WORKING PAPERS
Price Impact Costs and the Limit of Arbitrage
Abstract
This paper investigates whether one can profit from the size, book-to-market, or
momentum anomaly, when price-impact costs are taken into account. A non-linear
price-impact function is individually estimated for 5173 stocks to assess the magnitude
of trading costs. Compared to constant proportional transaction costs (as typically
assumed in the literature), a concave price-impact function tends to assign a higher
impact cost to mid-size trades and a lower impact to large-size trades. We implement
long-short arbitrage strategies based on each such anomaly, and estimate the maximal
fund size possible before excess returns become negative. For all anomalies, the maximal
fund sizes are small in order to remain profitable. Markets are therefore
bounded-rational: price-impact costs deter agents from exploiting the anomalies.
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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.
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Optimal Liquidity Trading
Abstract
A liquidity trader wishes to trade a fixed number of shares within a certain time
horizon and to minimize the mean and variance of the costs of trading. Explicit
formulas for the optimal trading strategies show that risk-averse liquidity traders
reduce their order sizes over time and execute a higher fraction of their total
trading volume in early periods when price volatility or liquidity increases. In
the presence of transaction fees, numerical simulations suggest that traders want
to trade more frequently when price volatility goes up or liquidity declines. In
the multi-asset case, price effects across assets have a substantial impact on
trading behavior, as does continuous-time trading.
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