Sorry for the confusion. I was talking about the Then part
It is not the condition
But just as you posted, let f=x-y, and g=x-2y, then
COV(f, g)=V(x)+2V(y)-3COV(x,y).
If COV(x,y) is positive and large enough, COV(f,g) can be negative.
So COV(f, g)>=0 is not guaranteed.
But just as you posted, let f=x-y, and g=x-2y, then
COV(f, g)=V(x)+2V(y)-3COV(x,y).
If COV(x,y) is positive and large enough, COV(f,g) can be negative.
So COV(f, g)>=0 is not guaranteed.