Information content of liquidity and volatility measures

Highlights

• We investigate mutual information shared by volatility and liquidity.

• We study transfer entropy between the measures.

• Volatility estimators are more coherent than the liquidity ones.

• Garman–Klass is the most comprehensive volatility estimator.

• Volatility over volume shares more information with volatility than with liquidity.

Abstract

This paper aims to compare the mutual information shared by various liquidity and volatility estimators within each group separately. Our sample covers forty one blue-chip companies from the Warsaw Stock Exchange. In terms of their information content, volatility measures are much more coherent, while liquidity ones are more dispersed. The Garman–Klass volatility estimator seems to be the broadest measure of volatility, while Amihud illiquidity and Volatility over volume share the highest amount of mutual information among liquidity proxies. The latter proxy shares approximately the same amount of information with both volatility estimates and liquidity proxies. The possibility to forecast volatility or liquidity, measured by the transfer entropy, with the help of the other volatility or liquidity proxies is limited.

Introduction

Volatility and liquidity are intrinsic characteristics of financial markets, which share common properties: they are latent and related to the price formation process. The task of a perfect distinction between liquidity and volatility measures seems to be challenging [1]. Volatility focuses on the dispersion of returns and as such is a one-dimensional measure, while liquidity might be examined in various dimensions, focusing on the market depth, width, price impact or transaction costs [2]. Although both volatility and liquidity could be estimated in several ways, estimates of the former are based on prices only, while liquidity proxies require prices, quotes, and volumes. Karpoff [3] shows that large changes of prices or volumes have common sources in the information flow process. This study aims to investigate various volatility and liquidity measures to find one with the broadest information content. It also verifies how much information contained in one group is observed in the other. To achieve this, we refer to the information theory [4] and focus on the mutual information and transfer entropy of various volatility estimators and liquidity proxies. To identify whether volatility and liquidity estimates capture similar information, we consider nonparametric measures. From the broad set of volatility estimators we choose two which are based on high-low-open-close daily prices, namely Garman-Klass [5] and Parkinson [6] ones, as well as two measures computed based on intradaily data, the realized variance [7], and the bipower variation [8]. In the case of liquidity measures we focus on percent-cost and cost-per-dollar-volume proxies [9]. The former are represented by the Effective Quoted Spread [10] and the Closing Percent Quoted Spread [11], while the latter are Amihud illiquidity (2002) and Volatility over volume [13]. Based on these two sets of measures we examine the amount of mutual information shared by liquidity proxies and volatility estimates. By employing transfer entropy, we determine whether there is any information transfer between these measures, both in terms of linear or non-linear dependencies.

We offer several contributions to the existing literature. Many previous works aimed to indicate the best volatility estimators or liquidity proxies [14], [15]. Our study employs less popular approach which is related to the information theory [16]. On the one hand, we show that volatility measures share a significant amount of mutual information, much exceeding the one shared by liquidity proxies. The Garman–Klass estimator seems to be the leader among volatility proxies, as it shares the highest amount of information with every other volatility measure. On the other hand, liquidity proxies are loosely connected with their counterparts. The relationship between two liquidity proxies: Volatility over volume and Amihud illiquidity, seems to be most pronounced. However, the amount of mutual information shared by these proxies is roughly the same as the one shared by Volatility over volume and Garman–Klass or Parkinson estimators (both are volatility estimators). Thus, Volatility over volume might be considered as either a liquidity or volatility measure. Furthermore, we offer an extension to the causality studies by investigating the transfer entropy. The latter can be interpreted as a broader measure of causality, since it takes into account not only the linear, but also non-linear dependencies. We find that the transfer of information between various pairs of volatility estimates or liquidity proxies is limited. Most often the transfer from Parkinson estimator to Garman–Klass estimator is observed.

We employ data from the Warsaw Stock Exchange, which is a fast-growing European emerging market. We consider highly liquid stocks that have been included in the blue-chip index, WIG20, during the sample period 2006–2016 (or at least in some part of it). This study extends our understanding of how markets operate, showing the relations between liquidity and volatility. It also enhances the process of finding the best proxies and estimates.

The remainder of the paper is as follows: Section 2 shortly presents related works, Section 3 discusses the methodology, Section 4 describes data and the approach to measure liquidity and volatility, and Section 5 shows the empirical results. The paper ends up with conclusions.