Package 'Risk' reference manual

Title:	Computes 26 Financial Risk Measures for Any Continuous Distribution
Description:	Computes 26 financial risk measures for any continuous distribution. The 26 financial risk measures include value at risk, expected shortfall due to Artzner et al. (1999) <DOI:10.1007/s10957-011-9968-2>, tail conditional median due to Kou et al. (2013) <DOI:10.1287/moor.1120.0577>, expectiles due to Newey and Powell (1987) <DOI:10.2307/1911031>, beyond value at risk due to Longin (2001) <DOI:10.3905/jod.2001.319161>, expected proportional shortfall due to Belzunce et al. (2012) <DOI:10.1016/j.insmatheco.2012.05.003>, elementary risk measure due to Ahmadi-Javid (2012) <DOI:10.1007/s10957-011-9968-2>, omega due to Shadwick and Keating (2002), sortino ratio due to Rollinger and Hoffman (2013), kappa due to Kaplan and Knowles (2004), Wang (1998)'s <DOI:10.1080/10920277.1998.10595708> risk measures, Stone (1973)'s <DOI:10.2307/2978638> risk measures, Luce (1980)'s <DOI:10.1007/BF00135033> risk measures, Sarin (1987)'s <DOI:10.1007/BF00126387> risk measures, Bronshtein and Kurelenkova (2009)'s risk measures.
Authors:	Saralees Nadarajah, Stephen Chan
Maintainer:	Saralees Nadarajah <[email protected]>
License:	GPL (>= 2)
Version:	1.0
Built:	2024-11-17 03:38:50 UTC
Source:	https://github.com/cran/Risk

Computes 26 Financial Risk Measures for Any Continuous Distribution

Description

Computes 26 financial risk measures, including value at risk, expected shortfall due to Artzner et al. (1999) <DOI:10.1007/s10957-011-9968-2>, tail conditional median due to Kou et al. (2013) <DOI:10.1287/moor.1120.0577>, expectiles due to Newey and Powell (1987) <DOI:10.2307/1911031>, beyond value at risk due to Longin (2001) <DOI:10.3905/jod.2001.319161>, expected proportional shortfall due to Belzunce et al. (2012) <DOI:10.1016/j.insmatheco.2012.05.003>, elementary risk measure due to Ahmadi-Javid (2012) <DOI:10.1007/s10957-011-9968-2>, omega due to Shadwick and Keating (2002), sortino ratio due to Rollinger and Hoffman (2013), kappa due to Kaplan and Knowles (2004), Wang (1998)'s <DOI:10.1080/10920277.1998.10595708> risk measures, Stone (1973)'s <DOI:10.2307/2978638> risk measures, Luce (1980)'s <DOI:10.1007/BF00135033> risk measures, Sarin (1987)'s <DOI:10.1007/BF00126387> risk measures, Bronshtein and Kurelenkova (2009)'s risk measures.

Details

Package:	Risk
Type:	Package
Version:	1.0
Date:	2017-06-05
License:	GPL(>=2)

financial risk measures

Author(s)

Saralees Nadarajah, Stephen Chan

Maintainer: Saralees Nadarajah <[email protected]>

References

A. Ahmadi-Javid, Entropic value-at-risk: A new coherent risk measure, Journal of Optimization Theory and Applications, 155, 2012, 1105-1123 <DOI:10.1007/s10957-011-9968-2>

P. Artzner, F. Delbaen, J. M. Eber and D. Heath, Coherent measures of risk, Mathematical Finance, 9, 1999, 203-228 <DOI:10.1007/s10957-011-9968-2>

F. Belzunce, J. F. Pinar, J. M. Ruiz and M. A. Sordo, Comparison of risks based on the expected proportional shortfall, Insurance: Mathematics and Economics, 51, 2012, 292-302 <DOI:10.1016/j.insmatheco.2012.05.003>

E. Bronshtein and J. Kurelenkova, Complex risk measures in portfolio optimization, Ufa State Aviation Technical University, Russia, 2009

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

P. D. Kaplan and J. A. Knowles, Kappa: A generalized downside risk-adjusted performance measure, Miscellaneous Publication, Morningstar Associates and York Hedge Fund Strategies, 2004

S. Kou, X. Peng and C. C. Heyde, External risk measures and Basel accords, Mathematics of Operations Research, 38, 2013, 393-417 <DOI:10.1287/moor.1120.0577>

