Intelligent Hedge Fund Investing
Successfully Avoiding Pitfalls through Better Risk Evaluation
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CHAPTER 6

INTRODUCTION

BIBLIOGRAPHY

ERRATA AND OTHER MATERIAL

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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.

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BIBLIOGRAPHY

  1. 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.
    download
  2. Burghardt, G., Duncan, R. and L. Liu, 2003, "Deciphering Drawdown", Risk Supplement: Risk Management for Investors, September, S16-S20.
  3. 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)
  4. 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)
  5. 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.
    purchase from publisher
  6. 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).
    download
  7. Tabachnick, B.G. and L.S. Fidell 1996, Using Multivariate Statistics, 3rd Edition, New York, Harper Collins.
    view at Amazon.com

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ERRATA AND OTHER MATERIAL

  1. Errata:
    p.160: Table 1, the fourth row of numbers should read as follows: -0.20, -0.10, 0.00, +0.10, +0.20.
  2. Related research:
    • Bailey, D. and M. Lopez de Prado, 2013, "Drawdown-Based Stop-Outs and the 'Triple Penance' Rule", working paper (June)
      download (pdf 894K)
    • Belentepe, C. Y., 2003, "Expected Drawdowns", working paper, University of Pennsylvania (December)
      download (pdf 204K)
    • Berkelaar, Arjan and Roy Kouwenberg, 2010, "A Liability-Relative Drawdown Approach to Pension Asset Liability Management", Journal of Asset Management (vol. 11, nos. 2-3), pp. 194-217.
      download (pdf 381K)
    • Burghardt, G., Duncan, R. and L. Liu, 2003, "Understanding Drawdowns", working paper, Carr Futures (September 4)
      download (pdf 499K)
    • Carr, P., H. Zhang and O. Hadjiliadis, 2012, "Maximum Drawdown Insurance", International Journal of Theoretical and Applied Finance 14(8), 1195-1230.
      publisher's site
    • 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)
    • Cheridito, P., A. Nikeghbali, and E. Platen, 2009, "Processes of Class (Σ), Last Passage Times and Drawdowns", working paper, (October)
      download (pdf 314)
    • 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 324K)
    • Eckholdt, H., 2004, "Risk Management: Using SAS to Model Portfolio Drawdown, Recovery and Value at Risk" (February)
      download (pdf 258K)
    • Gray, Wesley and J. Vogel, 2013, "Using Maximum Drawdowns to Capture Tail Risk", working paper (Feburary)
      download (pdf 180K)
    • Grossman, S. J. and Z. Zhou, 1993, "Optimal Investment Strategies for Controlling Drawdowns", Mathematical Finance 3, pp. 241-276.
      download (pdf 781K)
    • Hadjiliadis, Olympia and Jan Vecer, 2006, "Drawdowns Preceding Rallies in the Brownian Motion Model", Quantitative Finance (October), 403-409.
      download (pdf 142K)
    • Hamelink, F. and M. Hoesli, 2004, "Maximum Drawdown and the Allocation to Real Estate", Journal of Property Research (vol 21, no 1) (March), pp. 5-29.
      purchase from publisher
    • Hamelink, F. and M. Hoesli, 2003, "The Maximum Drawdown as a Risk Measure: The Role of Real Estate in the Optimal Portfolio Revisited", working paper (June 24).
      download (pdf 101K)
    • 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)
    • Hayes, B. T., 2006, "Maximum Drawdowns of Hedge Funds with Serial Correlation", Journal of Alternative Investments (vol 8, no 4) (Spring), pp. 26-38.
      purchase from publisher
    • Kim, Daehwan, 2010, "Relevance of Maximum Drawdown in the Investment Fund Selection Problem when Utility is Nonadditive", working paper (July).
      download (pdf 290K)
    • Klein Rivera, Raphael, 2011, "Extreme Price Drawdowns in Financial Markets with Time-Varying Volatilities", master's thesis (January).
