Turnover Risk Measure Constraints

PortfolioOptimisers.set_risk_constraints! Method

set_risk_constraints!(
    model::Model,
    i,
    r::TurnoverRiskMeasure,
    opt::RiskJuMPOptimisationEstimator,
    ::AbstractPriorResult,
    args...;
    prefix,
    kwargs...
) -> VariableRef

Add turnover risk constraints to model.

Introduces a scalar variable turnover_risk and the L1-norm cone constraint [sc * turnover_risk; sc * (w - benchmark * k)] in NormOneCone(1 + N) where benchmark is the reference weight vector from r.w.

Mathematical definition

$$\begin{array}{rl}\mathrm{Turnover}(\mathit{w})& =\parallel \mathit{w}-{\mathit{w}}_{b}k{\parallel }_1.\end{array}$$

Where:

• $\mathrm{Turnover}(\mathit{w})$: Portfolio turnover.

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

• ${\mathit{w}}_b$: Benchmark weight vector.

• $k$: Rebalancing factor (0 or 1).

• $\parallel \cdot {\parallel }_1$: L1 norm.

where ${\mathit{w}}_b$ is the benchmark weight vector and $k$ is the budget scaling variable.

Arguments

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

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

• r::TurnoverRiskMeasure: Turnover risk measure instance carrying the benchmark weights.

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

Returns

• nothing.

Related

• set_risk_bounds_and_expression!

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