Base Distance

julia

struct SimpleDistance <: AbstractDistanceAlgorithm

Simple distance algorithm for portfolio optimization.

\begin{aligned} d_{i, j} & = \sqrt{\frac{1 - ρ_{i, j}}{2}}, \end{aligned}

where $d$ is the distance, $ρ$ is the correlation coefficient, and each subscript denotes an asset.

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PortfolioOptimisers.SimpleAbsoluteDistance Type

julia

struct SimpleAbsoluteDistance <: AbstractDistanceAlgorithm

Simple absolute distance algorithm for portfolio optimization.

\begin{aligned} d_{i, j} & = \sqrt{1 - | ρ_{i, j} |}, \end{aligned}

where $d$ is the distance, $ρ$ is the correlation coefficient, and each subscript denotes an asset.

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PortfolioOptimisers.LogDistance Type

julia

struct LogDistance <: AbstractDistanceAlgorithm

Logarithmic distance algorithm for portfolio optimization.

\begin{aligned} d_{i, j} & = - \log | ρ_{i, j} |, \end{aligned}

where $d$ is the distance, $ρ$ is the correlation coefficient, and each subscript denotes an asset.

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PortfolioOptimisers.CorrelationDistance Type

julia

struct CorrelationDistance <: AbstractDistanceAlgorithm

Correlation distance algorithm for portfolio optimization.

\begin{aligned} d_{i, j} & = \sqrt{1 - ρ_{i, j}}, \end{aligned}

where $d$ is the distance, $ρ$ is the correlation coefficient, and each subscript denotes an asset.

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PortfolioOptimisers.VariationInfoDistance Type

julia

struct VariationInfoDistance{__T_bins, __T_normalise} <: AbstractDistanceAlgorithm

Variation of Information (VI) distance algorithm for portfolio optimization.

VariationInfoDistance specifies the use of the Variation of Information (VI) metric, an information-theoretic distance based on entropy and mutual information.

Fields

bins: Binning algorithm or fixed number of bins.
normalise: Whether to normalise the mutual and/or variation of information calculation.

Constructors

julia

VariationInfoDistance(;
    bins::Int_Bin = HacineGharbiRavier(),
    normalise::Bool = true
) -> VariationInfoDistance

Keywords correspond to the struct's fields.

Validation

If bins is an integer, bins > 0.

Examples

julia

julia> VariationInfoDistance()
VariationInfoDistance
       bins ┼ HacineGharbiRavier()
  normalise ┴ Bool: true

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PortfolioOptimisers.CanonicalDistance Type

julia

struct CanonicalDistance <: AbstractDistanceAlgorithm

Canonical distance algorithm for portfolio optimization.

Defines the canonical distance metric for a given covariance estimator. The resulting distance metric is consistent with the properties of the covariance estimator (relevant when the covariance estimator is MutualInfoCovariance).

Covariance Estimator	Distance Metric
`MutualInfoCovariance`	`VariationInfoDistance`
`LowerTailDependenceCovariance`	`LogDistance`
`DistanceCovariance`	`CorrelationDistance`
`StatsBase.CovarianceEstimator`	`SimpleDistance`

The table also applies to PortfolioOptimisersCovariance where ce is one of the aforementioned estimators.

When used with a covariance matrix directly, uses SimpleDistance.

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PortfolioOptimisers.AbstractDistanceEstimator Type

julia

abstract type AbstractDistanceEstimator <: AbstractEstimator

Abstract supertype for all distance estimator types in PortfolioOptimisers.jl.

All concrete and/or abstract types implementing distance-based estimation algorithms should be subtypes of AbstractDistanceEstimator.

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PortfolioOptimisers.AbstractDistanceAlgorithm Type

julia

abstract type AbstractDistanceAlgorithm <: AbstractAlgorithm

Abstract supertype for all distance algorithm types in PortfolioOptimisers.jl.

All concrete and/or abstract types implementing specific distance-based algorithms (such as correlation distance, absolute distance, log distance, or information-theoretic distances) should be subtypes of AbstractDistanceAlgorithm.

Related

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Base Distance ​

Base Distance