This paper studies an order-driven stock market where agents have heterogeneous estimates of the fundamental value of the risky asset. The agents are budget-constrained and follow a value-based trading strategy which buys or sells depending on whether the price of the asset is below or above its risk-adjusted fundamental value. This environment generates returns that are remarkably leptokurtic and fat-tailed. By extending the study over a grid of different parameters for the fundamentalist trading strategy, we exhibit the existence of monotone relationships between the bid-ask spread demanded by the agents and several statistics of the returns. We conjecture that this effect, coupled with positive dependence of the risk premium on the volatility, generates positive feedbacks that might explain volatility bursts.