The Battle Between Competing Models: What causes price to move, Information or Trader Impact? 

The following post is derived from a research paper published in January 2022 by Jean-Philippe Bouchaud titled “The Inelastic Market Hypothesis: A Microstructural Interpretation”. You can listen to a conversation with Jean-Philippe here.

Under the traditional viewpoint of the Efficient Market Hypothesis, information is seen as the primary driver of price movement. Under this theoretical framework it is assumed that all investors are rational participants seeking to optimise their utility function. These rational investors can all accurately determine the fundamental value of an asset based on the information that is available to them.  

A financial market is therefore regarded as a consolidation device which aggregates all these private estimates of an asset’s value to derive a consolidated result.

Under this ‘efficient’ model investors cannot obtain any arbitrage opportunity from this relationship between new information and the degree of price movement as ‘new information’ is by definition unpredictable. The model assumes that the information-price update function is immediate. 

The market price under this viewpoint is therefore considered to represent fundamental value at all times. Any change in price solely arises from new information made available to rational participants who immediately update market price through their altered private estimates of value.

Under EMH all new information is therefore regarded as being exogenous in origin. When new information is made available, rational participants quickly absorb that new information and update their value estimates. 

The immediate nature of the price update function means that there is no prior price dependence reflected in a time series. Each interval in a price series is therefore independent to each other and EMH stridently opposes the view of the existence of serial correlation in a time series.  

This absence of serial correlation in a time series of price data makes speculation a fruitless exercise. Any form of trading arbitrage depends on serial correlation where price updates are not immediately updated. Lags in price updating are a necessary ingredient for speculators to possess an edge.

While the EMH has had a dominant role in traditional economic theory, it is now being seriously challenged by alternative market models that see the causal reasons for price movement arising from the mechanics of collective trader impacts as opposed to factors arising from informational sources. These alternative models see impacts such as order flow imbalances, crowd behaviour and feedback loops as taking a primary role in driving price mechanics.

A leading contributor to these alternate models of market behaviour is Jean-Philippe Bouchaud (JPB) who appeared on our Volatility series podcast of TTU who has undertaken extensive research into understanding the microstructural behaviour of large price moves. JPB’s research provides a strong foundation that lend credibility to the growing movement of alternative ‘trader Impact’ models such as that proposed in the recent ‘Inelastic Market Hypothesis’ proposed by Xavier Gabaix and Ralph Koijen.

Microstructural Research

To be in a position to challenge the assumptions of the EMH, it is necessary to demonstrate that price moves are not causally linked to information, or to the actions of rational investors. If research can demonstrate that new information which the market receives is not the dominant contributor of price moves, then this would be sufficient to at least strongly challenge traditional orthodoxy.

JPB undertook extensive research using 1 minute data of major price moves in equity markets, where it could be demonstrated that most major price moves could not be accounted for through exogenous news sources. 

His research investigated directional price moves of +/- 4 standard deviations whereby greater than 90% of these events could not be assigned to ‘news events’ released via Bloomberg, Reuters and other major investor information sources. Only approximately 10% of the major price moves could be accounted for by these ‘Exogenous factors’. The balance of greater than 90% of all material price moves could only be therefore explained through sources arising from within the behaviour of markets themselves. These internal causal factors were assigned to ‘endogenous factors’. 

This is not to say that Exogenous news events don’t have a causal impact on moving price. They clearly do, but the degree to which ‘news events’ contribute to major price moves is clearly over-stated by traditional economic models. 

Furthermore, in a model which explains price moves as arising from collective trader impacts, it is inevitable that exogenous news events such as the declaration of war, the discovery of a new vaccine etc. will all contribute to altered trader behaviour. So, the question needs to be asked, does information have a primary causal role to play at all in driving price movement? Could it all be attributed to collective trader impacts?

