You are trying to develop a strategy for investing in two different stocks. The

Question

You are trying to develop a strategy for investing in two different stocks. The anticipated annual return for a $1,000 investment in each Returns p-stock under four different economic conditions has the probability distribution shown to the right. Complete parts (a) through (c) below. (a) The expected return for stock X and for stock Y. (b) The standard deviation for stock X and for stock Y. (c) The covariance of stock X and stock Y. Describe the relationship between stock X and stock Y. (d) Would you invest in stock X or stock Y? Explain.

Explanation / Answer

Expected Rate of Return Y = Probability * Future expected returns of stock Y

Expected Rate of Return Y = 0.1(-100) + 0.2(50) + 0.4(150) + 0.3(190) =117

b.X^2 =[ E(r)X -E(r)Y]^2 * probability

X^2 = (-70 - 89)^2(0.1) + (20 - 89)^2(0.2) + (110 - 89)^2(0.4)+ (160 - 89)^2(0.3) = 5169

X = 71.895

CVX = X/R X = 71.895/89 = 0.807, while

CVY = 87.41/117 = 0.747

If Stock Y is less highly correlated with the market than X, then it might have a lower beta than Stock X, and hence be less risky in a portfolio sense.

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