|
MAXUMUM DRAWDOWN: FURTHER RESULTS
Emmanuel Acar and Amy Middleton
INTRODUCTION
Acar and Middleton remind us of an important lesson, namely a statistic is not necessarily meaningful just because you can calculate it.
Evaluating performance should be easy. It isn’t. For example, much recent research, and not a little common sense, has robbed the Sharpe Ratio of some of its luster as a performance measure. Non-normal returns, illiquid or smoothed pricing, and the effects of estimation errors all negatively affect its usefulness.
In the hedge fund universe the use of maximum drawdown is as ubiquitous as the use of the Sharpe Ratio is in traditional portfolio analysis. If I did not ask a prospective manager “what has been your largest drawdown,” I would almost surely be considered by my peers to be derelict in my assessment of the manager’s potential.
Yet we see in this paper that the popular maximum drawdown statistic has not very much power in identifying relatively more skilled managers. The problem begins when you realize that it is not sufficient to simply examine observed drawdowns in assessing performance.
Observed or experienced maximum drawdowns will, other things equal, be larger the longer is the time interval over which you observe returns for a manager. The longer the observation interval, the greater is the opportunity to experience a drawdown worse than previously known. For this reason, to use maximum drawdown as a performance measure one needs to evaluate drawdown in relation to some absolute or idealized benchmark, such as the maximum drawdown expected from a passive buy-and-hold strategy (appropriately defined). This is what Acar and Middleton do, and find that unless markets are inefficient, it can be difficult for maximum drawdown as a statistic to successfully detect managers with superior skill at generating returns while controlling drawdowns.
In the best tradition of the “belt-and-suspenders” approach to risk management, it is common to use multiple performance statistics, in part to overcome the lack of power or potential biases in individual statistics. Therefore statistics based on maximum drawdown, such as the Calmar Ratio, are commonly looked at along with others, such as the Sharpe Ratio, Information Ratio, Sortino Ratio, or M-Squared.
The danger here, of course, is that these statistics are not independent. That is, they do not provide independent information about performance. For example, the ordering of portfolio managers that would be obtained from the Sharpe Ratio is the same as that obtained from M-Squared. Several authors have also shown, as discussed by Acar and Middleton, that Maximum Drawdown can be stated as a function of the portfolio standard deviation (in a nonlinear way), meaning that it may contain very similar information.
The take-away from the lesson of this paper, as in a lot of the research presented in this volume, is not “don’t go there”, but rather “use with care.” Maximum drawdown can be a useful diagnostic, used intelligently, by keeping the limitations in mind at all times.
return to top
BIBLIOGRAPHY
- Acar, E. and S. James, 1997, "Maximum Loss and Maximum Drawdown in Financial Markets", Presented at the “Forecasting Financial Markets Conference” in London, May, 1997.
http://www.GloriaMundi.org/picsresources/easj.pdf
- Burghardt, G., Duncan, R. and L. Liu, 2003, “Deciphering Drawdown”, Risk Supplement: Risk Management for Investors, September, S16-S20.
- Douady, R., Shiryaev, A. and M. Yor, 2000, “On Probability Characteristics of Downfalls in a Standard Brownian Motion”, Siam, Theory Probability Appl, 44(1), 29–38.
download (pdf 152K)
- Harding, D., Nakou, G., and A. Nejjar, 2003, “The Pros and Cons of 'Drawdown' as a Statistical Measure of Risk for Investments”, AIMA Journal, April, 16-17.
download (pdf 1,138K)
- Levich, R.M. and L.R. Thomas, 1993, "The Significance of Technical Trading-rule Profits in the Foreign Exchange Market: a Bootstrap Approach", Journal of International Money and Finance, 12, 451-474.
- Magdon-Ismail, M., Atiya, A.F., Pratap, A. and Y.S. Abu-Mostafa, 2004, “On the Maximum Drawdown of a Brownian Motion”, Journal of Applied Probability, 41(1).
http://www.GloriaMundi.org/picsresources/miapam.pdf
- Tabachnick, B.G. and L.S. Fidell 1996, Using Multivariate Statistics, 3rd Edition, New York, Harper Collins.
view at Amazon.com
return to top
ERRATA AND OTHER MATERIAL
- Errata:
p.160: Table 1, the fourth row of numbers should read as follows: -0.20, -0.10, 0.00, +0.10, +0.20.
