Why are Limit Orders Always Linear?

8 Pages Posted: 19 Mar 2008

See all articles by Andre Levy

Andre Levy

UNSW Business School

Peter L. Swan

University of New South Wales (UNSW Sydney; Financial Research Network (FIRN)

Date Written: March 11, 2008

Abstract

A number of results in liquidity asset pricing and market microstructure depend on the assumption that, when investors trade strategically, recognizing limited market participation (i.e. thin markets), trade volume impacts prices linearity with respect to order size. The assumption is usually made explicitly or implicitly in the traders' linear investment demand schedules or limit order books. Yet, in the reviewed literature, this assumption on investment demand is always imposed, rather than derived from investors' endowments and preferences for risk. In many cases, the result is that the lack of market depth has little or no impact on asset prices. We first show that the validity of these results depends strongly on the linearity assumption, as we demonstrate that investment demand linearity is equivalent to investors being homogenously price-sensitive regardless of endowment heterogeneity. We then eliminate the need for the assumption, endogenizing investment demand schedules from risk preferences instead, and show that, in the case of CARA investors facing a stream of normally distributed instantaneous dividends, the equilibrium demand is necessarily linear on prices, and thus that investors, regardless of differences in endowments, are all equally price-sensitive. This result reconciles the theory with both economic intuition and with empirical studies on price impact functions.

Suggested Citation

Levy, Andre and Swan, Peter Lawrence, Why are Limit Orders Always Linear? (March 11, 2008). Available at SSRN: https://ssrn.com/abstract=1107845 or http://dx.doi.org/10.2139/ssrn.1107845

Andre Levy

UNSW Business School ( email )

UNSW Business School
High St
Sydney, NSW 2052
Australia

Peter Lawrence Swan (Contact Author)

University of New South Wales (UNSW Sydney ( email )

School of Banking and Finance
UNSW Business School
Sydney NSW, NSW 2052
Australia
+61 2 9385 5871 (Phone)
+61 2 9385 6347 (Fax)

HOME PAGE: http://https://www.business.unsw.edu.au/our-people/peterswan

Financial Research Network (FIRN)

C/- University of Queensland Business School
St Lucia, 4071 Brisbane
Queensland
Australia

HOME PAGE: http://www.firn.org.au

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