Consider the following information on Stocks I and II: State of Economy Probabil
ID: 2751556 • Letter: C
Question
Consider the following information on Stocks I and II: State of Economy Probability of State of Economy Rate of Return if State Occurs Stock I Stock II Recession .24 .065 .29 Normal .69 .365 .21 Irrational exuberance .07 .225 .49 The market risk premium is 11.9 percent, and the risk-free rate is 4.9 percent.
Requirement 1:
(a) Calculate the beta and standard deviation of Stock I.
Stock I Beta Standard deviation %
(b) Calculate the beta and standard deviation of Stock II.
Stock II Beta Standard deviation %
Requirement 2:
(a) Which stock has the most systematic risk?
(b) Which one has the most unsystematic risk? (c) Which stock is “riskier”?
Explanation / Answer
.49
Expected return on stock I=0.24*0.065+0.69*.365+.07*.225
=0.2832
=28.32%
Expected return on stock II=0.24*-0.29+0.69*.21+.07*.49
=0.1096
=10.96%
Standard deviation of stock 1= [0.24*(0.065-0.2832)+0.69*(0.365-0.2832)+0.07*(0.225-0.2832)]^0.5
=0
Standard Deviation of stock is 0%
Using CAPM
Expected return=rf+ beta*(market risk premium)
28.32=4.9+beta*11.9
Beta of stock 1=1.97
Standard deviation of stock 2= [0.24*(-0.29-0.1096)+0.69*(0.21-0.1096)+0.07*(0.49-0.1096)]^0.5
=0
Standard Deviation of stock is 0%
Using CAPM
Expected return=rf+ beta*(market risk premium)
10.96=4.9+beta*11.9
Beta of stock 2=0.51
a)Stock I has the most systematic risk because beta is higher than stock II.
b) Stock I is most riskier.
State of Economy Probability of State of Economy Rate of Return if State Occurs Stock I Rate of Return if State Occurs Stock II Recession .24 .065 -.29 Normal .69 .365 .21 Irrational exuberance .07 .225.49
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