Consider the following information on Stocks I and II: State of Economy Probabil
ID: 2720042 • 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 .21 .050 .26 Normal .66 .350 .18 Irrational exuberance .13 .210 .46 The market risk premium is 11.6 percent, and the risk-free rate is 4.6 percent.
Requirement 1: (a) Calculate the beta and standard deviation of Stock I. (Do not round intermediate calculations. Enter the standard deviation as a percentage. Round your answers to 2 decimal places (e.g., 32.16).) Stock I Beta Standard deviation % (b) Calculate the beta and standard deviation of Stock II. (Do not round intermediate calculations. Enter the standard deviation as a percentage. Round your answers to 2 decimal places (e.g., 32.16).) 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
We first need to compute expected return:
ER= sum of Px R
Stock A
State
P
R Stock I
P x R
Recession
0.21
0.05
0.0105
Normal
0.66
0.35
0.231
Irrational ex
0.13
0.21
0.0273
0.2688
ER = 26.88%
State
P
R Stock I
P x R
R-ER
Px (R-ER)^2
Recession
0.21
0.05
0.0105
-0.2188
0.010053422
Normal
0.66
0.35
0.231
0.0812
0.00435167
Irrational ex
0.13
0.21
0.0273
-0.0588
0.000449467
0.2688
0.01485456
Variance = 0.01485456
Standard deviation = (0.01485456)^0.50
= 12.19%
Beta = (ER- Rf)/MRP
= (26.88%-4.60%)/11.6%
=1.92
Stock II
State
P
R Stock II
P x R
R-ER
Px (R-ER)^2
Recession
0.21
-0.26
-0.0546
-0.384
0.03096576
Normal
0.66
0.18
0.1188
0.056
0.00206976
Irrational ex
0.13
0.46
0.0598
0.336
0.01467648
0.124
0.047712
ER= 0.124
Variance = 0.047712
SD = (0.047712^0.50
=21.84%
Beta = (ER- Rf)/MRP
= (12.4%-4.60%)/11.6%
=0.67
Since Stock A has higher Beta, it has higher systematic risk.
Stock B has higher unsystematic risk. Stock B has higher total risk,
State
P
R Stock I
P x R
Recession
0.21
0.05
0.0105
Normal
0.66
0.35
0.231
Irrational ex
0.13
0.21
0.0273
0.2688
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