Question

Calculate the expected return and standard deviation for the following single stock:

State of economy	Probability of state of economy	Return if state of economy occurs
Recession	.15	.02
Normal	.25	.08
Boom	.60	.12

The expected return and standard deviation, respectively, are:

9.8%, 2.95%

7.33%, 4.18%

9.50%, 3.57%

9.50%, 4.18%

7.33%, .1275%

Answer 1

Expected return=Respective return*Respective probability

=(0.15*2)+(0.25*8)+(0.6*12)

=9.5%

Probability	Return	Probability*(Return-Expected return)^2
0.15	2	0.15*(2-9.5)^2=8.4375
0.25	8	0.25*(8-9.5)^2=0.5625
0.6	12	0.6*(12-9.5)^2=3.75
		Total=12.75%

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

=(12.75)^(1/2)

=3.57%(Approx)

Hence the correct option is:

9.5%;3.57%