Effective Number of Assets Constraints

PortfolioOptimisers.set_number_effective_assets! Function

set_number_effective_assets!(args...)

Add an effective number of assets constraint to the JuMP optimisation model.

The fall-through method does nothing. The concrete method introduces an auxiliary variable nea and enforces ‖w‖₂ ≤ nea via a SecondOrderCone constraint, combined with nea * √val ≤ k. This is equivalent to requiring the effective number of assets to be at least val.

Mathematical definition

$$\begin{array}{r}\mathrm{nea}\ge \parallel \mathit{w}{\parallel }_2,\\ \mathrm{nea}\cdot \sqrt{\mathrm{val}}\le k\iff \mathrm{ENA}(\mathit{w})& =\frac{1}{\parallel \mathit{w}{\parallel }_2^2}\ge \mathrm{val}.\end{array}$$

Where:

• $\mathrm{nea}$: Auxiliary variable upper-bounding $\parallel \mathit{w}{\parallel }_2$.

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

• $k$: Budget scaling / homogenisation variable.

• $\mathrm{ENA}(\mathit{w})$: Effective number of assets.

• $\mathrm{val}$: Minimum required effective number of assets.

Arguments

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

• val::Number: Minimum required effective number of assets.

Returns

• nothing.

Related

• number_effective_assets

• EqualRiskMeasure

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