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The Limits of Leverage

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  • Paolo Guasoni
  • Eberhard Mayerhofer

Abstract

When trading incurs proportional costs, leverage can scale an asset's return only up to a maximum multiple, which is sensitive to its volatility and liquidity. In a model with one safe and one risky asset, with constant investment opportunities and proportional costs, we find strategies that maximize long term returns given average volatility. As leverage increases, rising rebalancing costs imply declining Sharpe ratios. Beyond a critical level, even returns decline. Holding the Sharpe ratio constant, higher asset volatility leads to superior returns through lower costs.

Suggested Citation

  • Paolo Guasoni & Eberhard Mayerhofer, 2015. "The Limits of Leverage," Papers 1506.02802, arXiv.org, revised Oct 2017.
    • Handle: RePEc:arx:papers:1506.02802
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    References listed on IDEAS

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    1. Andrea Frazzini & Lasse Heje Pedersen, 2022. "Embedded Leverage [Asset pricing with liquidity risk]," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 12(1), pages 1-52.
    2. Kevin Guo & Tim Leung, 2016. "Understanding the Tracking Errors of Commodity Leveraged ETFs," Papers 1610.09404, arXiv.org.
    3. Michael Taksar & Michael J. Klass & David Assaf, 1988. "A Diffusion Model for Optimal Portfolio Selection in the Presence of Brokerage Fees," Mathematics of Operations Research, INFORMS, vol. 13(2), pages 277-294, May.
    4. Tang, Hongfei & Xu, Xiaoqing Eleanor, 2013. "Solving the Return Deviation Conundrum of Leveraged Exchange-Traded Funds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(1), pages 309-342, February.
    5. 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.
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    Cited by:

    1. Ibrahim Ekren & Ren Liu & Johannes Muhle-Karbe, 2015. "Optimal Rebalancing Frequencies for Multidimensional Portfolios," Papers 1510.05097, arXiv.org, revised Sep 2017.
    2. Ibrahim Ekren & Johannes Muhle-Karbe, 2017. "Portfolio Choice with Small Temporary and Transient Price Impact," Papers 1705.00672, arXiv.org, revised Apr 2020.
    3. Tim Leung & Hyungbin Park, 2017. "LONG-TERM GROWTH RATE OF EXPECTED UTILITY FOR LEVERAGED ETFs: MARTINGALE EXTRACTION APPROACH," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(06), pages 1-33, September.

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