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Imagine pouring sand onto a pile, one grain at a time. As the individual particles of sand are added, the pile grows larger, but seems to be otherwise stable. But as time goes by, something changes within that seemingly stable system. Instead of settling on the surface of the pile, adding another grain of sand causes an avalanche as rivers of sand suddenly break loose and rush down the surface of the pile.

What's happening in this scenario is some very complex and chaotic physics. Millions of individual particles are dynamically interacting with each other to produce this effect after they reach what's called a self-organized criticality. Once they reach this point, instead of acting like a somewhat solid and stable object, the individual grains of stand start moving together and flow like a fluid. That change is called a phase transition and its something of a signature of a system that's affected by quantum dynamics.

Of all the inventions humans have created, the stock market perhaps comes closest to sharing the same quantum-like properties at play in a sand pile. Every day, people engage in millions if not billions of transactions and, when all is going well, the value of their investments rise over time. Metaphorically much like a pile of sand. Until....

There's a new paper, published earlier this year, that caught our attention because it focused on the quantum-like properties of stock prices to explain why they suddenly break from their stable rising pattern, with investors randomly reacting to new information, and start behaving chaotically instead, with investors rushing for the proverbial exits all at the same time.

Here's an excerpt from the introduction of paper published by Kwangwon Ahn, Linxiao Cong, Hanwool Jang, and Daniel Sungyeon Kim that gets into the work they did to describe that phenomenon using the tools of quantum physics:

Stock markets exhibit universal characteristics similar to physical systems with considerable interacting units, for which several microscopic models have been developed (Shalizi 2001; Lux and Marchesi 1999). For example, the return distribution presents pronounced tails that are thicker than those of the Gaussian distribution (Shalizi 2001; Lux 1996; Mantegna and Stanley 1995). Several models have been proposed that phenomenologically show fat-tail distributions induced by investors’ herding behavior (Banerjee 1993; Topol 1991). Furthermore, Cont and Bouchaud (2000), Orĺean (1995), Banerjee (1993), and Topol (1991) showed that market participants’ interactions through imitation can lead to large fluctuations in aggregate demand and heavy tails in the distribution of returns. This approach had been formalized as a power law exponent at the tail of the distribution with a smaller magnitude associated with stronger herding behavior in stock returns (Nirei et al. 2020; Gabaix et al. 2005; Plerou et al. 1999; Gopikrishnan et al. 1999), trading volumes (Gabaix et al. 2006; Gopikrishnan et al. 2000), and commodity returns (Joo et al. 2020), which have been empirically investigated. Another stream of literature theoretically explains the power law in firm size distribution (Ji et al. 2020; Luttmer 2007) and trading volume (Nirei et al. 2020). However, these studies are limited to providing a connection between the power law exponent and other external factors, such as the business cycles and economic uncertainty.

We contribute to literature by explaining the role of economic uncertainty as a bridge between business cycles and investors’ herding behavior. Specifically, we propose a parsimonious model that employs quantum mechanics as an intermediate step to obtain the final solution and justify the power law distribution in stock returns. We start with the Fokker–Planck (FP) equation to model the dynamics of stock return distribution and derive the Schrödinger equation for a particular external potential (Ahn et al. 2017). The form of the potential is postulated based on empirical evidence of the evolution of stock returns in the marketplace. The solution suggests the existence of a power law for the tail distribution of stock returns. This also predicts a positive association between business cycles and the power law exponent. Our model provides new insights into existing research that models stock prices using random walks (Bartiromo 2004; Ma et al. 2004), quantum oscillators (Ahn et al. 2017; Ye and Huang 2008), quantum wells (Pedram 2012; Zhang and Huang 2010), and quantum Brownian motions (Meng et al. 2016).

We provide further empirical evidence on whether herding behavior in stock returns is negatively associated with business cycles. Furthermore, business cycles, which are often used as proxies for economic growth, are closely related to economic uncertainty, whereby it is believed that recessions are accompanied by higher economic uncertainty (Bloom 2014). Moreover, greater economic uncertainty leads to higher levels of uncertainty in the stock market. With greater uncertainty in the stock market, investors are more likely to mimic others because increased information asymmetry leads to fewer investors having confidence in their valuations (Alhaj-Yaseen and Yau 2018; Park and Sabourian 2011; Devenow and Welch 1996), amplifying investors’ herding behavior in the tail. As hypothesized, we find that herding behavior is stronger during recessions than booms and that economic uncertainty causes significant herding behavior.

In normal circumstances, individual investors respond to the random onset of new information and their responses are generally not synchronized with each other. And why would they be? For example, Investor A may be seeking to build their portfolio of dividend stocks to provide income in their near retirement. Meanwhile, Investor B may be focused on investing in growth stocks because it will be years before they retire. Investor C, on the other hand, is excited to speculate and chases after the hottest stocks. Investors D through Z, and millions more, approach their investments differently and, most importantly, mostly at random with respect to each other.

But when recessionary conditions take hold, which have the potential to affect millions simultaneously, the onset of new information associated with that developing state and the decreased certainty of continued stability would appear to prompt investors to act more like a herd, which is one of their two main macro-level findings.

Their other main finding is that applying a quantum model to stock prices can explain the tendency of investors to cluster around the center but also allows for "local" herding among extreme investors. That sounds very much like what you get from a stock market whose variation is best described with a Lévy stable distribution, which came up when we recently described the day-to-day volatility of the S&P 500 since 3 January 1950.

Going beyond the paper, we should note that such herd behavior doesn't only arise with developing recessionary conditions. Since 2008, we've regularly documented how investors alter the trajectory of the S&P 500 in response to market moving news, such as changes in the expected timing of interest rate changes. These changes arising from the same phenomenon can drive either rising or falling stock prices depending on other underlying factors. Since many of these changes aren't tied to any significant changes in investor uncertainty, there are still big research opportunities in this area.

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