Question

You are expecting either a recession or steady growth next year. Recession has a 41% probability of happening. In steady growth, stock ABC returns 10.00% and stock XYZ returns 7.00%. In a recession, stock ABC returns -5.40% and stock XYZ returns -3.20%. You are going to put together a portfolio of these two stocks with positive portfolio weight in each and allocate 39% of the portfolio to ABC with the remainder to XYZ. What is the variance of the portfolio?

Question 15 options:

	0.00353
	0.00362
	0.00371
	0.00380
	0.00389

Answer 1

0.00362

Step-1:Calculation of expected return
Expected Return of :
Stock ABC	=	(41%*-5.40%)+(59%*10%)	=	3.69%
Stock XYZ	=	(41%*-3.2%)+(59%*7%)	=	2.82%
Step-2:Calculation of variance
Stock ABC	Chance	Return	Expected Return
	a	b	c	d=((b-c)^2)*a
	41%	-5.40%	3.69%	0.003384771
	59%	10.00%	3.69%	0.002352129
	Variance			0.0057369
Stock XYZ	Chance	Return	Expected Return
	a	b	c	d=((b-c)^2)*a
	41%	-3.20%	2.82%	0.001484869
	59%	7.00%	2.82%	0.001031858
	Variance			0.002516728
Step-3:Calculation of Standard deviation
Standard Deviation of :
Stock ABC	=	Variance^(1/2)	=	0.0057369	^(1/2)	=	7.57%
Stock XYZ	=	Variance^(1/2)	=	0.002516728	^(1/2)	=	5.02%
Step-4:Calculation of covariance
	Chance	Return of Stock A	Expected return of Stock A	Return of Stock B	Expected return of Stock B
	x	a	b	c	d	e=((a-b)*(c-d))*x
	41%	-5.40%	3.69%	-3.20%	2.82%	0.002241861
	59%	10.00%	3.69%	7.00%	2.82%	0.001557904
	Covariance				0.003799765
Step-5:Calculation of correlation coefficient
Correlation Coefficient	=	Covariance between Stock A and Stock B	/	(Standard deviation of Stock A*Standard deviation of Stock B)
	=	0.003799765	/	(7.57%*5.02%)
	=	0.003799765	/	0.003799765
	=	1.0000
Step-6: Calculation of Variance of portfolio
Variance of portfolio	=	(WA)^2*(SDA)^2+(WB)^2*(SDB)^2+2*WA*WB*SDA*SDB*CorrA,B
	=	(39%)^2*(7.57%)^2+(61%)^2*(5.02%)^2+2*39%*61%*7.57%*5.02%*1.00
	=	0.00362
Where,
WA	=	Weight of Stock ABC		=	39%
WB	=	Weight of Stock XYZ		=	61%
SDA	=	Standard deviation of Stock ABC	=	7.57%
SDB	=	Standard deviation of Stock XYZ	=	5.02%
CorrA,B	=	Correlation Coefficient		=	1.0000