Don’t blame HFT: plug liquidity gaps for market stability

Dynamic fees could incentivise liquidity when and where it’s most needed, writes quant fund founder Bouchaud

High-frequency trading, often accused of upsetting the status quo in traded markets, in fact brings a dynamism that helps them function better.

Yet when markets move erratically and volatility jumps occur with no apparent financial or economic explanation, fingers are quick to point in HFT’s direction. Critics hold it responsible for variously rigging and destabilising markets, as epitomised in flash crashes. Research confirms, however, that HFT results in significantly lower bid-ask spread costs. And, barring any technological glitches, does not increase the frequency of large price jumps.

We also know the real reason is that market liquidity is intrinsically unstable. Recent models demonstrate that managing the risks associated with market-making, whether by humans or by computers, unavoidably creates destabilising feedback loops.

Since orders to buy or sell arrive at random times, financial markets are always unbalanced. In such conditions, market-makers play a crucial role in allowing smooth trading and continuous prices. They act as liquidity buffers, which absorb any temporary surplus of buy or sell orders.

Their reward for providing such a service is the bid/ask spread – systematically buying a shade lower and selling a shade higher – and pocketing the difference.

So, what is the fair value of the bid/ask spread? Well, it must at least compensate the cost of providing liquidity, which is adverse selection.

Value proposition

Indeed, market-makers must post prices that can be picked up if deemed advantageous by traders with superior information. The classic Glosten-Milgrom model provides an elegant conceptual framework to rationalise the trade-off between adverse selection and bid/ask spread, but fails to give a quantitative, operational answer.

In a 2008 study by Capital Fund Management researchers, we came up with a remarkably simple answer: the fair value of the bid/ask spread is equal to the ratio of the volatility to the square-root of the trade frequency. This simple rule of thumb has many interesting consequences.¹  First, it tells us that, for a fixed level of volatility, increasing the trade frequency allows market-makers to reduce the spread – and hence the trading costs – for final investors. The logic is that trading smaller chunks more often reduces the risk of adverse selection.

This explains in part the rise of HFT in modern market-making, and the corresponding reduction in spreads. Throughout the period 1900 to 1980, the spread on US stocks was generally a whopping 60 basis points – reduced now to only a few basis points.

The fair value of the bid/ask spread is equal to the ratio of the volatility to the square-root of the trade frequency

Jean-Phillipe Bouchaud, Capital Fund Management

In the meantime, volatility has always hovered around 40% per year – with occasional troughs and spikes, of course.

In other words, investors were paying a much higher price for liquidity before HFT – confounding wild assertions that today’s electronic markets are rigged.

In fact – a few prosperous years before 2012 aside – high frequency market-making has become extremely competitive, and average spreads are now compressed to minimal values.

From this perspective, then, the economic rents available to liquidity providers have greatly decreased since the advent of HFT. But has this made markets more stable, or has the decrease in the profitability of market-making also made them more fragile?

This important question relates to the second consequence of our simple relation between spread and volatility. This relationship can be viewed from two angles.

Clearly, when volatility increases, the impact of adverse selection can be dire for market-makers, who therefore mechanically increase their spreads. Periods of high volatility can, however, be quite profitable for HFT since competition for providing liquidity then becomes less fierce.

But higher spreads by themselves lead to higher volatility, since transactions generate larger price jumps – or even crashes, when liquidity is low, and the order book is sparse. So, we can diagnose a fundamental destabilising feedback loop, intrinsic to any market-making activity:

volatility -> higher spreads & lower liquidity -> more volatility

This type of loop can be included in stochastic order-book models, such as the now commonly used family of Hawkes processes. As the strength of the feedback increases, one finds a phase transition between a stable market and a market prone to spontaneous liquidity crises, even in the absence of exogenous shocks or news.²

This theoretical result suggests that when market-makers – whether human or machine – react too strongly to unexpected events, liquidity can enter a death spiral. But who can blame them?

As the traders’ maxim goes: liquidity’s a coward; it’s never there when it’s needed.

Such a paradigm allows one to understand why a large fraction of price jumps occur without any significant news – rather, they result from endogenous, unstable feedback loops.

Intrinsic instability

Empirically, the frequency of 10-sigma daily moves of US stock prices has been fairly constant over the past 30 years, with no significant change between the pre-HFT era and more recent years.

There was even a precursor and a pre-HFT foreshadower of the infamous May 6, 2010 flash crash: on May 28, 1962, the stock market plunged 9% within a matter of minutes – for no apparent reason – before recovering in much the same, weird price trajectory as in 2010.

Our conjecture: markets are intrinsically unstable and have always been so.

So, to make markets more resilient, research should focus on better market design and/or adapted regulation that nips these intrinsic instabilities in the bud.

Is it possible to engineer a smart solution to make markets less prone to such dislocations? From the arguments above, we know the objective would be to crush the volatility/liquidity feedback loop – by promoting liquidity provision when it is on the verge of disappearing.

One idea would be to introduce dynamic make/take fees, which would make cancellations more costly and limit-order posting more profitable, depending on the current state of the order book.

These fees would then funnel into the HFT’s optimisation algorithms, and – one would hope – deflect the system away from the regime of recurrent endogenous liquidity crisis.

Jean-Phillipe Bouchaud is chairman of Capital Fund Management and member of the Académie des Sciences

Footnotes

¹ See: Wyart, M; Bouchaud, JP; Kockelkoren, J; Potters, M; and Vettorazzo, M (2008) – Relation between bid–ask spread, impact and volatility in order-driven markets. Quantitative finance, 8(1), 41–57.

² See: Fosset, A; Bouchaud, JP; and Benzaquen, M (2020) – Endogenous liquidity crises. Journal of Statistical Mechanics: Theory and Experiment, 2020(6), 063401.