Average Drawdown

PortfolioOptimisers.AverageDrawdown Type

struct AverageDrawdown{__T_settings, __T_w} <: RiskMeasure

Represents the Average Drawdown risk measure.

AverageDrawdown computes the mean of the absolute drawdown series of the portfolio returns. It provides a measure of the average magnitude of drawdowns over the sample period.

Mathematical definition

Define the absolute drawdown series:

$$\begin{array}{rl}{c}_t& =\sum _{s=1}^t{x}_s,\\ d_t& =c_t-\underset{0\le s\le t}{max}{c}_s\le 0.\end{array}$$

Where:

• $\mathit{x}$: Portfolio returns vector $T\times 1$.

• $c_t$: Cumulative simple portfolio return at period $t$.

• $d_t\le 0$: Absolute drawdown at period $t$.

The Average Drawdown is:

$$\begin{array}{rl}\mathrm{ADD}(\mathit{x})& =-\frac{1}{T}\sum _{t=1}^T{d}_t.\end{array}$$

Where:

• $\mathrm{ADD}(\mathit{x})$: Average drawdown.

• $T$: Number of observations.

• $d_t\le 0$: Absolute drawdown at period $t$.

For observation-weighted samples, the weighted mean is used instead.

Fields

• settings: Risk measure settings.

• w: Optional portfolio weights.

Constructors

AverageDrawdown(;
    settings::RiskMeasureSettings = RiskMeasureSettings(),
    w::Option{<:ObsWeights} = nothing
) -> AverageDrawdown

Keywords correspond to the struct's fields.

Validation

• If w is not nothing: !isempty(w).

Functor

(r::AverageDrawdown)(x::VecNum)

Computes the Average Drawdown of a portfolio returns vector x.

Arguments

• x::VecNum: Portfolio returns vector.

Examples

julia> AverageDrawdown()
AverageDrawdown
  settings ┼ RiskMeasureSettings
           │   scale ┼ Float64: 1.0
           │      ub ┼ nothing
           │     rke ┴ Bool: true
         w ┴ nothing

Related

• RiskMeasure

• RiskMeasureSettings

• MaximumDrawdown

• UlcerIndex

• ConditionalDrawdownatRisk

• RelativeAverageDrawdown

source

PortfolioOptimisers.factory Method

factory(
    r::AverageDrawdown,
    pr::AbstractPriorResult,
    args...;
    kwargs...
) -> AverageDrawdown{RiskMeasureSettings{__T_scale, __T_ub, __T_rke}} where {__T_scale, __T_ub, __T_rke}

Create an instance of AverageDrawdown by selecting observation weights from the risk-measure instance or falling back to the prior result.

Related

• AverageDrawdown

• AbstractPriorResult

• factory

• nothing_scalar_array_selector

source

PortfolioOptimisers.RelativeAverageDrawdown Type

struct RelativeAverageDrawdown{__T_settings, __T_w} <: HierarchicalRiskMeasure

Represents the Relative Average Drawdown risk measure for hierarchical optimisation.

RelativeAverageDrawdown computes the mean of the relative (compounded) drawdown series of the portfolio returns.

Mathematical definition

Define the compounded wealth process and relative drawdown series:

$$\begin{array}{rl}{C}_t& =\prod _{s=1}^t(1+x_s),\\ r{d}_t& =\frac{C_t}{\underset{0\le s\le t}{max}{C}_s}-1\le 0.\end{array}$$

Where:

• $\mathit{x}$: Portfolio returns vector $T\times 1$.

• $C_t$: Compound wealth process at period $t$.

• $r{d}_t\le 0$: Relative drawdown at period $t$.

The Relative Average Drawdown is:

$$\begin{array}{rl}\mathrm{RADD}(\mathit{x})& =-\frac{1}{T}\sum _{t=1}^{T}r{d}_t.\end{array}$$

Where:

• $\mathrm{RADD}(\mathit{x})$: Relative average drawdown.

• $T$: Number of observations.

• $r{d}_t\le 0$: Relative drawdown at period $t$.

Fields

• settings: Risk measure settings.

• w: Optional portfolio weights.

Constructors

RelativeAverageDrawdown(;
    settings::HierarchicalRiskMeasureSettings = HierarchicalRiskMeasureSettings(),
    w::Option{<:ObsWeights} = nothing
) -> RelativeAverageDrawdown

Keywords correspond to the struct's fields.

Validation

• If w is not nothing: !isempty(w).

Functor

(r::RelativeAverageDrawdown)(x::VecNum)

Computes the Relative Average Drawdown of a portfolio returns vector x.

Arguments

• x::VecNum: Portfolio returns vector.

Examples

julia> RelativeAverageDrawdown()
RelativeAverageDrawdown
  settings ┼ HierarchicalRiskMeasureSettings
           │   scale ┴ Float64: 1.0
         w ┴ nothing

Related

• HierarchicalRiskMeasure

• HierarchicalRiskMeasureSettings

• AverageDrawdown

• RelativeMaximumDrawdown

source

PortfolioOptimisers.factory Method

factory(
    r::RelativeAverageDrawdown,
    pr::AbstractPriorResult,
    args...;
    kwargs...
) -> RelativeAverageDrawdown{HierarchicalRiskMeasureSettings{__T_scale}} where __T_scale

Create an instance of RelativeAverageDrawdown by selecting observation weights from the risk-measure instance or falling back to the prior result.

Related

• RelativeAverageDrawdown

• AbstractPriorResult

• factory

• nothing_scalar_array_selector

source