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On the foundation of performance measures under asymmetric returns
Abstract
We examine two performance measures advocated for asymmetric return distributions: the Sortino ratio—originally introduced by Sortino and Price (Sortino F and Price L 1994 J. Investing 59–65)—and a measure based on power utility introduced in Leland (Leland H 1999 Financial Analysts J. 27–36). In particular, we investigate the role of the maximum principle in this context, and assess the conditions under which the measures satisfy it. Our results add further motivation for the use of a modified Sortino ratio, by placing it on a sound theoretical foundation. In this light, we discuss its relative merits compared with alternative approaches.
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The Sortino ratio is more appropriate than the Sharpe ratio when returns are asymmetric, as it focuses on negative volatility.
“This metric is more appropriate than the Sharpe ratio when returns are asymmetric, as it focuses on negative volatility (Sortino and Van der Meer, 1991; Pedersen and Satchell, 2002).”
From StockBench: Can LLM Agents Trade Stocks Profitably In Real-world Markets? (2025) · cites this paper as Pedersen and Satchell, 2002
Citations
Cites
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StockBench: Can LLM Agents Trade Stocks Profitably In Real-world Markets?
Chen, Y., Yao, Z., Liu, Y., Xin, A., Ye, J., Yu, J., Hou, L., & Li, J. (2025) · arXiv · Cited by 62
“…metric is more appropriate than the Sharpe ratio when returns are asymmetric, as it focuses on negative volatility (Sortino and Van der Meer, 1991; Pedersen and Satchell, 2002 After computing these metrics for each model, we derive a composite rank by leveraging the z-score of each metric,…”
Metadata
- Authors
- Pedersen, C. S., & Satchell, S. E.
- Affiliations
- University of Cambridge (GB)
- ORCID
- Satchell, Stephen E
- Venue
- Quantitative Finance
- Publisher
- Informa UK Limited
- Published
- 2002-06
- Volume
- 2
- Issue
- 3
- Pages
- 217-223
- ISSN
- 1469-7688 (ISSN-L)
- 1469-7696
- OpenAlex
- W1998506499
- Cited by
- 97
- References
- 1
- Citations by year
- 2024: 3 · 2023: 1 · 2021: 2 · 2020: 4 · 2019: 2 · 2018: 3 · 2017: 7 · 2016: 4 · 2015: 6 · 2014: 5 · 2013: 3 · 2012: 3
- FWCI
- 4.91
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Quantitative Finance (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Risk and Portfolio Optimization
- Social Sciences › Economics, Econometrics and Finance › Finance › Financial Markets and Investment Strategies
- Social Sciences › Economics, Econometrics and Finance › Finance › Stochastic processes and financial applications
- Keywords
- performance indicators, Sortino ratio, asymmetric returns, downside risk, electric utilities, maximum principle, risk-adjusted performance
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