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Methodology of measuring performance in alternative investment



The development of alternative investment has highlighted the limitations of standard performance measures like the Sharpe ratio, primarily because alternative strategies yield returns distributions which can be far from gaussian. In this paper, we propose a new framework in which trades, portfolios or strategies of various types can be analysed regardless of assumptions on payoff. The proposed class of measures is derived from natural and simple properties of the asset allocation. We establish representation results which allow us to describe our set of measures and involve the log-Laplace transform of the asset distribution. These measures include as particular cases the squared Sharpe ratio, Stutzer's rank ordering index and Hodges' Generalised Sharpe Ratio. Any measure is shown to be proportional to the squared Sharpe ratio for gaussian distributions. For non gaussian distributions, asymmetry and fat tails are taken into account. More precisely, the risk preferences are separated into gaussian and non-gaussian risk aversions.

Suggested Citation

  • Alexis Bonnet & Isabelle Nagot, 2005. "Methodology of measuring performance in alternative investment," Cahiers de la Maison des Sciences Economiques b05078, Université Panthéon-Sorbonne (Paris 1).
  • Handle: RePEc:mse:wpsorb:b05078

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    References listed on IDEAS

    1. Carlo Acerbi, 2001. "Risk Aversion and Coherent Risk Measures: a Spectral Representation Theorem," Papers cond-mat/0107190,
    2. Stutzer, Michael, 2003. "Portfolio choice with endogenous utility: a large deviations approach," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 365-386.
    3. Bertsimas, Dimitris & Lauprete, Geoffrey J. & Samarov, Alexander, 2004. "Shortfall as a risk measure: properties, optimization and applications," Journal of Economic Dynamics and Control, Elsevier, vol. 28(7), pages 1353-1381, April.
    4. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 26(01), pages 71-92, May.
    5. Acerbi, Carlo, 2002. "Spectral measures of risk: A coherent representation of subjective risk aversion," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1505-1518, July.
    6. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    7. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    8. Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191,
    9. Gerber, Hans U., 1974. "On Additive Premium Calculation Principles," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 7(03), pages 215-222, March.
    10. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    11. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304,
    12. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
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    More about this item


    Alternative investment; performance measure; additive independence condition; generalised Sharpe ratio; portfolio optimization.;

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools

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