As reported by Bloomberg, David Easley, Marcos Mailoc Lopez de Prado and Maureen O’Hara have published a paper titled The Microstructure of the ‘Flash Crash’: Flow Toxicity, Liquidity Crashes and the Probability of Informed Trading:

The ‘flash crash’ of May 6th 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, $1 trillion in market value vanished. In this paper, we argue that the ‘flash crash’ is the result of the new dynamics at play in the current market structure, not conjunctural factors, and therefore similar episodes are likely to occur again. We highlight the role played by order toxicity in affecting liquidity provision, and we provide compelling evidence that the collapse could have been anticipated with some degree of confidence given the increasing toxicity of the order flow in the hours and days prior to collapse. We also show that a measure of this toxicity, the Volume-Synchronized Probability of Informed Trading (the VPIN* informed trading metric), Granger-causes volatility, while the reciprocal is less likely, and that it takes on average 1/10 of a session’s volume for volatility to adjust to changes in the VPIN metric. We attribute this cause-effect relationship to the impact that flow toxicity has on market makers’ willingness to provide liquidity. Since 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’, which would allow them to dynamically monitor and manage their risks.

They make the point:

Providing liquidity in a high frequency environment introduces new risks for market makers. When order flows are essentially balanced, high frequency market makers have the potential to earn razor thin margins on massive numbers of trades. When order flows become unbalanced, however, market makers face the prospect of losses due to adverse selection. The market makers’ estimate of the toxicity (the expected loss from trading with position takers) of the flow directed to them by position takers now becomes a crucial factor in determining their participation. If they believe that this toxicity is too high, they will liquidate their positions and leave the market.

In summary, we see three forces at play in the recent market structure:

Concentration of liquidity provisioninto a small number of highly specialized firms.Reduced participation of retail investorsresulting in increased toxicity of the flow received by market makers.High sensitivity of liquidity providers to intraday losses, as a result of the liquidity providers low capitalization, high turnover, increased competition and small profit target.

Quick! Sign up the big banks to provide liquidity through proprietary trading! Oh … wait ….

Further, they make the point about market-making:

To understand why toxicity of order flow can induce such behavior from market makers, let us return to the role that information plays in affecting liquidity in the market. Easley and O’Hara (1992) sets out the mechanism by which informed traders extract wealth from liquidity providers. For example, if a liquidity provider trades against a buy order he loses the difference between the ask price and the expected value of the contract if the buy is from an informed trader. On the other hand, he gains the difference between the ask price and the expected value of the contract if the buy is from an uninformed trader. This loss and gain, weighted by the probabilities of the trade arising from an informed trader or an uninformed trader just balance due to the intense competition between liquidity providers.

[Formula]

If flow toxicity unexpectedly rises (a greater than expected fraction of trades arises from informed traders), market makers face losses. Their inventory may grow beyond their risk limits, in which case they are forced to withdraw from the side of the market that is being adversely selected. Their withdrawal generates further weakness on that side of the market and their inventories keep accumulating additional losses. At some point they capitulate, dumping their inventory and taking the loss. In other words, extreme toxicity has the ability of transforming liquidity providers into liquidity consumers.

The earlier paper by these authors, detailing the calculation of VPIN, was titled Measuring Flow Toxicity in a High Frequency World:

Order flow is regarded as toxic when it adversely selects market makers, who are unaware that they are providing liquidity at their own loss. Flow toxicity can be expressed in terms of Probability of Informed Trading (PIN). We present a new procedure to estimate the Probability of Informed Trading based on volume imbalance (the VPIN* informed trading metric). An important advantage of the VPIN metric over previous estimation procedures comes from being a direct analytic procedure which does not require the intermediate estimation of non-observable parameters describing the order flow or the application of numerical methods. It also renders intraday updates mutually comparable in a frequency that matches the speed of information arrival (stochastic time clock). Monte Carlo experiments show this estimate to be accurate for all theoretically possible combinations of parameters, even for statistics computed on small samples. Finally, the VPIN metric is computed on a wide range of products to show that this measure anticipated the ‘flash crash’ several hours before the markets collapsed

Although the calibration is interesting and perhaps valuable, the underlying theory is pretty simple:

classify each transaction as buy or sell initiated:[Footnote]

a. A transaction i is a buy if either:

i. [Price increases], or

ii. [Price unchanged] and the [previous transaction] was also a buy.

b. Otherwise, the transaction is a sell.

Footnote: According to Lee and Ready (1991), 92.1% of all buys at the ask and 90.0% of all sells at the bid are correctly classified by this simple procedure. See Lee, C.M.C. and M.J. Ready (1991): “Inferring trade direction from intraday data”, The Journal of Finance, 46, 733-746. Alternative trade classification algorithms could be used.

and VPIN is simply the absolute value of the difference between buy-volume and sell-volume, expressed as a fraction of total volume. Yawn.

The VPIN indicator is very similar to Joe Granville’s Technical Analysis indicator On-Balance Volume. While Easley, Lopez de Prado and O’Hara have dressed it up with a little math and illustrated it in the glorious TA tradition of anecdotal cherry picking, they have neither provided anything particularly new nor proved their case.

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