Factor risk contribution

PortfolioOptimisers.FactorRiskContributionResult Type

struct FactorRiskContributionResult{__T_jr, __T_rr, __T_frc_plr, __T_fb} <: RiskJuMPOptimisationResult

Result type for Factor Risk Contribution portfolio optimisation.

Fields

• jr: Shared JuMP result core, see JuMPOptimisationResult.

• rr: Regression result.

• frc_plr: Factor risk contribution placeholder result.

• fb: Fallback result or estimator.

Property access delegates to the embedded JuMPOptimisationResult; unknown properties forward into rr first, then through jr (including the virtual :w and the pa fall-through).

Related

• FactorRiskContribution

• RiskJuMPOptimisationResult

• JuMPOptimisationResult

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PortfolioOptimisers.factory Method

factory(a::Union{Nothing, <:AbstractEstimator, <:AbstractAlgorithm,
                 <:AbstractResult}, args...; kwargs...) -> a

No-op factory function for constructing objects with a uniform interface.

Defining methods which dispatch on the first argument allows for a consistent factory interface across different types.

Arguments

• a: Indicates no object should be constructed.

• args...: Arbitrary positional arguments (ignored).

• kwargs...: Arbitrary keyword arguments (ignored).

Returns

• a: The input unchanged.

Examples

julia> factory(nothing, 1, 2; x = 3)

julia> factory(MeanValue())
MeanValue
  w ┴ nothing

Related

• AbstractEstimator

• AbstractAlgorithm

• AbstractResult

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factory(res::NonFiniteAllocationOptimisationResult, fb::Option{<:OptE_Opt})

Rebuild a continuous optimisation result with an updated fallback optimiser fb.

Every optimisation result carries fb as its last field, so the generic rebuild copies all fields unchanged except the trailing fb. Concrete result types may override this method when rebuilding requires more than swapping fb.

Related

• OptE_Opt

• NonFiniteAllocationOptimisationResult

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factory(
    opt::Union{NonFiniteAllocationOptimisationEstimator, NonFiniteAllocationOptimisationResult},
    _
) -> RandomWeighted{_A, var"#s179", _B, _C, _D, var"#s1791", _E, Bool} where {_A, var"#s179"<:AbstractRNG, _B, _C, _D, var"#s1791"<:WeightFinaliser, _E}

Return opt unchanged.

Default pass-through factory for optimisation estimators and results. Overridden for estimators that carry parameters requiring update at each optimisation step.

Related

• OptE_Opt

• factory

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Base.getproperty Method

getproperty(
    r::FactorRiskContributionResult,
    sym::Symbol
) -> Any

Access properties of FactorRiskContributionResult. Unique fields rr/frc_plr resolve directly; unknown properties forward into rr first, then delegate to the embedded JuMPOptimisationResult jr (the virtual :w and pa fall-through).

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PortfolioOptimisers.FactorRiskContribution Type

struct FactorRiskContribution{__T_opt, __T_re, __T_r, __T_obj, __T_frc_ple, __T_sets, __T_wi, __T_flag, __T_fb} <: RiskJuMPOptimisationEstimator

Factor Risk Contribution (FRC) portfolio optimiser.

FactorRiskContribution allocates portfolio weights so that each factor (and the idiosyncratic component) contributes a target proportion to the total portfolio risk. It combines factor regression with a JuMP-based risk budgeting optimisation.

Mathematical definition

Factor model:

$$\begin{array}{rl}{\mathit{r}}_i& ={\alpha }_i+\mathbf{F}{\mathit{\beta }}_i+{\mathit{\epsilon }}_i.\end{array}$$

Factor risk contribution for factor $k$:

$$\begin{array}{rl}R{C}_k& ={\beta }_{k,\mathit{w}}\cdot \frac{\partial \mathcal{R}(\mathit{w})}{\partial {\beta }_{k,\mathit{w}}},\\ {\beta }_{k,\mathit{w}}& ={\mathit{w}}^{⊺}{\mathit{\beta }}_k.\end{array}$$

Where:

• ${\mathit{r}}_i$: Return vector of asset $i$.

• ${\alpha }_i$: Intercept (idiosyncratic return) for asset $i$.

• $\mathbf{F}$: Factor returns matrix.

• ${\mathit{\beta }}_i$: Factor loading vector for asset $i$.

• ${\mathit{\epsilon }}_i$: Idiosyncratic residual for asset $i$.

• $R{C}_k$: Risk contribution of factor $k$.

