Tracking Risk Measure Constraints

PortfolioOptimisers.set_risk_constraints! Method

set_risk_constraints!(
    model::Model,
    i,
    r::TrackingRiskMeasure{<:Any, <:Any, <:L1Tracking},
    opt::RiskJuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    args...;
    prefix,
    kwargs...
) -> Any

Add tracking risk constraints to model.

The L1Tracking overload uses an L1-norm cone. The L2Tracking / SquaredL2Tracking overload uses an SOC. The LpTracking overload uses power cones parameterised by r.alg.p. The LInfTracking overload uses an infinity-norm cone. The independent-variable overload shifts the weight vector by a benchmark before delegating to set_risk_tracking_risk_constraints!. The dependent-variable overload computes a benchmark risk and adds an L1-norm cone on the risk difference via set_risk_tracking_risk_constraints!.

Mathematical definition

$$\begin{array}{rl}{\mathrm{TR}}_p(\mathit{w})& =\frac{\parallel \mathbf{X}\mathit{w}-\mathit{b}k{\parallel }_p}{c_p}.\end{array}$$

Where:

• ${\mathrm{TR}}_p(\mathit{w})$: Tracking risk measure.

• $\mathbf{X}$: Return matrix $T\times N$.

• $\mathit{w}$: Portfolio weights vector $N\times 1$.

• $\mathit{b}$: Benchmark return series.

• $k$: Rebalancing factor (0 or 1).

• $c_p$: Normalisation constant depending on the norm order $p$.

where $\mathit{b}$ is the benchmark return series, $k$ is the budget scaling variable, and $c_p$ is the norm-order scaling factor ($T$, $\sqrt{T-d}$, etc.).

Arguments

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

• i: Constraint index for unique variable and constraint naming.

• r: Tracking risk measure instance.

• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.

• pr::AbstractPriorResult: Prior result containing the returns matrix X.

• pl: Optional phylogeny constraints.

• fees: Optional fees structure.

Returns

• nothing.

Related

• set_tracking_risk!

• set_risk_tr_constraints!

• set_risk_tracking_risk_constraints!

source

PortfolioOptimisers.set_risk_constraints! Method

set_risk_constraints!(
    model::Model,
    i,
    r::TrackingRiskMeasure{<:Any, <:Any, <:Union{var"#s2413", var"#s2412"} where {var"#s2413"<:L2Tracking, var"#s2412"<:SquaredL2Tracking}},
    opt::RiskJuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    args...;
    prefix,
    kwargs...
) -> Any

Add JuMP risk constraints for TrackingRiskMeasure with L2Tracking or SquaredL2Tracking to model.

Introduces a scalar variable and an SOC constraint to encode the L2 (root mean squared) tracking error between portfolio and benchmark returns.

Arguments

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

• i: Constraint index for unique variable and constraint naming.

• r::TrackingRiskMeasure{<:Any, <:Any, <:Union{<:L2Tracking, <:SquaredL2Tracking}}: The tracking risk measure.

• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.

• pr: Prior result.

Returns

• nothing.

Related

• TrackingRiskMeasure

• L2Tracking

• set_risk_constraints!

source

PortfolioOptimisers.set_risk_constraints! Method

set_risk_constraints!(
    model::Model,
    i,
    r::TrackingRiskMeasure{<:Any, <:Any, <:LpTracking},
    opt::RiskJuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    args...;
    prefix,
    kwargs...
) -> Any

Add JuMP risk constraints for TrackingRiskMeasure with LpTracking to model.

Introduces a scalar variable and power-cone constraints to encode the Lp-norm tracking error between portfolio and benchmark returns, scaled by (T - ddof)^(1/p).

Arguments

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

• i: Constraint index for unique variable and constraint naming.

• r::TrackingRiskMeasure{<:Any, <:Any, <:LpTracking}: The tracking risk measure.

• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.

• pr: Prior result.

