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The Boiling Frog

September 29, 2023

The boiling frog is a somewhat morbid ‘apologue’ [1] that tells of how a frog will sense and react to changes in temperature as opposed to its absolute level. This means that if you were to put a frog into tepid water and slowly raise the temperature, the frog would meet its demise, feeling no urge to leave the water as it slowly warmed to a boil.  While this fable is not true (rest assured that a frog will, in fact, jump out of water that has become uncomfortably warm, no matter how slowly the temperature is being raised), it serves as a colourful analogy for the inner workings of financial markets.

At its heart, investing in a financial asset (e.g., stock in a company, a government bond, etc.) requires that two parties – a buyer and a seller – agree on a transaction price: the number of dollars that the buyer and seller agree that the asset is worth. This process begs the question of what exactly this price should be. Intuitively, it’s tied in some way to the so-called ‘fundamental value’ of the asset – an often vaguely defined (and unobserved) property of an asset related to a visceral and intrinsic attribute of quality. However, putting a number to this fundamental value is tricky, so much so that renowned economist Fischer Black famously said that we can’t know the fundamental value within more than a factor of two. (Black, 1986) Furthermore, while the amount and speed of information dissemination has increased exponentially since the time of Black, the inaccessibility if this fundamental measure of value still rings true. So, somewhat like the fabled frog, replacing temperatures with dollars, we have a poor sense for what the true value (temperature) of an asset is.

Sitting alongside the concept of fundamental value is another ubiquitous anchor point for analysis known as the efficient markets hypothesis. A champion of the theoretical underpinnings of economics, the story of efficient markets states that all market participants are rational actors who work in the process of price discovery, ingesting all available information as it emerges, and rapidly coming to a consensus about the correct price. [2] One of the crowning achievements of the efficient markets hypothesis from a quantitative perspective, is that it provides an explanation for the statistical properties of observed market dynamics (the day-to-day changes in asset prices), and serves as a basis for the absence of predictive information contained in past prices. However, upon further investigation, the precision and simplicity of such a picture may be a little too clean to be entirely true.

There are, for instance, rational limits on this sort of efficiency: on fast enough timescales – as market participants try to find the correct price of an asset in light of new information – there will be transient mispricing of the asset, which may result in exploitable trends in price. [3] However, as shown by physicist-turned-financier Jean-Philippe Bouchaud in a recent commentary article, these mispricings would need to be smaller than 0.05%, and only persist for around 10 minutes to be consistent with empirical data, which is a tough sell given the uncertainty in fundamental value. (Bouchaud, 2022)

A compelling explanation for this unreasonable speed of efficiency comes from the emerging field of microstructure theory, which focuses on modelling the dynamics of financial order books as a means of understanding the prevailing dynamics of markets. Here, the observed high level of efficiency is of a different origin. Specifically, high-frequency traders (known as liquidity providers in this context), who use algorithms to identify and execute on trading opportunities over very short timescales, are deciding which assets to buy and sell not on the real-world information that is entering the marketplace, but based solely on information about what other traders are doing. While the way that this strategy is borne out is rather technical, the effect of these liquidity providers is to remove any exploitable trends in prices over timescales much faster than markets would otherwise remain efficient. (Bouchaud, 2006) However, because of this, while markets may appear to be efficient from a statistical point of view, they need not be efficient in a ‘fundamental value’ sense.

There are many implications of this microstructural view, but one of the most interesting outcomes – that brings us eventually back to the frogs – has to do with what is called market impact. On its face, market impact simply reflects that the act of buying or selling an asset will impact its price. For instance, if I have to sell a large amount of a given asset over a short period of time, as I sell all of my assets, each successive trade will execute at a lower price. So, we are posed with an interesting situation when the market begins to digest a very large order for selling or buying an asset (often called a metaorder) that can be initiated for reasons unrelated to shifts in any fundamentals of the asset.  The impact of the order on the market price can be significant, and the response of market participants bears important implications for the fundamental efficiency of markets. In a somewhat recent article (Benzaquen & Bouchaud, 2018), it was shown that, in the presence of a metaorder, if market participants tend to re-orient their assessment of fundamental value in response to price changes (over some timescale), then markets can exhibit long-term price adjustments that are completely unrelated to changes in fundamental value. Furthermore, the ‘stickiness’ of people’s conviction that the pre-metaorder price is, in fact, correct will impact how large the long-term price change will be. Most importantly, however, is that this mechanism provides a concrete means by which market price can become untethered (at least partly so) from fundamental value, while remaining efficient (in a statistical sense). (Bouchaud, 2022) [4]

So, like the fabled frogs in the pot of water, doomed to meet a bubbly end, the problem of fundamental value versus order-flow based price changes sheds a bit of light on the inner complexities of markets in action. The intrinsic uncertainty of fundamental value can lead to scenarios where capital flows into and out of markets become the driving force for price adjustments.  Furthermore, this delicate balance between fundamentals-driven traders and high-frequency liquidity providers can have real, and potentially detrimental, impacts on the financial portfolio of an asset manager. Ultimately, while judgments of value could be 100% correct, the price can be distorted by order flows to appear as if it were not. So, while you may be right, as John Maynard Keynes famously said: “markets can remain irrational longer than you can remain solvent.”


  • F. Black, “Noise”, The Journal of Finance, 1986
  • J.P. Bouchaud, “The Inelastic Market Hypothesis: A Microstructural Interpretation”, Arxiv, 2022
  • J.P. Bouchaud, Y. Gefen, M. Potters, & M. Wyart, “Fluctuations and Response in Financial Markets”, Quantitative Finance, 2006
  • M. Benzaquen & J.P. Bouchaud, “Market Impact with Multi-Timescale Liquidity”, Quantitative Finance, 2018
  • X. Gabaix and R. Koijen, “In Search of the Origin of Financial Fluctuations: The Inelastic Markets Hypothesis”, SSRN, 2022


  • [1] Which is, apparently, a moral fable, and typically one containing animals.
  • [2] ‘Correct’ in the sense that the prevailing price reflects the fundamental value of the asset.
  • [3] For instance, in the minutes to hours following a new piece of news about a company, there will be some disagreement between what the implications are for asset value between market participants, leading to increases in price volatility over this timescale.
  • [4] In a rather awesome melding of the microstructural with the macroeconomic, this rather granular explanation of how prices can change in absence of shifts in fundamentals provides a microscopic backdrop for a previously written about article by Gabaix and Koijen (2022) studying the inelasticity of markets on a large scale, which is argued by Bouchaud to be a manifestation of the same underlying phenomenon.


Steve Large

Steve is a data scientist working on foundational research, using advanced quantitative methods to add value to VIP’s models and strategies. Steve holds a PhD in theoretical physics and uses his knowledge of stochastic processes and quantitative methods to develop unique and robust investment strategies that continually improve the strategies offered to VIP’s investors.


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