Mainstream macroeconomic theory predicts a rapid response of asset prices to monetary policy shocks, which conventional empirical models are unable to reproduce. We argue that this is due to a deficient information set: Forward-looking economic agents observe vastly more information than the handful of variables included in standard VAR models. Thus, small-scale VARs are likely to suffer from nonfundamentalness and yield biased results. We tackle this problem by estimating a Structural Factor Model for a large euro area dataset. We find quicker and larger effects of monetary policy shocks, consistent with mainstream theory and the observed large swings in asset prices. Our results point to stronger financial stability consequences of an exogenous monetary policy tightening, also in the form of a quicker than expected unwinding of QE, than commonly thought.