Returns

• nothing.

Related

• TrackingRiskMeasure

• LpTracking

• set_risk_constraints!

source

PortfolioOptimisers.set_risk_constraints! Method

set_risk_constraints!(
    model::Model,
    i,
    r::TrackingRiskMeasure{<:Any, <:Any, <:LInfTracking},
    opt::RiskJuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    args...;
    prefix,
    kwargs...
) -> Any

Add JuMP risk constraints for TrackingRiskMeasure with LInfTracking to model.

Introduces a scalar variable and an infinity-norm cone constraint to encode the L∞-norm (maximum) tracking error between portfolio and benchmark returns, scaled by T - ddof.

Arguments

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

• i: Constraint index for unique variable and constraint naming.

• r::TrackingRiskMeasure{<:Any, <:Any, <:LInfTracking}: The tracking risk measure.

• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.

• pr: Prior result.

Returns

• nothing.

Related

• TrackingRiskMeasure

• LInfTracking

• set_risk_constraints!

source

PortfolioOptimisers.set_risk_constraints! Method

set_risk_constraints!(
    model::Model,
    i,
    r::RiskTrackingRiskMeasure{<:Any, <:Any, <:Any, <:IndependentVariableTracking},
    opt::RiskJuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    pl::Union{Nothing, AbstractPhylogenyConstraintResult, AbstractVector{<:AbstractPhylogenyConstraintResult}},
    fees::Union{Nothing, Fees},
    args...;
    prefix,
    kwargs...
) -> Any

Add JuMP risk constraints for RiskTrackingRiskMeasure with IndependentVariableTracking to model.

Stores the benchmark-shifted weights w - wb*k at Symbol(tprefix, :w) under the composed tracking prefix tprefix = Symbol(prefix, :tr_iv_, i, :_), delegates to set_risk_tracking_risk_constraints! to build the inner risk on those weights under tprefix, then applies risk bounds and expression registration. The prefix namespacing replaces the former save/restore swap (ADR 0005) and is re-entrant.

Arguments

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

• i: Constraint index for unique variable and constraint naming.

• r::RiskTrackingRiskMeasure{<:Any, <:Any, <:Any, <:IndependentVariableTracking}: The risk-tracking risk measure.

• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.

• pr: Prior result.

• pl: Optional phylogeny constraints.

• fees: Optional fees structure.

Returns

• The tracking risk JuMP expression.

Related

• RiskTrackingRiskMeasure

• IndependentVariableTracking

• set_risk_tracking_risk_constraints!

• set_risk_constraints!

source

PortfolioOptimisers.set_risk_constraints! Method

set_risk_constraints!(
    model::Model,
    i,
    r::RiskTrackingRiskMeasure{<:Any, <:Any, <:Any, <:DependentVariableTracking},
    opt::RiskJuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    pl::Union{Nothing, AbstractPhylogenyConstraintResult, AbstractVector{<:AbstractPhylogenyConstraintResult}},
    fees::Union{Nothing, Fees},
    args...;
    prefix,
    kwargs...
) -> VariableRef

Add JuMP risk constraints for RiskTrackingRiskMeasure with DependentVariableTracking to model.

Computes the benchmark's expected risk value, stores the (unshifted) portfolio weights at Symbol(tprefix, :w) under the composed tracking prefix tprefix = Symbol(prefix, :tr_dv_, i, :_), delegates to set_risk_tracking_risk_constraints! to build the inner portfolio risk under tprefix, then adds an L1-norm cone constraint on the difference between the portfolio's risk expression and the benchmark's expected risk scaled by the allocation variable k. The prefix namespacing replaces the former save/restore swap (ADR 0005) and is re-entrant.

Arguments

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

• i: Constraint index for unique variable and constraint naming.

• r::RiskTrackingRiskMeasure{<:Any, <:Any, <:Any, <:DependentVariableTracking}: The risk-tracking risk measure.

• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.

• pr: Prior result.

• pl: Optional phylogeny constraints.

• fees: Optional fees structure.

Returns

• The tracking risk JuMP expression.

Related

• RiskTrackingRiskMeasure

• DependentVariableTracking

• set_risk_tracking_risk_constraints!

• set_risk_constraints!

source

PortfolioOptimisers.set_tracking_risk! Function

set_tracking_risk!(
    model::Model,
    r::TrackingRiskMeasure{<:Any, <:Any, <:L2Tracking},
    opt::RiskJuMPOptimisationEstimator,
    tracking_risk::AbstractJuMPScalar,
    key::Symbol
) -> AbstractJuMPScalar

Finalise the L2 or squared-L2 tracking risk expression and apply bounds.

The L2Tracking overload calls set_risk_bounds_and_expression! directly with the SOC variable. The SquaredL2Tracking overload squares it and applies a sqrt-converted upper bound to the original SOC variable.

Arguments

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

• r::TrackingRiskMeasure: Tracking risk measure instance.

• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.

• tracking_risk::JuMP.AbstractJuMPScalar: Normalised tracking-risk SOC variable.

• key::Symbol: Symbol used to name constraints or expressions in the model.

Returns

• nothing.

Related

• set_risk_constraints!

• variance_risk_bounds_val

source

PortfolioOptimisers.set_risk_tr_constraints! Function

set_risk_tr_constraints!(
    key,
    model::Model,
    r::RiskMeasure,
    opt::JuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    pl::Union{Nothing, AbstractPhylogenyConstraintResult, AbstractVector{<:AbstractPhylogenyConstraintResult}},
    fees::Union{Nothing, Fees},
    args...;
    kwargs...
) -> Any

Dispatch to indexed set_risk_constraints! for a single measure or iterate over a vector of measures, using a name prefix key for unique constraint naming.

Arguments

• key: Name prefix for unique constraint symbols.

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

• r: A RiskMeasure or a vector of risk measures.

• opt::JuMPOptimisationEstimator: JuMP optimisation estimator.

• pr: Prior result.

• pl: Optional phylogeny constraints.

• fees: Optional fees structure.

Returns

• nothing.

Related

• set_risk_constraints!

• set_risk_tracking_risk_constraints!

source

PortfolioOptimisers.set_risk_tracking_risk_constraints! Function

set_risk_tracking_risk_constraints!(
    model::Model,
    r,
    opt::RiskJuMPOptimisationEstimator,
    pr::AbstractPriorResult,
    pl::Union{Nothing, AbstractPhylogenyConstraintResult, AbstractVector{<:AbstractPhylogenyConstraintResult}},
    fees::Union{Nothing, Fees},
    tprefix::Symbol,
    args...;
    kwargs...
) -> Any

Build the inner risk expression for risk tracking under a namespaced tprefix.

The caller stores the tracking-difference weights at Symbol(tprefix, :w), so the inner set_risk_tr_constraints! build reads and writes ALL of its shared model-state keys (:w, :net_X, :W, :variance_flag, …) under tprefix and cannot collide with the outer model's keys. This replaces the former save/unregister/restore swap (ADR 0005): the prefix isolates the nested build structurally. Because tracking prefixes COMPOSE (tprefix = Symbol(prefix, :tr_iv_, i, :_)), tracking-nested-in-tracking is collision-free.

Arguments

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

• r: Inner risk measure (or vector of measures).

• opt::RiskJuMPOptimisationEstimator: Risk-based optimisation estimator.

• pr: Prior result.

• pl: Optional phylogeny constraints.

• fees: Optional fees structure.

• tprefix::Symbol: Composed tracking prefix namespacing the nested build's keys.

Returns

• The inner risk JuMP expression.

Related

• set_risk_tr_constraints!

source

<!– set_triv_risk_constraints! –> <!– set_trdv_risk_constraints! –>