Question

Answer the following question based on the information below:

State of Economy	Probability	Stock A’s return	Stock B’s return
Boom	.4	15%	- 30%
Recession	.6	5%	40%

Which of the following statements is true?

a) Stock A has higher expected return than stock B.

b) The actual return of stock A will always be greater than that of stock B.

c) Stock A has higher total risk than stock B.

d) Stocks A and B are positively correlated.

Answer 1

True statements are as follows:

• Stock B has higher expected return than stock A.
• The actual return of stock A will always be greater than that of stock B.
• Stock B has higher total risk than stock A.
• Stocks A and B are negatively correlated.

Working Note

1) Stock A

State of Economy	Probability (P)	Return(%)	Probability*Return	Deviation form expected return (D1)	PD1^2
Boom	0.4	15	6.00	6.00	14.40
Recession	0.6	5	3.00	-4.00	9.60

Expected return = Probability*Return

= 6+3

= 9%

Variance = PD^2

= 14.4+9.6

= 24

Standard Deviation = Variance

= 24

= 4.90%

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

2) Stock B

State of Economy	Probability (P)	Return(%)	Probability*Return	Deviation form expected return (D2)	PD2^2
Boom	0.4	-30	-12.00	-42.00	705.60
Recession	0.6	40	24.00	28.00	470.40

Expected return = Probability*Return

= -12+24

= 12%

Variance = PD^2

= 705.6+470.4

= 1176

Standard Deviation = Variance

= 1176

= 34.29%

Probability (P)	Deviation (D1)	Deviation (D2)	PD1D2
0.4	6.00	-42.00	-100.80
0.6	-4.00	28.00	-67.20

Covariance = PD1D2

= -100.80-67.20

= -168

Correlation = Covariance/SDA*SDB

= -168/(4.9*34.29)

= -0.99