      download (pdf 2400K)
    • Lehoczky, John, 1977, "Formulas for Stopped Diffusion Processes with Stopping Times Based on the Maximum", The Annals of Probability (vol 5, no 4), pp. 601-607.
      download (pdf 597K)
    • Lohre, Harald, Thorsten Neumann and Thomas Winterfeldt, 2007, "Portfolio Construction with Asymmetric Risk Measures", working paper (May).
      download (pdf 262K)
    • 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)
    • Maslov, Sergei and Zhang, Yi-Cheng, 1998, "Probability Distribution of Drawdowns in Risky Investments", working paper (August).
      download (pdf 205K)
    • 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.
    • Nouri, Suhila, 2006, "Expected Maximum Drawdowns under Constant and Stochastic Volatility", MS Thesis, Worcester Polytechnic Institute (May).
      download (pdf 125K)
    • 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, 2010, "Portfolio Sensitivity to Changes in the Maximum and the Maximum Drawdown", Quantitative Finance, vol. 10, no. 6, (June), pp. 617-627.
      download (pdf 678K)
    • Pospisil, Libor and Vecer, Jan, 2010, "Maximum Drawdown of a Jump-Diffusion Process and the Corresponding Partial Intego-Differential Equations", Columbia University working paper (June).
      download (pdf 191K)
    • Pospisil, Libor and Vecer, Jan, 2008, "PDE Methods for the Maximum Drawdown", Columbia University working paper (April).
      download (pdf 838K)
    • Pospisil, Libor, Vecer, Jan and Hadjiliadis, Olympia, 2009, "Formulas for Stopped Diffusion Processes with Stopping Times Based on Drawdowns and Drawups", Columbia University working paper (January).
      download (pdf 312K)
    • Reveiz, Alejandro and Leon, Carlos, 2008, "Efficient Portfolio Optimization in the Wealth Creation and Maximum Drawdown Space", working paper #520, Banco de la Republica Colombia (June)
      download (pdf 495K)
    • Rotundo, Giulia and Navarra, Mauro, 2007, "On the Maximum Drawdown During Speculative Bubbles", working paper (April).
      download (pdf 439K)
    • Salminen, Paavo and Pierre Vallois, 2007, "On the maximum increase and decrease of Brownian motion", Annales de l'Institut Henri Poincare (B) Probability and Statistics (vol 43, no 6) pp. 655-676
      download (pre-publication version) (pdf 338K)
    • Steiner, Andreas, 2010, "Ambiguity in Calculating and Interpreting Maximum Drawdown," working paper (December).
      download (pdf 174K)
    • Vecer, Jan, 2007, "Preventing Portfolio Losses by Hedging Maximum Drawdown", working paper, (June)
      download (pdf 430K)
    • 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)
    • Yang, Z. G. and Z. Liang, 2011, "Optimal Portfolio Strategy to Control Maximum Drawdown", working paper (Feburary)
      download (pdf 931K)
    • Zabarankin, M., K. Pavlikov and S. Uryasev, 2013, "Capital Asset Pricing Model (CAPM) with Drawdown Measure", European Journal of Operational Research.
      visit publication
    • Zhang, Hongzhong and Olympia Hadjiliadis, 2009, "Formulas for the Laplace Transform of Stopping Times Based on Drawdowns and Drawups", working paper.
      download (pdf 238K)
    • Zhang, Hongzhong and Olympia Hadjiliadis, 2009, "Drawdowns and rallies in a finite time-horizon", Methodology and Computing in Applied Probability.
      download pre-publication version) purchase from publisher) (pdf 178K)
  3. 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

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INSIDE REVIEWS PURCHASE

Introduction

Table of Contents

Contributors

"How exciting to read a book that is so timely and practical"
Tanya Styblo Beder, CEO, Tribeca Investments

Publisher: Risk Books
Hardcover: 470 pages
ISBN: 19044339220

Editor: Barry Schachter

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