Inference, arbitrage, and asset price volatility

This paper models the impact of arbitrageurs on stock prices when arbitrageurs are uncertain about the drift of the dividend process of a risky asset. Under perfect information, the presence of risk-neutral arbitrageurs unambiguously reduces the volatility of asset returns. When arbitrageurs are uncertain about the drift of the dividend process, they condition their investment strategy on the observation of dividends and trading volume. In such a setting, the presence of arbitrageurs can lead to an increase in the equilibrium volatility of asset returns. The arbitrageurs' inference problem gives rise to rich dynamics of asset prices and investment strategies: the optimal trading strategy of arbitrageurs can be upward sloping in prices, the response of prices to news can be nonlinear, and minor news can have large effects. These results are driven by the arbitrageurs' inability to perfectly distinguish temporary from permanent shocks. Arbitrageurs would like to sell assets in response to temporary price increases and buy assets in response to permanent price increases.