Student or educator? Sign up with your school email and get 6 months of Pro free.
CoChat
Sign Up
PreprintCited by 350Risk and Portfolio OptimizationFinancial Risk and Volatility ModelingProbability and Risk Models

The DOI matches its Crossref record.

Drawdown Measure in Portfolio Optimization

Open access
Chekhlov, Alexei, Uryasev, Stanislav P., Zabarankin, Michael·2004·International Journal of Theoretical and Applied Finance
DOI 10.2139/ssrn.544742
Open this paper in CoChat — free account

Abstract

A new one-parameter family of risk measures called Conditional Drawdown (CDD) has been proposed. These measures of risk are functionals of the portfolio drawdown (underwater) curve considered in active portfolio management. For some value of the tolerance parameter Alpha, in the case of a single sample path, drawdown functional is defined as the mean of the worst (1 - Alpha) 100% drawdowns. The CDD measure generalizes the notion of the drawdown functional to a multi-scenario case and can be considered as a generalization of deviation measure to a dynamic case. The CDD measure includes the Maximal Drawdown and Average Drawdown as its limiting cases. Mathematical properties of the CDD measure have been studied and efficient optimization techniques for CDD computation and solving asset-allocation problems with a CDD measure have been developed. The CDD family of risk functionals is similar to Conditional Value-at-Risk (CVaR), which is also called Mean Shortfall, Mean Excess Loss, or Tail Value-at-Risk. Some recommendations on how to select the optimal risk functionals for getting practically stable portfolios have been provided. A real-life asset-allocation problem has been solved using the proposed measures. For this particular example, the optimal portfolios for cases of Maximal Drawdown, Average Drawdown, and several intermediate cases between these two have been found.

Overview

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Integrity signals

Registry

Crossref · 10.2139/ssrn.544742

Cites

Statistics

Verification

Claims the paper makes

The claims and statistics of this paper haven’t been checked yet.

Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.

A few free checks a day · papers already verified open instantly · results are public

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

The self-check needs the paper’s full text.

Citations

Cites

Still being checked.

