Question

What is the standard deviation of the returns on a $40,000 portfolio which consists of stocks C and D? Stock C is valued at $22,000.

State of Economy	Probability of State of Economy	Returns if State Occurs
		Stock C	Stock D
Boom	20%	15%	4%
Normal	70%	9%	6%
Recession	10%	-2%	5%

Answer 1

Solution:
	Portfolio's Standard deviation	0.0231	in decimal
		2.31%	in %
Working Notes:
First of all	We calculate weight of each stock in the portfolio
	Weight of Stock C in portfolio
	= Stock C value/ portfolio value
	=22,000/40,000
	=0.55
	Weight of Stock D in portfolio
	= 1-Weight of Stock C in portfolio
	= 1 - 0.55
	=0.45
Then	We calculate Return of portfolio at each state of Economy.
Return at Boom (rb)	Return of portfolio at Boom (rb)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= 15% x 0.55 + 4% x 0.45
	=10.05%
Return at Normal   (r Normal)	Return at Normal   (r Normal) = Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= 9% x 0.55 + 6% x 0.45
	=7.65%
Return at Recession   (r Recession)	Return at Recession   (r Recession)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= -2% x 0.55 + 5% x 0.45
	=1.15%
Expected return of portfolio(Er) = Sum of ((prob of each state) x (Return of portfolio at each state))
	=0.20 x 10.05% + 0.70 x 7.65% + 10% x 1.15%
	=7.48%
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 ]
	=0.20 x (10.05% - 7.48%)^2 + 0.70 x (7.65% - 7.48%)^2 + 0.10 x (1.15% - 7.48%)^2
	=0.00053481000
	The standard deviation of Portfolio = Square root of the variance of portfolio
	The standard deviation of Portfolio = (0.00053481000)^(1/2)
	The standard deviation of Portfolio = 0.023125959
	The standard deviation of Portfolio = 0.0231
	The standard deviation of Portfolio	2.31%
Please feel free to ask if anything about above solution in comment section of the question.