# averageShortfall (3) - Linux Manuals

## averageShortfall: empirical-distribution risk measures

## NAME

QuantLib::GenericRiskStatistics - empirical-distribution risk measures

## SYNOPSIS

#include <ql/math/statistics/riskstatistics.hpp>

Inherits S.

### Public Types

typedef S::value_type **value_type**

### Public Member Functions

Real **semiVariance** () const

Real **semiDeviation** () const

Real **downsideVariance** () const

Real **downsideDeviation** () const

Real **regret** (Real target) const

Real **potentialUpside** (Real percentile) const

*potential upside (the reciprocal of VAR) at a given percentile *

Real **valueAtRisk** (Real percentile) const

*value-at-risk at a given percentile *

Real **expectedShortfall** (Real percentile) const

*expected shortfall at a given percentile *

Real **shortfall** (Real target) const

Real **averageShortfall** (Real target) const

## Detailed Description

### template<class S> class QuantLib::GenericRiskStatistics< S >

empirical-distribution risk measuresThis class wraps a somewhat generic statistic tool and adds a number of risk measures (e.g.: value-at-risk, expected shortfall, etc.) based on the data distribution as reported by the underlying statistic tool.

**Possible enhancements**

- add historical annualized volatility

**Examples: **

## Member Function Documentation

### Real semiVariance () const

returns the variance of observations below the mean, [ ac{N}{N-1} mathrm{E}

)^2 ;|; x <

ngle ight]. ]

### Real semiDeviation () const

returns the semi deviation, defined as the square root of the semi variance.

### Real downsideVariance () const

returns the variance of observations below 0.0, [ ac{N}{N-1} mathrm{E}

al downsideDeviation () const"

returns the downside deviation, defined as the square root of the downside variance.

### Real regret (Real target) const

returns the variance of observations below target, [ ac{N}{N-1} mathrm{E}

e Dembo and Freeman, 'The Rules Of Risk', Wiley (2001).

### Real potentialUpside (Real centile) const

potential upside (the reciprocal of VAR) at a given percentile

**Precondition:**

- percentile must be in range [90-100%)

### Real valueAtRisk (Real centile) const

value-at-risk at a given percentile

**Precondition:**

- percentile must be in range [90-100%)

### Real expectedShortfall (Real centile) const

expected shortfall at a given percentile

returns the expected loss in case that the loss exceeded a VaR threshold,

[ mathrm{E}

average of observations below the given percentile $ p $. Also know as conditional value-at-risk.

See Artzner, Delbaen, Eber and Heath, 'Coherent measures of risk', Mathematical Finance 9 (1999)

**Precondition:**

- percentile must be in range [90-100%)

### Real shortfall (Real target) const

probability of missing the given target, defined as [ mathrm{E}

ta ;|; (-infty,infty) ight] ] where [ Theta(x) =

al averageShortfall (Real target) const"

averaged shortfallness, defined as [ mathrm{E}

nerated automatically by Doxygen for QuantLib from the source code.