# maxdrawdown

Compute maximum drawdown for one or more price series

## Syntax

``MaxDD = maxdrawdown(Data)``
``MaxDD = maxdrawdown(___,Format)``
``[MaxDD,MaxDDIndex] = maxdrawdown(___)``

## 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

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

```load FundMarketCash 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

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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

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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.