Nested Clustered

PortfolioOptimisers.NestedClusteredResult Type

struct NestedClusteredResult{__T_oe, __T_pr, __T_clr, __T_wb, __T_fees, __T_resi, __T_reso, __T_cv, __T_retcode, __T_w, __T_fb} <: NonJuMPOptimisationResult

Result type for Nested Clustered Optimisation.

Fields

• oe: Type of the optimisation estimator that produced this result.

• pr: Prior result.

• clr: Clusters result.

• wb: Weight bounds.

• fees: Fees estimator or result.

• resi: Inner optimisation results.

• reso: Outer optimisation results.

• cv: Cross-validation estimator.

• retcode: Optimisation return code.

• w: Final aggregated portfolio weights.

• fb: Fallback result or estimator.

Related

• NestedClustered

• NonFiniteAllocationOptimisationResult

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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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PortfolioOptimisers.NestedClustered Type

struct NestedClustered{__T_pe, __T_cle, __T_wb, __T_fees, __T_sets, __T_opti, __T_opto, __T_cv, __T_wf, __T_ex, __T_fb, __T_brt, __T_cle_pr, __T_strict} <: ClusteringOptimisationEstimator

Nested Clustered Optimisation (NCO) portfolio optimiser.

NestedClustered implements the Nested Clustered Optimisation algorithm. It first clusters assets, then solves a within-cluster (inner) optimisation for each cluster independently, and finally solves an across-cluster (outer) optimisation to combine the cluster portfolios into a final portfolio.

Fields

• pe: Prior estimator.

• cle: Clusters estimator.

• wb: Weight bounds estimator or weight bounds.

• fees: Fees estimator.

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

• opti: Inner optimiser.

• opto: Outer optimiser.

• cv: Cross-validation estimator.

• wf: Weight finaliser.

• ex: Parallel execution strategy.

• fb: Fallback result or estimator.

• brt: Whether to use bootstrap returns.

• cle_pr: Whether to pass the prior result to the clustering estimator.

• strict: Whether to strictly enforce weight bounds.

Constructors

NestedClustered(;
    pe::PrE_Pr = EmpiricalPrior(),
    cle::ClE_Cl = ClustersEstimator(),
    wb::Option{<:WbE_Wb} = WeightBounds(),
    fees::Option{<:FeesE_Fees} = nothing,
    sets::Option{<:AssetSets} = nothing,
    opti::NonFiniteAllocationOptimisationEstimator,
    opto::NonFiniteAllocationOptimisationEstimator = opti,
    cv::Option{<:OptimisationCrossValidation} = nothing,
    wf::WeightFinaliser = IterativeWeightFinaliser(),
    ex::FLoops.Transducers.Executor = FLoops.ThreadedEx(),
    fb::Option{<:OptE_Opt} = nothing,
    brt::Bool = false,
    cle_pr::Bool = true,
    strict::Bool = false
) -> NestedClustered

Keywords correspond to the struct's fields.

Validation

• opto must pass assert_external_optimiser and assert_special_nco_requirements.

• If opti !== opto: opti must pass assert_internal_optimiser and assert_special_nco_requirements.

• If cv is provided: opti must also pass assert_external_optimiser and assert_special_nco_requirements.

Mathematical definition

Let clusters $C_1,\dots ,C_K$ partition the $N$ assets. The NCO algorithm:

1. Inner: for each cluster $k$, solve ${\mathit{w}}_{C_k}=\mathrm{opti}({\mathbf{X}}_{C_k})$ (sub-portfolio weights within $C_k$).

2. Outer: form a $T\times K$ synthetic returns matrix from cluster portfolios and solve $\mathit{a}=\mathrm{opto}({\mathbf{X}}_{\mathrm{cluster}})$ (allocation across clusters).

3. Combine: $w_i=a_k\cdot w_{C_k,i}$ for $i\in C_k$.

Related

• ClusteringOptimisationEstimator

• HierarchicalRiskParity

• Stacking

• NestedClusteredResult

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PortfolioOptimisers.factory Method

factory(
    nco::NestedClustered,
    w::AbstractVector
) -> NestedClustered{_A, _B, _C, _D, _E, var"#s179", var"#s1791", _F, var"#s1792", var"#s1793", _G, Bool, Bool, Bool} where {_A, _B, _C, _D, _E, var"#s179"<:NonFiniteAllocationOptimisationEstimator, var"#s1791"<:NonFiniteAllocationOptimisationEstimator, _F, var"#s1792"<:WeightFinaliser, var"#s1793"<:Transducers.Executor, _G}

Build an updated NestedClustered with all estimators that track previous weights updated via factory using w.

