= max [ sum[r(t)] ] - r(t)
t = 0..T
Given a time series with N log returns r(t) over t = 1 to T, we can define...
= min [r(1), r(1)+r(2), r(1)+r(2)+r(3), ..., r(1)+...+r(N)]
= min [ sum [r(i)] ]
In words: The minimum cumulated return from the beginning in a certain time period.
The maximum drawdown can be loosely defined as the largest drop from a peak to a bottom in a certain time period.
Maximum drawdown captures a path-dependant feature of a time series which is not represented in the histogram of the return time series.
= min [r(1), r(1)+r(2), r(1)+r(2)+r(3), ..., r(1)+...+r(N),
r(2), r(2)+r(3), r(2)+r(3)+r(4), ..., r(2)+...+r(N), ..., r(N)]
= min [ sum [r(j)] ]
i=1..t, t=1..N j=i..t
In words: The minimum cumulated return from any beginning points over a certain time period.
= max [ Drawdown(t) ]
...the last formula yields the end-point of the maximum
drawdown period. The starting point is found at the
last time point Drawdown(t) was equal to zero.
Maximum drawdown is always smaller than or equal to the difference between maximum loss and maximum gain.
Maximum loss & gain are the global extreme values, maximum drawdown is a concept base on the local minimum of a return time series.
Maximum drawdown is often used when not enough observations are available to calculate volatility measures (like for example standard deviation).
Maximum drawdown is highly dependent on the time interval chosen (annual, monthly, daily and so on) as well as the observation period.
Source ---> http://www.andreassteiner.net/performanceanalysis/?Risk_Measurement:Absolute_Riskrawdown