Question

Consider the following information on Stocks I and II:

				Rate of Return if State Occurs
State of	Probability of
Economy	State of Economy			Stock I			Stock II
Recession		.30			.05		−	.30
Normal		.45			.22			.10
Irrational exuberance		.25			.05			.50

The market risk premium is 6 percent, and the risk-free rate is 2 percent. (Do not round intermediate calculations. Enter your standard deviation answers as a percent rounded to 2 decimal places (e.g., 32.16). Round your beta answers to 2 decimal places (e.g., 32.16).)

  

The standard deviation on Stock I's expected return is  percent, and the Stock I beta is  . The standard deviation on Stock II's expected return is  percent, and the Stock II beta is  . Therefore, Stock  (Click to select)  II  I  is "riskier".

Answer 1

Standard Deviation:

Stock I=sqrt(0.30*(0.05-(0.30*0.05+0.45*0.22+0.25*0.05))^2+0.45*(0.22-(0.30*0.05+0.45*0.22+0.25*0.05))^2+0.25*(0.05-(0.30*0.05+0.45*0.22+0.25*0.05))^2)=0.084573932

Stock II=sqrt(0.30*(-0.30-(0.30*(-0.30)+0.45*0.10+0.25*0.50))^2+0.45*(0.10-(0.30*(-0.30)+0.45*0.10+0.25*0.50))^2+0.25*(0.50-(0.30*(-0.30)+0.45*0.10+0.25*0.50))^2)=0.295972972

Beta:
Stock I=((0.30*0.05+0.45*0.22+0.25*0.05)-2%)/6%=1.775

Stock II=((0.30*(-0.30)+0.45*0.10+0.25*0.50)-2%)/6%=1

Stock I is riskier