Worst Realisation

struct WorstRealisation{__T_settings} <: RiskMeasure

Represents the Worst Realisation risk measure.

WorstRealisation returns the maximum loss (i.e., the negative minimum return) over all observed scenarios. It is the most conservative risk measure, capturing the single worst outcome in the sample.

Mathematical definition

\[\begin{align} \mathrm{WR}(\boldsymbol{x}) &= -\min_{1 \leq t \leq T} x_t\,. \end{align}\]

Where:

• $\mathrm{WR}(\boldsymbol{x})$: Worst realisation of portfolio returns.
• $\boldsymbol{x}$: Portfolio returns vector $T \times 1$.
• $T$: Number of observations.

Fields

• settings: Risk measure settings.

Constructors

WorstRealisation(;    settings::RiskMeasureSettings = RiskMeasureSettings()) -> WorstRealisation

Keywords correspond to the struct's fields.

Functor

(r::WorstRealisation)(x::VecNum)

Computes the Worst Realisation of a portfolio returns vector x.

Arguments

• x::VecNum: Portfolio returns vector.

Examples

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

Related

• RiskMeasure
• RiskMeasureSettings
• Range
• ValueatRisk

References

• [115] M. R. Young. A minimax portfolio selection rule with linear programming solution. Management Science 44, 673–683 (1998).