Question

Consider the following information about Stocks I and II:

				Rate of Return if State Occurs
State of	Probability of
Economy	State of Economy			Stock I			Stock II
Recession		.26			.05		−	.31
Normal		.50			.22			.11
Irrational exuberance		.24			.05			.51

The market risk premium is 5 percent, and the risk-free rate is 3 percent. 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, based on the stock's systematic risk/beta, Stock one is "riskier".

Answer 1

Stock I:

Expected return=E= sum of( probability*returns of state)

=.26*.05+.5*.22+.24*.05 =.135= 13.5%

Variance= sum of ( probability*(E-returns)^2)

=.26*(.135-.05)^2+.5*(.135-.22)^2+.24*(.135-.05)^2

=.007225

Std dev= sqrt(variance)= sqrt(.007225)=.085=8.5%

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

13.5=3+beta*5

beta=10.5/5=2.1

-

Stock II:

Expected return=E= sum of( probability*returns of state)

=.26*.31+.5*.11+.24*.51=.258= 25.8%

Variance= sum of ( probability*(E-returns)^2)

=.26*(.258-.31)^2+.5*(.258-.11)^2+.24*(.258-.51)^2

=.026896

Std dev= sqrt(variance)= sqrt(0.026896)=.164=16.4%

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

25.8=3+beta*5

beta=22.8/5=4.56