Question

Consider the following information on Stocks I and II:

State of	Probability of			Rate of Return if State Occurs
Economy	State of Economy			Stock I				Stock II
Recession		.20				.010		−	.30
Normal		.55				.320			.22
Irrational exuberance		.25				.180			.40

The market risk premium is 11 percent, and the risk-free rate is 4 percent.

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.)

	Stock I
Beta
Standard deviation			%

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.)

	Stock II
Beta
Standard deviation			%

Answer 1

1.
Beta=(0.20*0.010+0.55*0.320+0.25*0.180-4%)/11%=1.663636364

Standard Deviation=sqrt(0.20*(0.010-(0.20*0.010+0.55*0.320+0.25*0.180))^2+0.55*(0.320-(0.20*0.010+0.55*0.320+0.25*0.180))^2+0.25*(0.180-(0.20*0.010+0.55*0.320+0.25*0.180))^2)=0.121288911

2.
Beta=(0.20*(-0.30)+0.55*0.22+0.25*0.40-4%)/11%=1.1

Standard Deviation=sqrt(0.20*(-0.30-(0.20*(-0.30)+0.55*0.22+0.25*0.40))^2+0.55*(0.22-(0.20*(-0.30)+0.55*0.22+0.25*0.40))^2+0.25*(0.40-(0.20*(-0.30)+0.55*0.22+0.25*0.40))^2)=0.242278765