# New Measures for Performance Evaluation

## Author Info

• Alexander Cherny
Registered author(s):

## Abstract

This paper characterizes performance measures satisfying a set of proposed axioms. We develop four new measures consistent with the axioms and show that they improve on the economic properties of the Sharpe Ratio and the Gain-Loss Ratio. In our treatment, the performance measures, or the indexes of acceptability, are linked to positive expectations resulting from a stressed sampling of the cash-flow distribution. Theoretically, it is shown that the level of acceptability varies directly with the amount of stress tolerated. In an empirical application, the performance measures are applied to cash flows generated by writing options on the SPX and the FTSE. This exercise reveals that acceptability levels are U-shaped in the strike direction. The Author 2008. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org, Oxford University Press.

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File URL: http://hdl.handle.net/10.1093/rfs/hhn081

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## Bibliographic Info

Article provided by Society for Financial Studies in its journal The Review of Financial Studies.

Volume (Year): 22 (2009)
Issue (Month): 7 (July)
Pages: 2371-2406

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Handle: RePEc:oup:rfinst:v:22:y:2009:i:7:p:2371-2406

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## Citations

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Cited by:
1. Madan, Dilip B. & Schoutens, Wim, 2013. "Systemic risk tradeoffs and option prices," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 222-230.
2. Volker Krätschmer & Alexander Schied & Henryk Zähle, 2014. "Comparative and qualitative robustness for law-invariant risk measures," Finance and Stochastics, Springer, vol. 18(2), pages 271-295, April.
3. Dilip B. Madan, 2010. "Conserving Capital by Adjusting Deltas for Gamma in the Presence of Skewness," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 3(1), pages 1-25, December.
4. Jan Voelzke, 2014. "Weakening the Gain-Loss-Ratio measure to make it stronger," CQE Working Papers 3114, Center for Quantitative Economics (CQE), University of Muenster.
5. Dilip Madan & Martijn Pistorius & Mitja Stadje, 2013. "On consistent valuations based on distorted expectations: from multinomial random walks to L\'{e}vy processes," Papers 1301.3531, arXiv.org.
6. David B. BROWN & Enrico G. DE GIORGI & Melvyn SIM, . "A Satiscing Alternative to Prospect Theory," Swiss Finance Institute Research Paper Series 09-19, Swiss Finance Institute.
7. Enrico G. De Giorgi & David B. Brown & Melvyn Sim, 2010. "Dual representation of choice and aspirational preferences," University of St. Gallen Department of Economics working paper series 2010 2010-07, Department of Economics, University of St. Gallen.
8. Cerrato, Mario & Crosby, John & Kaleem, Muhammad, 2011. "Measuring the Economic Significance of Structural Exchange Rate Models," SIRE Discussion Papers 2011-62, Scottish Institute for Research in Economics (SIRE).
9. Marco Frittelli & Marco Maggis, 2012. "Complete duality for quasiconvex dynamic risk measures on modules of the $L^{p}$-type," Papers 1201.1788, arXiv.org, revised Sep 2012.
10. Marco Frittelli & Marco Maggis & Ilaria Peri, 2012. "Risk Measures on $\mathcal{P}(\mathbb{R})$ and Value At Risk with Probability/Loss function," Papers 1201.2257, arXiv.org, revised Sep 2012.
11. Tomasz R. Bielecki & Igor Cialenco & Marcin Pitera, 2013. "Dynamic Limit Growth Indices in Discrete Time," Papers 1312.1006, arXiv.org.
12. Ernst Eberlein & Dilip Madan & Martijn Pistorius & Wim Schoutens & Marc Yor, 2014. "Two price economies in continuous time," Annals of Finance, Springer, vol. 10(1), pages 71-100, February.
13. Sara Biagini & Jocelyne Bion-Nadal, 2012. "Dynamic quasi-concave performance measures," Papers 1212.3958, arXiv.org.
14. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
15. Tomasz R. Bielecki & Igor Cialenco & Ismail Iyigunler & Rodrigo Rodriguez, 2012. "Dynamic Conic Finance: Pricing and Hedging in Market Models with Transaction Costs via Dynamic Coherent Acceptability Indices," Papers 1205.4790, arXiv.org, revised Jun 2013.
16. Volker Kr\"atschmer & Alexander Schied & Henryk Z\"ahle, 2012. "Comparative and qualitative robustness for law-invariant risk measures," Papers 1204.2458, arXiv.org, revised Jan 2014.
17. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Feb 2014.

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