The non-random walk of stock prices: The long-term correlation between signs and sizes

TL;DR

This paper reveals that stock prices exhibit long-range correlations between the signs and sizes of returns, challenging the random walk assumption and highlighting the importance of long-memory effects for market efficiency.

Contribution

It introduces a simple model linking signs and sizes of returns to volatility and demonstrates the existence of long-range correlations that the model cannot reproduce.

Findings

The simple model overestimates volatility by about 70% at one-hour intervals.

Long-range correlations between signs and sizes of returns are identified.

These correlations are linked to long-memory of transaction signs and market efficiency.

Abstract

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about 70%, and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.