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PortfolioOptimisers.port_opt_view Method

port_opt_view(
    nco::NestedClustered,
    i,
    X::AbstractMatrix{<:Union{var"#s20", var"#s19"} where {var"#s20"<:Number, var"#s19"<:AbstractJuMPScalar}},
    args...
) -> NestedClustered{_A, _B, _C, _D, _E, var"#s179", var"#s1791", _F, var"#s1792", var"#s1793", _G, Bool, Bool, Bool} where {_A, _B, _C, _D, _E, var"#s179"<:NonFiniteAllocationOptimisationEstimator, var"#s1791"<:NonFiniteAllocationOptimisationEstimator, _F, var"#s1792"<:WeightFinaliser, var"#s1793"<:Transducers.Executor, _G}

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

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PortfolioOptimisers.predict_outer_nco_estimator_returns Function

predict_outer_nco_estimator_returns(
    nco::NestedClustered,
    rd::ReturnsResult,
    pr::AbstractPriorResult,
    fees::Option{<:Fees},
    wi::MatNum,
    resi::VecOpt,
    cls::VecVecInt
)

Predict outer portfolio returns for NestedClustered optimisation. Overload this using nco.cv for custom cross-validation prediction.

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PortfolioOptimisers.optimise Method

optimise(nco::NestedClustered{<:Any, <:Any, <:Any, <:Any, <:Any, <:Any, <:Any,
                  <:Any, <:Any, <:Any, Nothing
              }, rd::ReturnsResult;
         dims::Int = 1, branchorder::Symbol = :optimal, str_names::Bool = false,
         save::Bool = true, kwargs...) -> NestedClusteredResult

Run the Nested Clustered Optimisation portfolio optimisation.

Arguments

• nco: The nested clustered optimiser to use.

• rd: The returns result to use.

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

• branchorder: Passed to the inner and outer optimisers. If this optimiser uses hierarchical clustering, this applies to the clusterisation. The branch order to use for the clusterisation.

• str_names: Passed to the inner and outer optimisers. Whether to use string names for the assets in the optimisation.

• save: Passed to the inner and outer optimisers. Whether to save the JuMP model in the optimisation result.

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

Related

• NestedClustered

• NestedClusteredResult

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PortfolioOptimisers.needs_previous_weights Method

needs_previous_weights(opt::NestedClustered) -> Any

Return true if any sub-estimator of opt requires previous portfolio weights (fees, inner optimiser, outer optimiser, or fallback).

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PortfolioOptimisers.assert_rc_pl Method

assert_rc_pl(opt)

Assert that the optimiser does not use phylogeny risk contribution for NCO outer optimisation.

Checks that factor risk contribution optimisers do not use phylogeny-based constraints when used as the outer optimiser in NCO.

Arguments

• opt: Optimisation estimator.

Returns

• nothing.

Related

• NestedClustered

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PortfolioOptimisers.assert_external_optimiser Method

assert_external_optimiser(opt)

Assert that the outer optimiser is valid for use in NCO.

Checks that the outer optimiser does not use pre-computed prior results, regression results, or unsupported variance/phylogeny risk contribution configurations.

Arguments

• opt: Outer optimisation estimator.

Returns

• nothing on success; throws ArgCheck error otherwise.

Related

• NestedClustered

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PortfolioOptimisers.RiskBudgetingOptimiser Type

const RiskBudgetingOptimiser = Union{<:RiskBudgeting, <:RelaxedRiskBudgeting}

Alias for risk budgeting JuMP optimisers.

Matches either RiskBudgeting or RelaxedRiskBudgeting. Used for dispatch in NCO validation and constraint generation.

Related

• RiskBudgeting

• RelaxedRiskBudgeting

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PortfolioOptimisers.assert_rc_variance Function

assert_rc_variance(opt)

Assert that the optimiser does not use variance risk contribution for NCO outer optimisation.

Checks that risk budgeting-based JuMP optimisers do not use variance for risk contribution when used as the outer optimiser in NCO.

Arguments

• opt: Optimisation estimator.

Returns

• nothing.

Related

• NestedClustered

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