Measuring Toxic Flow for Trading & Risk Management

A common theme of microstructure modeling is that trade flow is often predictive of market direction.  One concept in particular that has gained traction is flow toxicity, i.e. flow where resting orders tend to be filled more quickly than expected, while aggressive orders rarely get filled at all, due to the participation of informed traders trading against uninformed traders.  The fundamental insight from microstructure research is that the order arrival process is informative of subsequent price moves in general and toxic flow in particular.  This is turn has led researchers to try to measure the probability of informed trading  (PIN).  One recent attempt to model flow toxicity, the Volume-Synchronized Probability of Informed Trading (VPIN)metric, seeks to estimate PIN based on volume imbalance and trade intensity.  A major advantage of this approach is that it does not require the estimation of unobservable parameters and, additionally, updating VPIN in trade time rather than clock time improves its predictive power.  VPIN has potential applications both in high frequency trading strategies, but also in risk management, since highly toxic flow is likely to lead to the withdrawal of liquidity providers, setting up the conditions for a flash-crash” type of market breakdown.

The procedure for estimating VPIN is as follows.  We begin by grouping sequential trades into equal volume buckets of size V.  If the last trade needed to complete a bucket was for a size greater than needed, the excess size is given to the next bucket.  Then we classify trades within each bucket into two volume groups:  Buys (V(t)B) and Sells (V(t)S), with V = V(t)B + V(t)S
The Volume-Synchronized Probability of Informed Trading is then derived as:

Typically one might choose to estimate VPIN using a moving average over n buckets, with n being in the range of 50 to 100.

Another related statistic of interest is the single-period signed VPIN. This will take a value of between -1 and =1, depending on the proportion of buying to selling during a single period t.

Fig 1. Single-Period Signed VPIN for the ES Futures Contract

It turns out that quote revisions condition strongly on the signed VPIN. For example, in tests of the ES futures contract, we found that the change in the midprice from one volume bucket the next  was highly correlated to the prior bucket’s signed VPIN, with a coefficient of 0.5.  In other words, market participants offering liquidity will adjust their quotes in a way that directly reflects the direction and intensity of toxic flow, which is perhaps hardly surprising.

Of greater interest is the finding that there is a small but statistically significant dependency of price changes, as measured by first buy (sell) trade price to last sell (buy) trade price, on the prior period’s signed VPIN.  The correlation is positive, meaning that strongly toxic flow in one direction has a tendency  to push prices in the same direction during the subsequent period. Moreover, the single period signed VPIN turns out to be somewhat predictable, since its autocorrelations are statistically significant at two or more lags.  A simple linear auto-regression ARMMA(2,1) model produces an R-square of around 7%, which is small, but statistically significant.

A more useful model, however , can be constructed by introducing the idea of Markov states and allowing the regression model to assume different parameter values (and error variances) in each state.  In the Markov-state framework, the system transitions from one state to another with conditional probabilities that are estimated in the model.

An example of such a model  for the signed VPIN in ES is shown below. Note that the model R-square is over 27%, around 4x larger than for a standard linear ARMA model.

We can describe the regime-switching model in the following terms.  In the regime 1 state  the model has two significant autoregressive terms and one significant moving average term (ARMA(2,1)).  The AR1 term is large and positive, suggesting that trends in VPIN tend to be reinforced from one period to the next. In other words, this is a momentum state. In the regime 2 state the AR2 term is not significant and the AR1 term is large and negative, suggesting that changes in VPIN in one period tend to be reversed in the following period, i.e. this is a mean-reversion state.

The state transition probabilities indicate that the system is in mean-reversion mode for the majority of the time, approximately around 2 periods out of 3.  During these periods, excessive flow in one direction during one period tends to be corrected in the
ensuring period.  But in the less frequently occurring state 1, excess flow in one direction tends to produce even more flow in the same direction in the following period.  This first state, then, may be regarded as the regime characterized by toxic flow.

