Standard deviation expected returns

PortfolioOptimisers.StandardDeviationExpectedReturns Type

struct StandardDeviationExpectedReturns{__T_ce} <: AbstractExpectedReturnsEstimator

Expected returns estimator that returns the asset standard deviations.

StandardDeviationExpectedReturns computes "expected returns" as the standard deviation of each asset, as estimated by the underlying covariance estimator. This can be useful in certain risk-based portfolio construction approaches where the expected return proxy is the asset's volatility.

Fields

• ce: Covariance estimator.

Constructors

StandardDeviationExpectedReturns(;
    ce::StatsBase.CovarianceEstimator = PortfolioOptimisersCovariance()
) -> StandardDeviationExpectedReturns

Keywords correspond to the struct's fields.

Propagated parameters

When factory is called on this type, the following @fprop-tagged fields are automatically propagated:

• ce: Recursively updated via factory.

View parameters

When port_opt_view is called on this type, the following @vprop-tagged fields are automatically subset to the selected indices:

• ce: Recursively viewed via port_opt_view.

Examples

julia> StandardDeviationExpectedReturns()
StandardDeviationExpectedReturns
  ce ┼ PortfolioOptimisersCovariance
     │   ce ┼ Covariance
     │      │    me ┼ SimpleExpectedReturns
     │      │       │   w ┴ nothing
     │      │    ce ┼ GeneralCovariance
     │      │       │   ce ┼ StatsBase.SimpleCovariance: StatsBase.SimpleCovariance(true)
     │      │       │    w ┴ nothing
     │      │   alg ┴ FullMoment()
     │   mp ┼ MatrixProcessing
     │      │     pdm ┼ Posdef
     │      │         │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton
     │      │         │   kwargs ┴ @NamedTuple{}: NamedTuple()
     │      │      dn ┼ nothing
     │      │      dt ┼ nothing
     │      │     alg ┼ nothing
     │      │   order ┴ NTuple{4, Symbol}: (:pdm, :dn, :dt, :alg)

Related

• AbstractExpectedReturnsEstimator

• PortfolioOptimisersCovariance

• factory

• port_opt_view

source

Statistics.mean Method

Statistics.mean(me::StandardDeviationExpectedReturns, X::MatNum;
                dims::Int = 1, kwargs...)

Compute expected returns as the standard deviation of each asset.

This method returns the standard deviation vector of X as estimated by the covariance estimator me.ce.

Mathematical definition

$$\begin{array}{rl}{\hat{\mu }}_j& ={\hat{\sigma }}_j=\sqrt{\frac{1}{T-c}\sum _{t=1}^T{w}_t(r_{tj}-{\hat{\mu }}_j^{(0)}{)}^2}.\end{array}$$

Where:

• ${\hat{\sigma }}_j$: Standard deviation of asset $j$.

• $c$: Bias correction ($c=1$ if corrected = true, else $c=0$).

• $T$: Number of observations.

• $w_t$: Observation weights.

Arguments

• me: Standard deviation expected returns estimator.

• X: Data matrix of asset returns (observations × assets).

• dims: Dimension along which to perform the computation.

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

Returns

• mu::Matrix{<:Number}: Standard deviation vector, shaped as (1, N) if dims == 1 or (N, 1) if dims == 2.

Related

• StandardDeviationExpectedReturns

source

PortfolioOptimisers.VarianceExpectedReturns Type

struct VarianceExpectedReturns{__T_ce} <: AbstractExpectedReturnsEstimator

Expected returns estimator that returns the asset variances.

VarianceExpectedReturns computes "expected returns" as the variance of each asset, as estimated by the underlying covariance estimator. This can be useful in certain risk-based portfolio construction approaches where the expected return proxy is the asset's variance. Variance is the square of volatility (standard deviation).

Fields

• ce: Covariance estimator.

Constructors

VarianceExpectedReturns(;
    ce::StatsBase.CovarianceEstimator = PortfolioOptimisersCovariance()
) -> VarianceExpectedReturns

Keywords correspond to the struct's fields.

Propagated parameters

When factory is called on this type, the following @fprop-tagged fields are automatically propagated:

• ce: Recursively updated via factory.

View parameters

When port_opt_view is called on this type, the following @vprop-tagged fields are automatically subset to the selected indices:

• ce: Recursively viewed via port_opt_view.

Examples

julia> VarianceExpectedReturns()
VarianceExpectedReturns
  ce ┼ PortfolioOptimisersCovariance
     │   ce ┼ Covariance
     │      │    me ┼ SimpleExpectedReturns
     │      │       │   w ┴ nothing
     │      │    ce ┼ GeneralCovariance
     │      │       │   ce ┼ StatsBase.SimpleCovariance: StatsBase.SimpleCovariance(true)
     │      │       │    w ┴ nothing
     │      │   alg ┴ FullMoment()
     │   mp ┼ MatrixProcessing
     │      │     pdm ┼ Posdef
     │      │         │      alg ┼ UnionAll: NearestCorrelationMatrix.Newton
     │      │         │   kwargs ┴ @NamedTuple{}: NamedTuple()
     │      │      dn ┼ nothing
     │      │      dt ┼ nothing
     │      │     alg ┼ nothing
     │      │   order ┴ NTuple{4, Symbol}: (:pdm, :dn, :dt, :alg)

Related

• AbstractExpectedReturnsEstimator

• PortfolioOptimisersCovariance

• factory

• port_opt_view

source

PortfolioOptimisers.factory Method

factory(a::Union{Nothing, <:AbstractEstimator, <:AbstractAlgorithm,
                 <:AbstractResult}, args...; kwargs...) -> a

No-op factory function for constructing objects with a uniform interface.

Defining methods which dispatch on the first argument allows for a consistent factory interface across different types.

factory and port_opt_view are the two propagation mechanisms in this library. They are duals: factory threads runtime values (prior moments, observation weights, previous portfolio weights) down through a composed struct tree; port_opt_view threads an index selection (a subset of assets or observations) down through the same tree.

Arguments

• a: Indicates no object should be constructed.

• args...: Arbitrary positional arguments (ignored).

• kwargs...: Arbitrary keyword arguments (ignored).

Returns

• a: The input unchanged.

Examples

julia> factory(nothing, 1, 2; x = 3)

julia> factory(MeanValue())
MeanValue
  w ┴ nothing

Related

• port_opt_view

• AbstractEstimator

• AbstractAlgorithm

• AbstractResult

source

Statistics.mean Method

Statistics.mean(me::VarianceExpectedReturns, X::MatNum;
                dims::Int = 1, kwargs...)

Compute expected returns as the variance of each asset.

This method returns the variance vector of X as estimated by the covariance estimator me.ce.

Arguments

• me: Variance expected returns estimator.

• X: Data matrix of asset returns (observations × assets).

• dims: Dimension along which to perform the computation.

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

Returns

• mu::Matrix{<:Number}: Variance vector, shaped as (1, N) if dims == 1 or (N, 1) if dims == 2.

Related

• VarianceExpectedReturns

source