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Extreme Risk, excess return and leverage: the LP formula

Author

Listed:
  • Olivier Le Marois

    (fluks - FLUKS)

  • Julia Mikhalevsky

    (FEDERIS Gestion d'Actifs - Federis Gestion d'Actifs)

  • Raphaël Douady

    (Riskdata - Financial Risk Management Software, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

The LP formula is based upon the substitution of the exogenous risk aversion hypothesis by a credit equilibrium hypothesis. This leads to a trade-off between expected blue-sky return – the expected return excluding default scenarios – and extreme risk estimated from scenarios leading to default. An empirical study on the past 90 years shows that this trade-off curve is almost identical across asset classes. In equilibrium, an asset expected blue-sky return is proportional to its contribution to extreme risk. Assuming normal returns, we obtain CAPM as a sub-case of the LP relation. This relationship makes extreme risk underestimation a strong driver of asset price bubbles.

Suggested Citation

  • Olivier Le Marois & Julia Mikhalevsky & Raphaël Douady, 2014. "Extreme Risk, excess return and leverage: the LP formula," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01151376, HAL.
    • Handle: RePEc:hal:cesptp:hal-01151376
    Note: View the original document on HAL open archive server: https://hal.science/hal-01151376
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    References listed on IDEAS

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    1. Victor DeMiguel & Lorenzo Garlappi & Francisco J. Nogales & Raman Uppal, 2009. "A Generalized Approach to Portfolio Optimization: Improving Performance by Constraining Portfolio Norms," Management Science, INFORMS, vol. 55(5), pages 798-812, May.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
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    More about this item

    Keywords

    asset allocation; extreme risk; CAPM; risk budgeting; equilibrium;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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