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smilefish · 2025年02月16日

Cov(A,B) = E(AB) - E(A)*E(B)请老师讲一下这个公式是怎么来的,谢谢

NO.PZ2019040801000072

问题如下:

Analyst Amy gathers the follwing data for the return on the market and the return on Crude Oil. Please calculate the covariance of returns between Crude Oil and the market.

Probability Matrix

选项:

A.

0.66%

B.

1.05%

C.

0.28%

D.

2.68

解释:

A is correct.

考点:Covariance

解析: Cov(A,B) = E(AB) - E(A)*E(B)

E(AB) = 30%*25%*0.3+15%*20%*0.4 +10%*0*0.3 = 3.45%

E(A) = 30%*30%+15%*40%+10%*30%= 18%

E(B) = 25%*30%+20%*40%+0*30%=15.5%

所以Cov(A,B) = E(AB) - E(A)*E(B)=0.66%

Cov(A,B) = E(AB) - E(A)*E(B)请老师讲一下这个公式是怎么来的,谢谢

1 个答案

李坏_品职助教 · 2025年02月16日

嗨,从没放弃的小努力你好:


这个公式在FRM的Quantitiative Analysis的原版书教材里面有:


原版书里面没有给出证明过程,FRM不会考查数学推导。如果感兴趣的话可以看下面这个过程:




然后:

----------------------------------------------
就算太阳没有迎着我们而来,我们正在朝着它而去,加油!

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