arXiv subjects

Jean-Philippe Bouchaud

Publications and source records attributed to Jean-Philippe Bouchaud.

At least 109 records · Page 6Linked to original sources

arXiv2018

Co-impact: Crowding effects in institutional trading activity

This paper is devoted to the important yet unexplored subject of crowding effects on market impact, that we call "co-impact". Our analysis is based on a large database of metaorders by institutional investors in the U.S. equity market. We find that the market chiefly reacts to the net order flow of ongoing metaorders, without individually distinguishing them. The joint co-impact of multiple contemporaneous metaorders depends on the total number of metaorders and their mutual sign correlation. Using a simple heuristic model calibrated on data, we reproduce very well the different regimes of the empirical market impact curves as a function of volume fraction $ϕ$: square-root for large $ϕ$, linear for intermediate $ϕ$, and a finite intercept $I_0$ when $ϕ\to 0$. The value of $I_0$ grows with the sign correlation coefficient. Our study sheds light on an apparent paradox: How can a non-linear impact law survive in the presence of a large number of simultaneously executed metaorders?

q-fin.TR↗

arXiv2018

Can the glass transition be explained without a growing static length scale?

It was recently discovered that SWAP, a Monte Carlo algorithm that involves the exchange of pairs of particles of differing diameters, can dramatically accelerate the equilibration of simulated supercooled liquids in regimes where the normal dynamics is glassy. This spectacular effect was subsequently interpreted as direct evidence against a static, cooperative explanation of the glass transition such as the one offered by the random first-order transition (RFOT) theory. We review several empirical facts that support the opposite view, namely, that a local mechanism cannot explain the glass transition phenomenology. We explain the speedup induced by SWAP within the framework of the RFOT theory. We suggest that the efficiency of SWAP stems from a postponed onset of glassy dynamics, which allows the efficient exploration of configuration space even in the regime where the physical dynamics is dominated by activated events across free-energy barriers. We describe this effect in terms of `crumbling metastability' and use the example of nucleation to illustrate the possibility of circumventing free-energy barriers of thermodynamic origin by a change of the local dynamical rules.

cond-mat.stat-mech↗

arXiv2018

Greedy algorithms and Zipf laws

We consider a simple model of firm/city/etc. growth based on a multi-item criterion: whenever entity B fares better that entity A on a subset of $M$ items out of $K$, the agent originally in A moves to B. We solve the model analytically in the cases $K=1$ and $K \to \infty$. The resulting stationary distribution of sizes is generically a Zipf-law provided $M > K/2$. When $M \leq K/2$, no selection occurs and the size distribution remains thin-tailed. In the special case $M=K$, one needs to regularise the problem by introducing a small "default" probability $ϕ$. We find that the stationary distribution has a power-law tail that becomes a Zipf-law when $ϕ\to 0$. The approach to the stationary state can also been characterized, with strong similarities with a simple "aging" model considered by Barrat & Mézard.

cond-mat.stat-mech↗

arXiv2018

Optimal Inflation Target: Insights from an Agent-Based Model

Which level of inflation should Central Banks be targeting? We investigate this issue in the context of a simplified Agent Based Model of the economy. Depending on the value of the parameters that describe the behaviour of agents (in particular inflation anticipations), we find a rich variety of behaviour at the macro-level. Without any active monetary policy, our ABM economy can be in a high inflation/high output state, or in a low inflation/low output state. Hyper-inflation, deflation and "business cycles" between coexisting states are also found. We then introduce a Central Bank with a Taylor rule-based inflation target, and study the resulting aggregate variables. Our main result is that too-low inflation targets are in general detrimental to a CB-monitored economy. One symptom is a persistent under-realisation of inflation, perhaps similar to the current macroeconomic situation. Higher inflation targets are found to improve both unemployment and negative interest rate episodes. Our results are compared with the predictions of the standard DSGE model.

econ.GN↗

arXiv2018

The short-term price impact of trades is universal

We analyze a proprietary dataset of trades by a single asset manager, comparing their price impact with that of the trades of the rest of the market. In the context of a linear propagator model we find no significant difference between the two, suggesting that both the magnitude and time dependence of impact are universal in anonymous, electronic markets. This result is important as optimal execution policies often rely on propagators calibrated on anonymous data. We also find evidence that in the wake of a trade the order flow of other market participants first adds further copy-cat trades enhancing price impact on very short time scales. The induced order flow then quickly inverts, thereby contributing to impact decay.