Markov State Regime-Switching Model

Markov Transition Probabilities

P(.|1)       P(.|2)

P(1|.)        0.54916      0.27782

P(2|.)       0.45084      0.7221

Regime 1:

AR1           1.35502    0.02657   50.998        0

AR2         -0.33687    0.02354   -14.311        0

MA1          0.83662    0.01679   49.828        0

Error Variance^(1/2)           0.36294     0.0058

Regime 2:

AR1      -0.68268    0.08479    -8.051        0

AR2       0.00548    0.01854    0.296    0.767

MA1     -0.70513    0.08436    -8.359        0

Error Variance^(1/2)           0.42281     0.0016

Log Likelihood = -33390.6

Schwarz Criterion = -33445.7

Hannan-Quinn Criterion = -33414.6

Akaike Criterion = -33400.6

Sum of Squares = 8955.38

R-Squared =  0.2753

R-Bar-Squared =  0.2752

Residual SD =  0.3847

Residual Skewness = -0.0194

Residual Kurtosis =  2.5332

Jarque-Bera Test = 553.472     {0}

Box-Pierce (residuals):         Q(9) = 13.9395 {0.124}

Box-Pierce (squared residuals): Q(12) = 743.161     {0}


A Simple Trading Strategy

One way to try to monetize the predictability of the VPIN model is to use the forecasts to take directional positions in the ES
contract.  In this simple simulation we assume that we enter a long (short) position at the first buy (sell) price if the forecast VPIN exceeds some threshold value 0.1  (-0.1).  The simulation assumes that we exit the position at the end of the current volume bucket, at the last sell (buy) trade price in the bucket.

This simple strategy made 1024 trades over a 5-day period from 8/8 to 8/14, 90% of which were profitable, for a total of $7,675 – i.e. around ½ tick per trade.

The simulation is, of course, unrealistically simplistic, but it does give an indication of the prospects for  more realistic version of the strategy in which, for example, we might rest an order on one side of the book, depending on our VPIN forecast.

Figure 2 – Cumulative Trade PL


Easley, D., Lopez de Prado, M., O’Hara, M., Flow Toxicity and Volatility in a High frequency World, Johnson School Research paper Series # 09-2011, 2011

Easley, D. and M. O‟Hara (1987), “Price, Trade Size, and Information in Securities Markets”, Journal of Financial Economics, 19.

Easley, D. and M. O‟Hara (1992a), “Adverse Selection and Large Trade Volume: The Implications for Market Efficiency”,
Journal of Financial and Quantitative Analysis, 27(2), June, 185-208.

Easley, D. and M. O‟Hara (1992b), “Time and the process of security price adjustment”, Journal of Finance, 47, 576-605.


Forecasting Financial Markets – Part 1: Time Series Analysis

The presentation in this post covers a number of important topics in forecasting, including:

  • Stationary processes and random walks
  • Unit roots and autocorrelation
  • ARMA models
  • Seasonality
  • Model testing
  • Forecasting
  • Dickey-Fuller and Phillips-Perron tests for unit roots

Also included are a number of detailed worked examples, including:

  1. ARMA Modeling
  2. Box Jenkins methodology
  3. Modeling the US Wholesale Price Index
  4. Pesaran & Timmermann study of excess equity returns
  5. Purchasing Power Parity



    Resources for Quantitative Analysts

    Two of the smartest econometricians I know are Prof. Stephen Taylor of Lancaster University, and Prof. James Davidson of Exeter University.

    I recall spending many profitable hours in the 1980′s with Stephen’s book Modelling Financial Time Series, which I am pleased to see has now been reprinted in a second edition.  For a long time this was the best available book on the topic and it remains a classic. It has been surpassed by very few books, one being Stephen’s later work Asset Price Dynamics, Volatility and Prediction.  This is a superb exposition, one that will repay close study.    

    James Davidson is one of the smartest minds in econometrics. Not only is his research of the highest caliber, he has somehow managed (in his spare time!) to develop one of the most advanced econometrics packages available.  Based on Jurgen Doornik’s Ox programming system, the Time Series Modelling package covers almost every conceivable model type, including regression models, ARIMA, ARFIMA and other single equation models, systems of equations, panel data models, GARCH and other heteroscedastic models and regime switching models, accompanied by very comprehensive statistical testing capabilities.  Furthermore, TSM is very well documented and despite being arguably the most advanced system of its kind it is inexpensive relative to alternatives.  James’s research output is voluminous and often highly complex.  His book, Econometric Theory, is an excellent guide to the state of the art, but not for the novice (or the faint hearted!).

    Those looking for a kinder, gentler introduction to econometrics would do well to acquire a copy of Prof. Chris Brooks’s Introductory Econometrics for Finance. This covers most of the key ideas, from regression, through ARMA, GARCH, panel data models, cointegration, regime switching and volatility modeling.  Not only is the coverage comprehensive, Chris’s explanation of the concepts is delightfully clear and illustrated with interesting case studies which he analyzes using the EViews econometrics package.    Although not as advanced as TSM, EViews has everything that most quantitative analysts are likely to require in a modeling system and is very well suited to Chris’s teaching style.  Chris’s research output is enormous and covers a great many topics of interest to financial market analysts, in the same lucid style.