In a dynamic stochastic exchange economy where, due to beliefs heterogeneity, agents engage in speculative trade, I investigate the Market Selection Hypothesis that speculation rewards the agent with the most accurate beliefs. Assuming that agents maximize Epstein-Zin preferences and that markets are complete, I derive sufficient conditions for agents' survival in terms of their saving and portfolio rules, and use them to show that the Market Selection Hypothesis fails generically. Beliefs heterogeneity and speculation may persist in the long-run or, even when discount factors and intertemporal elasticities of substitution are homogeneous, speculation may cause the agent with the most accurate beliefs to vanish. Failures occur because agents' portfolio returns depend not only on beliefs accuracy but also on risk preferences, through the comparison to the optimal growth portfolio. The latter plays no role in CRRA economies because, due to the interdependence of relative risk aversion and intertemporal elasticity of substitution, portfolio returns not related to beliefs accuracy are compensated by the precautionary component of saving.