Question

You are expecting either a recession or steady growth next year. Recession has a 29% probability of happening. In steady growth, stock ABC returns 11.50% and stock XYZ returns 8.50%. In a recession, stock ABC returns -6.00% and stock XYZ returns -3.80%. You are going to put together a portfolio of these two stocks with positive portfolio weight in each and allocate 51% of the portfolio to ABC with the remainder to XYZ. What is the variance of the portfolio?

Question 1 options:

	0.00449
	0.00460
	0.00472
	0.00483
	0.0049

Answer 1

State of economy	Probability	ABC	XYZ
Recession	29.00%	-6.00%	-3.80%
Steady	71.00%	11.50%	8.50%
Computation of expected return (ABC-51%, XYZ-49%)
		51%	49%		Average return= Probability * return	Deviation= Return less average return	Deviation^2	Deviation^2*Probability
State of economy	Probability	ABC	XYZ	Portfolio	Portfolio	Portfolio	Portfolio	Stock A
		Return*weight
Recession	29.00%	-3.060%	-1.86%	-4.922%	-1.43%	-10.62%	1.127%	0.3268%
Steady	71.00%	5.865%	4.17%	10.030%	7.12%	4.34%	0.188%	0.1335%
				Total	5.69%			0.4603%
Expected return-Portfolio	5.69%
Variance-Portfolio	0.00460