Question

State of Economy		Prob. of State of Economy		Rate of Return if State occurs
				Stock A	Stock B	Stock C
Boom		0.75		0.07	0.15	0.33
Bust		0.25		0.13	0.03	–0.06

- Portfolio expected return:

State	pi	RP,i	pi X RP,i
1	0.75
2	0.25

b. Variance of a portfolio invested 20% each in A and B and 60% in C

- Portfolio expected return for each state:

- Portfolio expected return and variance:

State	pi	RP,i	pi X RP,i	RP,i–E(RP)	[RP,i–E(RP)]2	pi X [RP,i–E(RP)]2
1
2

Answer 1

Return In each situation:
Boom	0.07*0.20+0.15*0.2+0.33*0.6 =			24.2
Bust	0.13*0.2+0.03*0.2 -0.06*0.6 =			-0.4
Economy	Probability	Return
	(P)	( R)	(P) *(R )
Boom	0.75	24.2	18.15
Bust	0.25	-0.4	-0.1
Expected return			18.05	%
Standard deviation
Economy	Probability	Return	Deviation	Squared	Sq. Deviation*(P)
	(P)	( R)	E - (R )	Deviation
Boom	0.75	24.2	-6.15	37.8225	28.36688
Bust	0.25	-0.4	18.45	340.4025	85.10063
			Variance		113.4675
Std deviation = (Variance ) ^ 2
		(113.4675)^2 = 10.65%