Question

State of the Economy		Probability of State of Economy		Rate of Return if State Occurs
Stock A			Stock B
Normal	0.82		0.12		0.14
Recession	0.18		-0.07		-0.10

You have a portfolio which is comprised of 45 percent of stock A and 55 percent of stock B.

a) What is the expected return for stock A? Please interpret your answer.

b) What is the standard deviation for stock A? Please interpret your answer.

c) What is the expected return for Sock B? Please interpret your answer.

d) What is the standard deviation for stock B? Please interpret your answer.

e) What is the expected return for this portfolio (i.e., Stock A and Stock B)? Please interpret your answer.

f) What is the standard deviation for this portfolio (i.e., Stock A and Stock B)? Please interpret your answer.

Answer 1

a)

The expected return is the sum of multiplying potential outcomes (i.e. return) by the chances of each outcome occurring.

Information given for Stock A is

State of Economy	Rate of return(%)	Probability
Normal	12	.82
Recession	-7	.18

Expected return of Stock A is

= (12*.82) + (-7*.18)

= 8.58%

Expected return is less than return of normal period but is more than return of recession period.

b)

Standard Deviation =

Σ Proυ και 2

State of economy	rate of return (1)	Expected return (2)	Deviation [d = (1) - (2)]	$d^{2}$
Normal	12	8.58	3.42	11.69
Recession	-7	8.58	-15.58	242.74

S.D. = .82 * 11.69) + (.18 * 242.74)

S.D. of Stock A = 7.30%

Stock A has a risk of 7.30%. Actual returns may vary 7.30% than expected return.

c)

The expected return is the sum of multiplying potential outcomes (i.e. return) by the chances of each outcome occurring.

Information given for Stock B is

State of Economy	Rate of return(%)	Probability
Normal	14	.82
Recession	-10	.18

Expected return of Stock A is

= (14*.82) + (-10*.18)

= 9.68%

Expected return is less than return of normal period but is more than return of recession period.

b)

Standard Deviation =

Σ Proυ και 2

State of economy	rate of return (1)	Expected return (2)	Deviation [d = (1) - (2)]	$d^{2}$
Normal	14	9.68	4.32	18.66
Recession	-10	9.68	-19.68	387.30

S.D. = 1.82 * 18.66) + (.18 * 387.30)

S.D. of Stock A = 9.22%

Stock A has a risk of 9.22%. Actual returns may vary 9.22% than expected return.

Please ask point (e) & (f) as separate question.