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

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%