Statistical properties of market collective responses

TL;DR

This paper empirically investigates how trade signs, volumes, and liquidity influence market responses, revealing the statistical structure of these responses and the critical role of traded volumes in price changes.

Contribution

It introduces a comprehensive analysis of market responses using singular value decomposition and characterizes their statistical properties with the $t$ distribution.

Findings

Price and liquidity responses are well described by the $t$ distribution.

Traded volumes significantly influence price changes and liquidity responses.

Price and liquidity factors are weakly overlapping when related to trade signs.

Abstract

We empirically analyze the price and liquidity responses to trade signs, traded volumes and signed traded volumes. Utilizing the singular value decomposition, we explore the interconnections of price responses and of liquidity responses across the whole market. The statistical characteristics of their singular vectors are well described by the $t$ location-scale distribution. Furthermore, we discuss the relation between prices and liquidity with respect to their overlapping factors. The factors of price and liquidity changes are non-random when these factors are related to the traded volumes. This means that the traded volumes play a critical role in the price change induced by the liquidity change. In contrast, the two kinds of factors are weakly overlapping when they are related to the trade signs and signed traded volumes. Hence, an imbalance of liquidity is related to the price change.