What is the standard deviation of the returns on a portfolio that is invested in stocks...

What is the standard deviation of the returns on a portfolio that is invested in stocks A, B, and C? 20 percent of the portfolio is invested in stock A and 45 percent is invested in stock C.

State of Economy

Boom Normal Bust

Probability of Returns if State Occurs

State of Economy Stock A Stock B Stock C 20% 9% 3% 11% 55%4%5%8% 25% -2% 10% -13%

Solutions

Expert Solution

Portion invested in B=	100%-(20%+45%)
Portion invested in B=	35.00%


State of economy	Probability	A	B	C
Boom	20.00%	9.00%	3.00%	11.00%
Normal	55.00%	4.00%	5.00%	8.00%
Bust	25.00%	-2.00%	10.00%	-13.00%



Computation of expected return (A-20%, B-35%, C-45%)
		20%	35%	45%		Average return= Probability * return	Deviation= Return less average return	Deviation^2	Deviation^2*Probability
State of economy	Probability	A	B	C	Portfolio	Portfolio	Portfolio	Portfolio	Stock A
		Return*weight
Boom	20.00%	1.800%	1.05%	4.95%	7.800%	1.56%	3.55%	0.126%	0.0251%
Normal	55.00%	0.800%	1.75%	3.60%	6.150%	3.38%	1.90%	0.036%	0.0198%
Bust	25.00%	-0.400%	3.50%	-5.85%	-2.750%	-0.69%	-7.01%	0.491%	0.1227%
					Total	4.26%			0.1676%
Expected return-Portfolio	4.26%

Variance-Portfolio	0.17%

Standard deviation-Portfolio	4.1%	Variance ^0.5

jeff jeffy answered 1 year ago

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