Budget Constraints

PortfolioOptimisers.BudgetConstraintEstimator Type

abstract type BudgetConstraintEstimator <: JuMPConstraintEstimator

Abstract supertype for all budget constraint estimators.

Related

• BudgetEstimator

• BudgetCostEstimator

• BudgetRange

source

PortfolioOptimisers.Num_BgtCE Type

const Num_BgtCE = Union{<:Number, <:BudgetConstraintEstimator}

Union of scalar budget values and BudgetConstraintEstimator instances.

source

PortfolioOptimisers.BudgetEstimator Type

abstract type BudgetEstimator <: BudgetConstraintEstimator

Abstract supertype for estimators that specify the portfolio budget range (sum of weights).

Related

• BudgetRange

source

PortfolioOptimisers.BudgetCostEstimator Type

abstract type BudgetCostEstimator <: BudgetConstraintEstimator

Abstract supertype for estimators that specify transaction cost budgets.

Related

• BudgetCosts

• BudgetMarketImpact

source

PortfolioOptimisers.set_budget_costs! Function

set_budget_costs!(args...)

Set transaction cost budget constraints in the JuMP model.

No-op fallback when no cost budget is specified.

Arguments

• args...: Arguments (ignored).

Returns

• nothing.

Related

• set_long_short_budget_constraints!

source

PortfolioOptimisers.BudgetRange Type

struct BudgetRange{__T_lb, __T_ub} <: BudgetEstimator

Specifies the portfolio budget constraint as a closed interval $[\mathrm{lb},\mathrm{ub}]$ on the sum of weights. At least one of lb or ub must be provided.

Fields

• lb: Lower bound.

• ub: Upper bound.

Constructors

BudgetRange(; lb::Option{<:Number} = 1.0, ub::Option{<:Number} = 1.0) -> BudgetRange

Keywords correspond to the struct's fields.

Validation

• At least one of lb, ub must not be nothing.

• lb and ub must be finite.

• lb <= ub when both are provided.

Related

• BudgetCosts

• BudgetMarketImpact

• set_weight_constraints!

source

PortfolioOptimisers.Num_BgtRg Type

const Num_BgtRg = Union{<:Number, <:BudgetRange}

Alias for a scalar budget value or budget range.

Matches either a plain number (fixed budget, e.g. 1.0) or a BudgetRange (interval budget constraint). Used for dispatch in budget constraint generation.

Related

• BudgetRange

• set_long_short_budget_constraints!

source

PortfolioOptimisers.BudgetCosts Type

struct BudgetCosts{__T_bgt, __T_w, __T_vp, __T_vn, __T_up, __T_un} <: BudgetCostEstimator

Budget constraint that accounts for linear transaction costs.

Mathematical definition

Models the portfolio budget as:

$$\begin{array}{r}{\mathit{v}}_p^{⊺}{\mathit{w}}_p+{\mathit{v}}_n^{⊺}{\mathit{w}}_n\in [\mathrm{lb},\mathrm{ub}].\end{array}$$

Where:

• ${\mathit{w}}_p$, ${\mathit{w}}_n$: Positive and negative weight increments.

• ${\mathit{v}}_p$, ${\mathit{v}}_n$: Cost coefficient vectors for positive and negative changes.

• $\mathrm{lb}$, $\mathrm{ub}$: Lower and upper budget bounds.

Fields

• bgt: Budget target or range.

• w: Portfolio weights vector assets × 1.

• vp: Cost coefficients for positive weight changes. Non-negative.

• vn: Cost coefficients for negative weight changes. Non-negative.

• up: Upper limit on positive weight changes. Non-negative.

• un: Upper limit on negative weight changes. Non-negative.

Constructors

BudgetCosts(;
    bgt::Num_BgtRg = 1.0,
    w::VecNum,
    vp::Num_VecNum = 1.0,
    vn::Num_VecNum = 1.0,
    up::Num_VecNum = 1.0,
    un::Num_VecNum = 1.0
) -> BudgetCosts

Keywords correspond to the struct's fields.

Validation

• !isempty(w).

• If vp is a vector: !isempty(vp) and all elements >= 0. If scalar: >= 0.

• If vn is a vector: !isempty(vn) and all elements >= 0. If scalar: >= 0.

• If up is a vector: !isempty(up) and all elements >= 0. If scalar: >= 0.

• If un is a vector: !isempty(un) and all elements >= 0. If scalar: >= 0.

View parameters

When port_opt_view is called on this type, the following @vprop-tagged fields are automatically subset to the selected indices:

• w: Sliced to the selected indices via port_opt_view.

• vp: Sliced to the selected indices via port_opt_view.

• vn: Sliced to the selected indices via port_opt_view.

• up: Sliced to the selected indices via port_opt_view.

• un: Sliced to the selected indices via port_opt_view.

Related

• BudgetRange

• BudgetMarketImpact

• port_opt_view

source

PortfolioOptimisers.BudgetMarketImpact Type

struct BudgetMarketImpact{__T_bgt, __T_w, __T_vp, __T_vn, __T_up, __T_un, __T_beta} <: BudgetCostEstimator

Budget constraint that accounts for non-linear (power-law) market impact costs. Extends BudgetCosts with a beta exponent controlling the concavity of the market impact function.

Fields

• bgt: Budget target or range.

• w: Portfolio weights vector assets × 1.

• vp: Cost coefficients for positive weight changes. Non-negative.

