Definitions

# Drawdown (economics)

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

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

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

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

$MDD\left(T\right)=Max_\left\{tauin \left(0,T\right)\right\}lbrack Max_\left\{t in \left(0,tau\right)\right\} X\left(t\right)- X\left(tau\right) rbrack$ 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]`
`endfor`

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 $X\left(T\right)$ 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

$X\left(t\right)=mu t+ sigma W\left(t\right),$

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

## References

• 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.
Search another word or see Drawdown_(economics)on Dictionary | Thesaurus |Spanish