Expected Returns

Public

julia

struct ExpectedReturn{__T_rt} <: NonOptimisationRiskMeasure

Return-based risk measure.

ExpectedReturn is a risk measure that uses the expected portfolio return as its risk metric. This is useful for algorithms or analyses where the risk is defined as the expected return, used in portfolio performance analysis.

Fields

rt: Returns estimator.

Constructors

julia

ExpectedReturn(;
    rt::JuMPReturnsEstimator = ArithmeticReturn()
) -> ExpectedReturn

Keywords correspond to the struct's fields.

Propagated parameters

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

rt: Recursively updated via factory.

Examples

julia

julia> ExpectedReturn()
ExpectedReturn
  rt ┼ ArithmeticReturn
     │   ucs ┼ nothing
     │    lb ┼ nothing
     │    mu ┴ nothing

Related

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PortfolioOptimisers.ExpectedReturnRiskRatio Type

julia

struct ExpectedReturnRiskRatio{__T_rt, __T_rk, __T_rf} <: NonOptimisationRiskMeasure

Ratio-based risk measure.

ExpectedReturnRiskRatio is a risk measure that computes the risk-adjusted return ratio, such as the Sharpe ratio, for a portfolio. It combines a return estimator, a risk measure, and a risk-free rate to produce a ratio metric, used in portfolio performance analysis.

Fields

rt: Returns estimator.
rk: Risk measure for ratio computation.
rf: Risk-free rate.

Constructors

julia

ExpectedReturnRiskRatio(;
    rt::JuMPReturnsEstimator = ArithmeticReturn(),
    rk::AbstractBaseRiskMeasure = Variance(),
    rf::Number = 0.0,
) -> ExpectedReturnRiskRatio

Keywords correspond to the struct's fields.

Propagated parameters

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

rt: Recursively updated via factory.
rk: Recursively updated via factory.

Examples

julia

julia> ExpectedReturnRiskRatio()
ExpectedReturnRiskRatio
  rt ┼ ArithmeticReturn
     │   ucs ┼ nothing
     │    lb ┼ nothing
     │    mu ┴ nothing
  rk ┼ Variance
     │   settings ┼ RiskMeasureSettings
     │            │   scale ┼ Float64: 1.0
     │            │      ub ┼ nothing
     │            │     rke ┴ Bool: true
     │      sigma ┼ nothing
     │       chol ┼ nothing
     │         rc ┼ nothing
     │        alg ┴ SquaredSOCRiskExpr()
  rf ┴ Float64: 0.0

Related

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PortfolioOptimisers.expected_risk Function

julia

expected_risk(r::ExpectedReturn, w::VecNum, pr::AbstractPriorResult;
              fees::Option{<:Fees} = nothing, kwargs...)

Compute the expected risk for a portfolio using a return-based risk measure.

expected_risk returns the expected portfolio return as the risk metric, using the specified return estimator in the ExpectedReturn. This is useful for algorithms where risk is defined as expected return.

Arguments

r: ExpectedReturn containing a return estimator.
w: Portfolio weights.
pr: Prior result.
fees: Optional transaction fees.
kwargs...: Additional keyword arguments.

Returns

risk::Number: Expected portfolio return (net of fees if provided).

Related

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PortfolioOptimisers.expected_risk Function

julia

expected_risk(r::ExpectedReturnRiskRatio, w::VecNum, pr::AbstractPriorResult;
              fees::Option{<:Fees} = nothing, kwargs...)

Compute the expected risk for a portfolio using a ratio-based risk measure.

expected_risk returns the risk-adjusted return ratio (e.g., Sharpe ratio) for the portfolio, using the specified return estimator, risk measure, and risk-free rate in the ExpectedReturnRiskRatio.

Arguments

r: ExpectedReturnRiskRatio containing a return estimator, risk measure, and risk-free rate.
w: Portfolio weights.
pr: Prior result.
fees: Optional transaction fees.
kwargs...: Additional keyword arguments.

Returns

risk::Number: Risk-adjusted return ratio.

