Markets never forget: the lasting impression of square-root impact

Inelasticity and illiquidity prolong the effects of flows; risk management needs to take this into account

Key points Summary Q&A

• Recent research shows that market impact can determine long‑term returns and create lasting gaps between market price and fundamental value.
• Sato and Kanazawa find the square‑root law of market impact holds across asset and trader types, reinforcing that impact is mechanical rather than informational.
• Gabaix and Koijen are among those who say that impact decays, but slowly – and only partially; Slade and Yan have also published on this point.
• Their arguments support Fisher Black’s idea that fundamental value is only vaguely known to market participants, who must use price as information about value.
• The author argues that long-term price impact is the lasting effect of short-term square-root impact, and that trading changes prices in a way that can persist and change the investment landscape.

These summaries are generated by an LLM, but edited by humans.

How should we characterise market impact? For practitioners, it’s an obstacle that considerably increases the cost of trading. For most financial economists, however, it’s a short-lived effect that has little economic relevance in the longer term.

Yet recent research – both theoretical and empirical – suggests this is not the case. It shows that impact is no second-order nuisance. Rather, it is a first-order determinant of long-horizon returns – and can generate lasting deviations between market price and fundamental value. 

It makes the perceived differential between trading and investing harder to defend, since one person’s impact is another’s alpha.

Long-term price impact is the lasting effect of short-term square-root impact

In my previous column for Risk.net, I discussed the striking Tokyo Stock Exchange study of Yuki Sato and Kiyoshi Kanazawa. Their key finding confirms that the square-root law of market impact holds not only across different assets, but also across decision-makers – be they retail or institutional, informed or not. It strongly supports the idea that the square-root law is mechanical – arising from order flow and liquidity – rather than informational.

So, the natural question then is: what happens when trading pressure ends? If impact is mechanical, why don’t prices quickly relax back to a level dictated by fundamentals?

Several empirical studies suggest impact does indeed decay post-trade, but slowly – over days or weeks – and only partially. In a remarkable paper, Xavier Gabaix and Ralph Koijen argue the impact multiplier, as they call it – the GK multiplier – is five (see also Morgan Slade and Seb Yan on the impact of institutional order flows). Thus, buying $1 of the US equity market, without any special information, increases total market capitalisation by about $5 in the long run – over a period of several months.

The Gabaix-Koijen interpretation of such extreme price inelasticity is that the portfolio composition of large mutual funds is constrained; to keep a target stock or bond allocation, these funds can only sell if prices go up sufficiently. Hence, when a new buy order arrives, it sets off a game of pass-the-parcel: liquidity providers absorb demand and gradually pass the instrument along to lower-frequency participants, until – finally – it ends up in the hands of long-term investors.

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Although this depiction likely captures some of the reality, I believe long-term impact is much more general: that it is not confined to stocks and bonds but extends to all asset classes. In my paper, ‘The Inelastic Market Hypothesis: A Microstructural Interpretation’, I argue that long-term price impact is the lasting effect of short-term square-root impact. 

The mechanism is simple, in essence, and hinges on Fisher Black’s idea that fundamental value is only vaguely known to market participants, who must heed the market price – itself a source of information about what other investors believe. Thus, once prices have been impacted by incoming flow – even uninformed – participants tend to revise their reservation prices in the direction of the newly traded price. Statistically, the whole supply-demand curve follows the realised price – sometimes with a delay.

This is enough, as I show in my paper, to explain both the slow relaxation of impact and its long-term, permanent component, which the theory predicts to be linear in quantity – even when the short-term impact is square-root. Perhaps more surprisingly, the model in fact predicts the correct O(1) magnitude for the GK multiplier, which is found to be the ratio of two small numbers of similar proportions – namely the daily volatility and the fraction of market capitalisation traded daily.

But once we accept this, the consequences are uncomfortable. Flows become a first-order determinant of long-horizon returns. Sustained buying pressure – be it from passive allocation, benchmark rebalancing, corporate buybacks, systematic strategies or liability-driven investing – can push prices up or down for extended periods without any corresponding news. 

Back to Black

Fundamentals still matter – particularly insofar as they affect flows – but many other motivations, including fads and manias, can be incorporated into prices. This leads to significant and persistent distortions between prices and value – precisely as anticipated by Black, and further discussed in a 2018 article I co-authored for Risk.net: ‘Black was right’. 

A direct piece of evidence that this picture makes sense is provided in ‘Ponzi funds’, a paper I recently co-wrote with Dario Villamaina and Philippe van der Beck. Using a detailed database of daily flows into exchange-traded funds, we quantitatively confirm that the impact of such flows is a primary determinant of ETF performance – in particular, for funds concentrated in illiquid assets. In other words, inflows can mechanically generate performance. Performance then attracts more inflows, which pushes prices up further – reinforcing performance – until flows reverse. 

This is not fraud, it is simply what happens in an inelastic market, when capital chases performance and the market’s risk-bearing capacity is limited. The unwind may then not be a gentle mean-reversion, but a sharp drop – when everyone wants to do the same trade. This is precisely what happened during the infamous quant quake of 2007, and it is the lurking risk embedded in many stat-arb and market-neutral books.

The upshot is that price impact is not merely about slippage around a ‘true’ price: when markets are inelastic, trading changes prices in a way that can persist and therefore changes the investment landscape itself. 

Capacity is not only an operational constraint, it’s a pricing constraint. Stress tests should include flow shocks – correlated redemptions, de-risking rules, benchmark effects – not just exogenous price shocks.

And perhaps most importantly, where long-term impact is a lingering effect of short-term impact, the connection between microstructure and macro finance is much stronger than we would like to think.

Editing by Louise Marshall