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Mid2Problems1A

# Mid2Problems1A - Midterm Exam 2 Practice Problems Answer...

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Midterm Exam 2 Practice Problems - Answer Key 1. Consider the following fictional joint probability distribution for returns on stocks and bonds. Stock returns are entered in the left most column and bond returns in the top most row. Stocks/Bonds - 10% 0% 10% - 10% 1 6 1 12 1 6 0% 1 12 0 1 12 10% 1 6 1 12 1 6 (a) What is the probability that stock returns are 10%? What is the probability that stock returns are 0%? What is the probability that stock returns are - 10%? Let S denote the returns to stocks and B the return to bonds. To find P ( S = 10) note that: P ( S = 10) = P ( S = 10 , B = - 10) + P ( S = 10 , B = 0) + P ( S = 10 , B = 10) = 1 6 + 1 12 + 1 6 = 5 12 Similarly we obtain P ( S = 0) = 1 6 and P ( S = 10) = 5 12 . (b) What is the mean of stock returns? Since S is a discrete random variables, we obtain the formula for the mean and obtain E [ S ] = - 10 × 5 12 + 0 × 1 6 + 10 × 5 12 = 0 (c) Are stock returns and bond returns independent? Justify your answer. They are not. Note that P ( S = 0) = 1 / 6 and P ( B = 0) = 1 / 6, but P ( S = 0 , B, = 0) = 0. Hence P ( S = 0 , B = 0) 6 = P ( S = 0) P ( B = 0) which is required for independence. (d) What is the covariance between stock and bond returns? It’s easier to use the formula for covariance σ SB = E [ SB ] - E [ S ] E [ B ]. Through calculations we obtain E [ SB ] = 0. Hence since from (b) E [ S ] = 0 and probabilities are the same for bonds we also have E [ B ] = 0. It follows that σ SB = 0.

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