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Measuring adequately the benefit of diversification in the extreme quantiles: An inquiry into covariation on the brink of catastrophe

Author

Listed:
  • Pierre-Charles Pradier

    (Centre d'Economie de la Sorbonne)

  • Guillaume Rideau

    (Groupe BPCE, Département Risques Participations Non Bancaires)

  • Sakina Rrguiti

    (Université Paris 1 Panthéon-Sorbonne, Centre d'Economie de la Sorbonne et Groupe BPCE)

Abstract
The aim of this work is to better understand the nature of covariation in the vicinity of extremes on financial data and assess whether the usual assumptions and covariation measures fits the actual data. For simplicity, we consider pairs of random variables. In order to identify the shape of the covariation all along the distribution, and particularly as the extreme quantiles are approached, we describe the contribution of each of the variables from a random couple to the quantiles of the weighted sum of these variables. This approach makes sense since it can be interpreted in terms of Value-at-Risk in a financial institution: the VaR of the sum of variables may represent the capital requiremet for a diversified conglomerate, while the sum of VaR of the variables would correspond to the capital requirements for the components of the conglomerate, without taking diversification into account. The ratio of these two quantities appears as a good measure of both the benefit of diversification and the decorrelation of variables. We thus compare the values of quantiles and ratio taken from a representative dataset to the values obtained from various simulations relying on the usual assumptions. The result of this comparison is that the usual assumptions do not correctly model the covariation of the real-word data. In particular, the usual assumptions tend to exaggerate the correlation in the vicinity of extreme loss while the benefit of diversification is uniform across distribution. Additional simulations and modelling assumptions may be required to assess the generality of this result

Suggested Citation

  • Pierre-Charles Pradier & Guillaume Rideau & Sakina Rrguiti, 2022. "Measuring adequately the benefit of diversification in the extreme quantiles: An inquiry into covariation on the brink of catastrophe," Documents de travail du Centre d'Economie de la Sorbonne 22021, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:22021
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    References listed on IDEAS

    as
    1. Smith, Keith V & Schreiner, John C, 1969. "A Portfolio Analysis of Conglomerate Diversification," Journal of Finance, American Finance Association, vol. 24(3), pages 413-427, June.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
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    More about this item

    Keywords

    Financial Conglomerates; Diversification; Value-at-Risk; Capital requirements;
    All these keywords.

    JEL classification:

    • G20 - Financial Economics - - Financial Institutions and Services - - - General
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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