- Related research:
- Belentepe, C. Y., 2003, "Expected Drawdowns", working paper, University of Pennsylvania (December)
download (pdf 204K)
- Burghardt, G., Duncan, R. and L. Liu, 2003, "Understanding Drawdowns", working paper, Carr Futures (September 4)
download (pdf 499K)
- Chekhlov, A., S. Uryasev and M. Zabarankin, 2000, "Portfolio Optimization with Drawdown Contraints", working paper, (April)
download (pdf 104K)
- Chekhlov, A., S. Uryasev and M. Zabarankin, 2003, "Drawdown Measure in Portfolio Optimization", working paper, (June)
download (pdf 437K)
- Cvitanic, J. and I. Karatzas, 1995, "On Portfolio Optimization Under 'Drawdown' Constraints", IMA Lecture Notes in Mathematics & Applications 65, pp. 77-88.
download (pdf 222K)
- Dacorogna, M., R. Gencay, U. Muller and O. Pictet, 1999, "Effective Return, Risk Aversion and Drawdowns", working paper (September)
download (pdf 328K)
- Eckholdt, H., 2004, "Risk Management: Using SAS to Model Portfolio Drawdown, Recovery and Value at Risk" (February)
download (pdf 258K)
- Grossman, S. J. and Z. Zhou, 1993, "Optimal Investment Strategies for Controlling Drawdowns", Mathematical Finance 3, pp. 241-276.
download (pdf 781K)
- Harmantzis, F. C. and L. Miao, 2005, "Empirical Study of Fat-Tails in Maximum Drawdown: The Stable Paretian Modelling Approach", working paper (June).
download (pdf 748K)
- Hadjiliadis, Olympia and Jan Veces, 2006, "Drawdowns Preceding Rallies in the Brownian Motion Model", Quantitative Finance (October), 403-409.
download (pdf 142K)
- Lopez do Prado, M. M. and A. Peijan, 2004, "Measuring Loss Potential of Hedge Fund Strategies", Journal of Alternative Investments, (Summer), pp. 7-31.
download (pdf 128K)
- Magdon-Ismail, Malik, 2004, "An Analysis of the Maximum Drawdown Risk Measure", presentation notes, (May 6)
download (pdf 128K)
- Magdon-Ismail, Malik and Atiya, Amir, 2004, "Maximum Drawdown", Risk (October).
download (pdf 135K)
- Magdon-Ismail, M., Atiya, A.F., Pratap, A. and Y.S. Abu-Mostafa, 2002, "The Sharpe Ratio, Range, and Maximal Drawdown of a Brownian Motion", working paper (September).
download (pdf 352K)
- Meilijson, Isaac, 2003, "The Time to a Given Drawdown in Brownian Motion", in Lecture Notes in Mathematics, v. 1832, Berlin: Springer, pp. 94-108.
follow link to paper
- Melo Mendes, B. V. de, and R. P. Camara Leal, 2005, "Maximum Drawdown: Models and Applications", Journal of Alternative Investments, (Spring).
download (pdf 400K)
- Melo Mendes, B. V. de, and R. Brandi, 2004, "Modeling Drawdowns and Drawups in Financial Markets", Journal of Risk (Spring), pp. 53-69.
- Pratap, Amrit, 2004, "Maximum Drawdown of a Brownian Motion and AlphaBoos: A Boosting Algorithm", MS Thesis, California Institute of Technology (May).
download (pdf 569K)
- Petroni, Filippo and Rotundo, Giulia, 2008, "Effectiveness of Measures of Performance During Speculative Bubbles", Physica A: Statistical Mechanics and its Applications (June), pp. 3942-3948.
download (pdf 834K)
- Pospisil, Libor and Vecer, Jan, 2008, "Portfolio Sensitivity to the Changes in the Maximum and the Maximum Drawdown", Columbia University working paper (March).
download (pdf 678K)
- Pospisil, Libor and Vecer, Jan, 2008, "PDE Methods for the Maximum Drawdown", Columbia University working paper (April).
download (pdf 838K)
- Rotundo, Giulia and Navarra, Mauro, 2007, "On the Maximum Drawdown During Speculative Bubbles", working paper (April).
download (pdf 439K)
- Vecer, Jan, 2006, "Maximum Drawdown and Directional Trading", Risk, (December), 88-92.
download (pdf 495K)
- Wilkins, K., C. Morales and L. Roman, 2005, "Maximum Drawdown Distributions with Volatility Persistence", working paper.
download (pdf 63K)
- Miscellaneous
- Maximum Drawdown demonstration in Mathematica
go to website
- Maximum Drawdown and Expected Maximum Drawdown in Matlab
go to website
- Andreas Steiner's Maximum Drawdown demonstration in MatLab
go to website
return to top
|