• vn: Cost coefficients for negative weight changes. Non-negative.

• up: Upper limit on positive weight changes. Non-negative.

• un: Upper limit on negative weight changes. Non-negative.

• beta: Market impact exponent in (0, 1].

Constructors

BudgetMarketImpact(;
    bgt::Num_BgtRg = 1.0,
    w::VecNum,
    vp::Num_VecNum = 1.0,
    vn::Num_VecNum = 1.0,
    up::Num_VecNum = 1.0,
    un::Num_VecNum = 1.0,
    beta::Number = 2/3
) -> BudgetMarketImpact

Keywords correspond to the struct's fields.

Validation

• !isempty(w).

• If vp is a vector: !isempty(vp) and all elements >= 0. If scalar: >= 0.

• If vn is a vector: !isempty(vn) and all elements >= 0. If scalar: >= 0.

• If up is a vector: !isempty(up) and all elements >= 0. If scalar: >= 0.

• If un is a vector: !isempty(un) and all elements >= 0. If scalar: >= 0.

• 0 <= beta <= 1.

View parameters

When port_opt_view is called on this type, the following @vprop-tagged fields are automatically subset to the selected indices:

• w: Sliced to the selected indices via port_opt_view.

• vp: Sliced to the selected indices via port_opt_view.

• vn: Sliced to the selected indices via port_opt_view.

• up: Sliced to the selected indices via port_opt_view.

• un: Sliced to the selected indices via port_opt_view.

Related

• BudgetRange

• BudgetCosts

• port_opt_view

source

PortfolioOptimisers.set_budget_constraints! Function

set_budget_constraints!(args...)
set_budget_constraints!(model::JuMP.Model, val::Number, w::VecNum)
set_budget_constraints!(model::JuMP.Model, bgt::BudgetRange, w::VecNum)
set_budget_constraints!(model::JuMP.Model, bgt::BudgetCosts, w::VecNum)
set_budget_constraints!(model::JuMP.Model, bgt::BudgetMarketImpact, w::VecNum)

Add budget constraints to the JuMP optimisation model.

The fall-through method does nothing. The concrete methods add the appropriate portfolio budget constraint based on the type of budget specification provided.

Mathematical definition

Fixed / range:

$$\begin{array}{rl}k\cdot \mathrm{lb}& \le \sum _i{w}_i\le k\cdot \mathrm{ub}.\end{array}$$

Where:

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

• $k$: Budget scaling / homogenisation variable.

• $\mathrm{lb}$, $\mathrm{ub}$: Lower and upper budget bounds.

Linear cost budget (BudgetCosts):

$$\begin{array}{r}\sum _i{w}_i+{\mathit{v}}_p^{⊺}{\mathit{w}}_p+{\mathit{v}}_n^{⊺}{\mathit{w}}_n\in [k\mathrm{lb},k\mathrm{ub}].\end{array}$$

Where:

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

• $k$: Budget scaling / homogenisation variable.

• ${\mathit{w}}_p$, ${\mathit{w}}_n$: Positive and negative weight increments.

• ${\mathit{v}}_p$, ${\mathit{v}}_n$: Cost coefficient vectors for positive and negative changes.

• $\mathrm{lb}$, $\mathrm{ub}$: Lower and upper budget bounds.

Power-law market-impact budget (BudgetMarketImpact):

$$\begin{array}{r}\sum _i{w}_i+{\mathit{v}}_p^{⊺}{\mathit{w}}_p^{\beta }+{\mathit{v}}_n^{⊺}{\mathit{w}}_n^{\beta }\in [k\mathrm{lb},k\mathrm{ub}].\end{array}$$

Where:

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

• $k$: Budget scaling / homogenisation variable.

• ${\mathit{w}}_p$, ${\mathit{w}}_n$: Positive and negative weight increments.

• ${\mathit{v}}_p$, ${\mathit{v}}_n$: Market-impact cost coefficient vectors.

• $\beta \in (0,1]$: Market-impact power exponent.

• $\mathrm{lb}$, $\mathrm{ub}$: Lower and upper budget bounds.

Arguments

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

• val::Number: Fixed budget scalar.

• bgt: Budget constraint specification (BudgetRange, BudgetCosts, or BudgetMarketImpact).

• w: Portfolio weight vector.

Returns

• nothing.

Related

• BudgetRange

• BudgetCosts

• BudgetMarketImpact

• set_weight_constraints!

source

PortfolioOptimisers.set_long_short_budget_constraints! Function

set_long_short_budget_constraints!(args...)

Set budget constraints for long and short portfolio positions in the JuMP model.

Various overloads handle different budget types (fixed, range), dispatching on the presence or absence of long/short budget configurations.

Arguments

• args...: JuMP model and budget parameters.

Returns

• nothing.

Related

• BudgetRange

• set_cost_budget_constraints!

source

PortfolioOptimisers.set_cost_budget_constraints! Function

set_cost_budget_constraints!(model, vp, vn, val_or_bgt, w)

Set cost-budget constraints in the JuMP model.

Various overloads handle different cost types (fixed value or BudgetRange).

Arguments

• model: JuMP optimisation model.

• vp: Positive cost vector or scalar.

• vn: Negative cost vector or scalar.

• val_or_bgt: Fixed budget value or BudgetRange.

• w: Portfolio weight vector.

Returns

• nothing.

Related

• set_budget_costs!

• set_long_short_budget_constraints!

source