Related

source

Private

PortfolioOptimisers.PerfRM Type

julia

const PerfRM = Union{...}

Union of performance risk measures used to compute portfolio performance metrics (returns and return/risk ratios).

Related

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PortfolioOptimisers.PrRM Type

julia

const PrRM = Union{<:ExpectedReturn, <:ExpectedReturnRiskRatio}

Union of prior-based return risk measures that are incompatible with PredictionResult inputs and require the use of MeanReturn or MeanReturnRiskRatio instead.

Related

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PortfolioOptimisers.expected_return Function

julia

expected_return(ret::ArithmeticReturn, w::VecNum, pr::AbstractPriorResult;
                fees::Option{<:Fees} = nothing, kwargs...)
expected_return(ret::LogarithmicReturn, w::VecNum, pr::AbstractPriorResult;
                fees::Option{<:Fees} = nothing, kwargs...)
expected_return(ret::JuMPReturnsEstimator, w::VecVecNum, pr::AbstractPriorResult;
                fees::Option{<:Fees} = nothing, kwargs...)

Compute the expected portfolio return using the specified return estimator.

expected_return computes the expected return for a portfolio given its weights, a prior result, and optional transaction fees. Supports arithmetic, logarithmic, and JuMP-based return estimators. For logarithmic returns, computes the mean log-growth rate. For JuMP-based estimators, returns a vector of expected returns for each portfolio.

Arguments

ret: Return estimator.
w: Portfolio weights.
pr: Prior result.
fees: Optional fees.
kwargs...: Additional keyword arguments passed to underlying routines.

Returns

rt::Num_VecNum: Expected portfolio return(s), net of fees if provided.

Details

For the third method, expected_return is broadcast over the vector of vectors of portfolio weights.

Related

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PortfolioOptimisers.expected_ratio Function

julia

expected_ratio(r::AbstractBaseRiskMeasure, ret::JuMPReturnsEstimator, w::VecNum,
               pr::AbstractPriorResult; fees::Option{<:Fees} = nothing, rf::Number = 0,
               kwargs...)

Compute the expected risk-adjusted return ratio for a portfolio.

expected_ratio computes the ratio of expected portfolio return (net of fees and risk-free rate) to expected portfolio risk, using the specified risk measure and return estimator.

Arguments

r: Risk measure.
ret: Return estimator.
w: Portfolio weights.
pr: Prior result.
fees: Optional transaction fees.
rf: Risk-free rate.
kwargs...: Additional keyword arguments.

Returns

ratio::Number: Risk-adjusted return ratio.

Related

source

PortfolioOptimisers.expected_risk_ret_ratio Function

julia

expected_risk_ret_ratio(r::AbstractBaseRiskMeasure, ret::JuMPReturnsEstimator, w::VecNum,
                        pr::AbstractPriorResult; fees::Option{<:Fees} = nothing,
                        rf::Number = 0, kwargs...)

Compute expected risk, expected return, and risk-adjusted return ratio for a portfolio.

expected_risk_ret_ratio returns a tuple containing the expected portfolio risk, expected portfolio return, and the risk-adjusted return ratio, using the specified risk measure and return estimator.

Arguments

r: Risk measure.
ret: Return estimator.
w: Portfolio weights.
pr: Prior result.
fees: Optional transaction fees.
rf: Risk-free rate.
kwargs...: Additional keyword arguments.

Returns

risk::Number: Expected portfolio risk.
return::Number: Expected portfolio return.
ratio::Number: Risk-adjusted return ratio.

Related

source

PortfolioOptimisers.expected_sric Function

julia

expected_sric(r::AbstractBaseRiskMeasure, ret::JuMPReturnsEstimator, w::VecNum,
              pr::AbstractPriorResult; fees::Option{<:Fees} = nothing, rf::Number = 0,
              kwargs...)

Compute the risk-adjusted ratio information criterion (SRIC) for a portfolio.

expected_sric computes the SRIC, which adjusts the risk-adjusted return ratio for estimation error, penalizing overfitting in portfolio optimization. The SRIC is computed as the risk-adjusted return ratio minus a penalty term based on the number of assets and sample size.

