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Long Horizons, High Risk Aversion, and Endogeneous Spreads

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  • Paolo Guasoni
  • Johannes Muhle-Karbe

Abstract

For an investor with constant absolute risk aversion and a long horizon, who trades in a market with constant investment opportunities and small proportional transaction costs, we obtain explicitly the optimal investment policy, its implied welfare, liquidity premium, and trading volume. We identify these quantities as the limits of their isoelastic counterparts for high levels of risk aversion. The results are robust with respect to finite horizons, and extend to multiple uncorrelated risky assets. In this setting, we study a Stackelberg equilibrium, led by a risk-neutral, monopolistic market maker who sets the spread as to maximize profits. The resulting endogenous spread depends on investment opportunities only, and is of the order of a few percentage points for realistic parameter values.

Suggested Citation

  • Paolo Guasoni & Johannes Muhle-Karbe, 2011. "Long Horizons, High Risk Aversion, and Endogeneous Spreads," Papers 1110.1214, arXiv.org, revised Jul 2012.
  • Handle: RePEc:arx:papers:1110.1214
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    File URL: http://arxiv.org/pdf/1110.1214
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    References listed on IDEAS

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    1. Stefan Gerhold & Johannes Muhle-Karbe & Walter Schachermayer, 2010. "The dual optimizer for the growth-optimal portfolio under transaction costs," Papers 1005.5105, arXiv.org, revised Oct 2010.
    2. Riccardo Giacomelli & Elisa Luciano, 2011. "Equilibrium price of immediacy and infrequent trade," Carlo Alberto Notebooks 221, Collegio Carlo Alberto, revised 2013.
    3. Dumas, Bernard & Luciano, Elisa, 1991. " An Exact Solution to a Dynamic Portfolio Choice Problem under Transactions Costs," Journal of Finance, American Finance Association, vol. 46(2), pages 577-595, June.
    4. Yuri M. Kabanov & Christophe Stricker, 2002. "On the optimal portfolio for the exponential utility maximization: remarks to the six-author paper," Mathematical Finance, Wiley Blackwell, vol. 12(2), pages 125-134.
    5. Stefan Gerhold & Paolo Guasoni & Johannes Muhle-Karbe & Walter Schachermayer, 2011. "Transaction Costs, Trading Volume, and the Liquidity Premium," Papers 1108.1167, arXiv.org, revised Jan 2013.
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