[CFA Level 1] 请教一个一级问题 between, perfect, following, statements, correct

victor2372

   which of the following statements about covariance and correlation is least likely correct?

            A. A zero covariance implies there is no linear relationship between the return on two assets

            B. if two assets have perfect negative correlation, the variance of returns for a portfolio that consists of these two assets will equal zero.

       敢问高人这题的B为什么是错的，correlation为-1的时候不是可以让风险变成0的吗？

jysavior

W1和W2就是weight

jysavior

 呵呵，B是一个容易混淆的概念。
注意， perfect negative correlation导致variance=0的情况，一定要考虑portfolio里两种assets的weight
看公式
if 
perfect negative correlation

then

sigma of portfolio= w1*sigma1-w2*sigma2. Do you agree with me? Sigam is the standard deviation, square root of variance.

so, when sigma of portfolio= w1*sigma1-w2*sigma2, 它一定为0？显然不可能，只有通过适当地选择W1和W2才可能是的sigma of portfolio =0。这是个偶然的结论，不总是成立的。