Arguments

r: Risk measure.
ret: Return estimator.
w: Portfolio weights.
pr: Prior result.
fees: Optional transaction fees.
rf: Risk-free rate.
kwargs...: Additional keyword arguments.

Returns

sric::Number: Sharpe Ratio Information Criterion.

Related

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PortfolioOptimisers.expected_risk_ret_sric Function

julia

expected_risk_ret_sric(r::AbstractBaseRiskMeasure, ret::JuMPReturnsEstimator, w::VecNum,
                       pr::AbstractPriorResult; fees::Option{<:Fees} = nothing,
                       rf::Number = 0, kwargs...)

Compute expected risk, expected return, and SRIC for a portfolio.

expected_risk_ret_sric returns a tuple containing the expected portfolio risk, expected portfolio return, and the Sharpe Ratio Information Criterion (SRIC), which adjusts the risk-adjusted return ratio for estimation error.

Arguments

r: Risk measure.
ret: Return estimator.
w: Portfolio weights.
pr: Prior result (must contain asset return matrix X).
fees: Optional transaction fees.
rf: Risk-free rate (default: 0).
kwargs...: Additional keyword arguments.

Returns

risk::Number: Expected portfolio risk.
return::Number: Expected portfolio return.
sric::Number: Sharpe Ratio Information Criterion.

Related

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PortfolioOptimisers.factory Method

julia

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.

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

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

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

Related

source

julia

factory(
    rs::AbstractBaseRiskMeasure,
    args...;
    kwargs...
) -> ConditionalValueatRiskRange{RiskMeasureSettings{__T_scale, __T_ub, __T_rke}, <:Number, <:Number} where {__T_scale, __T_ub, __T_rke}

Return the risk measure rs unchanged.

Identity pass-through used when a risk measure is provided in a context that calls factory.

Related

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PortfolioOptimisers.factory Method

julia

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.

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

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

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

Related

source

julia

factory(
    rs::AbstractBaseRiskMeasure,
    args...;
    kwargs...
) -> ConditionalValueatRiskRange{RiskMeasureSettings{__T_scale, __T_ub, __T_rke}, <:Number, <:Number} where {__T_scale, __T_ub, __T_rke}

Return the risk measure rs unchanged.

Identity pass-through used when a risk measure is provided in a context that calls factory.

Related

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PortfolioOptimisers.needs_previous_weights Method

julia

needs_previous_weights(r::AbstractBaseRiskMeasure) -> Bool
needs_previous_weights(r::VecBaseRM) -> Bool

Return whether risk measure r requires previous portfolio weights as input.

The default returns false. Override to true for risk measures such as turnover or tracking constraints that depend on prior weights. The VecBaseRM overload returns true if any element returns true.

Returns

Bool: true if prior weights are required; false otherwise.

Related

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PortfolioOptimisers.brinson_attribution Function

julia

brinson_attribution(X::TimeArray, w::VecNum, wb::VecNum,
                    asset_classes::DataFrame, col; date0 = nothing, date1 = nothing)

Compute Brinson performance attribution aggregated per asset class [3].

brinson_attribution generates a DataFrame summarizing the Brinson performance attribution, decomposing total excess return into asset allocation, security selection, interaction, and total effect for each asset class. The calculation is performed over the specified date range, using the provided asset weights, benchmark weights, and asset class assignments.

Arguments

X: TimeArray of asset prices or returns.
w: Vector of portfolio weights.
wb: Vector of benchmark weights.
asset_classes: DataFrame containing asset class assignments for each asset.
col: Column in asset_classes specifying the class for each asset.
date0: (Optional) Start date for the attribution period.
date1: (Optional) End date for the attribution period.

Returns

df::DataFrame: DataFrame with rows for asset allocation, security selection, interaction, and total effect, and columns for each asset class and the total.

Details

Computes returns for the specified period.
Aggregates attribution effects by asset class.
Supports custom date ranges via date0 and date1.
Returns a DataFrame with attribution breakdown for each class and the total.

Related

VecNum

References

[3] G. P. Brinson and N. Fachler. Measuring non-US. equity portfolio performance. The Journal of Portfolio Management 11, 73–76 (1985).

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Expected Returns

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