Assume $X_i$ and $X_j$ relate to market $M^a$ and $M^b$ $$X_i = \sqrt{\rho_a} M^a + \sqrt(1-\rho_a} Z_i $$ $$X_j = \sqrt{\rho_b} M^b + \sqrt(1-\rho_b} Z_j $$
Assume $X_i$ and $X_j$ relate to market $M^a$ and $M^b$ $$X_i = \sqrt{\rho_a} M^a + \sqrt(1-\rho_a} Z_i $$ $$X_j = \sqrt{\rho_b} M^b + \sqrt(1-\rho_b} Z_j $$