Relaxed risk budgeting

PortfolioOptimisers.RelaxedRiskBudgetingAlgorithm Type

abstract type RelaxedRiskBudgetingAlgorithm <: OptimisationAlgorithm

Abstract supertype for relaxed risk budgeting algorithm variants.

Related Types

• BasicRelaxedRiskBudgeting

• RegularisedRelaxedRiskBudgeting

• RegularisedPenalisedRelaxedRiskBudgeting

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PortfolioOptimisers.BasicRelaxedRiskBudgeting Type

struct BasicRelaxedRiskBudgeting <: RelaxedRiskBudgetingAlgorithm

Basic Relaxed Risk Budgeting formulation.

Uses the basic Second Order Cone (SOC) relaxation of the risk budgeting problem without additional regularisation.

Related Types

• RelaxedRiskBudgetingAlgorithm

• RegularisedRelaxedRiskBudgeting

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PortfolioOptimisers.RegularisedRelaxedRiskBudgeting Type

struct RegularisedRelaxedRiskBudgeting <: RelaxedRiskBudgetingAlgorithm

Regularised Relaxed Risk Budgeting formulation.

Extends the basic SOC formulation with a regularisation term to improve numerical stability.

Related Types

• RelaxedRiskBudgetingAlgorithm

• BasicRelaxedRiskBudgeting

• RegularisedPenalisedRelaxedRiskBudgeting

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PortfolioOptimisers.RegularisedPenalisedRelaxedRiskBudgeting Type

struct RegularisedPenalisedRelaxedRiskBudgeting{__T_p} <: RelaxedRiskBudgetingAlgorithm

Regularised and penalised Relaxed Risk Budgeting formulation.

Extends the regularised formulation with a penalty on deviations from target risk budgets, controlled by parameter p.

Fields

• p: Penalty parameter (positive finite number).

Constructors

RegularisedPenalisedRelaxedRiskBudgeting(;
    p::Number = 1.0
) -> RegularisedPenalisedRelaxedRiskBudgeting

Keywords correspond to the struct's fields.

Validation

• isfinite(p) and p > 0.

Related Types

• RelaxedRiskBudgetingAlgorithm

• RegularisedRelaxedRiskBudgeting

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PortfolioOptimisers.RelaxedRiskBudgeting Type

struct RelaxedRiskBudgeting{__T_opt, __T_rba, __T_wi, __T_alg, __T_fb} <: JuMPOptimisationEstimator

Relaxed Risk Budgeting (RRB) portfolio optimiser.

RelaxedRiskBudgeting implements a relaxed formulation of the risk budgeting problem using a Second Order Cone constraint on the portfolio variance. Unlike RiskBudgeting, it does not require a logarithmic or mixed-integer formulation, making it computationally more tractable.

Fields

• opt: JuMP optimiser configuration.

• rba: Risk budgeting algorithm.

• wi: Initial weights for warm-starting.

• alg: Relaxed risk budgeting algorithm variant.

• fb: Fallback optimiser.

Constructors

RelaxedRiskBudgeting(;
    opt::JuMPOptimiser = JuMPOptimiser(),
    rba::RiskBudgetingAlgorithm = AssetRiskBudgeting(),
    wi::Option{<:VecNum} = nothing,
    alg::RelaxedRiskBudgetingAlgorithm = BasicRelaxedRiskBudgeting(),
    fb::Option{<:OptE_Opt} = nothing
) -> RelaxedRiskBudgeting

Keywords correspond to the struct's fields.

Related

• JuMPOptimisationEstimator

• RiskBudgeting

• RelaxedRiskBudgetingAlgorithm

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PortfolioOptimisers.set_relaxed_risk_budgeting_alg_constraints! Function

set_relaxed_risk_budgeting_alg_constraints!(alg, model, w, sigma, chol)

Add algorithm-specific second-order cone constraints for Relaxed Risk Budgeting.

Dispatches based on the RRB algorithm variant. Adds second-order cone constraints implementing the basic, regularised, or regularised-penalised RRB formulation.

Arguments

• alg: RRB algorithm (BasicRelaxedRiskBudgeting, RegularisedRelaxedRiskBudgeting, or RegularisedPenalisedRelaxedRiskBudgeting).

• model::JuMP.Model: JuMP optimisation model.

• w::VecJuMPScalar: Portfolio weight variables.

• sigma::MatNum: Covariance matrix.

• chol::Option{<:MatNum}: Optional pre-computed Cholesky factor.

Returns

• nothing.

Related

• RelaxedRiskBudgeting

• set_relaxed_risk_budgeting_constraints!

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PortfolioOptimisers.set_relaxed_risk_budgeting_constraints! Function

set_relaxed_risk_budgeting_constraints!(model, rrb, pr, wb, args...)

Add Relaxed Risk Budgeting (RRB) constraints and weight variables to the JuMP model.

Dispatches based on the risk budgeting algorithm type. Configures weight variables, budget constraints, second-order cone constraints, and weight bounds.

Arguments

• model::JuMP.Model: JuMP optimisation model.

• rrb::RelaxedRiskBudgeting: RRB estimator configuration.

• pr::AbstractPriorResult: Prior result with asset moments.

• wb::WeightBounds: Weight bounds configuration.

• args...: Additional arguments (e.g. returns data for factor risk budgeting).

Returns

• Processed risk budgeting attributes.

Related

• RelaxedRiskBudgeting

• set_relaxed_risk_budgeting_alg_constraints!

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PortfolioOptimisers.optimise Function

optimise(rrb::RelaxedRiskBudgeting{<:Any, <:Any, <:Any, <:Any, Nothing},
         rd::ReturnsResult = ReturnsResult(); dims::Int = 1,
         str_names::Bool = false, save::Bool = true, kwargs...) -> RiskBudgetingResult

Arguments

• rrb: The relaxed risk budgeting optimiser to use.

• rd: The returns result to use. If isa(hec.opt.pe, AbstractPriorResult), rd is not necessary if doing a standalone optimisation, but may be required/desired by fallbacks and/or clusterisation.

• dims: The dimension along which observations advance in time.

• str_names: Whether to use string names for the assets in the optimisation.

• save: Whether to save the JuMP model in the optimisation result.

• kwargs: Additional keyword arguments passed to the optimisation function.

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