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HW1_sol - Purdue University Krannert School of Management...

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Purdue University Krannert School of Management MGMT 411: INVESTMENS Assignment #1 Solution 1. Consider the following situation in which you have 3 states (s1, s2, s3) and 3 securities (R 1 , R 2 , R 3 ): The probability of each state is given in the table. a) What is the expected return of each security? E(R 1 ) = 0.15*35% + 0.03*45% + 0.01*20% = 0.0680 E(R 2 ) = 0.09*35% + 0.12*45% + 0.14*20% = 0.1135 E(R 3 ) = 0.12*35% + 0.08*45% + 0.10*20% = 0.0980 b) What is the standard deviation of the return of each security? σ 1 2 = (0.15 - 0.0680) 2 *35% + (0.03 - 0.0680) 2 *45% + (0.01 - 0.0680) 2 *20% = 0.003676 σ 2 2 = (0.09 - 0.1135) 2 *35% + (0.12 - 0.1135) 2 *45% + (0.14 - 0.1135) 2 *20% = 0.000353 σ 3 2 = (0.12 - 0.0980) 2 *35% + (0.08 - 0.0980) 2 *45% + (0.10 - 0. 0980) 2 *20% = 0.001452 c) What is the covariance between the returns of R 1 and R 2 ? R 2 and R 3 ? R 1 and R 3 ? σ 12 = (0.15 - 0.0680)(0.09 - 0.1135)*35% + (0.03 - 0.0680)(0.12 - 0.1135)*45% + (0.01 - 0.0680)(0.14 - 0.1135)*20% = -0.001093 Similarly for the others… 2. Download the monthly historical prices of IBM from finance.yahoo for the period January 1, 2007 to December 31, 2010. a) Compute monthly realized returns for IBM for each month. Date Adj Close Retu rn 12/1/201 0 144.9 11/1/201 0 139.67 0.037 10/1/201 0 141.15 - 0.010 9/1/2010
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