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Transaction costs, trading volume, and the liquidity premium

Gerhold, Stefan ; Guasoni, Paolo ; Muhle-Karbe, Johannes ; Schachermayer, Walter

In: Finance and Stochastics, 2014, vol. 18, no. 1, p. 1-37

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    Title
    • Transaction costs, trading volume, and the liquidity premium
    Author
    • Gerhold, Stefan. Institut für Wirtschaftsmathematik, Technische Universität Wien, Wiedner Hauptstrasse 8-10, 1040, Wien, Austria
    • Guasoni, Paolo. Department of Mathematics and Statistics, Boston University, 111 Cummington Street, 02215, Boston, MA, USA
    • Muhle-Karbe, Johannes. Departement für Mathematik, and Swiss Finance Institute, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland
    • Schachermayer, Walter. Fakultät für Mathematik, Universität Wien, Nordbergstrasse 15, 1090, Wien, Austria
    Document Type
    • Postprint
    OAI-PMH Identifier
    • oai:doc.rero.ch:324750
    Summary
    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.