q-fin.TR↗

arXiv2017

Market impact with multi-timescale liquidity

We present an extended version of the recently proposed "LLOB" model for the dynamics of latent liquidity in financial markets. By allowing for finite cancellation and deposition rates within a continuous reaction-diffusion setup, we account for finite memory effects on the dynamics of the latent order book. We compute in particular the finite memory corrections to the square root impact law, as well as the impact decay and the permanent impact of a meta-order. The latter is found to be linear in the traded volume and independent of the trading rate, as dictated by no-arbitrage arguments. In addition, we consider the case of a spectrum of cancellation and deposition rates, which allows us to obtain a square root impact law for moderate participation rates, as observed empirically. Our multi-scale framework also provides an alternative solution to the so-called price diffusivity puzzle in the presence of a long-range correlated order flow.

q-fin.TR↗

arXiv2017

A fractional reaction-diffusion description of supply and demand

We suggest that the broad distribution of time scales in financial markets could be a crucial ingredient to reproduce realistic price dynamics in stylised Agent-Based Models. We propose a fractional reaction-diffusion model for the dynamics of latent liquidity in financial markets, where agents are very heterogeneous in terms of their characteristic frequencies. Several features of our model are amenable to an exact analytical treatment. We find in particular that the impact is a concave function of the transacted volume (aka the "square-root impact law"), as in the normal diffusion limit. However, the impact kernel decays as $t^{-β}$ with $β=1/2$ in the diffusive case, which is inconsistent with market efficiency. In the sub-diffusive case the decay exponent $β$ takes any value in $[0,1/2]$, and can be tuned to match the empirical value $β\approx 1/4$. Numerical simulations confirm our theoretical results. Several extensions of the model are suggested.

q-fin.MF↗

arXiv2017

Trends and Risk Premia: Update and Additional Plots

Recently, our group has published two papers that have received some attention in the finance community. One is about the profitability of trend following strategies over 200 years, the second is about the correlation between the profitability of "Risk Premia" and their skewness. In this short note, we present two additional plots that fully corroborate our findings on new data.

q-fin.PM↗

arXiv2017

The "Size Premium" in Equity Markets: Where is the Risk?

We find that when measured in terms of dollar-turnover, and once $β$-neutralised and Low-Vol neutralised, the Size Effect is alive and well. With a long term t-stat of $5.1$, the "Cold-Minus-Hot" (CMH) anomaly is certainly not less significant than other well-known factors such as Value or Quality. As compared to market-cap based SMB, CMH portfolios are much less anti-correlated to the Low-Vol anomaly. In contrast with standard risk premia, size-based portfolios are found to be virtually unskewed. In fact, the extreme risk of these portfolios is dominated by the large cap leg; small caps actually have a positive (rather than negative) skewness. The only argument that favours a risk premium interpretation at the individual stock level is that the extreme drawdowns are more frequent for small cap/turnover stocks, even after accounting for volatility. This idiosyncratic risk is however clearly diversifiable.

q-fin.PM↗

arXiv2017

Trading Lightly: Cross-Impact and Optimal Portfolio Execution

We model the impact costs of a strategy that trades a basket of correlated instruments, by extending to the multivariate case the linear propagator model previously used for single instruments. Our specification allows us to calibrate a cost model that is free of arbitrage and price manipulation. We illustrate our results using a pool of US stocks and show that neglecting cross-impact effects leads to an incorrect estimation of the liquidity and suboptimal execution strategies. We show in particular the importance of synchronizing the execution of correlated contracts.

q-fin.TR↗

arXiv2017

Quantum Mechanics with a non-zero quantum correlation time

We propose an extension of Quantum Mechanics based on the idea that the underlying "quantum noise" has a non-zero, albeit very small, correlation time $τ_c$. The standard (non-relativistic) Schrodinger equation is recovered to zeroth order in $τ_c$, and the first correction to energy levels is computed. Some consequences are discussed, in particular the violation of Heisenberg's uncertainty principle and the restoration of locality at short times.

quant-ph↗

arXiv2017

Universal scaling and nonlinearity of aggregate price impact in financial markets

How and why stock prices move is a centuries-old question still not answered conclusively. More recently, attention shifted to higher frequencies, where trades are processed piecewise across different timescales. Here we reveal that price impact has a universal non-linear shape for trades aggregated on any intra-day scale. Its shape varies little across instruments, but drastically different master curves are obtained for order-volume and -sign impact. The scaling is largely determined by the relevant Hurst exponents. We further show that extreme order flow imbalance is not associated with large returns. To the contrary, it is observed when the price is "pinned" to a particular level. Prices move only when there is sufficient balance in the local order flow. In fact, the probability that a trade changes the mid-price falls to zero with increasing (absolute) order-sign bias along an arc-shaped curve for all intra-day scales. Our findings challenge the widespread assumption of linear aggregate impact. They imply that market dynamics on all intra-day timescales are shaped by correlations and bilateral adaptation in the flows of liquidity provision and taking.

