Consider the following information Rate of Return if State Occurs State of Econo

Question

Consider the following information Rate of Return if State Occurs State of Economy Boom Bust Probability of State of Economy 0.66 0.34 Stock A 0.23 0.13 Stock B 0.25 0.13 Stock C 0.15 0.15 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 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)3

Explanation / Answer

a) We have to find expected return of portfolio if weight of all three stocks are equal

Therefore, Weight of stocks = 1/3 = 0.33

Expected return = wa*ra + wb*rb + wcrc

where w is weight of corresponding stock and r is return of return of corresponding stock

Expected return if state of economy is boom = 1/3*(0.23) + 1/3*(0.25) + 1/3*(0.15) = 0.21 = 21%

Expected return if state of economy is bust = 1/3*(0.13) + 1/3*(0.13) + 1/3*(0.15) = 0.1367 = 13.67%

So the expected return of portfolio = (probability of boom*rate of returm if economy is booming) + (probability of bust*rate of returm if economy is busting) = (0.66*0.21) + (0.34*0.1367) = 0.1851 = 18.51%

b) Now weight of stock A and B = 20% each = 0.2

Weight of stock C = 60% = 0.6

Expected return if state of economy is boom = 0.2*(0.23) + 0.2*(0.25) + 0.6*(0.15) = 0.186 = 18.60%

Expected return if state of economy is bust = 0.2*(0.13) + 0.2*(0.13) + 0.6*(0.15) = 0.1420 = 14.20%

Expected return of portfolio = (probability of boom*rate of returm if economy is booming) + (probability of bust*rate of returm if economy is busting) = (0.66*0.186) + (0.34*0.142) = 0.1710 = 17.10%

Variance of portfolio = probability of boom*(Expected return if state of economy is boom - expected return of portfolio)2 + probability of bust*(Expected return if state of economy is bust - expected return of portfolio)2

Variance of portfolio = 0.66*( 0.186 - 0.170)2 + 0.34*(0.142 - 0.170)2

Variance of portfolio = 0.00043

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