# maxdrawdown

Compute maximum drawdown for one or more price series

## Description

example

MaxDD = maxdrawdown(Data) computes maximum drawdown for each series in an N-vector MaxDD and identifies start and end indexes of maximum drawdown periods for each series in a 2-by-N matrix MaxDDIndex.

example

MaxDD = maxdrawdown(___,Format) adds an optional argument for Format.

example

[MaxDD,MaxDDIndex] = maxdrawdown(___) adds an optional output for MaxDDIndex.

## Examples

collapse all

Calculate the maximum drawdown (MaxDD) using example data with a fund, market, and cash series:

MaxDD = maxdrawdown(TestData)
MaxDD = 1×3

0.1658    0.3381         0

The maximum drop in the given time period was 16.58% for the fund series, and 33.81% for the market series. There was no decline in the cash series, as expected, because the cash account never loses value.

## Input Arguments

collapse all

Total return price series, specified as a T-by-N matrix with T samples of N total return price series.

Data Types: double

Format of Data, specified as character vector with the following possible values:

• 'return' (default) — Maximum drawdown in terms of maximum percentage drop from a peak.

• 'arithmetic'

— Maximum drawdown of an arithmetic Brownian motion with drift (differences of data from peak to trough) using the equation

$dX\left(t\right)=\mu dt+\sigma dW\left(t\right).$

• 'geometric'

— Maximum drawdown of a geometric Brownian motion with drift (differences of log of data from peak to trough) using the equation

$dS\left(t\right)={\mu }_{0}S\left(t\right)dt+{\sigma }_{0}S\left(t\right)dW\left(t\right)$

Data Types: char

## Output Arguments

collapse all

Maximum drawdown, returned as a 1-by-N vector with maximum drawdown for each of N time series.

Note

• Drawdown is the percentage drop in total returns from the start to the end of a period. If the total equity time series is increasing over an entire period, drawdown is 0. Otherwise, it is a positive number. Maximum drawdown is an ex-ante proxy for downside risk that computes the largest drawdown over all intervals of time that can be formed within a specified interval of time.

• Maximum drawdown is sensitive to quantization error.

Start and end indexes for each maximum drawdown period for each total equity time series, returned as a 2-by-N vector of start and end indexes. The first row of the vector contains the start indexes and the second row contains the end indexes of each maximum drawdown period.

## References

[1] Christian S. Pederson and Ted Rudholm-Alfvin. "Selecting a Risk-Adjusted Shareholder Performance Measure." Journal of Asset Management. Vol. 4, No. 3, 2003, pp. 152–172.