Novel scaling law governing stock price dynamics

A stock market is typically modeled as a complex system where the purchase, holding or selling of individual stocks affects other stocks in nonlinear and collaborative ways that cannot be always captured using succinct models. Such complexity arises due to several latent and confounding factors, such as variations in decision making because of incomplete information, and differing short/long-term objectives of traders. While few emergent phenomena such as seasonality and fractal behaviors in individual stock price data have been reported, universal scaling laws that apply collectively to the market are rare. In this paper, we consider the market-mode adjusted pairwise correlations of returns over different time scales ($\tau$), $c_{i,j}(\tau)$, and discover two such novel emergent phenomena: (i) the standard deviation of the $c_{i,j}(\tau)$'s scales as $\tau^{-\lambda}$, for $\tau$ larger than a certain return horizon, $\tau_0$, where $\lambda$ is the scaling exponent, (ii) moreover, the scaled and zero-shifted distributions of the $c_{i,j}(\tau)$'s are invariant of $\tau > \tau_0$. Our analysis of S\&P500 market data collected over almost $20$ years ($2004-2020$) demonstrates that the twin scaling property holds for each year and across $2$ decades (orders of magnitude) of $\tau$. Moreover, we find that the scaling exponent $\lambda$ provides a summary view of market volatility: in years marked by unprecedented financial crises -- for example $2008$ and $2020$ -- values of $\lambda$ are substantially higher. As for analytical modeling, we demonstrate that such scaling behaviors observed in data cannot be explained by existing theoretical frameworks such as the single- and multi-factor models. To close this gap, we introduce a promising agent-based model -- inspired by literature on swarming -- that displays more of the emergent behaviors exhibited by the real market data.