q-fin.TR↗

arXiv2017

Nonlinear price impact from linear models

The impact of trades on asset prices is a crucial aspect of market dynamics for academics, regulators and practitioners alike. Recently, universal and highly nonlinear master curves were observed for price impacts aggregated on all intra-day scales [1]. Here we investigate how well these curves, their scaling, and the underlying return dynamics are captured by linear "propagator" models. We find that the classification of trades as price-changing versus non-price-changing can explain the price impact nonlinearities and short-term return dynamics to a very high degree. The explanatory power provided by the change indicator in addition to the order sign history increases with increasing tick size. To obtain these results, several long-standing technical issues for model calibration and -testing are addressed. We present new spectral estimators for two- and three-point cross-correlations, removing the need for previously used approximations. We also show when calibration is unbiased and how to accurately reveal previously overlooked biases. Therefore, our results contribute significantly to understanding both recent empirical results and the properties of a popular class of impact models.

q-fin.TR↗

arXiv2017

On the overlaps between eigenvectors of correlated random matrices

We obtain general, exact formulas for the overlaps between the eigenvectors of large correlated random matrices, with additive or multiplicative noise. These results have potential applications in many different contexts, from quantum thermalisation to high dimensional statistics. We find that the overlaps only depend on measurable quantities, and do not require the knowledge of the underlying "true" (noiseless) matrices. We apply our results to the case of empirical correlation matrices, that allow us to estimate reliably the width of the spectrum of the true correlation matrix, even when the latter is very close to the identity. We illustrate our results on the example of stock returns correlations, that clearly reveal a non trivial structure for the bulk eigenvalues. We also apply our results to the problem of matrix denoising in high dimension.

cond-mat.stat-mech↗

arXiv2017

You are in a drawdown. When should you start worrying?

Trading strategies that were profitable in the past often degrade with time. Since unlucky streaks can also hit "healthy" strategies, how can one detect that something truly worrying is happening? It is intuitive that a drawdown that lasts too long or one that is too deep should lead to a downward revision of the assumed Sharpe ratio of the strategy. In this note, we give a quantitative answer to this question based on the exact probability distributions for the length and depth of the last drawdown for upward drifting Brownian motions. We also point out that both managers and investors tend to underestimate the length and depth of drawdowns consistent with the Sharpe ratio of the underlying strategy.

q-fin.PM↗

arXiv2017

Genuine localisation transition in a long-range hopping model

We introduce and study a new class of Banded Random Matrix model describing sparse, long range quantum hopping in one dimension. Using a series of analytic arguments, numerical simulations, and mappings to statistical physics models, we establish the phase diagram of the model. A genuine localisation transition, with well defined mobility edges, appears as the hopping rate decreases slower than $\ell^{-2}$, where $\ell$ is the distance. Correspondingly, the decay of the localised states evolves from a standard exponential shape to a stretched exponential and finally to a novel $\exp(-C\ln^κ\ell)$ behaviour, with $κ> 1$.

cond-mat.stat-mech↗

arXiv2016

Dissecting cross-impact on stock markets: An empirical analysis

The vast majority of market impact studies assess each product individually, and the interactions between the different order flows are disregarded. This strong approximation may lead to an underestimation of trading costs and possible contagion effects. Transactions in fact mediate a significant part of the correlation between different instruments. In turn, liquidity shares the sectorial structure of market correlations, which can be encoded as a set of eigenvalues and eigenvectors. We introduce a multivariate linear propagator model that successfully describes such a structure, and accounts for a significant fraction of the covariance of stock returns. We dissect the various dynamical mechanisms that contribute to the joint dynamics of assets. We also define two simplified models with substantially less parameters in order to reduce overfitting, and show that they have superior out-of-sample performance.

q-fin.TR↗

arXiv2016

Agnostic Risk Parity: Taming Known and Unknown-Unknowns

Markowitz' celebrated optimal portfolio theory generally fails to deliver out-of-sample diversification. In this note, we propose a new portfolio construction strategy based on symmetry arguments only, leading to "Eigenrisk Parity" portfolios that achieve equal realized risk on all the principal components of the covariance matrix. This holds true for any other definition of uncorrelated factors. We then specialize our general formula to the most agnostic case where the indicators of future returns are assumed to be uncorrelated and of equal variance. This "Agnostic Risk Parity" (AGP) portfolio minimizes unknown-unknown risks generated by over-optimistic hedging of the different bets. AGP is shown to fare quite well when applied to standard technical strategies such as trend following.

q-fin.PM↗