Consider the following information on Stocks I and II: State of Economy Probabil

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 .030 ?.34 Normal .59 .340 .26 Irrational exuberance .17 .200 .44 The market risk premium is 11.4 percent, and the risk-free rate is 4.4 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?

Explanation / Answer

SOLUTION:

Requirement 1 (a):

Stock I:

E(R1) = Expected return on Stock I:

= (.24 * .030) + (.59 * .340) + (.17 * .200) = 0.2418

Now to compute the variance, it is the sum of the squared deviations from the mean (expected value) times the probability.

Variance of Stock I:

= (0.030-0.2418)^2 (0.24) + (0.340-0.2418)^2 (0.59) + (0.200-0.2418)^2 (0.17) = 0.0167

Standarad Deviation = Square root of Variance.

Standard Deviation Stock I = 0.1292 or 12.92%

By using cost and asset pricing model we find Beta as,

E(R) = rf +B (E(Rm) - rf)

Beta = ( 0.2418

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