Question

You decide to invest in a portfolio consisting of 33 percent Stock A, 44 percent Stock B, and the remainder in Stock C. Based on the following information, what is the variance of your portfolio? State of Economy Probability of State Return if State Occurs of Economy Stock A Stock B Stock C Recession .111 − 9.80% − 3.20% − 12.20% Normal .659 9.10% 10.60% 16.60% Boom .230 21.49% 24.99% 29.69% rev: 04_25_2019_QC_CS-167128 .00803 .01084 .00747 .00843 .00907

Answer 1

Solution:
	Answer is 1st option 0.00803
Working Notes:
	Portfolio consisting of 33% Stock A , 44% Stock B and remainder in stock C
	Total investment is 100% remainder in Stock C = 100% - Investment in Stock A - In Stock B
	% investment in stock C = 100% -33% - 44%
	% investment in stock C = 23%
	First of all we calculate Return of portfolio at each state of Economy.
Return at Recession   (r Recession)	Return at Recession   (r Recession)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= (33% x (-9.80%)) + (44% x (-3.20%)) + (23% x (-12.20%))
	= -0.07448
	-7.4480%
Return at Normal (rN)	Return of portfolio at Normal (rN)= Weighted average return of individual asset
	=Sum of ( return x weight of % invested)
	= (33% x (9.10%)) + (44% x (10.60%)) + (23% x (16.60%))
	= 0.114850
	11.4850%
Return at Boom (rb)	Return of portfolio at Boom (rb)= Weighted average return of individual asset
	= (33% x (21.49%)) + (44% x (24.99%)) + (23% x (29.69%))
	= 0.249160
	24.9160%
Expected return of portfolio(Er) = Sum of ((prob of each state) x (Return of portfolio at each state))
	=0.111 x (-7.4480%) + .659 x 11.4850% + .230 x 24.9160%
	=0.12472567
	12.4725670%
	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 ]
	=0.111 x (-7.4480% - 0.12472567)^2 + .659 x (11.4850% - 0.12472567)^2 + .230 x ( 24.9160% - 0.12472567)^2
	=0.008030371
	0.00803
Please feel free to ask if anything about above solution in comment section of the question.