Question

State of Economy	Probability of State	Return on Asset A in State	Return on Asset B in State	Return on Asset C in State
Boom	0.35	0.04	0.21	0.3
Normal	0.5	0.04	0.08	0.2
Recession	0.15	0.04	-0.01	-0.26

a.  What is the expected return of each​ asset?

b.  What is the variance of each​ asset?

c.  What is the standard deviation of each​ asset?

Answer 1

Expected Returns:

Asset A:
=0.35*0.04+0.5*0.04+0.15*0.04=0.04

Asset B:
=0.35*0.21+0.5*0.08+0.15*(-0.01)=0.112

Asset C:
=0.35*0.3+0.5*0.2+0.15*(-0.26)=0.166

Variance:

Asset A:
=0.35*(0.04-0.04)^2+0.5*(0.04-0.04)^2+0.15*(0.04-0.04)^2=0

Asset B:
=0.35*(0.21-0.112)^2+0.5*(0.08-0.112)^2+0.15*(-0.01-0.112)^2=0.006106

Asset C:
=0.35*(0.3-0.166)^2+0.5*(0.2-0.166)^2+0.15*(-0.26-0.166)^2=0.034084

Standard Deviation:

Asset A:
=SQRT(0)=0

Asset B:
=SQRT(0.006106)=0.0781408983823452

Asset C:
=SQRT(0.034084)=0.184618525614306