Finance and Stochastics

, Volume 18, Issue 1, pp 1–37 | Cite as

Transaction costs, trading volume, and the liquidity premium

  • Stefan Gerhold
  • Paolo Guasoni
  • Johannes Muhle-Karbe
  • Walter Schachermayer
Article

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. The 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 

Mathematics Subject Classification

91G10 91G80 

JEL Classification

G11 G12 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stefan Gerhold
    • 1
  • Paolo Guasoni
    • 2
    • 3
  • Johannes Muhle-Karbe
    • 4
  • Walter Schachermayer
    • 5
  1. 1.Institut für WirtschaftsmathematikTechnische Universität WienWienAustria
  2. 2.Department of Mathematics and StatisticsBoston UniversityBostonUSA
  3. 3.School of Mathematical SciencesDublin City UniversityDublin 9Ireland
  4. 4.Departement für Mathematik, and Swiss Finance InstituteETH ZürichZürichSwitzerland
  5. 5.Fakultät für MathematikUniversität WienWienAustria

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