Base Distance

PortfolioOptimisers.SimpleDistance Type

struct SimpleDistance <: AbstractDistanceAlgorithm end

Simple distance algorithm for portfolio optimization.

$$\begin{array}{rl}{d}_{i,j}& =\sqrt{{\displaystyle \frac{1-{\rho }_{i,j}}{2}}},\end{array}$$

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

Related

• AbstractDistanceAlgorithm

• AbstractDistanceEstimator

• distance

• cor_and_dist

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PortfolioOptimisers.SimpleAbsoluteDistance Type

struct SimpleAbsoluteDistance <: AbstractDistanceAlgorithm end

Simple absolute distance algorithm for portfolio optimization.

$$\begin{array}{rl}{d}_{i,j}& =\sqrt{1-|{\rho }_{i,j}|},\end{array}$$

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

Related

• AbstractDistanceAlgorithm

• AbstractDistanceEstimator

• distance

• cor_and_dist

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PortfolioOptimisers.LogDistance Type

struct LogDistance <: AbstractDistanceAlgorithm end

Logarithmic distance algorithm for portfolio optimization.

$$\begin{array}{rl}{d}_{i,j}& =-\log |{\rho }_{i,j}|,\end{array}$$

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

Related

• AbstractDistanceAlgorithm

• AbstractDistanceEstimator

• distance

• cor_and_dist

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PortfolioOptimisers.CorrelationDistance Type

struct CorrelationDistance <: AbstractDistanceAlgorithm end

Correlation distance algorithm for portfolio optimization.

$$\begin{array}{rl}{d}_{i,j}& =\sqrt{1-{\rho }_{i,j}},\end{array}$$

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

Related

• AbstractDistanceAlgorithm

• AbstractDistanceEstimator

• distance

• cor_and_dist

source

PortfolioOptimisers.VariationInfoDistance Type

struct VariationInfoDistance{T1, T2} <: AbstractDistanceAlgorithm
    bins::T1
    normalise::T2
end

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 strategy or number of bins. If an integer, must be strictly positive.

• normalise: Whether to normalise the VI distance to the range [0, 1].

Constructor

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

Keyword arguments correspond to the fields above.

Validation

• If bins is an integer, bins > 0.

Examples

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

Related

• AbstractDistanceAlgorithm

• distance

• cor_and_dist

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PortfolioOptimisers.CanonicalDistance Type

struct CanonicalDistance <: AbstractDistanceAlgorithm end

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.

Related

• AbstractDistanceAlgorithm

• AbstractDistanceEstimator

• MutualInfoCovariance

• LowerTailDependenceCovariance

• DistanceCovariance

• VariationInfoDistance

• LogDistance

• CorrelationDistance

• SimpleDistance

• distance

• cor_and_dist

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PortfolioOptimisers.AbstractDistanceEstimator Type

abstract type AbstractDistanceEstimator <: AbstractEstimator end

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.

Related

• AbstractEstimator

• AbstractDistanceAlgorithm

• distance

• cor_and_dist

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PortfolioOptimisers.AbstractDistanceAlgorithm Type

abstract type AbstractDistanceAlgorithm <: AbstractAlgorithm end

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

• AbstractDistanceEstimator

• SimpleDistance

• SimpleAbsoluteDistance

• LogDistance

• CorrelationDistance

• CanonicalDistance

• VariationInfoDistance

• distance

• cor_and_dist

source