Mini Case Chapter 5 Assume that you recently graduated and you just landed a job
ID: 2791360 • Letter: M
Question
Mini Case Chapter 5
Assume that you recently graduated and you just landed a job as a financial planner with the Cleveland Clinic. Your first assignment is to invest $100,000. Because the funds are to be invested at the end of one year, you have been instructed to plan for a one-year holding period. Further, your boss has restricted you to the following investment alternatives, shown with their probabilities and associated outcomes.
State of Economy
Probability
T-Bills
Alta Inds.
Repo Men
American Foam
Market Port.
Recession
0.1
8.00%
-22.0%
28.0%
10.0%
-13.0%
Below Average
0.2
8.00%
-2.0%
14.7%
-10.0%
1.0%
Average
0.4
8.00%
20.0%
0.0%
7.0%
15.0%
Above Average
0.2
8.00%
35.0%
-10.0%
45.0%
29.0%
Boom
0.1
8.00%
50.0%
-20.0%
30.0%
43.0%
Barney Smith Investment Advisors recently issued estimates for the state of the economy and the rate of return on each state of the economy. Alta Industries, Inc. is an electronics firm; Repo Men Inc. collects past due debts; and American Foam manufactures mattresses and various other foam products. Barney Smith also maintains an "index fund" which owns a market-weighted fraction of all publicly traded stocks; you can invest in that fund and thus obtain average stock market results. Given the situation as described, answer the following questions.
a. Calculate the expected rate of return on each alternative.
b. Calculate the standard deviation of returns on each alternative.
c. Calculate the coefficient of variation on each alternative.
d. Calculate the beta on each alternative.
e. Do the SD, CV, and beta produce the same risk ranking? Why or why not?
f. Suppose you create a two-stock portfolio by investing $50,000 in Alta Industries and $50,000 in Repo Men. Calculate the expected return, standard deviation, coefficient of variation, and beta for this portfolio. How does the risk of this two-stock portfolio compare with the risk of the individual stocks if they were held in isolation?
State of Economy
Probability
T-Bills
Alta Inds.
Repo Men
American Foam
Market Port.
Recession
0.1
8.00%
-22.0%
28.0%
10.0%
-13.0%
Below Average
0.2
8.00%
-2.0%
14.7%
-10.0%
1.0%
Average
0.4
8.00%
20.0%
0.0%
7.0%
15.0%
Above Average
0.2
8.00%
35.0%
-10.0%
45.0%
29.0%
Boom
0.1
8.00%
50.0%
-20.0%
30.0%
43.0%
Explanation / Answer
EXPECTED RETURN ON EACH ALTERNATIVE A B C=A*B D E=A*D F G=A*F H I=A*H J K=A*I T Bills Alta Inds Repo Men Americal Foam Market portfolio State of Economy Probability T-Bills Probability*Return Alta Inds. Probability*Return Repo Men Probability*Return American Foam Probability*Return Market Port. Probability*Return Recession 0.1 8.00% 0.80% -22.00% -2.20% 28.00% 2.80% 10.00% 1.00% -13.00% -1.30% Below Average 0.2 8.00% 1.60% -2.00% -0.40% 14.70% 2.94% -10.00% -2.00% 1.00% 0.20% Average 0.4 8.00% 3.20% 20.00% 8.00% 0.00% 0.00% 7.00% 2.80% 15.00% 6.00% Above Average 0.2 8.00% 1.60% 35.00% 7.00% -10.00% -2.00% 45.00% 9.00% 29.00% 5.80% Boom 0.1 8.00% 0.80% 50.00% 5.00% -20.00% -2.00% 30.00% 3.00% 43.00% 4.30% TOTAL 8.00% 17.40% 1.74% 13.80% 15.00% a. Investment Expected Return T-Bills 8% Alta Inds. 17.40% Repo Men 1.74% American Foam 13.80% Market Port. 15.00% b STANDARD DEVIATION OF EACH ALTERNATIVE STANDARD DEVIATION OF ALTA INDUSTRIES A B C=B-17.4 D=C^2 E=D*A State of Economy Probability Return ofAlta Inds.