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PS2Solutions_09

# PS2Solutions_09 - Solutions to Problem Set 2 Investments...

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Solutions to Problem Set 2 Investments Prof. Pierre-Olivier Weill Consider the following probability distribution for stock ABC and XYZ: Scenario Probability Return of ABC Return of XYZ 1 0.3 0.07 -0.09 2 0.5 0.11 0.14 3 0.2 -0.16 0.26 1. Calculate the expected return of stocks ABC and XYZ: the expected return of ABC is E ( R ABC ) = 0 . 3(0 . 07) + 0 . 5(0 . 11) + 0 . 2( - 0 . 16) = 0 . 044 . Similarly, the expected return of XYZ is E ( R XY Z ) = 0 . 3( - 0 . 09) + 0 . 5(0 . 14) + 0 . 2(0 . 26) = 0 . 095 . 2. Calculate the variance and standard deviation of stocks ABC and XYZ. The variance of ABC is σ 2 ABC = 0 . 3(0 . 07 - 0 . 044) 2 + 0 . 5(0 . 11 - 0 . 044) 2 + 0 . 2 * ( - 0 . 16 - 0 . 044) 2 = 0 . 010704 , and the standard deviation is σ ABC = 0 . 010704 = 0 . 10346 . The variance of XYZ is σ 2 XY Z = 0 . 3( - 0 . 09 - 0 . 095) 2 + 0 . 5(0 . 14 - 0 . 095) 2 + 0 . 2(0 . 26 - 0 . 095) 2 = 0 . 016725 , and the standard deviation is σ XY Z = 0 . 016725 = 0 . 129325 . 3. Calculate the covariance and correlation of stocks ABC and XYZ: cov( R ABC , R XY Z ) = 0 . 3(0 . 07 - 0 . 044)( - 0 . 09 - 0 . 095) +0 . 5(0 . 11 - 0 . 044)(0 . 14 - 0 . 095) +0 . 2( - 0 . 16 - 0 . 044)(0 . 26 - 0 . 095) = - 0 . 00669 .

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Thus, the correlation is cov( R ABC , R XY Z ) σ ABC σ XY Z = - 0 . 00669 (0 . 10346)(0 . 129325) = - 0 . 5 .
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