Consider the following information about Stocks I and II: Rate of Return If Stat

Question

Consider 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 .20 .09 .26 Normal .60 .18 .13 Irrational exuberance .20 .12 .46 The market risk premium is 5 percent, and the risk-free rate is 4 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 1 "riskier".

Explanation / Answer

Computation of standard deviation and beta of stock I.We have,

Standard deviation = sqrt ( 0.00144)

Standard deviation = 0.0379*100 = 3.79%

Using the CAPM,

Expected return = Risk free return + beta x market risk premium

0.15 = 0.04 + beta x 0.05

Beta = 0.11/0.05 = 2.2

Computation of standard deviation and beta of stock II.We have,

Standard deviation = sqrt ( 0.05308)

Standard deviation = 0.02303*100 = 2.30%

Using the CAPM,

Expected return = Risk free return + beta x market risk premium

0.15 = 0.04 + beta x 0.05

Beta = 0.11/0.05 = 2.2

State of economy Probability of state of economy Rate of return of Stock I Rate of return of Stock II Expected return of stock I Expected return of stockII Recession 0.20 0.09 - 0.26 0.018 - 0.0234 Normal 0.60 0.18 0.13 0.108 0.078 Irrational exuberance 0.20 0.12 0.46 0.024 0.092 0.15 0.15

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