Tackling nonlinear price impact with linear strategies
研究发现，对于非线性价格冲击（幂律指数0.4-0.7），通过选择适当的有效二次成本参数，线性策略也能达到近乎最优的表现，性能损失低于2%。
Abstract Empirical studies in various contexts find that the price impact of large trades approximately follows a power law with exponent between 0.4 and 0.7. Yet, tractable formulas for the portfolios that trade off predictive trading signals, risk, and trading costs in an optimal manner are only available for quadratic costs corresponding to linear price impact. In this paper, we show that the resulting linear strategies allow to achieve virtually optimal performance also for realistic nonlinear price impact, if the “effective” quadratic cost parameter is chosen appropriately. To wit, for a wide range of risk levels, this leads to performance losses below 2% compared to a numerical algorithm proposed by Kolm and Ritter, run at very high accuracy. The effective quadratic cost depends on the portfolio risk and concavity of the impact function, but can be computed without any sophisticated numerics by simply maximizing an explicit scalar function.