Turnover risk measure

PortfolioOptimisers.TurnoverRiskMeasure Type

struct TurnoverRiskMeasure{__T_settings, __T_w, __T_fixed} <: RiskMeasure

Represents the Turnover risk measure.

TurnoverRiskMeasure penalises portfolio rebalancing by measuring the $L^1$ distance between the new portfolio weights and a reference weight vector. It is used to control trading costs or limit portfolio drift.

Mathematical Definition

Let $\mathit{w}$ be the new portfolio weights and ${\mathit{w}}_0$ the reference (previous or target) weights:

$$\mathrm{Turnover}(\mathit{w})=\Vert {\mathit{w}}_0-\mathit{w}{\Vert }_1=\sum _{i=1}^N|w_{0,i}-w_i|.$$

Fields

• settings: Risk measure configuration.

• w: Reference weight vector (previous or benchmark portfolio weights).

• fixed: If true, the reference weights are fixed and not updated between optimisations. If false, the reference weights are updated to the previous optimisation result.

Constructors

TurnoverRiskMeasure(;
    settings::RiskMeasureSettings = RiskMeasureSettings(),
    w::VecNum,
    fixed::Bool = false
) -> TurnoverRiskMeasure

Keywords correspond to the struct's fields.

Validation

• !isempty(w).

Functor

(r::TurnoverRiskMeasure)(w::VecNum)

Computes the Turnover risk of a portfolio weight vector w.

Arguments

• w::VecNum: New portfolio weights vector.

Examples

julia> TurnoverRiskMeasure(; w = [0.5, 0.5])
TurnoverRiskMeasure
  settings ┼ RiskMeasureSettings
           │   scale ┼ Float64: 1.0
           │      ub ┼ nothing
           │     rke ┴ Bool: true
         w ┼ Vector{Float64}: [0.5, 0.5]
     fixed ┴ Bool: false

Related

• RiskMeasure

• RiskMeasureSettings

• TrackingRiskMeasure

source