correlation: the difference of two correlations is positive, but the correlation of the difference is negative? There are 3 random variables, $X_1$, $X_2$ and $Y$. We know $$corr(X_2, Y)>corr(X_1, Y)>0$$, but $$corr(X_2 - X_1, Y)<0$$
In other words, $X_2$ is more positively correlated to $Y$ than $X_1$, but the difference ($X_2-X_1$) is actually negatively correlated with $Y$.
Is this possible? and can you construct such random variables?

A small example in R:
X1 <- c(0, 1, 3)
X2 <- c(0, 1, 2)
Y  <- c(0, 1, 2)

cor(X1, Y)
# 0.9819805  # sqrt(27/28)
cor(X2, Y)
# 1
cor(X2-X1,Y)
# -0.8660254 # -sqrt(3/4)

It would not be possible with covariance, as cov(X2-X1, Y) = cov(X2, Y) - cov(X1, Y)