F. M. Longin, Beyond the VaR, Journal of Derivatives, 8, 2001, 36-48 <DOI:10.3905/jod.2001.319161>

R. D. Luce, Several possible measures of risk, Theory and Decision, 12, 1980, 217-228 <DOI:10.1007/BF00135033>

W. K. Newey and J. L. Powell, Asymmetric least squares estimation and testing, Econometrica, 55, 1987, 819-847 <DOI:10.2307/1911031>

T. Rollinger and S. Hoffman, Sortino ratio: A better measure of risk, Risk Management, 2013, 40-42

R. K. Sarin, Some extensions of Luce's measures of risk, Theory and Decision, 22, 1987, 125-141 <DOI:10.1007/BF00126387>

W. F. Shadwick and C. Keating, A universal performance measure, Journal of Performance Measurement, 2002

B. K. Stone, A general class of three-parameter risk measures, The Journal of Finance, 28, 1973, 675-685 <DOI:10.2307/2978638>

S. Wang, An actuarial index of the right-tail risk, North American Actuarial Journal, 2, 1988, 88-101 <DOI:10.1080/10920277.1998.10595708>

Bronshtein And Kurelenkova (2009)'s First Risk Measure

Description

Computes the first risk measure due to Bronshtein and Kurelenkova (2009)

Usage

BKg1(spec, alpha, a, b, ...)
BKg1(spec, alpha, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter taking values in (0, 1), see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving Bronshtein and Kurelenkova (2009)'s first risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

E. Bronshtein and J. Kurelenkova, Complex risk measures in portfolio optimization, Ufa State Aviation Technical University, Russia, 2009

Examples

BKg1("norm", 0.9, -Inf, Inf)BKg1("norm", 0.9, -Inf, Inf)

Bronshtein And Kurelenkova (2009)'s Second Risk Measure

Description

Computes the second risk measure due to Bronshtein and Kurelenkova (2009)

Usage

BKg2(spec, alpha, a, b, ...)
BKg2(spec, alpha, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter taking values in (0, 1), see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving Bronshtein and Kurelenkova (2009)'s second risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

E. Bronshtein and J. Kurelenkova, Complex risk measures in portfolio optimization, Ufa State Aviation Technical University, Russia, 2009

Examples

BKg2("norm", 0.9, -Inf, Inf)BKg2("norm", 0.9, -Inf, Inf)

Bronshtein And Kurelenkova (2009)'s Third Risk Measure

Description

Computes the third risk measure due to Bronshtein and Kurelenkova (2009)

Usage

BKg3(spec, alpha, a, b, beta, ...)
BKg3(spec, alpha, a, b, beta, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter taking values in (0, 1), see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`beta`	a non-negative real valued parameter, see Chan and Nadarajah for details
`...`	other parameters

Value

An object of the same length as alpha, giving Bronshtein and Kurelenkova (2009)'s third risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

E. Bronshtein and J. Kurelenkova, Complex risk measures in portfolio optimization, Ufa State Aviation Technical University, Russia, 2009

Examples

BKg3("norm", 0.9, -Inf, Inf, 1)BKg3("norm", 0.9, -Inf, Inf, 1)

Bronshtein And Kurelenkova (2009)'s Fourth Risk Measure

Description

Computes the fourth risk measure due to Bronshtein and Kurelenkova (2009)

Usage

BKg4(spec, alpha, a, b, beta, ...)
BKg4(spec, alpha, a, b, beta, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter taking values in (0, 1), see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`beta`	a non-negative real valued parameter, see Chan and Nadarajah for details
`...`	other parameters

Value

An object of the same length as alpha, giving Bronshtein and Kurelenkova (2009)'s fourth risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

E. Bronshtein and J. Kurelenkova, Complex risk measures in portfolio optimization, Ufa State Aviation Technical University, Russia, 2009

Examples

BKg4("norm", 0.9, -Inf, Inf, 1)BKg4("norm", 0.9, -Inf, Inf, 1)

Beyond Value At Risk Due To Longin (2001)

Description

Computes beyond value at risk for a given ditribution

Usage

bvar(spec, alpha, a, ...)
bvar(spec, alpha, a, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	the probabilities associated with beyon values at risk
`a`	the lower end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving beyond values ar risk computed.

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

F. M. Longin, Beyond the VaR, Journal of Derivatives, 8, 2001, 36-48 <DOI:10.3905/jod.2001.319161>

Examples

bvar("norm", 0.9, a=-Inf)bvar("norm", 0.9, a=-Inf)

Expected Proportional Shortfall Due To Belzunce et al. (2012)

Description

Computes expected proportional shortfall for a given ditribution

Usage

epsg(spec, alpha, ...)
epsg(spec, alpha, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	the probabilities associated with expected proportional shortfalls
`...`	other parameters

Value

An object of the same length as alpha, giving expected proportional shortfalls computed.

