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

financial risk measures

Author(s)

Saralees Nadarajah, Stephen Chan

Maintainer: Saralees Nadarajah <Saralees.Nadarajah@manchester.ac.uk>

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, ...)

Arguments

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)

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, ...)

Arguments

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)

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, ...)

Arguments

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)

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, ...)

Arguments

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)

Beyond Value At Risk Due To Longin (2001)

Description

Computes beyond value at risk for a given ditribution

Usage

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

Arguments

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)

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

Description

Computes expected proportional shortfall for a given ditribution

Usage

epsg(spec, alpha, ...)

Arguments

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

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>

Examples

epsg("norm", 0.9)

Expected Shortfall Due To Artzner et al. (1999)

Description

Computes expected shortfall for a given ditribution

Usage

esg(spec, alpha, ...)

Arguments

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)

Expectation

Description

Computes expectation for a given ditribution

Usage

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

Arguments

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)

Expectiles Due To Newey And Powell (1987)

Description

Computes expectiles for a given ditribution

Usage

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

Arguments

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)

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, ...)

Arguments

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)

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, ...)

Arguments

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)

Luce (1980)'s First Risk Measure

Description

Computes the first risk measure due to Luce (1980)

Usage

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

Arguments

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)

Luce (1980)'s Second Risk Measure

Description

Computes the second risk measure due to Luce (1980)

Usage

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

Arguments

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)

Luce (1980)'s Third Risk Measure

Description

Computes the third risk measure due to Luce (1980)

Usage

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

Arguments

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)

Luce (1980)'s Fourth Risk Measure

Description

Computes the fourth risk measure due to Luce (1980)

Usage

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

Arguments

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)

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, ...)

Arguments

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)

Sarin (1987)'s First Risk Measure

Description

Computes the first risk measure due to Sarin (1987)

Usage

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

Arguments

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)

Sarin (1987)'s Second Risk Measure

Description

Computes the second risk measure due to Sarin (1987)

Usage

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

Arguments

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)

Sarin (1987)'s Third Risk Measure

Description

Computes the third risk measure due to Sarin (1987)

Usage

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

Arguments

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)

Sortino Ratio Due To Rollinger And Hoffman (2013)

Description

Computes the Sortino ratio for a given ditribution

Usage

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

Arguments

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)

Stone (1973)'s First Risk Measure

Description

Computes the first risk measure due to Stone (1973)

Usage

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

Arguments

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)

Stone (1973)'s Second Risk Measure

Description

Computes the second risk measure due to Stone (1973)

Usage

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

Arguments

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)

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

Description

Computes tail conditional median for a given ditribution

Usage

tcm(spec, alpha, ...)

Arguments

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)

Value At Risk

Description

Computes value at risk for a given ditribution

Usage

varg(spec, alpha, ...)

Arguments

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)

Wang (1998)'s First Risk Measure

Description

Computes the first risk measure due to Wang (1998)

Usage

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

Arguments

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)

Wang (1998)'s Second Risk Measure

Description

Computes the second risk measure due to Wang (1998)

Usage

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

Arguments

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)