Trade Clustering and Power Laws in Financial Markets
Theoretical Economics 15 (2020), 1365–1398 1555-7561/20201365 Trade clustering and power laws in financial markets Makoto Nirei Graduate School of Economics, University of Tokyo John Stachurski Research School of Economics, Australian National University Tsutomu Watanabe Graduate School of Economics, University of Tokyo This study provides an explanation for the emergence of power laws in asset trad- ing volume and returns. We consider a two-state model with binary actions, where traders infer other traders’ private signals regarding the value of an asset from their actions and adjust their own behavior accordingly. We prove that this leads to power laws for equilibrium volume and returns whenever the number of traders is large and the signals for asset value are sufficiently noisy. We also provide nu- merical results showing that the model reproduces observed distributions of daily stock volume and returns. Keywords. Herd behavior, trading volume, stock returns, fat tail, power law. JEL classification. G14. 1. Introduction Recently, the literature on empirical finance has converged on a broad consensus: Daily returns on equities, foreign exchange, and commodities obey a power law. This striking property of high-frequency returns has been found across both space and time through a variety of statistical procedures, from conditional likelihood methods and nonpara- metric tail decay estimation to straightforward log-log regression.1 A power law has also been found for trading volume by Gopikrishnan et al. (2000)andPlerou et al. (2001). Makoto Nirei: nirei@e.u-tokyo.ac.jp John Stachurski: john.stachurski@anu.edu.jp Tsutomu Watanabe: watanabe@e.u-tokyo.ac.jp We have benefited from comments by the anonymous referees, Daisuke Oyama, and especially Koichiro Takaoka.
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