Question

You recently purchased a stock that is expected to earn 20 percent in a booming economy, 10 percent in a normal economy, and lose 30 percent in a recessionary economy. There is a 5 percent probability of a boom and an 80 percent chance of a normal economy. What is the expected rate of return and standard deviation on this stock?

Answer 1

	Probability	Return
Boom	5%	20%
Normal	80%	10%
Recession	(100-5-80)=15%	-30%

Expected Return=Respective return*Respective Probability

=(0.05*20)+(0.8*10)+(0.15*-30)=4.5%

Probability	Return	Probability*(Return-Expected Return)^2
0.05	20	0.05*(20-4.5)^2=12.0125
0.8	10	0.8*(10-4.5)^2=24.2
0.15	-30	0.15*(-30-4.5)^2=178.5375
		Total=214.75%

Standard deviation=[Total Probability*(Return-Expected Return)^2/Total probability]^(1/2)

=14.65%(Approx).