• ${\beta }_{k,\mathit{w}}$: Portfolio-level exposure to factor $k$.

• $\mathcal{R}(\mathit{w})$: Portfolio risk measure.

• $\mathit{w}$: Portfolio weight vector.

Fields

• opt: JuMP optimiser configuration.

• re: Regression estimator.

• r: Risk measure or vector of risk measures.

• obj: Portfolio objective function.

• frc_ple: Factor risk contribution placeholder constraints.

• sets: Sets used to map estimator values to features.

• wi: Initial portfolio weights for warm-starting the solver.

• flag: Algorithm selection flag.

• fb: Fallback result or estimator.

Constructors

FactorRiskContribution(;
    opt::JuMPOptimiser = JuMPOptimiser(),
    re::RegE_Reg = StepwiseRegression(),
    r::RM_VecRM = Variance(),
    obj::ObjectiveFunction = MinimumRisk(),
    frc_ple::Option{<:PlCE_PhC_VecPlCE_PlC} = nothing,
    sets::Option{<:AssetSets} = nothing,
    wi::Option{<:VecNum} = nothing,
    flag::Bool = false,
    fb::Option{<:OptE_Opt} = nothing
) -> FactorRiskContribution

Keywords correspond to the struct's fields.

Validation

• If r is a vector: !isempty(r).

• If wi is provided: !isempty(wi).

Propagated parameters

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

• opt: Recursively updated via factory.

• r: Recursively updated via factory.

• fb: Recursively updated via factory.

Related

• RiskJuMPOptimisationEstimator

• MeanRisk

• RiskBudgeting

• factor_risk_contribution

• factory

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PortfolioOptimisers.needs_previous_weights Method

needs_previous_weights(opt::FactorRiskContribution) -> Any

Return true if any sub-estimator of opt requires previous portfolio weights (JuMP optimiser, risk measure, or fallback).

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PortfolioOptimisers.port_opt_view Method

port_opt_view(
    frc::FactorRiskContribution,
    i,
    X::AbstractMatrix{<:Union{var"#s20", var"#s19"} where {var"#s20"<:Number, var"#s19"<:AbstractJuMPScalar}},
    args...
) -> FactorRiskContribution{JuMPOptimiser{__T_pe, __T_slv, __T_wb, __T_bgt, __T_sbgt, __T_lt, __T_st, __T_lcse, __T_cte, __T_gcarde, __T_sgcarde, __T_smtx, __T_sgmtx, __T_slt, __T_sst, __T_sglt, __T_sgst, __T_tn, __T_fees, __T_sets, __T_tr, __T_ple, __T_ret, __T_sca, __T_ccnt, __T_cobj, __T_sc, __T_so, __T_ss, __T_card, __T_scard, __T_nea, __T_l1, __T_l2, __T_linf, __T_lp, __T_brt, __T_cle_pr, __T_strict}, _A, _B, var"#s179", _C, _D, _E, Bool} where {__T_pe, __T_slv, __T_wb, __T_bgt, __T_sbgt, __T_lt, __T_st, __T_lcse, __T_cte, __T_gcarde, __T_sgcarde, __T_smtx, __T_sgmtx, __T_slt, __T_sst, __T_sglt, __T_sgst, __T_tn, __T_fees, __T_sets, __T_tr, __T_ple, __T_ret, __T_sca, __T_ccnt, __T_cobj, __T_sc, __T_so, __T_ss, __T_card, __T_scard, __T_nea, __T_l1, __T_l2, __T_linf, __T_lp, __T_brt, __T_cle_pr, __T_strict, _A, _B, var"#s179"<:ObjectiveFunction, _C, _D, _E}

Return a cluster-sliced copy of FactorRiskContribution for asset index set i and returns matrix X.

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PortfolioOptimisers.set_factor_risk_contribution_constraints! Method

set_factor_risk_contribution_constraints!(model, re, ...)

Add factor risk contribution constraints to the JuMP model.

Sets up the factor-level risk budgeting constraints in the optimisation model, using the regression result or estimator re to specify factor loadings.

Arguments

• model: JuMP model.

• re: Regression result or estimator (RegE_Reg).

• Additional risk and budget parameters.

Returns

• nothing.

Related

• FactorRiskContribution

• RegE_Reg

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PortfolioOptimisers.optimise Function

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

Run the Factor Risk Contribution portfolio optimisation.

Arguments

• frc: The factor risk contribution optimiser to use.

• rd: The returns result to use. If isa(frc.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.

Related

• FactorRiskContribution

• FactorRiskContributionResult

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