Question

You decide to invest in a portfolio consisting of 24 percent Stock X, 45 percent Stock Y, and the remainder in Stock Z. Based on the following information, what is the standard deviation of your portfolio?

State of Economy	Probability of State			Return if State Occurs
	of Economy
				Stock X			Stock Y			Stock Z
Normal		.78			9.90%			3.30%			12.30%
Boom		.22			17.20%			25.20%			16.70%

Answer 1

deviation “2x probability state of economy rate of return if state occurs Stock X Stock Y Stock Z Normal 9.9% 3.3% 12.3% Boom 17.2% 25.2% 16.7% weighted return (weight x return) StockX Stock y Stock Z 2.376% 1.485% 3.813% 4.128% 11.340% 5.177% weighted sum probability expected return (sum of weighted return) 7.674% 0.78 5.99% 20.645% 4.54% 10.53% deviation (weighted return- deviation^2 expected return) -2.854% 0.081431% 10.117% 1.023614% 0.000635165 0.00225195 Weight 24.00% 45.00% 31.00% Variance Standard deviation = variance10.5 0.00289 5.37% Standard deviation = 5.37%