Assume that you recently graduated and landed a job as a fin

Assume that you recently graduated and landed a job as a financial planner with Cicero Services, an investment advisory company. Your first client recently inherited some assets and has asked you to evaluate them. The client presently owns a bond portfolio with $1million invested in zero coupon Treasury bonds that mature in 10 years. The client also has $2 million invested in the stock of Blandy, Inc., a company that produces meat-and- potatoes frozen dinners. Blandy’s slogan is, Solid food for shaky times. Unfortunately, Congress and the President are engaged in an acrimonious dispute over the budget and the debt ceiling. The outcome of the dispute, which will not be resolved until the end of the year, will have a big impact on interest rates one year from now. Your first task is to determine the risk of the client’s bond portfolio. After consulting with the economists at your firm, you have specified five possible scenarios for the resolution of the dispute at the end of the year. For each scenario, you have estimated the probability of the scenario occurring and the impact on interest rates and bond prices if the scenario occurs. Given this information, you have calculated the rate of return on 10-year zero coupon for each scenario. The probabilities and returns are shown below:

Scenario

Probability of Scenario

Return on a 10 year Zero coupon treasury bond during the next year

Worst case

.10

-14%

Poor Case

.20

-4%

Most Likely

.40

6%

Good Case

.20

16%

Best Case

.10

26%

You have also gathered historical returns for the past 10 years for Blandy, Gourmange
Corporation (a producer of gourmet specialty foods), and the stock market.

                                                                   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

                                                 Market                       Blandy                      Gourmange

Average return:                         8%                               ?                                  9.2%

Standard Deviation:                 20.1%                           ?                                 38.6%

Correlation with the market:     1.00                              ?                                  0.678

Beta:                                         1.00                              ?                                1.30

The risk-free rate is 4% and the market risk premium is 5%.

Questions:

1) Your client decides to invest $1.4 million in Blandy stock and $0.6 million in Gourmange stock. What are the weights of the portfolio? What is the portfolio\'s beta? What is the required return for this portfolio?

Scenario	Probability of Scenario	Return on a 10 year Zero coupon treasury bond during the next year
Worst case	.10	-14%
Poor Case	.20	-4%
Most Likely	.40	6%
Good Case	.20	16%
Best Case	.10	26%

Solution

Total investment = 1.4 + 0.6 = 2 mn

So, weights in the portfolio :

Blandy : 1.4 / 2.0 =0.7

Gourmange: 0.6 / 2.0 = 0.3

Beta = correlation (market returns, stock returns) * stdev(stock returns) / stdev (market returns)

Thus, portfolio beta :

0.7 * 0.6 + 0.3*1.3 = 0.42 + 0.39

= 0.61 is the portfolio beta (weighted average of the individual beta)

Required return can be calculated using the CAPM model:

Re = Rf + b (risk premium)

= 4 + 0.61 (5)

= 4 + 3.05

= 7.05% is the expected return on the portfolio

Hope this helps. Ask if you have any doubts

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
Mean	8	6.4	9.2
Stdev	20.1	25.2	38.6
Correl	1	0.481	0.678
Beta	1	0.60	1.30