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Homework answers / question archive / Consider the following information: State of the Economy Probability of the State of the Economy Rate of Return if State occurs Stock A Stock B Stock C 0
Consider the following information: State of the Economy Probability of the State of the Economy Rate of Return if State occurs Stock A Stock B Stock C 0.18 0.04 0.31 0.03 0.16 -0.11 Boom 0.60 0.40 Bust (a) What is the expected return on an equally weighted portfolio of these three stocks? (b) What is the variance of a portfolio invested 20 percent each in stock A and B and 60% in C?
Part a)
The expected return on an equally weighted portfolio of three stocks is calculated as below:
Expected Return (Boom) = (Rate of Return of Stock A + Rate of Return of Stock B + Rate of Return of Stock C)/3 = (0.18 + 0.04 + 0.31)/3 = 0.1767
Expected Return (Bust) = (Rate of Return of Stock A + Rate of Return of Stock B + Rate of Return of Stock C)/3 = (0.18 + 0.04 + 0.31)/3 = (0.03 + 0.16 - 0.11)/3 = 0.0267
Expected Return on an Equally Weighted Portfolio of Three Stocks = Probability of Boom*Expected Return (Boom) + Probability of Bust*Expected Return (Bust) = 0.60*0.1767 + 0.40*0.0267 = 11.67% or. 1167
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Part b)
The variance of the portfolio is determined as follows:
Expected Return (Boom) = Rate of Return of Stock A*Investment Percentage in Stock A + Rate of Return of Stock B*Investment Percentage in Stock B + Rate of Return of Stock C*Investment Percentage in Stock C = 20%*0.18 + 20%*0.04 + 60%*0.31 = 0.23
Expected Return (Bust) = Rate of Return of Stock A*Investment Percentage in Stock A + Rate of Return of Stock B*Investment Percentage in Stock B + Rate of Return of Stock C*Investment Percentage in Stock C = 20%*0.03 + 20%*0.16 + 60%*(-0.11) = -0.028
Expected Return (Portfolio) = Probability of Boom*Expected Return (Boom) + Probability of Bust*Expected Return (Bust) = 0.60*0.23 + 0.40*(-0.028) = 0.1268
Variance of Portfolio = Probability of Boom*[Expected Return (Boom) - Expected Return (Portfolio)]^2 + Probability of Bust*[Expected Return (Bust) - Expected Return (Portfolio)]^2 = 0.60*[0.23 - 0.1268]^2 + 0.40*[-0.028 - 0.1268]^2 = 0.01598 or 1.598%
