Chp 9- Risk, Return and the Opportunity Cost of capital
The following table is given for stocks A and B. Using the data given and answer the
questions 1 thru 6.
Scenario
Recession
Normal
Boom
Probability
25%
40%
35%
Return on A
-4%
8%
20%
Return on B
9%
4%
-4%
1. What is the expected return on Stock A?
a. 9.2 %
b. 8.0 %
c. 24.0 %
d. 11.3 %
2. What is the expected return on Stock B?
a. 3.0 %
b. 2.45 %
c. 4.33 %
d. 6.33 %
3. What is the standard deviation of Stock A?
a. 4.33 %
b. 6.22 %
c. 9.22 %
d. 0 %
4. What is the standard deviation of Stock B?
a. 0 %
b. 4.33 %
c. 6.22 %
d. 5.12%
5. What is the expected return of a portfolio if you invest %50 of your wealth in Stock A and
%50 in Stock B?
a. 5.83 %
b. 5.5 %
c. 11.0 %
d. 0 %
6. What is the standard deviation of the portfolio if you invest %50 of your wealth in Stock A
and %50 in Stock B?
a. 0 %
b. 5 %
c. 2.1 %
d. 10 %
CHP 09
Calculate the expected return, variance, and standard deviations for investments in
either stock A or stock B, or an equally weighted portfolio of both.
Scenario
Recession
Normal
Boom
Probability
25%
40%
35%
Return on A
-4%
8%
20%
Return on B
9%
4%
-4%
Answer:
Stock A:
Expected return = (.25 x –4%) + (.40 x 8%) + (.35 x 20%) = 9.2%
Variance = .25(-4% - 9.2%) + .4(8% - 9.2%)2 + .35(20% - 9.2%)2
= 43.56 + .58 + 40.82 = 84.96
Standard deviation = (84.92)2 = 9.22%
Stock B:
Expected return = (.25 x 9%) + (.40 x 4%) + (.35 x -4%) = 2.45%
Variance = .25(9% - 2.45%) + .4(4% - 2.45%)2 + .35(-4% - 2.45%)2
= 10.73 + .96 + 14.56 = 26.25
Standard deviation = (26.25)2 = 5.12%
Portfolio:
Expected return = (.5 x 9.2%) + (.5 x 2.45%) = 5.83%
Variance = .25(((-4% + 9%) x. 5) – 5.83%)2 + .4(((8% + 4%) x.5) – 5.83%)2
+ .35 ((20% - 4%) x.5) – 5.83%)2
= 2.77 + .01 + 1.65 = 4.43
Standard deviation = (4.43)2 = 2.1%
Note that the standard deviation of the portfolio is considerably less than that of either
Stock A or Stock B.