Question

Consider the following information:

  

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	0.78	0.15	0.07	0.25
Bust	0.22	0.15	0.09	-0.01

  

Requirement 1:

What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.)

(Click to select)13.91%16.41%25.94%28.71%8.18%

  

Requirement 2:

What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round your intermediate calculations.)

(Click to select)0.0074650.0094650.0119650.0116650.003965

Answer 1

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Answer:

Answer to Part a.

First we have to Calculate, Expected Return of Boom Economy,

Expected Return of Economy:

Expected Return = Sum the returns of each asset / Number of assets

Expected Return of Boom Economy = (0.15 +0.07 + 0.25) / 3 = 15.67%

Expected Return of Bust Economy = (0.15 +0.09 - 0.01) / 3 = 7.67%

Expected Return of Portfolio:

Expected Return of Portfolio = (0.78 * 15.67) + (0.22 * 7.67)

Expected Return of Portfolio =13.91%

Answer to Part b.

This portfolio does not have an equal weight in each asset. We need to find the return of the portfolio in each state of the economy.

For that, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:


Boom: RP = 0.20(0.15) +0.20(0.07) + 0.60(0.25) =19.4%
Bust: RP = 0.20(0.15) +0.20(0.09) + 0.60(−0.01) =4.2%


And the expected return of the portfolio is:


E(RP) = 0.78(0.194) + 0.22(0.042) = 16.056%

Variance of the portfolio is:

σp2 = 0.78(0.194 − 0.16056)^2 + 0.22(0.042 − 0.16056)^2 = 0.003965