Question

You decide to invest in a portfolio consisting of 22 percent Stock X, 43 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		.83			9.70%			3.10%			12.10%
Boom		.17			17.00%			25.00%			16.50%

6.88%

1.67%

4.72%

2.23%

5.90%

Answer 1

Weight of Stock Z =1-Weight of Stock X-Stock Y =1-22%-43% =35%
Expected return in Normal =weight of Stock X*return in Normal+Weight of Stock Y*Return in Normal+Weight of Stock Z*Return in Normal =22%*9.70%+43%*3.10%+35%*12.10% =7.7020%
Expected return in Boom =weight of Stock X*return in Boom+Weight of Stock Y*Return in Boom+Weight of Stock Z*Return in Boom =22%*17%+43%*25%+35%*16.50% =20.2650%

Expected return in portfolio =Probability of Normal*Expected return in Normal+Probability of Boom*Expected return in Boom
=0.83*7.7020%+0.17*20.2650% =0.83*7.7020%+0.17*20.2650%=9.8377%

Standard Deviation of Portfolio =(0.83*(7.7020%-9.8377%)^2+0.17*(20.2650%-9.8377%)^2)^0.5 = 4.72%

Option c is correct option