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

Examples

epsg("norm", 0.9)epsg("norm", 0.9)

Expected Shortfall Due To Artzner et al. (1999)

Description

Computes expected shortfall for a given ditribution

Usage

esg(spec, alpha, ...)
esg(spec, alpha, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	the probabilities associated with expected shortfall
`...`	other parameters

Value

An object of the same length as alpha, giving expected shortfall computed.

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

P. Artzner, F. Delbaen, J. M. Eber and D. Heath, Coherent measures of risk, Mathematical Finance, 9, 1999, 203-228 <DOI:10.1111/1467-9965.00068>

Examples

esg("norm", 0.9)esg("norm", 0.9)

Expectation

Description

Computes expectation for a given ditribution

Usage

expect(spec, a, b, ...)
expect(spec, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving the expected value of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

Examples

expect("norm", -Inf, Inf)expect("norm", -Inf, Inf)

Expectiles Due To Newey And Powell (1987)

Description

Computes expectiles for a given ditribution

Usage

expp(spec, alpha, a, b, ...)
expp(spec, alpha, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	the probabilities associated with expectiles
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving expectiles computed.

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

W. K. Newey and J. L. Powell, Asymmetric least squares estimation and testing. Econometrica, 55, 1987, 819-847 <DOI:10.2307/1911031>

Examples

expp("norm", 0.9, a=-Inf, b=Inf)expp("norm", 0.9, a=-Inf, b=Inf)

An Elementary Risk Measure Due To Ahmadi-Javid (2012)

Description

Computes the elementary risk measure for a given ditribution

Usage

expvar(spec, alpha, a, b, ...)
expvar(spec, alpha, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a positive valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving the elementary risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

A. Ahmadi-Javid, Entropic value-at-risk: A new coherent risk measure. Journal of Optimization Theory and Applications, 155, 2012, 1105-1123 <DOI:10.1007/s10957-011-9968-2>

Examples

expvar("norm", 0.9, -Inf, Inf)expvar("norm", 0.9, -Inf, Inf)

Kappa Risk Measure Due To Kaplan And Knowles (2004)

Description

Computes the Kappa risk measure for a given ditribution

Usage

kappag(spec, alpha, n, a, b, ...)
kappag(spec, alpha, n, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter, see Chan and Nadarajah for details
`n`	a positive integer valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving the Kappa risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

P. D. Kaplan and J. A. Knowles, Kappa: A generalized downside risk-adjusted performance measure, Miscellaneous Publication, Morningstar Associates and York Hedge Fund Strategies, 2004

Examples

kappag("norm", 2, 5, -Inf, Inf)kappag("norm", 2, 5, -Inf, Inf)

Luce (1980)'s First Risk Measure

Description

Computes the first risk measure due to Luce (1980)

Usage

luceg1(spec, a, b, aa, bb, ...)
luceg1(spec, a, b, aa, bb, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`aa`	a positive valued parameter, see Chan and Nadarajah for details
`bb`	a non-negative valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Luce (1980)'s first risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

R. D. Luce, Several possible measures of risk, Theory and Decision, 12, 1980, 217-228 <DOI:10.1007/BF00135033>

Examples

luceg1("unif", 0, 1, 1, 0)luceg1("unif", 0, 1, 1, 0)

Luce (1980)'s Second Risk Measure

Description

Computes the second risk measure due to Luce (1980)

Usage

luceg2(spec, a, b, aa, bb, ...)
luceg2(spec, a, b, aa, bb, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`aa`	a positive valued parameter, see Chan and Nadarajah for details
`bb`	a positive valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Luce (1980)'s second risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

R. D. Luce, Several possible measures of risk, Theory and Decision, 12, 1980, 217-228 <DOI:10.1007/BF00135033>

Examples

luceg2("unif", 0, 1, 1, 0)luceg2("unif", 0, 1, 1, 0)

Luce (1980)'s Third Risk Measure

Description

Computes the third risk measure due to Luce (1980)

Usage

luceg3(spec, a, b, aa, bb, ...)
luceg3(spec, a, b, aa, bb, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`aa`	a positive valued parameter, see Chan and Nadarajah for details
`bb`	a non-negative valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Luce (1980)'s third risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

