Marcos Lopez de Prado

The Microstructure of the ‘Flash Crash’: Flow Toxicity, Liquidity Crashes and the Probability of Informed Trading

The “flash crash” of May 6, 2010, was the second-largest point swing (1,010.14 points) and the biggest one-day point decline (998.5 points) in the history of the Dow Jones Industrial Average. For a few minutes,

The Volume Clock: Insights into the High Frequency Paradigm

1 trillion in market value vanished. In this article, the authors argue that the flash crash was the result of the new dynamics at play in the current market structure. They highlight the role played by order toxicity in affecting liquidity provision, and they show that a measure of this toxicity, the volume synchronized probability of informed trading (VPIN), captures the increasing toxicity of the order flow in the hours and days prior to collapse. Because the flash crash might have been avoided had liquidity providers remained in the marketplace, a solution is proposed in the form of a “VPIN contract” that would allow liquidity providers to dynamically monitor and manage their risks.

Pseudo-Mathematics and Financial Charlatanism: The Effects of Backtest Overfitting on Out-of-Sample Performance

Over the last two centuries, technological advantages have allowed some traders to be faster than others. In this article, the authors argue that contrary to popular perception, speed is not the defining characteristic that sets high-frequency trading (HFT) apart. HFT is the natural evolution of a new trading paradigm that is characterized by strategic decisions made in a volume-clock metric. Even if the speed advantage disappears, HFT will evolve to continue exploiting structural weaknesses of low-frequency trading (LFT).LFT practitioners are not defenseless against HFT players, however, and this article offers options that can help them survive and adapt to this new environment.

The Sharpe Ratio Efficient Frontier

Most firms and portfolio managers rely on backtests (or historical simulations of performance) to select investment strategies and allocate them capital. We prove that after trying only 7 strategy configurations, a researcher is expected to identify at least one 2-year long backtest with an annualized Sharpe ratio of over 1, when the expected out of sample Sharpe ratio is 0. If the researcher tries a large enough number of strategy configurations, a backtest can always be fit to any desired performance for a fixed sample length. We find that there is a minimum backtest length (MinBTL) that should be required for a given number of trials. A Sharpe ratio of 10 over 50 years requires more overfitting effort than a Sharpe ratio of 2 over 5 years, but nowadays’ computational power makes backtest overfitting a relatively easy task. The practical totality of published backtests do not report the number of trials involved, thus we suspect that many backtests may be substantially overfit. Standard statistical techniques designed to prevent regression overfitting, such as holdout, tend to be unreliable and inaccurate in the context of investment backtests. We propose a framework that estimates the probability of backtest overfitting (PBO) specifically in the context of investment simulations, through a numerical method that we call combinatorially symmetric cross-validation (CSCV). We show that CSCV produces accurate estimates of the probability that a particular backtest is overfit.

Discerning Information from Trade Data

We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns. We show that this new uncertainty-adjusted investment skill metric (called Probabilistic Sharpe ratio, or PSR) has a number of important applications: First, it allows us to establish the track record length needed for rejecting the hypothesis that a measured Sharpe ratio is below a certain threshold with a given confidence level. Second, it models the trade-off between track record length and undesirable statistical features (e.g., negative skewness with positive excess kurtosis). Third, it explains why track records with those undesirable traits would benefit from reporting performance with the highest sampling frequency such that the IID assumption is not violated. Fourth, it permits the computation of what we call the Sharpe ratio Efficient Frontier (SEF), which lets us optimize a portfolio under non-Normal, leveraged returns while incorporating the uncertainty derived from track record length. Results can be validated using the Python code in the Appendix.

The Exchange of Flow Toxicity

How best to discern trading intentions from market data? We examine the accuracy of three methods for classifying trade data: bulk volume classification (BVC), tick rule and aggregated tick rule. We develop a Bayesian model of inferring information from trade executions and show the conditions under which tick rules or bulk volume classification predominates. Empirically, we find that tick rule approaches and BVC are relatively good classifiers of the aggressor side of trading, but bulk volume classifications are better linked to proxies of information-based trading. Thus, BVC would appear to be a useful tool for discerning trading intentions from market data.

The Probability of Backtest Overfitting

Flow toxicity can be measured in terms of the probability that a liquidity provider is adversely selected by informed traders. In previous papers we introduced the concept of Volume-synchronized Probability of Informed Trading (the VPIN* metric), and provided a robust estimation procedure. In this study, we discuss the asymmetric impact that an incorrect estimation of the VPIN metric has on a market maker’s performance. This asymmetry may be part of the explanation for the evaporation of liquidity witnessed on May 6th 2010. To mitigate that undesirable behavior, we present the specifications of a VPIN contract, which could be used to hedge against the risk of higher than expected levels of toxicity, as well as to monitor such risk. Among other applications, it would also work as an execution benchmark, and a price discovery mechanism, since it allows for the externalization of market participants’ views of future toxicity.

The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting and Non-Normality

Most firms and portfolio managers rely on backtests (or historical simulations of performance) to select investment strategies and allocate them capital. Standard statistical techniques designed to prevent regression over-fitting, such as hold-out, tend to be unreliable and inaccurate in the context of investment backtests. We propose a framework that estimates the probability of backtest over-fitting (PBO) specifically in the context of investment simulations, through a numerical method that we call combinatorially symmetric cross-validation (CSCV). We show that CSCV produces accurate estimates of the probability that a particular backtest is over-fit.The appendices for this paper are available at the following URL: http://ssrn.com/abstract=2568435

Optimal Execution Horizon

With the advent in recent years of large financial data sets, machine learning, and high-performance computing, analysts can back test millions (if not billions) of alternative investment strategies. Backtest optimizers search for combinations of parameters that maximize the simulated historical performance of a strategy, leading to back test overfitting. The problem of performance inflation extends beyond back testing. More generally, researchers and investment managers tend to report only positive outcomes, a phenomenon known as selection bias. Not controlling for the number of trials involved in a particular discovery leads to overly optimistic performance expectations. The deflated Sharpe ratio (DSR) corrects for two leading sources of performance inflation: Selection bias under multiple testing and non-normally distributed returns. In doing so, DSR helps separate legitimate empirical findings from statistical flukes.

Building Diversified Portfolios that Outperform Out-of-Sample

Execution traders know that market impact greatly depends on whether their orders lean with or against the market. We introduce the OEH model, which incorporates this fact when determining the optimal trading horizon for an order, an input required by many sophisticated execution strategies. This model exploits the traders private information about her trades side and size, and how it will shift the prevailing order flow. From a theoretical perspective, OEH explains why market participants may rationally “dump” their orders in an increasingly illiquid market. We argue that trade side and order imbalance are key variables needed for modeling market impact functions, and their dismissal may be the reason behind the apparent disagreement in the literature regarding the functional form of the market impact function. We show that in terms of its information ratio OEH performs better than participation rate schemes and VWAP strategies. Our backtests suggest that OEH contributes substantial “execution alpha” for a wide variety of futures contracts. An implementation of OEH is provided in Python language.