Research works printed but not linked: 69

  1. translation: CV@R ? (? + const) = CV@R ? (?) + const, 10.1093/benz/9780199773787.article.b00120285 · DOI
  2. Positive homogeneity: CV@R ? (? ?) = ? CV@R ? (?), ?? ? 0 and ?? ?, 10.17509/ije.v10i1.5042.s446 · doi:10.17509/ije.v10i1.5042.s446
  3. Monotonicity: if ? k ? ? k , ?k1, k, then CV@R ? (?) ? CV@R ? (?)
  4. ? ?) ? b is a linear combination of any two drawdown sample paths ? a and ? b with ? ?, Convexity: if ? ? = ? ? a +
  5. Proof, Based on linear relation between CV@R ? and CVaR ? , given by (15), properties 1-4 are direct consequence of CVaR ? properties, 22
  6. Proposition 3. The CDD = ? ? (w) satisfies the properties of deviation measures
  7. Insensitivity to constant shift: ? ? (w + const) = ? ? (w)
  8. Positive homogeneity: ? ? (? w) = ? ? ? (w), ?? ? 0 and ?? ?, 10.1016/0167-6687(89)90007-3 · DOI
  9. ? ?) w b is a linear combination of any two sample paths of uncompounded cumulative rate of returns w a and w b with ? ?, Convexity: if w ? = ? w a +
  10. Proof. Properties 1 -4 follow from Propositions 1 and 2. Indeed, based on the relation between the CDD and CV@R, i.e. ? ? (w) = CV@R ? (AD(w)), the first property is a direct consequence of AD(w) nonnegativity. Properties 2 -4 are proved, respectively, ? ? (w + c) = CV@R ? (AD(w + c)) = CV@R ? (AD(w)) = ? ? (w), 10.1163/2468-0303-cohu_31-015 · DOI
  11. ? ? (? w) = CV@R ? (AD(? w)) = CV@R ? (? AD(w)) = ? CV@R ? (AD(w)) = ? ? ? (w), 10.1163/2468-0303-cohu_31-015 · DOI
  12. ? ? (w ? ) = CV@R ? (AD(? w a + (1 ? ?)w b )) ? CV@R ? (? AD(w a ) + (1 ? ?)AD(w b )) ? ? CV@R ? (AD(w a )) + (1 ? ?)CV@R ? (AD(w b ), 10.1163/2468-0303-cohu_31-015 · DOI
  13. = ? ? ? (w a ) + (1 ? ?)? ? (w b )
  14. Note that the monotonicity property of CV@R is used in the first line of the proof of CDD convexity
  15. MaDD (8) and AvDD (9) are the special cases of the ?-CDD functional (this notation is used to emphasize CDD dependence on ?), namely, MaxDD(w) = ? 1 (w)
  16. S Bd -U, 30-Year) Treasury Bond Futures (CBT)
  17. Bp -British, Pound Sterling Currency Futures (CME)
  18. CD -Canadian Dollar Currency Futures (CME)
  19. CP -Copper Futures (COMEX)
  20. Dgb -German, 10-Year Bond (Bund) Futures (LIFFE)
  21. S Dx -U, Dollar Index Currency Futures (FNX)
  22. ED -90-Day Euro Dollar Futures (CME)
  23. S Fv -U, 5-Year Treasury Note Futures (CBT)
  24. Japanese Yen Cross Currency Forward (OTC)
  25. Fxbpjy -British, Japanese Yen Cross Currency Forward (OTC)
  26. Fxeubp -Euro Vs, British Pound Sterling Cross Currency Forward (OTC)
  27. Fxeujy -Euro Vs, Japanese Yen Cross Currency Forward (OTC)
  28. Fxeusf -Euro Vs, 10.7551/mitpress/10939.003.0005 · DOI
  29. Fxussg -Singaporean, Dollar Currency Forward (OTC)
  30. FXUSSK -Swedish Krona Currency Forward (OTC)
  31. GC -Gold 100 Oz. Futures (COMEX)
  32. JY -Japanese Yen Currency Futures (CME)
  33. LBT -Italian 10-Year Bond Forward (OTC)
  34. LFT -FTSE-100 Index Futures (LIFFE)
  35. Lgl -Long Gilt, 10-Year Bond) Futures (LIFFE)
  36. LML -Aluminum Futures (COMEX)
  37. Mnn -French, 10.1002/9781119208426.ch1 · DOI
  38. SF -Swiss Franc Currency Futures (CME)
  39. Si -Silver, Futures (COMEX)
  40. Sjb -Jgb, Japanese 10-Year Government Bond) Futures (TSE)
  41. SNI -NIKKEI-225 Index Futures (SIMEX)
  42. international equity indices, currencies and crosscurrencies, and metals. Given set of 32 time series with daily rates of return covers a period of time between 6/12/1995 and 12/13/1999. Time is measured in trading days only, with a convention of 5 workdays per week, with adding previous day closing data for holidays with missing data. A basic version of non-parametric bootstrap re-sampling generates "children" samples from the original "father" sample in the following way: it fills out a "child" with father's daily rates of return in random order "with replacement", i.e. when the same daily rate of return can be pulled out twice or more. Well-known difficulty in obtaining a re-sampled probability distribution function by such a procedure is that if the original "father" time series has certain auto-correlation structure, Futures (CBT) These markets include most major asset classes traded through futures: fixed-income (short-term and long-term, both domestic and international)
  43. C Acerbi, 2002, On the Coherence of Expected Shortfall, Journal of Banking and Finance, 26, 1487, 10.1016/s0378-4266(02)00283-2 · DOI · Paper page
  44. P Artzner, 1999, Mathematical Finance, 9, 203, 10.1111/1467-9965.00068 · DOI · Paper page
  45. P Artzner, 2002, Multiperiod Risk and Coherent Multiperiod Risk Measurement
  46. F Delbaen, 2000, Coherent Risk Measures on General Probability Spaces, 10.1007/978-3-662-04790-3_1 · DOI · Paper page
  47. F Delbaen, 2000, Draft: Coherent Risk Measures, lecture notes
  48. A Chekhlov, 2003, Portfolio Optimization with Drawdown Constraints, Asset and Liability Management Tools, Risk Books, 263
  49. J Cvitanic, 1995, On Portfolio Optimization Under "Drawdown, Constraints, IMA Lecture Notes in Mathematics & Applications, 65, 77, 10.1007/978-1-4757-2435-6_3 · DOI
  50. R S Dembo, 1992, Tracking Models and the Optimal Regret Distribution in Asset Allocation, Applied Stochastic Models and Data Analysis, 8, 151, 10.1002/asm.3150080305 · DOI
  51. Bradley Efron, 1993, An Introduction to the Bootstrap, 10.1007/978-1-4899-4541-9 · DOI · Paper page
  52. P Jorion, 1996, Value at Risk : A New Benchmark for Measuring Derivatives Risk
  53. R C Grinold, 1999, Active Portfolio Management
  54. S J Grossman, 1993, Optimal Investment Strategies for Controlling Drawdowns, 3, 241, 10.1111/j.1467-9965.1993.tb00044.x · DOI · Paper page
  55. H Konno, 1991, Mean Absolute Deviation Portfolio Optimization Model and Its Application to Tokyo Stock Market, Management Science, 37, 519, 10.1287/mnsc.37.5.519 · DOI · Paper page
  56. H M Markowitz, 1952, Portfolio Selection, Journal of Finance, 7, 77, 10.1111/j.1540-6261.1952.tb01525.x · DOI · Paper page
  57. H Mausser, 1999, From Measuring Risk to Managing Risk, ALGO Research Quarterly, 1, 5, 10.1109/cifer.1999.771115 · DOI
  58. G C Pflug, 2001, Optimal scenario tree generation for multiperiod financial planning, Mathematical Programming, Ser. B, 89, 251, 10.1007/PL00011398 · DOI · Paper page
  59. G C Pflug, 2000, Some Remarks on the Value-at-Risk and the Conditional Value-at-Risk, Probabilistic Constrainted Optimization: Methodology and Applications, 278, 10.1007/978-1-4757-3150-7_15 · DOI · Paper page
  60. G C Pflug, 2004, A Risk Measure for Income Streams, in Risk Measures for the 21st Century
  61. R T Rockafellar, 1970, Convex Analysis, 10.1515/9781400873173 · DOI · Paper page
  62. R T Rockafellar, 2000, Optimization of Conditional Value-at-Risk, Journal of Risk, 2, 21, 10.21314/jor.2000.038 · DOI · Paper page
  63. R T Rockafellar, 2002, Conditional Value-at-Risk for General Loss Distributions, Journal of Banking and Finance, 26, 1443, 10.1016/s0378-4266(02)00271-6 · DOI · Paper page
  64. R T Rockafellar, 2002, Deviation Measures in Risk Analysis and Optimization, 10.2139/ssrn.365640 · DOI
  65. R T Rockafellar, 2002, Deviation Measures in Generalized Linear Regression
  66. R T Rockafellar, 2003, Portfolio Analysis with General Deviation Measures, 10.2139/ssrn.414268 · DOI
  67. M R Young, 1998, A Minimax Portfolio Selection Rule with Linear Programming Solution, Management Science, 44, 673, 10.1287/mnsc.44.5.673 · DOI · Paper page
  68. W T Ziemba, 1998, Asset and Liability Modeling
  69. 2000, Sound practices for hedge fund managers, A response to the President's Working Group (PWG) report on LTCM crisis by the leading hedge funds: Caxton Corporation, Kingdon Capital LLC, Soros Fund Management LLC, Tudor Investment Corporation