R. D. Luce, Several possible measures of risk, Theory and Decision, 12, 1980, 217-228 <DOI:10.1007/BF00135033>

Examples

luceg3("unif", 0, 1, 1, 0)luceg3("unif", 0, 1, 1, 0)

Luce (1980)'s Fourth Risk Measure

Description

Computes the fourth risk measure due to Luce (1980)

Usage

luceg4(spec, a, b, aa, bb, ...)
luceg4(spec, a, b, aa, bb, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`aa`	a positive valued parameter, see Chan and Nadarajah for details
`bb`	a positive valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Luce (1980)'s fourth risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

R. D. Luce, Several possible measures of risk, Theory and Decision, 12, 1980, 217-228 <DOI:10.1007/BF00135033>

Examples

luceg4("norm",-Inf, Inf, 1, 0)luceg4("norm",-Inf, Inf, 1, 0)

Omega Risk Measure Due To Shadwick And Keating (2002)

Description

Computes the omega risk measure for a given ditribution

Usage

omegag(spec, alpha, a, b, ...)
omegag(spec, alpha, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving the omega risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

W. F. Shadwick and C. Keating, A universal performance measure, Journal of Performance Measurement, 2002

Examples

omegag("norm", 2, -Inf, Inf)omegag("norm", 2, -Inf, Inf)

Sarin (1987)'s First Risk Measure

Description

Computes the first risk measure due to Sarin (1987)

Usage

saring1(spec, a, b, k, c, ...)
saring1(spec, a, b, k, c, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`k`	a non-zero real valued parameter, see Chan and Nadarajah for details
`c`	a non-zero real valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Sarin (1987)'s first risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

R. K. Sarin, Some extensions of Luce's measures of risk, Theory and Decision, 22, 1987, 125-141 <DOI:10.1007/BF00126387>

Examples

saring1("norm", -Inf, Inf, 1, 0)saring1("norm", -Inf, Inf, 1, 0)

Sarin (1987)'s Second Risk Measure

Description

Computes the second risk measure due to Sarin (1987)

Usage

saring2(spec, a, b, aa, bb1, bb2, ...)
saring2(spec, a, b, aa, bb1, bb2, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`aa`	a positive real valued parameter, see Chan and Nadarajah for details
`bb1`	a positive real valued parameter, see Chan and Nadarajah for details
`bb2`	a positive real valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Sarin (1987)'s second risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

R. K. Sarin, Some extensions of Luce's measures of risk, Theory and Decision, 22, 1987, 125-141 <DOI:10.1007/BF00126387>

Examples

saring2("norm",-Inf, Inf, 1, 1, 1)saring2("norm",-Inf, Inf, 1, 1, 1)

Sarin (1987)'s Third Risk Measure

Description

Computes the third risk measure due to Sarin (1987)

Usage

saring3(spec, a, b, aa, bb1, bb2, ...)
saring3(spec, a, b, aa, bb1, bb2, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`aa`	a positive real valued parameter, see Chan and Nadarajah for details
`bb1`	a positive real valued parameter, see Chan and Nadarajah for details
`bb2`	a positive real valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Sarin (1987)'s third risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

R. K. Sarin, Some extensions of Luce's measures of risk, Theory and Decision, 22, 1987, 125-141 <DOI:10.1007/BF00126387>

Examples

saring3("norm",-Inf, Inf, 1, 1, 1)saring3("norm",-Inf, Inf, 1, 1, 1)

Sortino Ratio Due To Rollinger And Hoffman (2013)

Description

Computes the Sortino ratio for a given ditribution

Usage

sortinog(spec, alpha, a, b, ...)
sortinog(spec, alpha, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving the Sortino ratio of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

T. Rollinger and S. Hoffman, Sortino ratio: A better measure of risk, Risk Management, 40-42, 2013

Examples

sortinog("norm", 2, -Inf, Inf)sortinog("norm", 2, -Inf, Inf)

Stone (1973)'s First Risk Measure

Description

Computes the first risk measure due to Stone (1973)

Usage

stoneg1(spec, x0, k, a, b, ...)
stoneg1(spec, x0, k, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`x0`	a real valued parameter, see Chan and Nadarajah for details
`k`	a positive valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Stone (1973)'s first risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

B. K. Stone, A general class of three-parameter risk measuresm, The Journal of Finance, 28, 1973, 675-685 <DOI:10.2307/2978638>

Examples

stoneg1("norm", 8, 3, -Inf, Inf)stoneg1("norm", 8, 3, -Inf, Inf)

