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	0.23	0.22	0.22
Normal	0.40	0.19	0.16
Recession	?	0.17	0.10

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 56% in A and 44% in B. (Round your answer to 2 decimal places.)

Answer 1

Here sum of all probability shall be equal to 1 so,

Here probability of recession = 1 - (0.23 + 0.40) = 0.37

(b) Expected return of Stock A = = Pr(Boom) * Return of A in boom condition + Pr(Normal) * return of A in Normal condition + Pr(Recession) * Return of A in Recession condition = 0.23 * 0.22 + 0.40 * 0.19 + 0.37 * 0.17 = 0.1895 or 18.95%

Expected return of Stock B = = Pr(Boom) * Return of B in boom condition + Pr(Normal) * return of B in Normal condition + Pr(Recession) * Return of B in Recession condition = 0.23 * 0.22 + 0.40 * 0.16 + 0.37 * 0.10 = 0.1516 or 15.16%

(c) Here Invested 56% in A and 44% in B

Expected return = 0.56 * expected return of A + 0.44 * expected return of B

= 0.56 * 0.1895 + 0.44 * 0.1516 = 0.1728 or 17.28%