Consider the following information on Stocks I and II: The market risk premium i

Question

Consider the following information on Stocks I and II: The market risk premium is 11.7 percent, and the risk-free rate is 4.7 percent. Requirement 1: 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).) 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).) Requirement 2: Which stock has the most systematic risk? Which one has the most unsystematic Which stock is "riskier"?

Explanation / Answer

Calculate the expected return stock 1

E(R1) = expected return on stock 1 = (0.22 x 0.045) +(0.62 x 0.355) + (0.16 x 0.215) = 0.2644

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

Var(1) = (0.045-0.2644)^2 (0.22) + (0.355-0.2644)^2 (0.62) + (0.215-0.2644)^2 (0.16) = 0.0161

Take sqrt of variance to get standard deviation

Standard Deviation Stock 1 = 0.12676= 12.68%

Then use CAPM to find beta

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

Solving for Beta

B= [ E(R) - rf] / [ E(Rm) - rf] = [ 0.2644-0.047]/ [0.117] = 1.858  

Calculate the expected return stock 2

E(R2) = expected return on stock 2 = (0.22 x- 0.37) +(0.62 x 0.29) + (0.16 x 0.47) = 0.1736

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

Var(1) = (-.037-0.1736)^2 (0.22) + (0.29-0.1736)^2 (0.62) + (0.47-0.1736)^2 (0.16) = 0.0322

Take sqrt of variance to get standard deviation

Standard Deviation Stock 1 = 0.1795= 17.95%

Then use CAPM to find beta

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

Solving for Beta

B= [ E(R) - rf] / [ E(Rm) - rf] = [ 0.1736-0.047]/ [0.117] = 1.0821

High-beta stocks are supposed to be riskier Stock 1

Higher beta stock is systematic Stock 1

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