Slow Decay of Impact in Equity Markets

Abstract

Using a proprietary dataset of meta-orders and prediction signals, and assuming a quasi-linear impact model, we deconvolve market impact from past correlated trades and a predictable return component to elicit the temporal dependence of the market impact of a single daily meta-order, over a ten day horizon in various equity markets. We find that the impact of single meta-orders is to a first approximation universal and slowly decays to zero (or to a small value), possibly as a power-law. We show that auto-correlated order-flows and trade information contents fully accounts for the apparent plateau observed in the raw data. We discuss the possible bias introduced by the quasi-linear assumption.PACS numbers:

A Fully Consistent, Minimal Model for Non-Linear Market Impact

“…However, our calculation shows that the empirical determination of the mechanical component of impact should carefully take into account any possible information content of the analyzed trades, as well as the possible auto-correlation of the trades. This parallels the discussion offered in [11,13], where attempts are made to measure the decay of mechanical impact I(Q, t > T ) in equity markets, with the conclusion that the mechanical component of impact seems indeed to relax to zero at large times.…”

“…We have shown that our model is free of price manipulation, which makes it the first consistent, non-linear and time dependent theory of impact. Our setting also suggests how prices can be naturally decomposed into a transient "mechanical impact" component and a permanent "informational" component, as initially proposed by Almgren et al [2], and recently exploited in [11,13] -see Section IX. Let us insist once again that this decomposition allowed us to construct diffusive prices (albeit with a generic short-term mean-reverting contribution).…”

“…time independent [7]. As now firmly established by many independent empirical studies, the average price change induced by the sequential execution of a total volume Q (which we call meta-order ) appears to follow a sub-linear, approximate √ Q law [2,3,5,[8][9][10][11][12][13]. At the end of the meta-order, impact is furthermore observed to decay (partially or completely) towards the unimpacted price [11][12][13][14].…”

“…As now firmly established by many independent empirical studies, the average price change induced by the sequential execution of a total volume Q (which we call meta-order ) appears to follow a sub-linear, approximate √ Q law [2,3,5,[8][9][10][11][12][13]. At the end of the meta-order, impact is furthermore observed to decay (partially or completely) towards the unimpacted price [11][12][13][14]. Quite strikingly, the square-root law appears to be universal, as it is to a large degree independent of details such as the type of contract traded (futures, stocks, options, Bitcoin [14]...), the geographical position of the market venue (US, Europe, Asia), the time period (1995 → 2014), the maturity of the market (e.g.…”

Market Impact with Multi-Timescale Liquidity

“…Equation (19) indicates that most of the incoming meta-order is executed against the rapid agents for t < t but the slow agents then take over for t > t (see Fig. 4).…”