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The solid line is an annual power-law index calculated by summarizing the daily normalized S&P 500 Index returns, with the dotted line being the uncertainty of the year. The shaded area indicates the recession period determined by the NBER recession indicator. **Financial Innovation (2024). doi： 10.1186/s40854-023-00540-z
A new study published in the journal Financial Innovation has developed a new quantum model for volatility that combines economic uncertainty and herd behavior. The study aims to gain a deeper understanding of the origin and impact of anomalies, such as fat tails, fluctuating clustering, and inverse effects.
In this study, quantum mechanics is the branch of physics that explains the behavior of subatomic particles and is the basis for simulating the dynamics of returns. "*Return drift is the result of external potentials that represent market forces, pulling short-term volatility back into long-term equilibrium," explains Dr. Kwangwon Ahn, first author of the study and associate professor of industrial engineering at Yonsei University.
They introduced the diffusion coefficient that captures the fluctuation of returns, and solved the Schrödinger equation, which is a fundamental quantum mechanical equation that produces a power-law distribution at the tail – a common feature of returns.
A power-law distribution means that extreme events, such as crashes, are more likely to occur in a normal distribution than expected. The researchers also showed that the power-law index, which measures the degree of obesity in tails, is inversely proportional to the diffusion coefficient and the external potential potential. This means that higher volatility and slower equilibrium regression lead to a stronger herd effect of returns, as investors tend to imitate others during periods of uncertainty and information asymmetry.
The researchers then used empirical data from the United States** to test their model. They use the growth rate of gross domestic product (GDP) and the uncertainty of the economy as the business cycle and economic uncertainty, respectively. They found that the power-law index was positively correlated with GDP growth rate and negatively correlated with the uncertainty of the **, which confirmed their theory**. They also found that economic uncertainty is the mediator that connects the business cycle with herd behavior in returns.
Our research shows that quantum mechanics can be a useful tool for understanding markets, which are complex systems with many interactions. We hope that our research will inspire more interdisciplinary research that combines physics and finance to explore the hidden patterns and mechanisms of markets," said corresponding author Dr. Daniel Sungyeon Kim, associate professor of finance at the university.
We show that economic uncertainty is at the root of counter-cyclical herd behavior in returns, which could have a significant impact on investors and policymakers.
More information: Kwangwon Ahn et al., Business Cycles and Herd Behavior in Returns: Theory and Evidence, Financial Innovation (2024). doi： 10.1186/s40854-023-00540-z