Question

XYZ Investment Corporation is considering a portfolio with 70% weighting in a cyclical stock and 30% weighting in a countercyclical stock. It is expected that there will be three economic states; Good, Average and Bad, each with equal probabilities of occurrence. The cyclical stock is expected to have returns of 25%, 5% and 1% in Good, Average and Bad economies respectively. The countercyclical stock is expected to have returns of -8%, 2% and 14% in Good, Average and Bad economies respectively. Given this information, what is the expected return of countercyclical stock?

Answer 1

Solution :

As per the information given in the question, It is expected that there will be three economic states; Good, Average, and Bad, each with equal probabilities of occurrence. Thus the probability of each state shall be = 1 / 3

Calculation of Expected Return of Countercyclical stock
Economic states	Probability	Rate of Return %	Expected Return %
(1)	(2)	(3)	(4) = (2) * (3)
Good	1/3	-8%	-2.6667%
Average	1/3	2%	0.6667%
Bad	1/3	14%	4.6667%
Expected Return of Countercyclical stock = - 2.6667 % + 0.6667 % + 4.6667 % = 2.6667 %	2.6667%

Thus the Expected Return of Countercyclical stock = 2.6667 %

= 2.67 % ( when rounded off to two decimal places )