Informed arbitrage with speculative noise trading

We consider speculative noise trading when some naïve speculators trade on noise as if it were information [Black, F., 1986. Noise. Journal of Finance 41, 529–543]. We examine the optimal trading strategy of an informed investor who faces such naïve speculators in the market. We find that the informed investor trades aggressively on her information and takes large, opposite positions against the naïve speculators. The trading volume is thereby drastically magnified. While such speculative noise trading enhances liquidity, it makes prices less efficient. The overall dynamic patterns that emerge from our model are most consistent with the evidence for interday variations in volume, volatility, and transaction costs.