An analyst has predicted the following returns for Stock A and Stock B in three

ID: 3439122 • Letter: A

Question

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

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

Calculate the expected return of Stocks A and B. (Round your answers to 2 decimal places.)

Calculate the expected return of a portfolio that is invested 58% in A and 42% in B. (Round your answer to 2 decimal places.)

State Probability A B Boom 0.29 0.24 0.23 Normal 0.41 0.20 0.13 Recession ? 0.15 0.07

The probabilities of boom, normal, and recession must add up to 1. Thus,

0.29 + 0.41 + P(rec) = 1

0.7 + P(rec) = 1

P(rec) = 0.30 [ANSWER]

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As E(x) = Sum [x P(x)]

For stock A,

P(x)   x   x P(x)
0.29   0.24   0.0696
0.41   0.2   0.082
0.3   0.15   0.045

Hence,

E(xA) = 0.1966 = 19.66% [ANSWER]

For stock B,

P(x)   x   x P(x)
0.29   0.23   0.0667
0.41   0.13   0.0533
0.3   0.07   0.021

E(xB) = 0.141 = 14.1% [ANSWER]

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E(xC) = 0.58 E(xA) + 0.42 E(xB) = 0.173248 = 17.3248% [ANSWER]