A natural conjecture is that speculative trade disappears when individual beliefs become correct through learning. Sandroni in  gives a counterexample in an economy with sunspots. We generalizenSandroni's result by showing that the conjecture holds for economies with complete markets only. We consider a standard finite-horizon General Equilibrium model with complete markets, where uncertaintynis represented by fluctuations in individual endowments. Individual beliefs are formed through arbitrary learning processes, and become eventually correct. We show that along every path of events, equilibrium prices of traded assets converge to rational expectations for the sup-norm. We also give a set of sufficient conditions on beliefs andnaggregate endowment leading to market crashes, as in Sandroni .nWe show that such situations are generically continuous perturbations of rational expectations behaviors when beliefs satisfy a requirementnintroduced here.