Suppose that Corporation A and Corporation B are in very different industries. I

Question

Suppose that Corporation A and Corporation B are in very different industries. In fact, the share price of Corporation A's stock is procyclical but the share price of Corporation B's stock is countercyclical. Corporation A's share price has an expected value of $60 per share and a standard deviation of $10 per share. Corporation B's share price has an expected value of $30 and a standard deviation of $5 per share. The covariance between these to stocks' prices is -125. An investor has 100 shares of Corporation A's stock and 200 shares of Corporation B's stock. What is the variance of the total value of this investor's portfolio?

Explanation / Answer

Solution

V(X+Y) = V(X) + V(Y) + 2cov(X,Y)

Variance (100A + 200B) = 10000V(A) + 40000V(B) + 2*100*200*Cov(A,B)

variance = 10000*100 + 40000*25 - 40000*1.25 = 1950000

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