PROBLEM ONE: The returns of Stock A and Stock B have the following distribution:
|
Demand for the
Company's Products
|
Probability of this
Demand Occurring
|
Rate of Return
Stock A
|
Rate of Return
Stock B
|
|
Weak
|
15.0%
|
(18.0%)
|
(24.0%)
|
|
Below Average
|
25.0%
|
(22.0%)
|
(4.0%)
|
|
Average
|
20.0%
|
44.0%
|
24.0%
|
|
Above Average
|
30.0%
|
22.0%
|
8.0%
|
|
Strong
|
10.0%
|
34.0%
|
56.0%
|
|
|
100.0%
|
|
|
a) Calculate the Expected Return for Stock A and Stock B
b) Calculate the Variance and the Standard Deviation for Stock A and Stock B
c) Calculate the Coefficient of Variation of each stock
d) Calculate the Correlation Coefficient between Stock A and Stock B
e) In which of the two stocks would you invest your money? Explain.
PROBLEM TWO: You have observed the following returns over time:
|
Year
|
Stock X
|
Stock Y
|
Stock Z
|
Market
|
|
2000
|
14%
|
13%
|
(18%)
|
12%
|
|
2001
|
19%
|
7%
|
33%
|
10%
|
|
2002
|
(16%)
|
(5%)
|
15%
|
(12%)
|
|
2003
|
3%
|
1%
|
(4%)
|
1%
|
|
2004
|
20%
|
11%
|
27%
|
15%
|
Assume that the risk-free rate is 6% and the market risk premium is 5%
a) What are the betas of Stocks X, Y and Z?
b) What are the required rates of return for Stocks X, Y and Z?
c) What are the standard deviations for Stocks X, Y and Z?
d) What is the required rate of return and standard deviation for a portfolio consisting of 20% invested in Stock X, 45% invested in Stock Y, and 35% invested in Stock Z?
e) If Stock X’s expected return is 22%, is Stock X under-or-over valued?