Question

Consider the following information on Stocks I and II: Probability of Rate of Retum if State State of Occurs State of Economy Economy Stock Stock | Recession Normal Irrational 45 exuberance The market risk premium is 7 percent, and the risk-free rate is 4 percent. a. Calculate the beta of each stock. (Do not round intermediate caldalations and round your answers to 2 decimal places, e.g., 32.16.) b. Calculate the standard deviation of each stock. (Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.) c. Which stock has the most systematic risk? d. Which one has the most unsystematic risk? e. Which stock is "riskier"?

Answer 1

Answer a.

Stock I:

Expected Return = 0.25 * 0.04 + 0.60 * 0.22 + 0.15 * 0.16
Expected Return = 0.1660 or 16.60%

Expected Return = Risk-free Rate + Beta * Market Risk Premium
16.60% = 4.00% + Beta * 7.00%
12.60% = Beta * 7.00%
Beta = 1.80

Stock II:

Expected Return = 0.25 * (-0.22) + 0.60 * 0.15 + 0.15 * 0.45
Expected Return = 0.1025 or 10.25%

Expected Return = Risk-free Rate + Beta * Market Risk Premium
10.25% = 4.00% + Beta * 7.00%
6.25% = Beta * 7.00%
Beta = 0.89

Answer b.

Stock I:

Variance = 0.25 * (0.04 - 0.166)^2 + 0.60 * (0.22 - 0.166)^2 + 0.15 * (0.16 - 0.166)^2
Variance = 0.005724

Standard Deviation = (0.005724)^(1/2)
Standard Deviation = 0.0757 or 7.57%

Stock II:

Variance = 0.25 * (-0.22 - 0.1025)^2 + 0.60 * (0.15 - 0.1025)^2 + 0.15 * (0.45 - 0.1025)^2
Variance = 0.045469

Standard Deviation = (0.045469)^(1/2)
Standard Deviation = 0.2132 or 21.32%

Answer c.

Stock I has most systematic risk than Stock II.

Answer d.

Stock II has most systematic risk than Stock I.

Answer e.

Stock I is more riskier.