Question

Consider the following information about Stocks I and II:

State of Economy	Probability of  Economy	Rate of Return if State Occurs Stock I	Rate of Return if State Occurs Stock II
Recession	.26	.06	- .21
Normal	.51	.18	.08
Irrational exuberance	.23	.07	.41

The market risk premium is 5 percent, and the risk-free rate is 4 percent. (Do not round intermediate calculations. Enter the standard deviations as a percent and round all answers to 2 decimal places, e.g., 32.16.)

The standard deviation on Stock I's return is (a)_______ percent, and the Stock I beta is (b)_______. The standard deviation on Stock II's return is (c)_______ percent, and the Stock II beta is (d)________ . Therefore, based on the stock's systematic risk/beta, Stock (e)__________ is "riskier".

Answer 1

State of Economy	Probability of Economy(X)	Rate of Return if State Occurs Stock I P(I)	Rate of Return if State Occurs Stock II P(II)
Recession	0.26	0.06	-0.21
Normal	0.51	0.18	0.08
Irrational exuberance	0.23	0.07	0.41
Expected return E(X)=sum of(x*P(X))		12.35%	8.05%
E(X^2)		0.018587	0.053393
Variance=E(X^2)-E(X)^2		0.00333475	0.04691275
Standard deviation=sqrt(Variance)		5.77%	21.66%

Expected return = risk free rate + beta * market risk premium

a) 5.77%

b)

12.35% = 4% + beta * 5%

=>

beta = 1.67

c) 21.66%

d)

8.05% = 4% + beta * 5%

=>

beta = 0.81

e)

Hence Stock I is riskier since it has high beta/systematic risk