Stone (1973)'s Second Risk Measure

Description

Computes the second risk measure due to Stone (1973)

Usage

stoneg2(spec, x0, k, a, b, ...)
stoneg2(spec, x0, k, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`x0`	a real valued parameter, see Chan and Nadarajah for details
`k`	a positive valued parameter, see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

A scalar, giving Stone (1973)'s second risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

B. K. Stone, A general class of three-parameter risk measuresm, The Journal of Finance, 28, 1973, 675-685 <DOI:10.2307/2978638>

Examples

stoneg2("norm", 8, 3, -Inf, Inf)stoneg2("norm", 8, 3, -Inf, Inf)

Tail Conditional Mean Due To Kou et al. (2013)

Description

Computes tail conditional median for a given ditribution

Usage

tcm(spec, alpha, ...)
tcm(spec, alpha, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	the probabilities associated with tail conditional median
`...`	other parameters

Value

An object of the same length as alpha, giving tail conditional medians computed.

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

S. Kou, X. Peng and C. C. Heyde, External risk measures and Basel accords, Mathematics of Operations Research, 38, 2013, 393-417 <DOI:10.1287/moor.1120.0577>

Examples

tcm("norm", 0.9)tcm("norm", 0.9)

Value At Risk

Description

Computes value at risk for a given ditribution

Usage

varg(spec, alpha, ...)
varg(spec, alpha, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	the probabilities associated with values at risk
`...`	other parameters

Value

An object of the same length as alpha, giving values at risk computed.

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

Examples

varg("norm", 0.9)varg("norm", 0.9)

Wang (1998)'s First Risk Measure

Description

Computes the first risk measure due to Wang (1998)

Usage

wangg1(spec, alpha, a, b, ...)
wangg1(spec, alpha, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter taking values in (0, 1), see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving Wang (1998)'s first risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

S. Wang, An actuarial index of the right-tail risk, North American Actuarial Journal, 2, 1998, 88-101 <DOI:10.1080/10920277.1998.10595708>

Examples

wangg1("lnorm", 0.9, 0, Inf)wangg1("lnorm", 0.9, 0, Inf)

Wang (1998)'s Second Risk Measure

Description

Computes the second risk measure due to Wang (1998)

Usage

wangg2(spec, alpha, a, b, ...)
wangg2(spec, alpha, a, b, ...)

Arguments

`spec`	a character string specifying the distribution (for example, "norm" corresponds to the standard normal)
`alpha`	a real valued parameter taking values in (0, 1), see Chan and Nadarajah for details
`a`	the lower end point of the distribution specified by `spec`
`b`	the upper end point of the distribution specified by `spec`
`...`	other parameters

Value

An object of the same length as alpha, giving Wang (1998)'s second risk measure of the distribution specified by spec

Author(s)

Stephen Chan, Saralees Nadarajah

References

S. Chan and S. Nadarajah, Risk: An R package for risk measures, submitted

S. Wang, An actuarial index of the right-tail risk, North American Actuarial Journal, 2, 1998, 88-101 <DOI:10.1080/10920277.1998.10595708>

Examples

wangg2("lnorm", 0.9, 0, Inf)wangg2("lnorm", 0.9, 0, Inf)

Package 'Risk'

Help Index

Computes 26 Financial Risk Measures for Any Continuous Distribution

Description

Details

Author(s)

References

Bronshtein And Kurelenkova (2009)'s First Risk Measure

Description

Usage

Arguments

Value

Author(s)

References

Examples

Bronshtein And Kurelenkova (2009)'s Second Risk Measure

Description

Usage

Arguments

Value

Author(s)

References

Examples

Bronshtein And Kurelenkova (2009)'s Third Risk Measure

Description

Usage

Arguments

Value

Author(s)

References

Examples

Bronshtein And Kurelenkova (2009)'s Fourth Risk Measure

Description

Usage

Arguments

Value

Author(s)

References

Examples

Beyond Value At Risk Due To Longin (2001)

Description

Usage

Arguments

Value

Author(s)

References

Examples

Expected Proportional Shortfall Due To Belzunce et al. (2012)

Description

Usage

Arguments

Value

Author(s)

References

Examples

Expected Shortfall Due To Artzner et al. (1999)

Description

Usage

Arguments

Value

Author(s)

References

Examples

Expectation

Description

Usage

Arguments

Value

Author(s)

References

Examples

Expectiles Due To Newey And Powell (1987)

Description

Usage

Arguments

Value

Author(s)

References

Examples

An Elementary Risk Measure Due To Ahmadi-Javid (2012)