Maximum Drawdown

PortfolioOptimisers.MaximumDrawdown Type

julia

struct MaximumDrawdown{__T_settings} <: RiskMeasure

Represents the Maximum Drawdown risk measure.

MaximumDrawdown computes the largest peak-to-trough decline in the cumulative portfolio returns. It captures the worst-case loss from a previous high.

Mathematical definition

Define the absolute drawdown series:

\begin{aligned} c_{t} & = \sum_{s = 1}^{t} x_{s}, \\ d_{t} & = c_{t} - max_{0 \leq s \leq t} c_{s} \leq 0 . \end{aligned}

Where:

$x$ : Portfolio returns vector $T \times 1$ .
$c_{t}$ : Cumulative simple portfolio return at period $t$ .
$d_{t} \leq 0$ : Absolute drawdown at period $t$ .

The Maximum Drawdown is the most negative value in the drawdown series:

\begin{aligned} MDD (x) & = - min_{1 \leq t \leq T} d_{t} . \end{aligned}

Where:

$MDD (x)$ : Maximum drawdown.
$T$ : Number of observations.
$d_{t} \leq 0$ : Absolute drawdown at period $t$ .

Fields

settings: Risk measure settings.

Constructors

julia

MaximumDrawdown(;
    settings::RiskMeasureSettings = RiskMeasureSettings()
) -> MaximumDrawdown

Keywords correspond to the struct's fields.

Functor

julia

(r::MaximumDrawdown)(x::VecNum)

Computes the Maximum Drawdown of a portfolio returns vector x.

Arguments

x::VecNum: Portfolio returns vector.

Examples

julia

julia> MaximumDrawdown()
MaximumDrawdown
  settings ┼ RiskMeasureSettings
           │   scale ┼ Float64: 1.0
           │      ub ┼ nothing
           │     rke ┴ Bool: true

Related

source

PortfolioOptimisers.RelativeMaximumDrawdown Type

julia

struct RelativeMaximumDrawdown{__T_settings} <: HierarchicalRiskMeasure

Represents the Relative Maximum Drawdown risk measure for hierarchical optimisation.

RelativeMaximumDrawdown computes the maximum of the relative (compounded) drawdown series.

Mathematical definition

Define the relative drawdown series:

\begin{aligned} C_{t} & = \prod_{s = 1}^{t} (1 + x_{s}), \\ r d_{t} & = \frac{C_{t}}{max_{0 \leq s \leq t} C_{s}} - 1 \leq 0 . \end{aligned}

Where:

$x$ : Portfolio returns vector $T \times 1$ .
$C_{t}$ : Compound wealth process at period $t$ .
$r d_{t} \leq 0$ : Relative drawdown at period $t$ .

The Relative Maximum Drawdown is:

\begin{aligned} RMDD (x) & = - min_{1 \leq t \leq T} r d_{t} . \end{aligned}

Where:

$RMDD (x)$ : Relative maximum drawdown.
$T$ : Number of observations.
$r d_{t} \leq 0$ : Relative drawdown at period $t$ .

Fields

settings: Risk measure settings.

Constructors

julia

RelativeMaximumDrawdown(;
    settings::HierarchicalRiskMeasureSettings = HierarchicalRiskMeasureSettings()
) -> RelativeMaximumDrawdown

Keywords correspond to the struct's fields.

Functor

julia

(r::RelativeMaximumDrawdown)(x::VecNum)

Computes the Relative Maximum Drawdown of a portfolio returns vector x.

Arguments

x::VecNum: Portfolio returns vector.

Examples

julia

julia> RelativeMaximumDrawdown()
RelativeMaximumDrawdown
  settings ┼ HierarchicalRiskMeasureSettings
           │   scale ┴ Float64: 1.0

Related

source

Maximum Drawdown ​

Maximum Drawdown