Fees Constraints

PortfolioOptimisers.add_to_fees! Function

julia

add_to_fees!(model::Model, expr::AbstractJuMPScalar)

Accumulate a JuMP expression into the :fees expression of the optimisation model.

Creates the :fees expression if it does not yet exist; otherwise adds expr to it in place.

Arguments

model::JuMP.Model: The JuMP optimisation model.
expr::JuMP.AbstractJuMPScalar: The fee expression to accumulate.

Returns

nothing.

Related

source

PortfolioOptimisers.set_turnover_fees! Function

julia

set_turnover_fees!(args...)

Add a turnover-based transaction fee expression to the JuMP optimisation model.

The fall-through method does nothing. The concrete method computes val' * |w - wt| via NormOneCone constraints and accumulates the result into the model's :fees expression via add_to_fees!.

Mathematical definition

\begin{aligned} t_{f t n, i} & \geq | w_{i} - w_{t, i} k |, \\ f_{t n} & = v^{⊺} t_{f t n} . \end{aligned}

Where:

$w_{i}$ : Portfolio weight for asset $i$ .
$w_{t, i}$ : Benchmark weight for asset $i$ .
$k$ : Budget scaling / homogenisation variable.
$v$ : Per-asset fee rate vector.
$t_{f t n}$ : Auxiliary absolute-deviation variable vector.
$f_{t n}$ : Total turnover fee.

Arguments

model::JuMP.Model: The JuMP optimisation model.
tn::Turnover: Turnover specification containing benchmark weights w and per-unit fee val.

Returns

nothing.

Related

source

PortfolioOptimisers.set_non_fixed_fees! Function

julia

set_non_fixed_fees!(args...)

Add all non-fixed (proportional and turnover) fee expressions to the JuMP optimisation model.

The fall-through method does nothing. The concrete method delegates to set_long_non_fixed_fees!, set_short_non_fixed_fees!, and set_turnover_fees!.

Arguments

model::JuMP.Model: The JuMP optimisation model.
fees::Fees: Fee specification containing long, short, and turnover fee rates.

Returns

nothing.

Related

source

PortfolioOptimisers.set_long_non_fixed_fees! Function

julia

set_long_non_fixed_fees!(args...)

Add proportional long-side fee expression to the JuMP optimisation model.

The fall-through method does nothing. The concrete method adds fl' * lw to the model's :fees expression via add_to_fees!.

Mathematical definition

\begin{aligned} f_{l} & = f_{l}^{⊺} l w . \end{aligned}

Where:

$f_{l}$ : Total long-side fee.
$f_{l}$ : Per-asset long-side fee rate vector.
$l w$ : Long-weight vector.

Arguments

model::JuMP.Model: The JuMP optimisation model.
fl: Long-side fee rate(s). Accepts a scalar Number or a VecNum.

Returns

nothing.

Related

source

PortfolioOptimisers.set_short_non_fixed_fees! Function

julia

set_short_non_fixed_fees!(args...)

Add proportional short-side fee expression to the JuMP optimisation model.

The fall-through method does nothing. The concrete method adds fs' * sw to the model's :fees expression via add_to_fees!. Does nothing when no short-weight variable :sw exists in the model.

Mathematical definition

\begin{aligned} f_{s} & = f_{s}^{⊺} s w . \end{aligned}

Where:

$f_{s}$ : Total short-side fee.
$f_{s}$ : Per-asset short-side fee rate vector.
$s w$ : Short-weight vector.

Arguments

model::JuMP.Model: The JuMP optimisation model.
fs: Short-side fee rate(s). Accepts a scalar Number or a VecNum.

Returns

nothing.

Related

source

PortfolioOptimisers.set_fixed_fees! Function

julia

set_fixed_fees!(
    model::Model,
    sp::AbstractMIPSpace,
    ind::AbstractMIPIndicators,
    ffl::Union{Nothing, Number, AbstractVector{<:Union{var"#s34", var"#s33"} where {var"#s34"<:Number, var"#s33"<:AbstractJuMPScalar}}},
    ffs::Union{Nothing, Number, AbstractVector{<:Union{var"#s34", var"#s33"} where {var"#s34"<:Number, var"#s33"<:AbstractJuMPScalar}}},
    ffl_flag::Bool,
    ffs_flag::Bool
)

Add fixed-fee expressions to the JuMP optimisation model.

A fixed fee is charged per position held, whatever its size, so unlike the proportional fees above it cannot be written against the weights — it needs a binary saying whether the position is there at all. That is the only reason this one takes an indicator bundle, and the only reason a MIP builder has to run before it.

Mathematical definition

\begin{aligned} f_{f l} & = f_{f l}^{⊺} b^{l}, & f_{f s} & = f_{f s}^{⊺} b^{s} . \end{aligned}

Where:

$b^{l}$ , $b^{s}$ : Long and short binaries (long_bin, short_bin). These are the binaries themselves, never the gates: a fee is incurred by the decision to hold, which is what the bit records, and the gates relax to continuous variables when the budget is free.
$f_{f l}$ , $f_{f s}$ : Long and short fixed-fee rates.

Under a long-only builder the held bit is the long bit (HeldIndicators), and there is no short side to charge.

Arguments

model::JuMP.Model: The JuMP optimisation model.
sp::AbstractMIPSpace: Weight space the fees are charged in.
ind::AbstractMIPIndicators: Indicator bundle supplying the binaries.
ffl::Option{<:Num_VecNum}: Long-side fixed fee rate(s).
ffs::Option{<:Num_VecNum}: Short-side fixed fee rate(s).
ffl_flag::Bool: Whether to add the long fixed-fee expression.
ffs_flag::Bool: Whether to add the short fixed-fee expression.

Returns

nothing.

Related

source

Fees Constraints ​

Fees Constraints