Appraisal data bias will lead to smaller correlation in absolute value than the true correlation?

CFA Level III
#1

Guys, please help me understand this feature.

I can understand appraisal data will lead to lower SD but why lower correlation? any formular ?

Thanks

#2

Capital markets reading

lower variance = lower std deviation

also leads to lower covariance - which leads to lower correlations.

#3

Not seeing this. If Correlation = COVx,y / STD DEVx STD DEVy

if the std deviation is lower, wont it increase the correlation with a lower denominator??

#4

CPK please check this again. Mathematically, a lower covariance by itself would lead to a lower correlation but in this case the lower covariance is combined with a lower std. Cov = sum(xi-xmean)(yi-ymean)/n^2 and std is ((sum(xi-xmean)^2)/n)^0.5. Changing the (xi-xmean) term will have an effect on both numerator and denominator of correlation so how do you figure which is affecting it more? I know what it says in the book but mathematically I dont see it.

#5

if you look at correlation as the extent to which two variables move together - and not as the “value” itself … then you have what the book is trying to say.

+1 correlation = when variable a increases - b also increases. (perfect positive correlation)

you seem to be looking at correlation as the value - but I guess it is the other meaning in which correlation is being used. due to lower volatility - the variables move less together with each other than before.

#6

CPK I think that both of your scenarios should have the same result. The value is also by definition the extent to which they move together?

#7

It could be that with more observations there are more variations with the other variable. This wouldnt be provable but likely shown through application.

#8

still donto get it. … does it matter that the correlation in this case is in absolute value according to the CFA book?

#9

lower variance = lower std deviation = > lower volatility … I think this sums it all.

Think of it in a rational way, you could even predict the correct answer from the choices given. Why would someone create a biase to achieve higher volatility, risk, or variance? Someone would have the tendency to shift risk down not up. That’s how i think of it.

#10

but lower correlation or a higher correlation is a good thing? for me higher means they tend to move toghther and it’s a good thing, lower means more disperse. so that’s a undesired situation. appraisal that means data are more similar and they should tend to move toghther…

#11

I try to remember it this way, not quite sure this is right though…

Appraised data means very low # of data which means the relationship is not going to be strong, because the R2 of the regression is going to be low. Hence low correlation! Atleast it helps me remember it :slight_smile:

#12

Hi, Sooraj ~ thanks for your tips. it seems nice for remembering .