nsider the following information about Stocks I and II: Rate of Return If State
ID: 2725388 • Letter: N
Question
nsider the following information about Stocks I and II: Rate of Return If State Occurs State of Probability of Economy State of Economy Stock I Stock II Recession .26 .05 .31 Normal .50 .22 .11 Irrational exuberance .24 .05 .51 The market risk premium is 5 percent, and the risk-free rate is 3 percent. (Do not round intermediate calculations. Round your answers to 2 decimal places, e.g., 32.16. Enter your return answers as a percent. ) The standard deviation on Stock I's return is percent, and the Stock I beta is . The standard deviation on Stock II's return is percent, and the Stock II beta is . Therefore, based on the stock's systematic risk/beta, Stock is "riskier".
Explanation / Answer
State of Economy Probability of State Return if State Occurs
Stock I Stock II
Recession .26 .05 .31
Normal .50 .22 .11
Irrational exuberance .24 .05 .51
The expected return of Stock I is:
E(R I ) = 0.26(0.050) + 0.50(0.220) + 0.24(0.05) = 0.135 or 13.5%
Using the CAPM to find the of Stock I, we find: Er=Rf+ (Rp)
risk-free rate is 3 percent
risk premium is 5 percent
0.135 = 0.030 + 0.05 I
I = (.135-.03)/.05
I =2.1
The total risk of the asset is measured by its standard deviation, so we need to calculate the standard deviation of Stock I. Beginning with the calculation of the stock's variance, we find:
i²= 0.26(0.050 - 0.135)² + 0.50(0.220 - 0.135)² + 0.24(0.050 - 0.135)² = 0.007225
i = (0.007225)1/²
Using the same procedure for Stock II, we find the expected return to be:
E(R II ) = 0.26(-.31) + 0.50(0.11) + 0.24(0.51) = 0.0968 or 9.68%
E(R II ) = 9.68%
Using the CAPM to find the of Stock II, we find:
.0968=0.030 + 0.05 I
II = (.0968-.03)/.05
II=(0.0668)/.05
II=1.336
The total risk of the asset is measured by its standard deviation, so we need to calculate the standard deviation of Stock I. Beginning with the calculation of the stock's variance, we find:
i²= 0.26(-.31 - 0.0968)²+0.50(0.11-0.0968)²+0.24(0.51 -0.0968)² = 0.0840
i = (0.0840)1/²
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