Transaction costs, trading volume, and the liquidity premium

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• 作者：Stefan Gerhold (1)
  Paolo Guasoni (2) (3)
  Johannes Muhle-Karbe (4)
  Walter Schachermayer (5)
  
• 关键词：Transaction costs ; Long ; run ; Portfolio choice ; Liquidity premium ; Trading volume ; 91G10 ; 91G80 ; G11 ; G12
• 刊名：Finance and Stochastics
• 出版年：2014
• 出版时间：January 2014
• 年：2014
• 卷：18
• 期：1
• 页码：1-37
• 全文大小：1,104 KB
• 作者单位：Stefan Gerhold (1)
  Paolo Guasoni (2) (3)
  Johannes Muhle-Karbe (4)
  Walter Schachermayer (5)
  
  1. Institut f眉r Wirtschaftsmathematik, Technische Universit盲t Wien, Wiedner Hauptstrasse 8-10, 1040, Wien, Austria
  2. Department of Mathematics and Statistics, Boston University, 111 Cummington Street, Boston, MA, 02215, USA
  3. School of Mathematical Sciences, Dublin City University, Glasnevin, Dublin 9, Ireland
  4. Departement f眉r Mathematik, and Swiss Finance Institute, ETH Z眉rich, R盲mistrasse 101, 8092, Z眉rich, Switzerland
  5. Fakult盲t f眉r Mathematik, Universit盲t Wien, Nordbergstrasse 15, 1090, Wien, Austria
  
• ISSN：1432-1122

文摘

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.