In addition to these powerful research findings regarding the links to causal exogenous or endogenous drivers of price mechanics, JPB’s research categorically concluded that the profile of price jumps from either exogenous or endogenous sources were not localised ‘immediate’ events. They were spread out in time and space (non-local in impact). The volatility surrounding these price jumps took time to decay. This makes us ‘smell a rat’ in regard to the assumption of EMH that new information immediately updates market prices.

While both exogenous and endogenous sources of price jump exhibited ‘delayed’ price properties, the research also found that the volatility profile of exogenous versus endogenous price jumps is different. 

• Exogenous impacts typically displayed low volatility up to the point of the price jump and then a fairly fast decay rate back to the prior volatility levels; while
• Endogenous impacts were far more symmetrical in nature. Starting from a small seed, the volatility reached a critical point over time and then slowly decays.

The particularly long decay rate exhibited by the volatility associated with endogenous price jumps reflects how considerable uncertainty remains for up to 300 minutes following the peak of the price jump. There is a degree of serial dependence exhibited through the extent of the price signal. 

This long period of decay following the initial signal provides an indication that major price moves are not ‘independent and localised’ events expected under EMH. The impact of these price shocks extends over time and space. Volatility associated with major price moves exhibits features of clustering. If these price volatility clusters can be shown to demonstrate serial correlation, this could lead to significant disparities arising between fundamental value and real value.

Excess Volatility Puzzle

These research findings at the microstructural level support findings of Robert Schiller who refers to the ‘Excess Volatility Puzzle’. The analysis of short-term price fluctuations indicates that price moves cannot be solely explained in terms of fluctuations of ‘fundamental value’. There is some other causal mechanism at work which adds additional volatility to the ‘informational model’ suggested by EMH. 

Alternative models arising from econophysics provide hints as to what this additional volatility may be attributed to. For example, positive or negative feedback loops demonstrate how signals could be amplified or dampened by the collective behaviour allowing for ‘lagged non-local’ effects and serially correlated price behaviour.

To understand this ‘excess volatility’, we need to depart from a model comprising rational market participants and introduce ‘noise traders’ to the mix of system participants. By introducing ‘non rational’ participants into the model we would then be able to evaluate how the presence or absence of information impacts the price update function. 

Under EMH the introduction of such uninformed noise traders should not have an impact on price volatility. Only ‘true information’ according to EMH can change prices.

If we found that non-rational agents also contributed to long-term price volatility this would put a final definitive nail in the EMH coffin. Instead of fundamental value determining prices, we would then need to embrace collective trader impacts (or the order flow itself) as the mechanism that drives future price. Whether informed or random, imbalances in collective trade activity is the causal agent that moves prices.

The ‘order-driven theory’ of price mechanics offers a solution to the excess-volatility puzzle. If trades by themselves move prices, then excess trading could create excess volatility. 

From Microstructure to Macrostructure

Now while these research studies relate to price microstructure, how could these principles scale up to create Macrostructural effects. Specifically, as Trend Followers we want to know how these volatility clusters at the microscale can lead to serially correlated clusters that can last many months or years in duration and lead to major price trends. What research do we have that lends support to the idea that trends persist?

A new model proposed by Gabaix and Koijen entitled “In Search of the Origins of Financial Fluctuations: The Inelastic Markets Hypothesis” finds that a trader buying or selling $1 of an individual stock on average increases or` decreases the market capitalisation of that stock by $1 in the long run. 

This model does not distinguish between informed traders or uninformed traders and highlights that it is the impact of the buying/selling activity itself that drives long term market capitalisation. 

The degree of price movement is even more profound when buying the market as a whole (an Index or basket of equities). The research concludes that the multiplier is not 1x but 5 x in terms of market capitalisation.

This research highlights that it is not information itself, which is driving price changes, but rather order-flow imbalances from trader impacts. 

Supporters of EMH would argue that if a participant received $1 worth of new information, then their models of fundamental value would also increase/decrease by a corresponding $1 (a linear relationship) but only if that price change related to genuinely new information received by the market. But their argument becomes tenuous when we introduce noise traders into the mix as an uninformed trader should not affect the market price in any way whatsoever.

