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	0.21	0.24	0.30
Normal	0.53	0.21	0.23
Recession	?	0.15	0.19

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

. 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 49% in A and 51% in B. (Round your answer to 2 decimal places.)

Answer 1

Solution:

(a) Total probability is 1.
Hence the probability of recession is given by
1- 0.21- 0.53 = 0.26
The probability of recession is 0.26

(b) The expected return of portfolio A is,
= 0.21(0.24) + 0.53(0.21) + 0.26(0.15)
= 0.0504 + 0.1113 + 0.039
= 0.2007
The expected return of portfolio A is 20.07%
The expected return of portfolio B is,
= 0.21(0.30) + 0.53(0.23) + 0.26(0.19)
= 0.063 + 0.1219 + 0.0494
= 0.2343
The expected return of portfolio B is 23.43%

(c) Expected return is = 0.2007(49%) + 0.2343(51%)
= 9.8343 + 11.9493
= 21.78%
Expected return of portfolio is 21.78%