Drawdown (economics)

The Drawdown is the measure of the decline from a historical peak in some variable (typically the cumulative profit or total open equity of a financial trading strategy).

Somewhat more formally, if X(t) is a random process [$X(0) = 0, t \geq 0$], the drawdown at any time, T, denoted D(T) is defined as

$D(T)=Max \lbrack 0, Max_{t \in (0,T)} X(t)- X(T) \rbrack$

The Maximum Drawdown (MDD) up to time T is the maximum of the Drawdown over the history of the variable. More formally,

$MDD(T)=Max_{\tau\in (0,T)}\lbrack Max_{t \in (0,\tau)} X(t)- X(\tau) \rbrack$

The following pseudocode computes the Drawdown ("DD") and Max Drawdown ("MDD") of the variable "NAV", the Net Asset Value of an investment. Drawdown and Max Drawdown are calculated as percentages:

MDD = 0
peak = -99999
for i = 1 to N step 1
  if (NAV[i] > peak) 
    peak = NAV[i]
  else
    DD[i] = 100.0 * (peak - NAV[i]) / peak
    if (DD[i] > MDD)
      MDD = DD[i]
    endif
  endif
endfor

López de Prado and Peijan (2008)^[1] have shown that Value at Risk substantially underestimates an investment's loss potential when its returns are incorrectly assumed to iid follow a Normal Distribution.

In finance, the use of the maximum drawdown as an indicator of risk is particularly popular in the world of commodity trading advisors through the widespread use of three performance measures: the Calmar ratio, the Sterling ratio and the Burke ratio. These measures can be considered as a modification of the Sharpe ratio in the sense that the numerator is always the excess of mean returns over the risk-free rate while the standard deviation of returns in the denominator is replaced by some function of the drawdown.

When X(T) is a standard Brownian motion, the expected behavior of the MDD as a function of time is known. A standard Brownian motion is represented as

X(t) = μt + σW(t),

where W(t) is a standard Wiener process. Then when μ > 0 the MDD grows logarithmically with time, μ = 0 the MDD grows as the square root of time and μ < 0 the MDD grows linearly with time.

Further reading

• Burghardt, G., Duncan, R. and L. Liu, "Understanding Drawdowns", working paper, Carr Futures (September 4), 2003 (http://www.intelligenthedgefundinvesting.com/pubs/rb-bdl.pdf)
• Eckholdt, H., "Risk Management: Using SAS to Model Portfolio Drawdown, Recovery and Value at Risk" (February), 2004. (http://www.intelligenthedgefundinvesting.com/pubs/rb-he.pdf)
• Grossman, S. J. and Z. Zhou, "Optimal Investment Strategies for Controlling Drawdowns", Mathematical Finance 3, pp. 241-276, 1993.
• Hamelink, F. and M. Hoesli, "The Maximum Drawdown as a Risk Measure: The Role of Real Estate in the Optimal Portfolio Revisited", working paper (June 24), 2003. (http://www.intelligenthedgefundinvesting.com/pubs/rb-fhmh.pdf)
• Hayes, B. T., "Maximum Drawdowns of Hedge Funds with Serial Correlation", Journal of Alternative Investments (vol 8, no 4) (Spring), pp. 26-38, 2006.
• Kim, Daehwan, "Relevance of Maximum Drawdown in the Investment Fund Selection Problem when Utility is Nonadditive", working paper (July), 2010. (http://www.intelligenthedgefundinvesting.com/pubs/dk_rmd.pdf)
• M. Magdon-Ismail, A. Atiya, A. Pratap, Y. Abu-Mostafa, On the Maximum Drawdown of a Brownian Motion, Journal of Applied Probability, Volume 41, Number 1, pages 147-161, March, 2004.
• M. Magdon-Ismail, A. Atiya, Maximum Drawdown, Risk Magazine, Volume 17, Number 10, pages 99-102, October, 2004.
• Steiner, Andreas, "Ambiguity in Calculating and Interpreting Maximum Drawdown," working paper (December), 2010. (http://www.intelligenthedgefundinvesting.com/pubs/as_acm.pdf)
• Wilkins, K., C. Morales and L. Roman, "Maximum Drawdown Distributions with Volatility Persistence", working paper, 2005. (http://www.intelligenthedgefundinvesting.com/pubs/rb-kwcmlr.pdf)

References

1. ^ López de Prado and Peijan (2008): "Measuring the Loss Potential of Hedge Fund Strategies", Journal of Alternative Investments (7)1, 7-31. http://ssrn.com/abstract=641702