Question

Calculate the standard deviation of the returns on Andrew’s Violins stock if projections include the following?

State of Economy	Probability of State Economy	Rate of Return if State Occurs
Boom	30%	15%
Normal	65%	12%
Recession	5%	6%

Answer 1

Expected return=Respective return*Respective probability

=(0.3*15)+(0.65*12)+(0.05*6)=12.6%

probability	Return	probability*(Return-Expected Return)^2
0.3	15	0.3*(15-12.6)^2=1.728
0.65	12	0.65*(12-12.6)^2=0.234
0.05	6	0.05*(6-12.6)^2=2.178
		Total=4.14%

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

=(4.14)^(1/2)

=2.03%(Approx).