Negative Skewness

PortfolioOptimisers.NSkeFormulations Type

const NSkeFormulations = Union{<:NSkeQuadFormulations, <:SOCRiskExpr}

Union of valid optimisation formulations for the NegativeSkewness risk measure.

Related

• NSkeQuadFormulations

• SOCRiskExpr

• NegativeSkewness

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PortfolioOptimisers.NegativeSkewness Type

struct NegativeSkewness{__T_settings, __T_mp, __T_sk, __T_V, __T_alg, __T_window} <: RiskMeasure

Represents the Negative Skewness risk measure.

NegativeSkewness quantifies the portfolio's exposure to negative asymmetry in returns by computing a quadratic or SOC (second-order cone) form of the coskewness matrix. It penalises portfolio constructions that exhibit heavy left-tail behaviour.

Mathematical Definition

Let $\mathit{w}$ be the portfolio weight vector and $\mathbf{V}$ the negative semi-definite coskewness matrix (spectral decomposition of the negative part of the sample coskewness tensor). The Negative Skewness risk measure is:

$$\mathrm{NSke}(\mathit{w})=\{\begin{array}{ll}\sqrt{{\mathit{w}}^{⊺}\mathbf{V}\mathit{w}}& \text{(SOC formulation)}\\ {\mathit{w}}^{⊺}\mathbf{V}\mathit{w}& \text{(Quadratic formulation)}\end{array}$$

Fields

• settings: Risk measure configuration.

• mp: Matrix processing estimator applied to the coskewness matrix.

• sk: Pre-computed coskewness matrix ($N\times N^2$). If nothing, it is computed from the prior.

• V: Pre-computed negative spectral coskewness matrix ($N\times N$). If nothing, it is computed from sk.

• alg: Optimisation formulation (SOCRiskExpr or a NSkeQuadFormulations subtype).

• window: Rolling window index or indices for time-series slicing.

Constructors

NegativeSkewness(;
    settings::RiskMeasureSettings = RiskMeasureSettings(),
    mp::AbstractMatrixProcessingEstimator = DenoiseDetoneAlgMatrixProcessing(),
    sk::Option{<:MatNum} = nothing,
    V::Option{<:MatNum} = nothing,
    alg::NSkeFormulations = SOCRiskExpr(),
    window::Option{<:Int_VecInt} = nothing
) -> NegativeSkewness

Keywords correspond to the struct's fields.

Validation

• If sk or V is provided, both must be provided, non-empty, with size(sk, 1)^2 == size(sk, 2) and V square.

• window is validated with assert_nonempty_nonneg_finite_val.

Functor

(r::NegativeSkewness)(w::VecNum)

Computes the Negative Skewness risk of a portfolio weight vector w.

Arguments

• w::VecNum: Portfolio weights vector.

Examples

julia> NegativeSkewness()
NegativeSkewness
  settings ┼ RiskMeasureSettings
           │   scale ┼ Float64: 1.0
           │      ub ┼ nothing
           │     rke ┴ Bool: true
        mp ┼ DenoiseDetoneAlgMatrixProcessing
           │     pdm ┼ Posdef
           │         │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton
           │         │   kwargs ┴ @NamedTuple{}: NamedTuple()
           │      dn ┼ nothing
           │      dt ┼ nothing
           │     alg ┼ nothing
           │   order ┴ DenoiseDetoneAlg()
        sk ┼ nothing
         V ┼ nothing
       alg ┼ SOCRiskExpr()
    window ┴ nothing

Related

• RiskMeasure

• RiskMeasureSettings

• Kurtosis

• HighOrderMoment

• NSkeQuadFormulations

• SOCRiskExpr

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