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 11.5 percent, and the risk-free rate is 4.5 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?

Explanation / Answer

Requirement 1:

Answer:(a) The amount of systematic risk is measured by the of an asset. Since we know the market risk premium and the risk-free rate, if we know the expected return of the asset we can use the CAPM to solve for the of the asset. The expected return of Stock I is:

E(RI) = .20(.035) + .60(.345) + .20(.205) = .255 or 25.5%

Using the CAPM to find the of Stock I, we find:

.255 = .045 + .115I

I = 1.83

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 = .20(.035 – .255)2 + .60(.345 – .255)2 + .20(.205 – .255)2

I2 = 0.01504

I= ( 0.01504)1/2 = .1226 or 12.26%

Answer:(b) Using the same procedure for Stock II, we find the expected return to be:

E(RII) = .20(–.35) + .60(.27) + .20(.45) = .182

Using the CAPM to find the of Stock II, we find:

.182 = .045 + .115II

II = 1.19

And the standard deviation of Stock II is:

II2 = .20(–.35 – .182)2 + .60(.27 – .182)2 + .20(.45 – .182)2

II2 = .075616

II = (.075616)1/2 = .27498 or 27.49%

Answer: Requirement 2:

(a) Although Stock II has more total risk than I, it has much less systematic risk, since its beta is much smaller than I’s. Thus, I has more systematic risk.

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