Generic Value at Risk Range

PortfolioOptimisers.GenericValueatRiskRange Type

struct GenericValueatRiskRange{__T_settings, __T_loss, __T_gain} <: RiskMeasure

Represents a generic Value-at-Risk range risk measure that combines any pair of XatRisk-type measures applied to the loss and gain sides of the return distribution.

GenericValueatRiskRange evaluates a loss-side XatRisk measure on the portfolio returns and a gain-side XatRisk measure on the negated portfolio returns, then sums the two to produce a symmetric tail-spread risk measure.

Mathematical definition

$$\begin{array}{rl}\mathrm{GenVaRRange}(\mathit{x})& ={\rho }_{\mathrm{loss}}(\mathit{x})+{\rho }_{\mathrm{gain}}(-\mathit{x}).\end{array}$$

Where:

• $\mathrm{GenVaRRange}(\mathit{x})$: Generic Value-at-Risk range.

• ${\rho }_{\mathrm{loss}}$: Loss-side XatRisk risk measure.

• ${\rho }_{\mathrm{gain}}$: Gain-side XatRisk risk measure.

• $\mathit{x}$: Portfolio returns vector $T\times 1$.

Fields

• settings: Risk measure settings.

• loss: Loss-side XatRisk risk measure applied to the portfolio returns.

• gain: Gain-side XatRisk risk measure applied to the negated portfolio returns.

Constructors

GenericValueatRiskRange(;
    settings::RiskMeasureSettings = RiskMeasureSettings(),
    loss::Union{<:ValueatRisk, <:ConditionalValueatRisk,
                <:DistributionallyRobustConditionalValueatRisk,
                <:EntropicValueatRisk, <:RelativisticValueatRisk,
                <:PowerNormValueatRisk} = ConditionalValueatRisk(),
    gain::Union{<:ValueatRisk, <:ConditionalValueatRisk,
                <:DistributionallyRobustConditionalValueatRisk,
                <:EntropicValueatRisk, <:RelativisticValueatRisk,
                <:PowerNormValueatRisk} = ConditionalValueatRisk()
) -> GenericValueatRiskRange

Keywords correspond to the struct's fields.

The constructor strips the rke flag from both loss and gain via no_risk_expr_risk_measure, since their risk expressions are combined into the outer settings-controlled expression.

Propagated parameters

When factory is called on this type, the following @fprop-tagged fields are automatically propagated:

• loss: Recursively updated via factory.

• gain: Recursively updated via factory.

View parameters

When port_opt_view is called on this type, the following @vprop-tagged fields are automatically subset to the selected indices:

• loss: Recursively viewed via port_opt_view.

• gain: Recursively viewed via port_opt_view.

Functor

(r::GenericValueatRiskRange)(x::VecNum)

Computes the GenericValueatRiskRange of a portfolio returns vector x.

Arguments

• x::VecNum: Portfolio returns vector.

Examples

julia> GenericValueatRiskRange()
GenericValueatRiskRange
  settings ┼ RiskMeasureSettings
           │   scale ┼ Float64: 1.0
           │      ub ┼ nothing
           │     rke ┴ Bool: true
      loss ┼ ConditionalValueatRisk
           │   settings ┼ RiskMeasureSettings
           │            │   scale ┼ Float64: 1.0
           │            │      ub ┼ nothing
           │            │     rke ┴ Bool: false
           │      alpha ┼ Float64: 0.05
           │          w ┴ nothing
      gain ┼ ConditionalValueatRisk
           │   settings ┼ RiskMeasureSettings
           │            │   scale ┼ Float64: 1.0
           │            │      ub ┼ nothing
           │            │     rke ┴ Bool: false
           │      alpha ┼ Float64: 0.05
           │          w ┴ nothing

Related

• RiskMeasure

• RiskMeasureSettings

• ValueatRisk

• ConditionalValueatRisk

• DistributionallyRobustConditionalValueatRisk

• EntropicValueatRisk

• RelativisticValueatRisk

• PowerNormValueatRisk

• no_risk_expr_risk_measure

• factory

• port_opt_view

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