Question

You are expecting either a recession or steady growth next year. Recession has a 33% probability of happening. In steady growth, stock ABC returns 11.00% and stock XYZ returns 8.00%. In a recession, stock ABC returns -5.80% and stock XYZ returns -3.60%. You are going to put together a portfolio of these two stocks with positive portfolio weight in each and allocate 47% of the portfolio to ABC with the remainder to XYZ. What is the variance of the portfolio?

Question 7 options:

	0.00403
	0.00414
	0.00425
	0.00436
	0.00447

Answer 1

Stock ABC :

State of Economy	Probability (P)	Return (x)	Px	x - sum of Px	(x - sum of Px)^2	P*(x - sum of Px)^2
Steady Growth	0.67	11	7.37	5.544	30.735936	20.59307712
Recession	0.33	-5.8	-1.914	-11.256	126.697536	41.81018688
Mean	5.456	Variance	62.403264

Stock XYZ :

State of Economy	Probability (P)	Return (y)	Py	y - sum of Py	(y - sum of Py)^2	P*(y - sum of Py)^2
Steady Growth	0.67	8	5.36	3.828	14.653584	9.81790128
Recession	0.33	-3.6	-1.188	-7.772	60.403984	19.93331472
Mean	4.172	Variance	29.751216

State of Economy	Probability (P)	x - sum of Px	y - sum of Py	P*(x - sum of Px * )(y - sum of Py)
Steady Growth	0.67	5.544	3.828	14.21902944
Recession	0.33	-11.256	-7.772	28.86893856
Covariance between ABC & XYZ	43.087968

Variance of the portfolio = weight of ABC^2*Variance of ABC + Weight of XYZ^2*Variance of XYZ + 2 * Weight of ABC * Weight of XYZ * Covariance between ABC and XYZ

= 0.47^2 * 62.40 + 0.53^2* 29.75 + 2 * 0.47*0.53*43.09

= 13.78 + 8.36 + 21.47 = 43.61