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 is a random process [], the drawdown at any time, T,
denoted
is defined as



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



The following pseudocode

Pseudocode

In computer science and numerical computation, pseudocode is a compact and informal high-level description of the operating principle of a computer program or other algorithm. It uses the structural conventions of a programming language, but is intended for human reading rather than machine reading...

 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) have shown that Value at Risk

Value at risk

In financial mathematics and financial risk management, Value at Risk is a widely used risk measure of the risk of loss on a specific portfolio of financial assets...

 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 advisor

Commodity trading advisor

A commodity trading advisor is an asset manager who follows a set of systematic investment strategies in futures contracts and options on futures contracts. The advisors originally operated predominantly in commodities markets, but today they invest in any liquid futures market. They are...

s through the widespread use of three performance measures: the Calmar ratio

Calmar Ratio

Calmar ratio is a performance measurement used to evaluate Commodity Trading Advisors and hedge funds. It was created by Terry W. Young and first published in 1991 in the trade journal Futures....

, the Sterling ratio

Sterling ratio

The Sterling ratio is a measure of the risk-adjusted return of an investment portfolio.Multiple definitions of the Sterling ratio exist...

 and the Burke ratio. These measures can be considered as a modification of the Sharpe ratio

Sharpe ratio

The Sharpe ratio or Sharpe index or Sharpe measure or reward-to-variability ratio is a measure of the excess return per unit of deviation in an investment asset or a trading strategy, typically referred to as risk , named after William Forsyth Sharpe...

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 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



where is a standard Wiener process. Then when the MDD grows logarithmically
with time, the MDD grows as the square root of time and
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)