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 computes the Drawdown ("DD") and Max Drawdown ("MDD") of the varialbe "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) then peak = NAV[i]
DD[i] = 100.0 * (peak - NAV[i]) / peak
if(DD[i] > MDD) then MDD = DD[i]
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 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.