Question

Use the following information to answer the questions.

State of Economy	Probability of State	Return on Asset d in State	Return on Asset e in State	Return on Asset f in State
Boom	0.32	0.07	0.28	0.16
Normal	0.46	0.07	0.19	0.08
Recession	0.22	0.07	-0.21	-0.07

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

Asset d

Since asset d has same return in all the three state of economy,

Expected return = 7%

variance = Standard deviation = 0

Asset e

State of Economy	Probability (P)	Return	Probability*Return	Deviation form expected return (D)	PD^2
Boom	0.32	0.28	0.0896	0.15	0.00712
Normal	0.46	0.19	0.0874	0.06	0.00161
Recession	0.22	-0.21	(0.0462)	-0.34	0.02555

Expected return = Probability*Return

= .0896+.0874-.0462

= .1308

= 13.08%

Variance = PD^2

= .00712+.00161+.02555

= .03429

Standard Deviation = Variance

= .03429

= 0.18517559234

= 18.52%

*Deviation form expected return = Rate of return -  expected return​

Asset f

State of Economy	Probability (P)	Return	Probability*Return	Deviation form expected return (D)	PD^2
Boom	0.32	0.16	0.0512	0.09	0.00244
Normal	0.46	0.08	0.0368	0.01	0.00003
Recession	0.22	-0.07	(0.0154)	-0.14	0.00447

Expected return = Probability*Return

= .0512+.0368-.0154

= .0726

= 7.26%

Variance = PD^2

= .00244+.00003+.00447

= .00694

Standard Deviation = Variance

= .00694

= 0.08330666239

= 8.33%