Question

Consider the following information:

State Probability Stock A Stock B Stock C

Boom 0.65 0.01 0.16 0.22

Bust 0.35 0.20 -0.06 0.10

What is the expected return on an equally weighted portfolio of these three stocks? (Hint: Equally means that each stock has the same weight. Given that there are only 3 stocks, each has a weight of 1/3) Enter the answer with 4 decimals (e.g. 0.1234).

Answer 1

weighted return when the state of the economy is boom:

stock	return	weight	weight * return
A	0.01	1/3	0.00333333
B	0.16	1/3	0.05333333
C	0.22	1/3	0.07333333
		Total weigheted return under boom	0.1299999

weighted return when economy is bust:

stock	return	weight	weight*return
A	0.20	1/3	0.0666666
B	-0.06	1/3	-0.02
C	0.10	1/3	0.033333
		total weighted return under bust	0.0799999

expected return on portfolio

=>[(probability of boom) * (weighted average return on boom)] + [(probability of bust)*(weighted average return on bust)]

=>[0.65 * 0.1299999] + [0.35*0.0799999]

=>0.11249999998

=>0.1125.....(rounded to four decimals)

expected return on an equally weighted portfolio of these three stocks =>0.1125.