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	.27	.030	−.22
Normal	.62	.330	.14
Irrational exuberance	.11	.190	.42

The market risk premium is 11.2 percent, and the risk-free rate is 4.2 percent.
a.	Calculate the beta and standard deviation of Stock I. (Do not round intermediate calculations. Enter the standard deviation as a percent and round both answers to 2 decimal places, e.g., 32.16.)
b.	Calculate the beta and standard deviation of Stock II. (Do not round intermediate calculations. Enter the standard deviation as a percent and round both answers 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

a)

Standard deviation of stock 1 = 15.01%

Expected return on stock 1 = 23.36%

Risk free rate = 4.2%

Market risk premium = 11.2%

23.36% = 4.2% + Beta * 11.2%

Beta = 1.71

b)

Standard deviation of stock 2 = 32.08%

Expected return = 7.36%

7.36% = 4.2% + beta* 11.2%

Beta = 0.28

c)

Beta is the measure of systematic risk, as Stock 1 has higher beta, Stock 1 has higher systematic risk.

d)

Standard deviation is the measure of unsystematic risk. Stock 2 has the highest unsystematic risk.

e)

Unsystematic risk can be mitigated through diversification however the systematic risk cannot be. Thus stock 1 is the riskier of the two.

Calculations