Ulcer Index

PortfolioOptimisers.UlcerIndex Type

struct UlcerIndex{__T_settings} <: RiskMeasure

Represents the Ulcer Index risk measure.

UlcerIndex measures the depth and duration of drawdowns in portfolio returns. It is defined as the root-mean-square of the absolute drawdown series, capturing both the magnitude and persistence of losses.

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 Ulcer Index is:

$$\mathrm{UI}(\mathit{x})=\sqrt{\frac{1}{T}\sum _{t=1}^T{d}_t^2}=\frac{\Vert \mathit{d}{\Vert }_2}{\sqrt{T}}.$$

Fields

• settings: Risk measure configuration.

Constructors

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

Keywords correspond to the struct's fields.

Functor

(r::UlcerIndex)(x::VecNum)

Computes the Ulcer Index of a portfolio returns vector x.

Arguments

• x::VecNum: Portfolio returns vector.

Examples

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

Related

• RiskMeasure

• RiskMeasureSettings

• AverageDrawdown

• MaximumDrawdown

• RelativeUlcerIndex

source

PortfolioOptimisers.RelativeUlcerIndex Type

struct RelativeUlcerIndex{__T_settings} <: HierarchicalRiskMeasure

Represents the Relative Ulcer Index risk measure for hierarchical optimisation.

RelativeUlcerIndex applies the Ulcer Index framework to 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 Ulcer Index is:

$$\mathrm{RUI}(\mathit{x})=\frac{\Vert \mathit{r}\mathit{d}{\Vert }_2}{\sqrt{T}}.$$

Fields

• settings: Hierarchical risk measure configuration.

Constructors

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

Keywords correspond to the struct's fields.

Functor

(r::RelativeUlcerIndex)(x::VecNum)

Computes the Relative Ulcer Index of a portfolio returns vector x.

Arguments

• x::VecNum: Portfolio returns vector.

Examples

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

Related

• HierarchicalRiskMeasure

• HierarchicalRiskMeasureSettings

• UlcerIndex

• RelativeAverageDrawdown

source