But the final blow to EMH is now being seen with research arising from observing price impacts through metaorders in high frequency price studies. Price changes do not follow a linear relationship with order execution, The research resoundingly concludes that price impact in the short term adopt a Square Root relationship.

This Square Root Law busts apart the assumption of EMH that market prices immediately adjust and re-equilibrate in accordance with the receipt of new information to the market. 

The Square Root Law in the short term suggests that the underlying mechanism is not information but rather the delayed impact in the short term of price adjustments associated with trader impacts. This small lag effect from correlated feedback effects is sufficient to embed arbitrage potential into the market for the speculator whereby a trader can exploit this arbitrage opportunity. 

The Square Root Law

Studies of large trades in high frequency trading reflect the impact of Metaorders. Traders or trading algos do not execute large trades via single market orders, but instead split up their trades into many small pieces. These pieces are executed incrementally over a period of several minutes to several days. The collection of all such individual orders belonging to the same trading decision is called a metaorder. 

So, to understand if price is linearly or nonlinearly related to trade activity, we can evaluate how much does a metaorder of total volume Q, executed over a period of duration T, affect the price on average? 

It is intuitive for us to believe that the impact of a metaorder would scale linearly with Q but surprisingly, empirical analysis reveals that in real markets, this scaling is not linear, but rather is approximately square root. In all metaorder cases, the average (relative) price change between the beginning and the end of a metaorder with volume Q is well-described by the “square-root law.

Metaorder impact is not additive. Instead, one finds that the second half of a metaorder impacts the price much less than the first half. 

For this square root impact to occur in the short term there must be some kind of liquidity memory time (or memory window) such that the influence of past trades cannot be neglected during this memory time. 

Over time horizons that exceed this memory time all memory of past trades is lost. One therefore expects that beyond the memory time, impact must become linear in Q. This is indeed what one finds within a model describing the dynamics of liquidity, which reproduces the square-root law at short times and a linear impact law at longer time.

The altering nature of the trade impact on price over time leads to a notion that a traders estimate of value remains ‘sticky’ over a short duration whereby this estimate has a tendency to distribute around the new updated price for a period of time before an new estimate is revised.

Recent theories that support this notion of a ‘memory time’ which makes price moves inelastic in nature and more discreet and ‘jump-like’ in nature rather than smooth and continuous is Latent Liquidity Theory.

Latent Liquidity Theory

Latent Liquidity Theory (LLT) of price impact,argues that the underlying mechanism for the inelasticity in price dynamics relates to how an investor updates their price estimates of an assets value. The theory recognises a memory time whereby price moves tend to hover around a single estimate for a period of time before discreetly jumping to a new reservation price. 

The theory assumes that each long-term investor in the market has a reservation price (to buy or to sell) that he or she updates as a function of time, due to incoming news, price changes, noise, etc. The collection of all these trading intentions constitutes the available liquidity at any instant of time – although most of it remains “latent”, i.e., is not immediately posted in the public order book.

Conclusion

This summary of recent research highlights a growing trend towards a model that seeks to explain price moves, not as a result of rational investors all homogenously acting with a shared utility towards the information that is made available to them to value a market price, but as a more realistic model that assesses the heterogeneous effects of collective trader impacts.

If collective trader impact (order flow) is the dominant cause of price changes, arbitrage is created through the ability of a trader to correctly anticipate the behaviour of others. These alternate models give hope to the FM’s seeking ‘alpha’ through models that exploit trader behaviour.

For example, when all market participants interpret a positive piece of news as negative and sell accordingly, the correct move for an arbitrageur is to interpret the news as negative, even if doing so does not make economic sense. 

The idea that it is the order-flow and not the information content that holds primacy in moving future price resonates well with the intuition of finance professionals and allows one to understand why statistical regularities might exist and be exploited by quant firms.