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Equilibrium returns with transaction costs

Author

Listed:
  • Bruno Bouchard

    (Université Paris-Dauphine)

  • Masaaki Fukasawa

    (Osaka University
    Tokyo Metropolitan University)

  • Martin Herdegen

    (University of Warwick)

  • Johannes Muhle-Karbe

    (Carnegie Mellon University)

Abstract

We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean–variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward–backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case, expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time.

Suggested Citation

  • Bruno Bouchard & Masaaki Fukasawa & Martin Herdegen & Johannes Muhle-Karbe, 2018. "Equilibrium returns with transaction costs," Finance and Stochastics, Springer, vol. 22(3), pages 569-601, July.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:3:d:10.1007_s00780-018-0366-6
    DOI: 10.1007/s00780-018-0366-6
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    References listed on IDEAS

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    1. Brennan, Michael J. & Subrahmanyam, Avanidhar, 1996. "Market microstructure and asset pricing: On the compensation for illiquidity in stock returns," Journal of Financial Economics, Elsevier, vol. 41(3), pages 441-464, July.
    2. Martin Herdegen & Johannes Muhle-Karbe, 2018. "Stability of Radner equilibria with respect to small frictions," Finance and Stochastics, Springer, vol. 22(2), pages 443-502, April.
    3. Dylan Possamai & H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs: the multidimensional case," Papers 1212.6275, arXiv.org, revised Jan 2013.
    4. Ludovic Moreau & Johannes Muhle-Karbe & H. Mete Soner, 2017. "Trading With Small Price Impact," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 350-400, April.
    5. Jean-Luc Vila & Dimitri Vayanos, 1999. "Equilibrium interest rate and liquidity premium with transaction costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 13(3), pages 509-539.
    6. Vayanos, Dimitri, 1998. "Transaction Costs and Asset Prices: A Dynamic Equilibrium Model," The Review of Financial Studies, Society for Financial Studies, vol. 11(1), pages 1-58.
    7. Pastor, Lubos & Stambaugh, Robert F., 2003. "Liquidity Risk and Expected Stock Returns," Journal of Political Economy, University of Chicago Press, vol. 111(3), pages 642-685, June.
    8. George M. Constantinides, 2005. "Capital Market Equilibrium with Transaction Costs," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 7, pages 207-227, World Scientific Publishing Co. Pte. Ltd..
    9. Sannikov, Yuliy & Skrzypacz, Andrzej, 2016. "Dynamic Trading: Price Inertia and Front-Running," Research Papers 3487, Stanford University, Graduate School of Business.
    10. Buss, Adrian & Uppal, Raman & Vilkov, Grigory, 2015. "Asset prices in general equilibrium with recursive utility and illiquidity induced by transactions costs," SAFE Working Paper Series 41, Leibniz Institute for Financial Research SAFE, revised 2015.
    11. Amihud, Yakov & Mendelson, Haim, 1986. "Asset pricing and the bid-ask spread," Journal of Financial Economics, Elsevier, vol. 17(2), pages 223-249, December.
    12. Jan Kallsen & Johannes Muhle-Karbe, 2017. "The General Structure Of Optimal Investment And Consumption With Small Transaction Costs," Mathematical Finance, Wiley Blackwell, vol. 27(3), pages 659-703, July.
    13. Heaton, John & Lucas, Deborah J, 1996. "Evaluating the Effects of Incomplete Markets on Risk Sharing and Asset Pricing," Journal of Political Economy, University of Chicago Press, vol. 104(3), pages 443-487, June.
    14. Subrahmanyam, Avanidhar, 1998. "Transaction Taxes and Financial Market Equilibrium," The Journal of Business, University of Chicago Press, vol. 71(1), pages 81-118, January.
    15. Jin Choi & Kasper Larsen, 2015. "Taylor approximation of incomplete Radner equilibrium models," Finance and Stochastics, Springer, vol. 19(3), pages 653-679, July.
    16. Anthony W. Lynch & Sinan Tan, 2011. "Explaining the Magnitude of Liquidity Premia: The Roles of Return Predictability, Wealth Shocks, and State‐Dependent Transaction Costs," Journal of Finance, American Finance Association, vol. 66(4), pages 1329-1368, August.
    17. Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
    18. Peter O. Christensen & Kasper Larsen, 2014. "Incomplete Continuous-Time Securities Markets with Stochastic Income Volatility," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 4(2), pages 247-285.
    19. Paolo Guasoni & Marko Weber, 2017. "Dynamic Trading Volume," Mathematical Finance, Wiley Blackwell, vol. 27(2), pages 313-349, April.
    20. Richard Martin & Torsten Schoneborn, 2011. "Mean Reversion Pays, but Costs," Papers 1103.4934, arXiv.org.
    21. Wachter, Jessica A., 2002. "Portfolio and Consumption Decisions under Mean-Reverting Returns: An Exact Solution for Complete Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 37(1), pages 63-91, March.
    22. Min Dai & Peifan Li & Hong Liu & Yajun Wang, 2016. "Portfolio Choice with Market Closure and Implications for Liquidity Premia," Management Science, INFORMS, vol. 62(2), pages 368-386, February.
    23. Kohlmann, Michael & Tang, Shanjian, 2002. "Global adapted solution of one-dimensional backward stochastic Riccati equations, with application to the mean-variance hedging," Stochastic Processes and their Applications, Elsevier, vol. 97(2), pages 255-288, February.
    24. Bong‐Gyu Jang & Hyeng Keun Koo & Hong Liu & Mark Loewenstein, 2007. "Liquidity Premia and Transaction Costs," Journal of Finance, American Finance Association, vol. 62(5), pages 2329-2366, October.
    25. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    26. Delarue, François, 2002. "On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case," Stochastic Processes and their Applications, Elsevier, vol. 99(2), pages 209-286, June.
    27. Constantinos Kardaras & Hao Xing & Gordan v{Z}itkovi'c, 2015. "Incomplete stochastic equilibria for dynamic monetary utility," Papers 1505.07224, arXiv.org, revised Feb 2017.
    28. Gordan Žitković, 2012. "An example of a stochastic equilibrium with incomplete markets," Finance and Stochastics, Springer, vol. 16(2), pages 177-206, April.
    29. Gârleanu, Nicolae & Pedersen, Lasse Heje, 2016. "Dynamic portfolio choice with frictions," Journal of Economic Theory, Elsevier, vol. 165(C), pages 487-516.
    30. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2014. "Transaction costs, trading volume, and the liquidity premium," Finance and Stochastics, Springer, vol. 18(1), pages 1-37, January.
    31. H. Mete Soner & Nizar Touzi, 2012. "Homogenization and asymptotics for small transaction costs," Papers 1202.6131, arXiv.org, revised Jun 2013.
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    More about this item

    Keywords

    Equilibrium; Transaction costs; FBSDEs;
    All these keywords.

    JEL classification:

    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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