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Modern quantitative trading systems implicitly assume that predictive accuracy implies economic control. This paper proves that assumption is false. We formalize a fundamental separation between predictability—an observer-centric statistical property—and controllability—an actuator-centric dynamical property of trading under feedback, frictions, and competition. Using tools from stochastic control, market microstructure, and performative economics, we establish a negative result: high predictive power is neither sufficient for nor monotone in profitability and can, under realistic regimes of convex execution costs and feedback, strictly accelerate P&L erosion. We model markets as closed-loop dynamical systems in which agents’ actions alter the state conditional on which predictions are made. We characterize exploitable alpha via a controllability condition and show that prediction-optimal policies are generically antioptimal under feedback. Finally, we propose a control-theoretic replacement for prediction-centric trading could specify that this replaces MSE-centric optimization to emphasize the practical takeaway.