(Percent) Deviation from expected Deviation squared (Deviation squared)*(Probability) Recession 0.1 (22.00) (39.40) 1,552.36 155.24 Below Average 0.2 (2.00) (19.40) 376.36 75.27 Average 0.4 20.00 2.60 6.76 2.70 Above Average 0.2 35.00 17.60 309.76 61.95 Boom 0.1 50.00 32.60 1,062.76 106.28 TOTAL 401.44 VARIANCE 401.44 STANDARD DEVIATION 20.04% (SQUARE ROOT OF VARIANCE =SQRT(401.44)= 20.04 STANDARD DEVIATION OF REPO MEN A B C=B-1.74 D=C^2 E=D*A State of Economy Probability Return ofRepo Men.(Percent) Deviation from expected Deviation squared (Deviation squared)*(Probability) Recession 0.1 28.00 26.26 689.59 68.96 Below Average 0.2 14.70 12.96 167.96 33.59 Average 0.4 - (1.74) 3.03 1.21 Above Average 0.2 (10.00) (11.74) 137.83 27.57 Boom 0.1 (20.00) (21.74) 472.63 47.26 TOTAL 178.59 VARIANCE 178.59 STANDARD DEVIATION 13.36% (SQUARE ROOT OF VARIANCE =SQRT(178.59)=13.36) STANDARD DEVIATION OF AMERICAN FOAM A B C=B-13.8 D=C^2 E=D*A State of Economy Probability Return ofAmerican Foam(Percent) Deviation from expected Deviation squared (Deviation squared)*(Probability) Recession 0.1 10.00 (3.80) 14.44 1.44 Below Average 0.2 10.00 (3.80) 14.44 2.89 Average 0.4 7.00 (6.80) 46.24 18.50 Above Average 0.2 45.00 31.20 973.44 194.69 Boom 0.1 30.00 16.20 262.44 26.24 TOTAL 243.76 VARIANCE 243.76 STANDARD DEVIATION 15.61% (SQUARE ROOT OF VARIANCE =SQRT(243.76)=15.61) STANDARD DEVIATION OF MARKET PORTFOLIO A B C=B-15 D=C^2 E=D*A State of Economy Probability Return of Market Portfolio(Percent) Deviation from expected Deviation squared (Deviation squared)*(Probability) Recession 0.1 (13.00) (28.00) 784.00 78.40 Below Average 0.2 1.00 (14.00) 196.00 39.20 Average 0.4 15.00 - - - Above Average 0.2 29.00 14.00 196.00 39.20 Boom 0.1 43.00 28.00 784.00 78.40 TOTAL 235.20 VARIANCE 235.20 STANDARD DEVIATION 15.34% (SQUARE ROOT OF VARIANCE =SQRT(235.20)=15.34) STANDARD DEVIATION OF T-BILLS= 0 T Bills returns do not change Return=Expected Return =8% Deviation from expected =0 Deciation squared=0 Sum of Deviation squared=0 Square root of sum=0 Investment Standard Deviation T-Bills 0% Alta Inds. 20.04% Repo Men 13.36% American Foam 15.61% Market Port. 15.34% c COEFFICIENT OF VARIATION Coefficient of variation=(Standard Deviation)/(Expected Return) A B C=A/B Investment Standard Deviation Expected Return Coefficient of Variation Coefficient of variation(percentage) T-Bills - 8.00 - 0% Alta Inds. 20.04 17.40 1.15 115% Repo Men 13.36 1.74 7.68 768% American Foam 15.61 13.80 1.13 113% Market Port. 15.34 15.00 1.02 102% d BETA OF EACH ALTERNATIVE INVESTMENT RETURN=RETURN ON T-BILL+BETA* (MARKET RETURN-RETURN ON T-BILLS) BETA=(INVESTMENT RETURN-8)/(15-8)=(INVESTMENT RETURN-8)/7 A B C=B-8 D=C/7 Investment Expected Return Investment premium BETA T-Bills 8.00 - - Alta Inds. 17.40 9.40 1.34 Repo Men 1.74 (6.26) (0.89) American Foam 13.80 5.80 0.83 Market Port. 15.00 7.00 1.00