Maximum Drawdown

PortfolioOptimisers.MaximumDrawdown Type

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:

$$c_t=\sum _{s=1}^t{x}_s,d_t=c_t-\underset{0\le s\le t}{max}{c}_s\le 0.$$

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

$$\mathrm{MDD}(\mathit{x})=-\underset{1\le t\le T}{min}{d}_t.$$

Fields

• settings: Risk measure configuration.

Constructors

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

Keywords correspond to the struct's fields.

Functor

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

Computes the Maximum Drawdown of a portfolio returns vector x.

Arguments

• x::VecNum: Portfolio returns vector.

Examples

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

Related

• RiskMeasure

• RiskMeasureSettings

• AverageDrawdown

• DrawdownatRisk

• RelativeMaximumDrawdown

source

PortfolioOptimisers.RelativeMaximumDrawdown Type

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:

$$C_t=\prod _{s=1}^t(1+x_s),r{d}_t=\frac{C_t}{\underset{0\le s\le t}{max}{C}_s}-1\le 0.$$

The Relative Maximum Drawdown is:

$$\mathrm{RMDD}(\mathit{x})=-\underset{1\le t\le T}{min}r{d}_t.$$

Fields

• settings: Hierarchical risk measure configuration.

Constructors

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

Keywords correspond to the struct's fields.

Functor

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

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

Arguments

• x::VecNum: Portfolio returns vector.

Examples

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

Related

• HierarchicalRiskMeasure

• HierarchicalRiskMeasureSettings

• MaximumDrawdown

• RelativeAverageDrawdown

source