Variance and Standard Deviation

PortfolioOptimisers.SimpleVariance — Type
SimpleVariance{T1 <: Union{Nothing, <:AbstractExpectedReturnsEstimator},
               T2 <: Union{Nothing, <:AbstractWeights}, T3 <: Bool}

A flexible variance estimator for PortfolioOptimisers.jl supporting optional expected returns estimators, observation weights, and bias correction.

SimpleVariance enables users to specify an expected returns estimator (for mean-centering), optional observation weights, and whether to apply bias correction (Bessel's correction). This type is suitable for both unweighted and weighted variance estimation workflows.

Fields

  • me::Union{Nothing, <:AbstractExpectedReturnsEstimator}: Optional expected returns estimator. If nothing, the mean is not estimated.
  • w::Union{Nothing, <:AbstractWeights}: Optional observation weights. If nothing, the estimator is unweighted.
  • corrected::Bool: Whether to apply Bessel's correction (unbiased variance).

Constructor

SimpleVariance(; me::Union{Nothing, <:AbstractExpectedReturnsEstimator} = SimpleExpectedReturns(),
                w::Union{Nothing, <:AbstractWeights} = nothing,
                corrected::Bool = true)

Construct a SimpleVariance estimator with the specified expected returns estimator, optional weights, and bias correction flag.

Related

source
PortfolioOptimisers.SimpleVariance — Method
SimpleVariance(; me::Union{Nothing, <:AbstractExpectedReturnsEstimator} = SimpleExpectedReturns(),
                w::Union{Nothing, <:AbstractWeights} = nothing,
                corrected::Bool = true)

Construct a SimpleVariance estimator for flexible variance estimation with optional mean-centering, observation weights, and bias correction.

This constructor creates a SimpleVariance object using the specified expected returns estimator for mean-centering, optional observation weights, and a flag for Bessel's correction (bias correction). If no weights are provided, the estimator defaults to unweighted variance estimation. If weights are provided, they must not be empty.

Arguments

  • me::Union{Nothing, <:AbstractExpectedReturnsEstimator}: Expected returns estimator. Necessary when estimating the variance or standard deviation along the dimension of a matrix. Not used when computed on a vector.
  • w::Union{Nothing, <:AbstractWeights}: Optional observation weights. If nothing, the estimator is unweighted.
  • corrected::Bool: Whether to apply Bessel's correction.

ReturnsResult

  • SimpleVariance: A variance estimator configured with the specified mean estimator, weights, and bias correction flag.

Validation

  • If w is provided, it must not be empty.

Examples

julia> using StatsBase

julia> sv = SimpleVariance()
SimpleVariance
         me | SimpleExpectedReturns
            |   w | nothing
          w | nothing
  corrected | Bool: true

julia> w = Weights([0.2, 0.3, 0.5]);

julia> svw = SimpleVariance(; w = w, corrected = false)
SimpleVariance
         me | SimpleExpectedReturns
            |   w | nothing
          w | StatsBase.Weights{Float64, Float64, Vector{Float64}}: [0.2, 0.3, 0.5]
  corrected | Bool: false

Related

source
Statistics.std — Method
std(ve::SimpleVariance, X::AbstractArray; dims::Int = 1, mean = nothing, kwargs...)

Compute the standard deviation using a SimpleVariance estimator for an array.

This method computes the standard deviation of the input array X using the configuration specified in ve, including optional mean-centering (via ve.me), observation weights (ve.w), and bias correction (ve.corrected). If a mean is not provided, it is estimated using the expected returns estimator in ve.me.

Arguments

  • ve::SimpleVariance: Variance estimator specifying the mean estimator, weights, and bias correction.
  • X::AbstractArray: Data array (vector or matrix) for which to compute the standard deviation.
  • dims::Int: Dimension along which to compute the standard deviation (for matrices).
  • mean: Optional mean value or vector for centering. If not provided, estimated using ve.me.
  • kwargs...: Additional keyword arguments passed to the mean estimator.

ReturnsResult

  • Standard deviation of X, computed according to the estimator configuration.

