Question

Consider the following information:

  

				Rate of Return if State Occurs
State of	Probability of
Economy	State of Economy			Stock A			Stock B			Stock C
Boom		.20			.32			.42			.22
Good		.50			.17			.13			.11
Poor		.25		–	.04		–	.07		–	.05
Bust		.05		–	.12		–	.17		–	.09

  

a.	Your portfolio is invested 28 percent each in A and C, and 44 percent in B. What is the expected return of the portfolio? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Expected return

%

  

b-1.	What is the variance of this portfolio? (Do not round intermediate calculations and round your answer to 5 decimal places, e.g., 32.16161.)

Variance

b-2.	What is the standard deviation? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation

%

Answer 1

State of	Probability of
Economy	State of Economy		Stock A		Stock B			stock C
Boom		0.2		0.32		0.42		0.22
good		0.5		0.17		0.13		0.11
poor		0.25		-0.04		-0.07		-0.05
bust		0.05		-0.12		-0.17		-0.09
		weight		0.28		0.44		0.28
		return		0.133		0.123		0.082
		weight * return		0.03724		0.05412		0.02296
		Expected return of portfolio E(X)	11.43%
		weight * return^2		0.00495292		0.00665676		0.00188272
		E(X^2)	0.0134924
		variance of portfolio	0.00042
		standard deviation of portfolio	2.06%