PortfolioOptimisers.jl

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Equilibrium expected returns ​

PortfolioOptimisers.EquilibriumExpectedReturns Type
julia
struct EquilibriumExpectedReturns{T1, T2, T3} <: AbstractShrunkExpectedReturnsEstimator
    ce::T1
    w::T2
    l::T3
end

Container type for equilibrium expected returns estimators.

EquilibriumExpectedReturns encapsulates the covariance estimator, equilibrium weights, and risk aversion parameter for computing equilibrium expected returns (e.g., as in Black-Litterman). This enables modular workflows for reverse optimization and equilibrium-based return estimation.

Fields

  • ce: Covariance estimator.

  • w: Equilibrium portfolio weights. If nothing, uses equal weights.

  • l: Risk aversion parameter.

Constructor

julia
EquilibriumExpectedReturns(;
                           ce::StatsBase.CovarianceEstimator = PortfolioOptimisersCovariance(),
                           w::Union{Nothing, <:AbstractVector} = nothing, l::Real = 1)

Keyword arguments correspond to the fields above.

Validation

  • If w is provided, !isempty(w).

Examples

julia
julia> EquilibriumExpectedReturns()
EquilibriumExpectedReturns
  ce ┼ PortfolioOptimisersCovariance
     │   ce ┼ Covariance
     │      │    me ┼ SimpleExpectedReturns
     │      │       │   w ┴ nothing
     │      │    ce ┼ GeneralCovariance
     │      │       │   ce ┼ StatsBase.SimpleCovariance: StatsBase.SimpleCovariance(true)
     │      │       │    w ┴ nothing
     │      │   alg ┴ Full()
     │   mp ┼ DefaultMatrixProcessing
     │      │       pdm ┼ Posdef
     │      │           │   alg ┴ UnionAll: NearestCorrelationMatrix.Newton
     │      │   denoise ┼ nothing
     │      │    detone ┼ nothing
     │      │       alg ┴ nothing
   w ┼ nothing
   l ┴ Int64: 1

Related

source
Statistics.mean Method
julia
mean(me::EquilibriumExpectedReturns, X::AbstractMatrix; dims::Int = 1, kwargs...)

Compute equilibrium expected returns from a covariance estimator, weights, and risk aversion.

This method computes equilibrium expected returns as λ * Σ * w, where λ is the risk aversion parameter, Σ is the covariance matrix, and w are the equilibrium weights. If w is not provided in the estimator, equal weights are used.

Arguments

  • me: Equilibrium expected returns estimator.

  • X: Data matrix (observations × assets).

  • dims: Dimension along which to compute the covariance.

  • kwargs...: Additional keyword arguments passed to the covariance estimator.

Returns

  • mu::AbstractArray: Equilibrium expected returns vector.

Related

source