Question

You decide to invest in a portfolio consisting of 15 percent Stock X, 51 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		.77			10.50%			3.90%			12.90%
Boom		.23			17.80%			25.80%			17.30%

2.51%

8.44%

7.24%

3.35%

5.79%

Answer 1

Solution:
	Answer is the 5th option 5.79%
Working Notes:
	First of all we calculate Return of portfolio at each state of Economy.
	Weight of stock in the portfolio are 15% in Stock X , 51% in stock Y and remainder (100-15-51 = 34%) in stock Z
Then	We will calculate expected return of the portfolio and variance and at last standard deviation of the portfolio the required.
Return at Normal (rn)	Return of portfolio at Normal (rn)= Weighted average return of individual stock
	=Sum of ( return x weight of % invested)
	= (10.50% x 15%) + (3.90% x 51%) + (12.90% x 34%)
	=0.07950
	=7.95%
Return at Boom (rb)	Return of portfolio at Boom (rb)= Weighted average return of individual stock
	=Sum of ( return x weight of % invested)
	= (17.80% x 15%) + (25.80% x 51%) + (17.30% x 34%)
	=0.21710
	=21.71%
Expected return of portfolio(Er) = Sum of ((prob of each state) x (Return of portfolio at each state))
	=0.77 x (7.95%) + 0.23 x (21.71%)
	=0.11114800
	=11.11480%
The variance of this portfolio = Sum of [(Prob. Of each state) x ( (Return of the portfolio at each state) - (Expected return of the portfolio))^2 ]
	=0.77 x (7.95% - 11.11480%)^2 + 0.23 x (21.71% - 11.11480%)^2
	=0.00335316890
	0.00335316890
	The standard deviation of Portfolio = Square root of the variance of Portfolio
		=(0.00335316890)^(1/2)
		=0.057906553
		0.0579
		=5.79%
Hence	The standard deviation of the portfolio is 5.79% , so answer is the 5th option
	Please feel free to ask if anything about above solution in comment section of the question.