We analyze the stability of financial investment networks, where financial institutions hold overlapping portfolios of assets. We consider the effect of portfolio diversification and heterogeneous investments using a random matrix dynamical model driven by portfolio rebalancing. The stability/instability transition is dictated by the largest eigenvalue of the random matrix governing the time evolution of the endogenous components of the returns, for which we will propose two different approximation schemes, and finally explore the replica method calculations that underpin one of the approximation schemes