An interesting corelation question

Today, I was confronted by an interesting macroeconomic question, which turns out to be a statistical question. The setup of the question is as follows: say x, and z are procyclical for y (output), that is, cov(x,y)>0 and cov(z,y)>0. Is it possible that cov(x,z)<0? If it is, find out the conditions for this to hold. Note that the covariance operator only captures the linear relationship while the nonlinear relationship is here to paly a role to make x and z negatively related. The solution would simplify once we assume that y is a symmetrically distributed random variable with mean zero. Also, the relationship between x and y and that between z and y are charactorized by x=f(y), z=g(y), respectively. Assuming f() and g() having zero derivatives for order higher than 2 will easily give the following condition for cov(x,z)<0 to hold:
00 and g'>0.
That is, the curvature of f and g must be different, with one being convex and the other being concave. Other than this, we need have abs(f ''(0)g''(0)) very large or y with high kurtosis for the condition to hold.