We use a cointegrated structural vector autoregressive model to investigate the relation between monetary policy in the euro area and the stock market. Since there may be an instantaneous causal relation, we consider long-run identifying restrictions for the structural shocks and also used (conditional) heteroscedasticity in the residuals for identification purposes. Heteroscedasticity is modelled by a Markov-switching mechanism. We find a plausible identification scheme for stock market and monetary policy shocks which is consistent with the second-order moment structure of the variables. The model indicates that contractionary monetary policy shocks lead to a long-lasting downturn of real stock prices.