12_Correlation from PDF_sol

12_Correlation from PDF_sol - Corr(r A , r I...

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BM 410 HW #12 For problems 1-4 below: A) Calculate the correlation. B) If the return on stock A is independent from the return on the index fund, verify that joint probabilities are the product of the unconditional probabilities. C) If the returns on stock A and the index fund perfectly linear dependent , find the constants m and b in the equation r A =mr I +b, where r I represents the return on the index fund, and r A represents the return on stock A. 1. 2. 3. 4. 1

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#1 Solution A) Since correlation by definition is Cov(r I ,r A )/( σ I * A ), the correlation must also be zero. B) In this case, the stock and the index fund are independent. C) The stock and index fund are not perfectly linear dependent. #2 Solution E[r A ]=.47*25+.53*(-15)=3.8 E[r I ]=.47*10+.53*(-2)=3.64 stdev[r A ]=sqrt(0.47*(25-3.8)^2+0.53*(-15-3.8)^2)=19.96 stdev[r I ]=sqrt(0.47*(10-3.64)^2+0.53*(-2-3.64)^2)=5.99

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Unformatted text preview: Corr(r A , r I )=109.968/(19.96*5.99)=0.92 B) Not independent. C) Not perfectly linear dependent. 2 #3 Solution A) E[r A ]=.70*25+.30*(-15)=13 E[r I ]=.70*10+.30*(-2)=6.4 stdev[r A ]=sqrt(0.70*(25-13)^2+0.30*(-15-13)^2)=18.33 stdev[r I ]=sqrt(0.70*(10-6.4)^2+0.30*(-2-6.4)^2)=5.5 Corr[r A , r I ]=100.8/(18.33*5.5)=1.0 B) Not independent. C) Yes, this is an example of perfect linear dependence. 3 25 3 10 10 25 3 10 12 40 2 15 10 25-= + = = = +-=-+ = b b m m b m b m 3 #4 Solution A) E[r A ]=.35*25+.65*(-15)=-1 E[r I ]=.65*10+.35*(-2)=5.8 Var[r A ]=sqrt(0.35*(25-(-1))^2+0.65*(-15-(-1))^2)=19.09 Var[r I ]=sqrt(0.65*(10-5.8)^2+0.35*(-2-5.8)^2)=5.72 Corr[r A , r I ]=-85.2/(19.09*5.72)=-0.7803 B) Not independent. C) Not perfectly linear dependent. 4...
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12_Correlation from PDF_sol - Corr(r A , r I...

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