英文标题：
《Are trading invariants really invariant? Trading costs matter》
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作者：
Fr\\\'ed\\\'eric Bucci, Fabrizio Lillo, Jean-Philippe Bouchaud and Michael
Benzaquen
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最新提交年份：
2019
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英文摘要：
We revisit the trading invariance hypothesis recently proposed by Kyle and Obizhaeva by empirically investigating a large dataset of bets, or metaorders, provided by ANcerno. The hypothesis predicts that the quantity $I:=\\ri/N^{3/2}$, where $\\ri$ is the exchanged risk (volatility $\\times$ volume $\\times$ price) and $N$ is the number of bets, is invariant. We find that the $3/2$ scaling between $\\ri$ and $N$ works well and is robust against changes of year, market capitalisation and economic sector. However our analysis clearly shows that $I$ is not invariant. We find a very high correlation $R^2>0.8$ between $I$ and the total trading cost (spread and market impact) of the bet. We propose new invariants defined as a ratio of $I$ and costs and find a large decrease in variance. We show that the small dispersion of the new invariants is mainly driven by (i) the scaling of the spread with the volatility per transaction, (ii) the near invariance of the distribution of metaorder size and of the volume and number fractions of bets across stocks.
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中文摘要：
我们通过实证研究安切诺提供的大量下注数据集或元指令，重新审视了凯尔和奥比扎耶娃最近提出的交易不变性假设。该假设预测数量$I：=\\ri/N ^{3/2}$，其中$\\ri$是交换风险（波动率$\\乘以$交易量$\\乘以$价格），而$N$是下注数量，是不变的。我们发现，在$\\ ri$和$\\ N$之间的3/2$缩放效果良好，并且对年度、市值和经济部门的变化具有鲁棒性。然而，我们的分析清楚地表明，I$并不是不变的。我们发现，在I$和赌注的总交易成本（价差和市场影响）之间，R^2>0.8$的相关性非常高。我们提出了新的不变量，定义为I$和成本的比率，并发现方差有很大的减少。我们发现，新不变量的微小分散主要是由（i）利差随每笔交易的波动率的缩放，（ii）亚阶大小分布以及股票间下注量和分数的近似不变性所驱动。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Trading and Market Microstructure 交易与市场微观结构
分类描述：Market microstructure, liquidity, exchange and auction design, automated trading, agent-based modeling and market-making
市场微观结构，流动性，交易和拍卖设计，自动化交易，基于代理的建模和做市
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一级分类：Physics 物理学
二级分类：Statistical Mechanics 统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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