Examples

julia> sv = SimpleVariance()
SimpleVariance
         me | SimpleExpectedReturns
            |   w | nothing
          w | nothing
  corrected | Bool: true

julia> Xmat = [1.0 2.0; 3.0 4.0];

julia> std(sv, Xmat; dims = 1)
1×2 Matrix{Float64}:
 1.41421  1.41421

Related

source
Statistics.std — Method
std(ve::SimpleVariance, X::AbstractVector; mean = nothing)

Compute the standard deviation using a SimpleVariance estimator for a vector.

This method computes the standard deviation of the input vector X using the configuration specified in ve, including optional observation weights (ve.w) and bias correction (ve.corrected). If a mean is provided, it is used for centering; otherwise, the default mean is used.

Arguments

  • ve::SimpleVariance: Variance estimator specifying weights and bias correction.
  • X::AbstractVector: Data vector for which to compute the standard deviation.
  • mean: Optional mean value for centering. If not provided, the default mean is used.

ReturnsResult

  • Standard deviation of X, computed according to the estimator configuration.

Examples

julia> using StatsBase

julia> sv = SimpleVariance()
SimpleVariance
         me | SimpleExpectedReturns
            |   w | nothing
          w | nothing
  corrected | Bool: true

julia> X = [1.0, 2.0, 3.0];

julia> std(sv, X)
1.0

julia> w = Weights([0.2, 0.3, 0.5]);

julia> svw = SimpleVariance(; w = w, corrected = false)
SimpleVariance
         me | SimpleExpectedReturns
            |   w | nothing
          w | StatsBase.Weights{Float64, Float64, Vector{Float64}}: [0.2, 0.3, 0.5]
  corrected | Bool: false

julia> std(svw, X)
0.7810249675906654

Related

source
Statistics.var — Method
var(ve::SimpleVariance, X::AbstractArray; dims::Int = 1, mean = nothing, kwargs...)

Compute the variance using a SimpleVariance estimator for an array.

This method computes the variance of the input array X using the configuration specified in ve, including optional mean-centering (via ve.me), observation weights (ve.w), and bias correction (ve.corrected). If a mean is not provided, it is estimated using the expected returns estimator in ve.me.

Arguments

  • ve::SimpleVariance: Variance estimator specifying the mean estimator, weights, and bias correction.
  • X::AbstractArray: Data array (vector or matrix) for which to compute the variance.
  • dims::Int: Dimension along which to compute the variance (for matrices).
  • mean: Optional mean value or vector for centering. If not provided, estimated using ve.me.
  • kwargs...: Additional keyword arguments passed to the mean estimator.

ReturnsResult

  • Variance of X, computed according to the estimator configuration.

Examples

julia> sv = SimpleVariance()
SimpleVariance
         me | SimpleExpectedReturns
            |   w | nothing
          w | nothing
  corrected | Bool: true

julia> Xmat = [1.0 2.0; 3.0 4.0];

julia> var(sv, Xmat; dims = 1)
1×2 Matrix{Float64}:
 2.0  2.0

Related

source
Statistics.var — Method
var(ve::SimpleVariance, X::AbstractVector; mean = nothing)

Compute the variance using a SimpleVariance estimator for a vector.

This method computes the variance of the input vector X using the configuration specified in ve, including optional observation weights (ve.w) and bias correction (ve.corrected). If a mean is provided, it is used for centering; otherwise, the default mean is used.

Arguments

  • ve::SimpleVariance: Variance estimator specifying weights and bias correction.
  • X::AbstractVector: Data vector for which to compute the variance.
  • mean: Optional mean value for centering. If not provided, the default mean is used.

ReturnsResult

  • Variance of X, computed according to the estimator configuration.

Examples

julia> using StatsBase

julia> sv = SimpleVariance()
SimpleVariance
         me | SimpleExpectedReturns
            |   w | nothing
          w | nothing
  corrected | Bool: true

julia> X = [1.0, 2.0, 3.0];

julia> var(sv, X)
1.0

julia> w = Weights([0.2, 0.3, 0.5]);

julia> svw = SimpleVariance(; w = w, corrected = false)
SimpleVariance
         me | SimpleExpectedReturns
            |   w | nothing
          w | StatsBase.Weights{Float64, Float64, Vector{Float64}}: [0.2, 0.3, 0.5]
  corrected | Bool: false

julia> var(svw, X)
0.61

Related

source