ZERO BETA = Partial correlation?

broadex

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In CFAI material - In Reading 16 –we are given that Market A has zero BETA (sensitivity) to global bonds and a positive sensitivity to global equity.
The curriculum goes to explain that a zero sensitivity to global bonds does not mean that Market A is uncorrelated with global bonds, although it does mean that its partial correlation with bonds (the correlation after removing the influence of the other markets) is zero and that global bonds are not one of Market A’s return drivers……
I don’t understand this…I always thought zero sensitivity (zero beta) means no correlation!!!
 
go back to your days of multiple regression and think about beta being the partial coefficient.
 
I dont get the answer above. Could someone please with more insight assist.
 
I could be wrong so hopefully someone else chims in:
Market A’s movement does not determine Market B’s movement.
However, market C may influence market A and market B’s movements, therefore they have some degree of correlation, even if their sensitivity to eachother is zero.
 
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