Question

There are three possible states of nature--boom, normality, and bust--with probabilities .2, .6, and .2. In these three states, Stock A has expected future returns of -16.8, 6.6, and 19.8 percent. Stock B has expected future returns of -16.5, 9.9, and 16.7 percent. What is the expected return on a portfolio invested half in Stock A and half in Stock B in percent?

Answer 1

Expected Return = Respective Weight * Respective Returns

= 0.5 * 4.56% + 0.5 * 5.98%

= 5.27%

Hence the correct answer is 5.27%

Note :

	Probability	Stock   A Return	Expected Return ( Probability * Expected Return)
Boom	0.20	(16.80)	-3.36
Normality	0.60	6.60	3.96
Bust	0.20	19.80	3.96
	Expected Return		4.5600
	Expected Return   %		4.56

	Probability	Stock B	Expected Return   ( Probability * Expected Return
Boom	0.20	-16.50	-3.3000
Normality	0.60	9.90	5.9400
Bust	0.20	16.7	3.3400
		Expected Return	5.98
		Expected Return  %	5.98