Question

Stock A pays 40% in a boom, 5% in a normal economy, and -20% in a recession. Stock B pays -10% in a boom, 10% in a normal economy, and 15% in a recession. If all three states of the economy are equally likely next year, what is the one-year expected return on a portfolio that is 70% stock A and 30% stock B? Enter your answer as a percentage point without the % sign, and round it to the second decimal point (i.e., if the answer is 10.3456%, enter it as 10.34).

Answer 1

As all the three states are equally likely in next years means the probability of each state occurring is 1/3.

Stock A

Stock A pays 40% in a boom

5% in a normal economy

and -20% in a recession.

Expected return = Probability of boom period * return expected in boom period + Probability of normal period * return expected in normal period + Probability of recession period * return expected in recession period

Expected return on Stock A = 8.33 % (approx)

Stock B

Expected return = Probability of boom period * return expected in boom period + Probability of normal period * return expected in normal period + Probability of recession period * return expected in recession period

Stock B pays -10% in a boom,

10% in a normal economy,

and 15% in a recession.

Expected return on Stock B = 5 %

Expected return on portfolio = Wa ∗Ra + Wb ∗Rb
Where,
Ra = Return on stock A
Rb = Return on stock B
Wa = Weight of stock A in portfolio
Wb = Weight of stock B in portfolio

Expected return on portfolio = 0.70 * 8.33 + 0.30 *5

= 5.831 + 1.5

= 7.331 %

Expected return on portfolio = 7.33

Hope it helps !