correlation between first order difference of two group variables

Question

I am doing correlation test on a factor and stock price(both are numerical values). I calculate the correlation from the following two ways:

1. Pearson correlation between factor value and stock price
2. Pearson correlation between factor value and first order difference of stock price(i.e., price[i+1] - price[i])

It turns out correlations in two cases vary a lot. Any explanation on the difference between the two approaches? I used to suppose they are very close.

Answer 1

Price and it's first order difference are not very close (maybe they're even independent!), so their correlations with any other variable do not have to be close. Toy example:

factor   price[i]   price[i+1]   difference
     1          1            3            2
     2          2            3            1
     3          3            3            0

Then correlation between factor value and stock price is 1 and correlation between factor value and first order difference of stock price is -1.