We contribute to the debate on whether central banks should respond to financial factors in monetary policy rules, by evaluating equilibrium determinacy and E-stability in the presence of a financial accelerator. Policies responding to lagged asset prices either reduce the region of determinacy or E-stability in the parameter space. However, a response to current asset prices expands both regions of determinacy and E-stability. Policy rules reacting to credit volume constrict the determinacy region. Most policies responding to credit spreads expand determinacy and E-stability regions. We favor the inclusion of current asset prices or credit spreads in monetary policy rules.