Question

An analyst has predicted the following returns for Stock A and Stock B in three possible states of the economy.

State	Probability	A	B
Boom	0.20	0.24	0.24
Normal	0.44	0.18	0.17
Recession	?	0.12	0.14

a. What is the probability of a recession? (Round your answer to 2 decimal places.)

b. Calculate the expected return for Stock A and Stock B. (Round your answers to 2 decimal places.)

c. Calculate the expected return for a portfolio that is invested 43% in A and 57% in B. (Round your answer to 2 decimal places.)

Answer 1

a) P(recession) = 1 - P(boom) - P(normal)

= 1 - 0.20 - 0.44

= 0.36

b) Expected return for Stock A = Sum of (return x corresponding probability)

= 0.24x0.20 + 0.18x0.44 + 0.12x0.36

= 0.17

Expected return for Stock B = 0.24x.0.20 + 0.17x0.44 + 0.14x0.36

= 0.17

c) Expected return from the portfolio = Percentage of investment in Stock A x Expected return from stock A + Percentage of investment in Stock B x Expected return from stock B

= 0.43x0.17 + 0.57x0.17

= 0.17