Quasi-Arbitrage and Price Manipulation

Abstract

In an environment where trading volume affects security prices and where prices are uncertain when trades are submitted, quasi-arbitrage is the availability of a series of trades which generate infinite expected profits with an infinite Sharpe ratio. We show that when the price impact of trades is time stationary, only linear price-impact functions rule out quasi-arbitrage and thus support viable market prices. This holds whether a single asset or a portfolio of assets is traded. When the temporary and permanent effects of trades on prices are independent, only the permanent price impact must be linear while the temporary one can be of a more general form. We also extend the analysis to a nonstationary framework.