Financial markets are commonly regarded as chaotic, yet the physics of complex systems continues to uncover stable patterns within them. Japanese researchers Yuki Sato and Kiyoshi Kanazawa of Kyoto University have published empirical evidence of the so-called Square-Root Law (SRL) using data from the Tokyo Stock Exchange in Physical Review Letters.
The essence of the law is simple and at the same time inconvenient for large players: the price impact of a large trade grows not linearly, but in proportion to the square root of the trade size. This means that to double the price effect, an investor must increase the volume of a buy or sell order not twofold, but fourfold. In other words, the market “dampens” aggressive capital inflows faster than might appear at first glance.
Importantly, the study is based not on models or simulations, but on real data from one of the world’s largest exchanges. This strengthens the status of SRL as a universal law applicable not only to the Japanese market, but to global financial systems as a whole.
For investors and algorithmic trading, this has practical implications: large positions become an increasingly inefficient tool for influencing prices, and market liquidity behaves like a physical medium with its own constraints. Financial markets remain risky—but are looking less and less completely random.
Link to the publication: journals.aps.org — continuation in the article
