Question

Consider the following information:

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	0.70	0.29	0.21	0.27
Bust	0.30	0.09	0.13	0.07

Requirement 1: What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.)

Requirement 2: What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round your intermediate calculations.)

Answer 1

Requirement 1:

State of economy	Probability	A	PA	B	PB	C	PC
Boom	0.70	0.29	0.203	0.21	0.147	0.27	0.189
Bust	0.30	0.09	0.027	0.13	0.039	0.07	0.021
Total			0.23		0.186		0.21
Weights			0.3333		0.3333		0.3333
E(r)			0.077		0.062		0.069

Total return on portfolio is 20.8%

Requirement 2:

1) Calculation of variance of stock A:

State of economy	P	A	PA	D= A-E(r)	D2	PD2
Boom	0.7	0.29	0.203	0.06	0.0036	0.00252
Bust	0.3	0.09	0.027	-0.14	0.0196	0.042
E(r)			0.23
Var.						0.04452
Weighted Var.(20%)						0.008904

Calculate for B and C in similar fashion, then add up all the weighted variances to arrive at portfolio variance