Transaction Costs, Trading Volume, and the Liquidity Premium

30 Pages Posted: 4 Aug 2011 Last revised: 5 Feb 2013

See all articles by Stefan Gerhold

Stefan Gerhold

Vienna University of Technology

Paolo Guasoni

Boston University - Department of Mathematics and Statistics; Dublin City University - School of Mathematical Sciences

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics

Walter Schachermayer

Universität Wien, Fakultät für Mathematik

Date Written: January 12, 2013

Abstract

In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs. We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. Results are robust to consumption and finite-horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly.

Keywords: transaction costs, long-run, portfolio choice, liquidity premium, trading volume

JEL Classification: G11, G12

Suggested Citation

Gerhold, Stefan and Guasoni, Paolo and Guasoni, Paolo and Muhle-Karbe, Johannes and Schachermayer, Walter, Transaction Costs, Trading Volume, and the Liquidity Premium (January 12, 2013). Boston U. School of Management Research Paper No. 2011-16, Available at SSRN: https://ssrn.com/abstract=1905077 or http://dx.doi.org/10.2139/ssrn.1905077

Stefan Gerhold

Vienna University of Technology ( email )

Karlsplatz 13
Vienna
Austria

Paolo Guasoni (Contact Author)

Dublin City University - School of Mathematical Sciences ( email )

Dublin
Ireland

HOME PAGE: http://www.guasoni.com

Boston University - Department of Mathematics and Statistics ( email )

Boston, MA 02215
United States

Johannes Muhle-Karbe

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
Imperial College
LONDON, SW7 2AZ
United Kingdom

Walter Schachermayer

Universität Wien, Fakultät für Mathematik ( email )

Oskar-Morgenstern-Platz 1
Vienna, A-1090
Austria
(+43-1) 4277-50723 (Phone)
(+43-1) 4277-850723 (Fax)

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