Question

2. Carry all calculations to 4 digits (4 digit accuracy)

State	Probability	Return: Stock A	Return: Stock B
Bear	.25	-.02	.05
Normal	.50	.14	.16
Bull	.25	.28	.10

1. Calculate the expected return for each stock

2. Calculate the variance of return for each stock

3. Calculate the covariance of return between Stock A and Stock B.

4. If you combine the stocks into a portfolio, will you obtain diversification benefits? Why, or why not (be sure to provide quantitative justification for your answer)?

5. What is the variance of return for a portfolio that invests 50% of wealth in Stock 1 and 50% in Stock 2.

Answer 1

	(a)	(b)	('c)	(a*b)	(a*c)
State	Probability (p)	Return: Stock A (rA)	Return: Stock B (rB)	Weighted return stock A	Weighted return Stock B	rA-E(rA)	rB-E(rB)	p*(rA-E(rA))(rB-E(rB))
Bear	0.25	-0.02	0.05	-0.0050	0.0125	-0.1550	-0.0675	0.0026
Normal	0.50	0.14	0.16	0.0700	0.0800	0.0050	0.0425	0.0001
Bull	0.25	0.28	0.10	0.0700	0.0250	0.1450	-0.0175	-0.0006
Total				0.1350	0.1175	-0.0050	-0.0425
							Covariance	0.0021

State	Probability (p)	rA-E(rA)	rB-E(rB)	p*(rA-E(rA))^2	p*(rB-E(rB))^2
Bear	0.25	-0.1550	-0.0675	0.0060	0.0011
Normal	0.50	0.0050	0.0425	0.0000	0.0009
Bull	0.25	0.1450	-0.0175	0.0053	0.0001
Total			Variance	0.0113	0.0021

Calculated values are:

	Stock A	Stock B
Expected return	0.1350	0.1175
Variance	0.0113	0.0021
Covariance	0.0021

On the face of it, it not appear that combining stock A and B into a portfolio will bring diversification benefits because the correlation between the two is (Covariance_A,B)/(variance_A^0.5*variance_B^0.5) = 0.0021/(0.0113^0.5*.0021^0.5) = 0.427. Both have a positive correlation with each other.

Porfolio	Stock A	Stock B
Weight	50%	50%
E('r)	0.1350	0.1175
Variance	0.0113	0.0021
Portfolio return	12.63%
Portfolio variance	0.0044