PortfolioOptimisers.jl

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Detone ​

Financial data is often responds to broad market conditions. This market-wide behaviour can obscure specific correlation signals. By removing the largest n eigenvalues, the idiosyncratic relationships between assets are allowed to shine through [1].

Detoned matrices may be non-positive definite, so they can be unsuitable for traditional optimisations, but they can be quite effective for clustering ones.

PortfolioOptimisers.AbstractDetoneEstimator Type
julia
abstract type AbstractDetoneEstimator <: AbstractEstimator end

Abstract supertype for all detoning estimators in PortfolioOptimisers.jl.

All concrete types representing detoning estimators (such as Detone) should subtype AbstractDetoneEstimator. This enables a consistent interface for detoning routines and downstream analysis.

Related

source
PortfolioOptimisers.Detone Type
julia
struct Detone{T1, T2} <: AbstractDetoneEstimator
    n::T1
    pdm::T2
end

A concrete detoning estimator for removing the largest n principal components (market modes) from a covariance or correlation matrix in detone! and detone.

For financial data, the leading principal components often represent market-wide movements that can obscure asset-specific signals. The Detone estimator allows users to specify the number of these leading components to remove, thereby enhancing the focus on idiosyncratic relationships between market members [1].

Detoned matrices may not be suitable for non-clustering optimisations because it can make the matrix non-positive definite. However, they can be quite effective for clustering optimsations.

Fields

  • n: Number of leading principal components to remove.

  • pdm: Optional Positive definite matrix estimator. If provided, ensures the output is positive definite.

Constructor

julia
Detone(; n::Integer = 1, pdm::Option{<:Posdef} = Posdef())

Keyword arguments correspond to the fields above.

Validation

  • n > 0.

Examples

julia
julia> Detone(; n = 2)
Detone
    n ┼ Int64: 2
  pdm ┼ Posdef
      │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton
      │   kwargs ┴ @NamedTuple{}: NamedTuple()

Related

References

  • [1] M. M. De Prado. Machine learning for asset managers (Cambridge University Press, 2020). Chapter 2.
source
PortfolioOptimisers.detone! Function
julia
detone!(dt::Detone, X::MatNum)
detone!(::Nothing, args...)

In-place removal of the top n principal components (market modes) from a covariance or correlation matrix.

For matrices without unit diagonal, the function converts them into correlation matrices i.e. matrices with unit diagonal, applies the algorithm, and rescales them back.

Arguments

  • dt: The estimator specifying the detoning algorithm.

    • dt::Detone: The top n principal components are removed from X in-place.

    • dt::Nothing: No-op and returns nothing.

  • X: The covariance or correlation matrix to be detoned (modified in-place).

Returns

  • nothing. The input matrix X is modified in-place.

Validation

  • 1 <= dt.n <= size(X, 2).

Examples

julia
julia> using StableRNGs

julia> rng = StableRNG(123456789);

julia> X = rand(rng, 10, 5);

julia> X = X' * X
5×5 Matrix{Float64}:
 3.29494  2.0765   1.73334  2.01524  1.77493
 2.0765   2.46967  1.39953  1.97242  2.07886
 1.73334  1.39953  1.90712  1.17071  1.30459
 2.01524  1.97242  1.17071  2.24818  1.87091
 1.77493  2.07886  1.30459  1.87091  2.44414

julia> detone!(Detone(), X)

julia> X
5×5 Matrix{Float64}:
  3.29494    -1.14673     0.0868439  -0.502106   -1.71581
 -1.14673     2.46967    -0.876289   -0.0864304   0.274663
  0.0868439  -0.876289    1.90712    -1.18851    -0.750345
 -0.502106   -0.0864304  -1.18851     2.24818    -0.0774753
 -1.71581     0.274663   -0.750345   -0.0774753   2.44414

Related

References

  • [1] M. M. De Prado. Machine learning for asset managers (Cambridge University Press, 2020). Chapter 2.
source
PortfolioOptimisers.detone Function
julia
detone(dt::Detone, X::MatNum)
detone(::Nothing, args...)

Out-of-place version of detone!.

Related

References

  • [1] M. M. De Prado. Machine learning for asset managers (Cambridge University Press, 2020). Chapter 2.
source