The Impact of Order Size on Stock Liquidity - A Representative Study

Abstract

Liquidity, the ease of trading an asset, strongly varies between di erent sizes of stock positions. We analyze this aspect using the Xetra Liquidity Measure (XLM), which calculates daily, weighted spread for impatient traders transacting against the limit order book. For this measure, we have data for 160 German stocks over 5.5 years, which allows us a representative analysis of the order-size impact on liquidity cost and its main statistical characteristics.We nd that in the sample period average liquidity costs rose to over 100bp in large DAX and to 460bp in large SDAX positions. Over the last 5.5 years, liquidity has equally improved across all order sizes. Liquid position sizes, however, su ered less badly during the recent sub-prime crises, which represents another type of the ight-to-liquidity.As the basis for further theoretical analysis, we nd that trends in liquidity levels and ine ciencies in liquidity prices of large positions generate non-normality in the liquidity distribution. We also show that -as a rule of thumb -liquidity of an order size relative to market value and transaction volume is constant across stocks and time. While order size is not the most important liquidity determinant, doubling order size increases liquidity cost by 5-10% on average when accounting for other di erences in stocks.

Liquidity Adjusted Value at Risk: Integrating the Uncertainty in Depth and Tightness

“…Similar to previous studies (Le Saout, 2002;FrancoisHeude and van Wynendaele, 2001;Giot and Grammig, 2002;Stange and Kaserer, 2008;Qi and Wing, 2009) we use the weighted spread in order to incorporate the endogenous effects. On the other hand, our spread calculation methodology differs slightly from the existing studies: we take price duration points as intervals for spread calculation, without relying on any specific intraday time interval, which is in line with the calculation methodology of , as described before.…”

“…More importantly, even though the computer technology is recently capable of handling large datasets, majority of these models are less straightforward to be implemented by finance practitioners, either due to time or hardware limitations or complexity or to some extent due to data availability/quality. On the other hand, exogenous models are straightforward in implementation and interpretation but come with a simplifying and often criticized assumption, implying a perfect competition in market, whereby no single investor would have significant impact on the market price (Bangia et al 1999;Stange and Kaserer, 2008;Ernst et al 2012).…”

“…In order to account for the uncertainty in the market depth, we use the net trading volume (VNET) indicator as an input, which was proposed by Engle and Lange (2001). The second model integrates also the tightness dimension of liquidity measured by the first two moments of weighted relative bid-ask spread as the proxy variable, similar to previous studies (Le Saout, 2002;Francois-Heude and van Wynendaele, 2001;Giot and Grammig, 2002;Stange and Kaserer, 2008;Qi and Wing, 2009). Results show that both parametric LVaR approaches are strictly superior to conventional Value at Risk (VaR) models, with respect to performance in terms of regulatory compliance and statistical coverage and the relative cost of liquidity vs. loss size given violation.…”

Assessing Performance of Liquidity Adjusted Value-at-Risk Models

“…The argument of non-normality holds equally for liquidity costs. Stange and Kaserer (2008) analyze the distributional properties of liquidity costs and show that they are heavily skewed and fat-tailed. Ernst et al (2012) suggest a parametric approach based on the Cornish-Fisher approximation to account for non-normality in liquidity risk.…”

Market Liquidity Risk - An Overview

“…However, Stange and Kaserer (2008a) show, that liquidity cost also greatly vary with market capitalization. Integration of this fact might possibly capture ight-to-liquidity eects but requires further research.…”