標題:
calculation of correlation coefficient of returns
發問:
Given follow information, what's the correlation coefficient of returns between investments A and B? Scenario I : probability 0.3 ; possible return (A) 28% , (B) 35% Scenario II: probability 0.4 ; possible return (A) 18% , (B) 15% Scenario III:probability 0.3 ; possible return (A) 6% , (B) 20%
最佳解答:
上面個位做錯了﹐既然要求the correlation coefficient of returns between investments A and B﹐無可能分開計 應該用公式 correlation coefficient = E(XY)-E(X)E(Y)/SD(X)SD(Y) E(A)=0.3*0.28+0.4*0.18+0.3*0.06=0.174 E(B)=0.3*0.35+0.4*0.15+0.3*0.2=0.225 E(A^2)=0.3*0.28^2+0.4*0.18^2+0.3*0.06^2=0.03756 E(B^2)=0.3*0.35^2+0.4*0.15^2+0.3*0.2^2=0.05775 VAR(A)=E(A^2)-[E(A)]^2=0.007284 VAR(B)=E(B^2)-[E(B)]^2=0.007125 SD(A)=0.08535 SD(B)=0.0844 E(AB)=0.3*0.28*0.35+0.4*0.18*0.15+0.3*0.06*0.2=0.0438 correlation coefficient = E(AB)-E(A)E(B)/SD(A)SD(B) =[0.0438-(0.174)(0.225)]/(0.08535)(0.0844) =0.6455
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