 75
Average 8.0% ? 9.2%
Standard 20.1% ? 38.6%
With Market 1.00 ? 0.678
Beta 1.00 ? 1.30
The Risk Free Rate is 4% and the market risk premium is 5%
A. -What are investments returns? What is the return on an investment that costs $1,000
B. -Graph the probability distribution for the binds returns based on the 5 scenarios. What might the graph of the probability distribution look like if there were an infinite number of scenarios if it were a continuous scenario.
C. -Use the scenario data to calculate the expected rate of return for the 10-year zero coupon Treasury bonds during the next year.
D. -What is stand-alone risk? Use the scenario data to calculate the standard deviation of the bond’s return for the next year.
E. -You client has decided that the risk of the bond portfolio is acceptable and wishes to leave it as it is. Now your client has asked you to use historical returns to estimate the standard deviation of Blandy’s stock returns. (Use Blandy’s 10 annual returns)
F. -Your client is shocked at how much risk Blandy’s stock has and would like to reduce the level of risk. You suggest that the client sell 25% of the Blandy stock and create a portfolio with 75% Blandy stock and 25% in the high risk Gourmange stock. How do you think the client will react to replacing some of the Blandy Stock with high Risk Stock? Show the client what the proposed portfolio return would have been in each of year of sample. Then calculate the s average return and standard deviation using the portfolios annual returns. How does the risk of the two-stock portfolio compare with the risk of the individual stocks if they were held in isolation?
G. -Explain correlation to your Client. Calcualet the estimate correlation between Blandy and Gourmange. Does this explain why the portfolio standard deviation was less than Blandy’s standard deviation?
H. -Suppose an investor starts with a portfolio consisting of one randomly selected stock. As more and morerandomly selected stocks are added to the portfolios, what happens to the portfolios risk?