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The best gain-loss ratio is a poor performance measure


  • Sara Biagini
  • Mustafa Pinar


The gain-loss ratio is known to enjoy very good properties from a normative point of view. As a confirmation, we show that the best market gain-loss ratio in the presence of a random endowment is an acceptability index and we provide its dual representation for general probability spaces. However, the gain-loss ratio was designed for finite $\Omega$, and works best in that case. For general $\Omega$ and in most continuous time models, the best gain-loss is either infinite or fails to be attained. In addition, it displays an odd behaviour due to the scale invariance property, which does not seem desirable in this context. Such weaknesses definitely prove that the (best) gain-loss is a poor performance measure.

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  • Sara Biagini & Mustafa Pinar, 2012. "The best gain-loss ratio is a poor performance measure," Papers 1209.6439,, revised Dec 2012.
  • Handle: RePEc:arx:papers:1209.6439

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    References listed on IDEAS

    1. PInar, Mustafa Ç. & Salih, AslIhan & CamcI, Ahmet, 2010. "Expected gain-loss pricing and hedging of contingent claims in incomplete markets by linear programming," European Journal of Operational Research, Elsevier, vol. 201(3), pages 770-785, March.
    2. John H. Cochrane & Jesus Saa-Requejo, 2000. "Beyond Arbitrage: Good-Deal Asset Price Bounds in Incomplete Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 79-119, February.
    3. Carr, Peter & Geman, Helyette & Madan, Dilip B., 2001. "Pricing and hedging in incomplete markets," Journal of Financial Economics, Elsevier, vol. 62(1), pages 131-167, October.
    4. Aytaç Ílhan & Mattias Jonsson & Ronnie Sircar, 2005. "Optimal investment with derivative securities," Finance and Stochastics, Springer, vol. 9(4), pages 585-595, October.
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