Cited by

  • 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

    “…decline in portfolio value from its peak to its trough throughout the evaluation period, providing a measure for down-side risk: 2) It highlights the worst loss an investor could have faced and is commonly used to assess risk and volatility (Magdon-Ismail et al., 2004; Chekhlov et al., 2005).”

See all 350

Metadata

Authors
Chekhlov, A., Uryasev, S. P., & Zabarankin, M.
Affiliations
University of Florida (US)
ORCID
Venue
International Journal of Theoretical and Applied Finance
Publisher
Elsevier BV
Published
2004
Volume
08
Issue
01
Pages
13-58
ISSN
0219-0249 (ISSN-L)
DOI
10.2139/ssrn.544742
OpenAlex
W3123675609
Cited by
350
References
0
Citations by year
2026: 34 · 2025: 24 · 2024: 20 · 2023: 31 · 2022: 15 · 2021: 16 · 2020: 19 · 2019: 14 · 2018: 10 · 2017: 16 · 2016: 20 · 2015: 18 · 2014: 15 · 2013: 30 · 2012: 17
FWCI
9.00
Type
journal article
Language
en
Open access
Locations
  • International Journal of Theoretical and Applied Finance (publishedVersion)
  • SSRN Electronic Journal (acceptedVersion)
  • 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 Risk and Volatility Modeling
  • Social Sciences › Decision Sciences › Management Science and Operations Research › Probability and Risk Models
Keywords
risk measures, portfolio optimization, asset allocation, conditional value at risk, deviation measures, active portfolio management

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review

How to cite

Cite CoChat for the checks on this page, and the paper for its own findings.

This page
CoChat. (2026). Citation check: Drawdown Measure in Portfolio Optimization. https://app.cochat.ai/papers/10.2139/ssrn.544742
The paper
Chekhlov, A., Uryasev, S. P., & Zabarankin, M. (2004). Drawdown Measure in Portfolio Optimization. International Journal of Theoretical and Applied Finance. https://doi.org/10.2139/ssrn.544742

Data sources

Bibliographic data: Semantic Scholar, OpenAlex, Crossref.

Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).

Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.