Consider the following information on Stocks I and II: Rate of Return if State O
ID: 2719941 • Letter: C
Question
Consider the following information on Stocks I and II:
Rate of Return if State Occurs State of Economy / Probability of State of Economy / Stock I / Stock II
Recession 0.11 0.05 -0.25
Normal 0.18 0.19 0.45
Irrational Exuberance .71 .25 .27
The market risk premium is 14 percent, and the risk-free rate is 8.4 percent.
For standard deviations: (Do not include the percent signs (%). Round your answers to 2 decimal places. (e.g., 32.16))
For betas: (Round your answers to 2 decimal places. (e.g., 32.16))
The standard deviation on Stock I's expected return is ??? percent, and the Stock I beta is ???. The standard deviation on Stock II's expected return is ??? percent, and the Stock II beta is ???
Explanation / Answer
Stock I
Expected return = Sum of P x R
State
P
RI
P x RI
Recession
0.11
0.05
0.0055
Normal
0.18
0.19
0.0342
Irrational Exuberance
0.71
0.25
0.1775
0.2172
Expected return = 0.2172
State
P
RI
P x RI
Ri-ERI
P x (RI-ERI)^2
Recession
0.11
0.05
0.0055
-0.1672
0.003075142
Normal
0.18
0.19
0.0342
-0.0272
0.000133171
Irrational Exuberance
0.71
0.25
0.1775
0.0328
0.000763846
0.2172
0.00397216
Variance = P x (R-ER)^2
Variance = 0.00397216
Standard Deviation = variance ^0.50
= 0.00397216^0.50
= 0.063025
Stock II
State
P
RII
P x RII
RII-ERII
P x (RII-ERII)^2
Recession
0.11
-0.25
-0.0275
-0.4952
0.026974534
Normal
0.18
0.45
0.081
0.2048
0.007549747
Irrational Exuberance
0.71
0.27
0.1917
0.0248
0.000436678
0.2452
0.03496096
Variance = 0.03496096
Standard deviation = 0.03496096^0.50
= 0.186979
Calculation of beta
Beta = (Stock return – Rf) /(Rm-Rf)
Beta (Stock I) = (0.2172-0.084)/0.14
=0.95
Beta (Stock II) = (0.2452-0.084)/0.14
=1.15
State
P
RI
P x RI
Recession
0.11
0.05
0.0055
Normal
0.18
0.19
0.0342
Irrational Exuberance
0.71
0.25
0.1775
0.2172
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