Question

You decide to invest in a portfolio consisting of 19 percent Stock X, 47 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		.80			11.10%			4.50%			13.50%
Boom		.20			18.40%			26.40%			17.90%

A. 5.27%

B. 6.59%

C. 7.69%

D. 2.78%

E. 2.08%

Answer 1

The Portfolio does not have equal weight in the each stock asset. We will calculate the return of the portfolio in each stock asset

Normal: E(RP) = 0.19(0.111)+0.47(0.045)+0.34(0.135) = 0.08814 = 8.814%

Boom: E(RP) = 0.19*0.184 + 0.47*0.264 + 0.34*0.179 = 0.2199 = 21.99% = 22% (approx)

Expected Return of the portfoli = (0.80*0.08814) + (0.20*0.2199) = 0.1144 = 11.45% (approx)

Scenario	Probability	Deviation from Expected Value %	Squared %	Probability * Squared %
Normal	0.8	(8.814%-11.45%) = -2.636	6.95	5.56
Boom	0.2	21.99%-11.45%) = 10.54	111.09	22.22
Total (Variance)				27.78
Standard Deviation = Square root of Variance				5.27

Standard Deviation = 5.27 %