Nassim&Taleb’s&The&Black&Swan&€¦ · Risk,&complex&systems,&failure& Outline:&...
Transcript of Nassim&Taleb’s&The&Black&Swan&€¦ · Risk,&complex&systems,&failure& Outline:&...
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!!!!!!!!Extreme!!!Statistics,!Black!Swans,!high5e!low5p!risk!!!!!!!!!!!!!!!!Latham!Stack,!MS,!CIA,!CGAP!
Value!V!
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Nassim&Taleb’s&The&Black&Swan&
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Criteria Cause
Risk-assessment
Recommendation
Effect
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Outline:&
Nassim&Taleb’s&The&Black&Swan&
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Outline:&
Nassim&Taleb’s&The&Black&Swan&
Risk,&complex&systems,&failure&
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Risk,&complex&systems,&failure&
Outline:&
Nassim&Taleb’s&The&Black&Swan&
Extreme&Value&Analysis&
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EVA&in&program&audiBng&I:&&&&quanBfying&exposure&&&p"
Risk,&complex&systems,&failure&
Outline:&
Nassim&Taleb’s&The&Black&Swan&
Extreme&Value&Analysis&
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EVA&in&program&audiBng:&II&&&&risk&miBgaBon&
Risk,&complex&systems,&failure&
Outline:&
Nassim&Taleb’s&The&Black&Swan&
Extreme&Value&Analysis&
EVA&in&pracBce,&program&audiBng&I&
5&
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Risk,&complex&systems,&failure&
Outline:&
Nassim&Taleb’s&The&Black&Swan&
Extreme&Value&Analysis&
EVA&in&pracBce,&program&audiBng&I&
EVA&in&pracBce,&program&audiBng&II&
Wrap,&Q&A&
Wrap&and&Q&&&A&6&
h"p://pixabay.com/en/black3swan3swans3birds3black3337967/<
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Risk,&complex&systems,&
failure,&lessons&from&accident&
invesBgaBon&and&safety&
engineering&
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simple&
complex&
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CC E
EEE
E CEE
C
E
CE E C
E
E
Simple&&&&&&&Complicated&&&&&&&&Complex&
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Fail Goal Goal Goal Goal
Complex&operations&
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h"ps://doctordeparture.files.wordpress.com/2011/07/swisscheese.png<
Swiss&Cheese&model&(Orlandella/Reason)&&
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Summary&
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Intended&
operaBng&
range&
Failure&Drift&into&failure&
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System:&Linear &Complex&
Coupling:&
Tight&&&
Loose&
James&Clerk&Maxwell&(1839N1879)&
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Complex&operations&
y<
Goal
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insert<slide:<
3<post3accident<a"ribuDon<to<human<error<
3<hindsight<bias<
3<human<factors<engineering<
3<photo<of<employee<
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Summary&Impact&on&auditing&
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Extreme&Value&Analysis&
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The!good!ol’!normal!distribution…!…often!doesn’t!work!
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Benoit&Mandelbrot!
•&Cotton&prices&exhibit&&&&&powerNlaw&behavior&
•&80N20&rule&of&thumb&
•&Fractal&phenomena&
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Vilfredo&Pareto,&1848N1923&
Generalized&Pareto&Distribution&&
80N20&rule&
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seven&years&of&records:&Frequency"distribu0on:"self5insurance"claims"200652012"
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seven&years&of&records:&
PercentilesObserved
100.0% maximum 194,89799.5% 54,34090.0% 11,51475.0% quartile 4,15050.0% median 1,45125.0% quartile 40110.0% 1300.5% 19
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normal&distribution&fits&poorly...&
PercentilesObserved Normal
100.0% maximum 194,897 47,00099.5% 54,340 34,00090.0% 11,514 19,30075.0% quartile 4,150 12,40050.0% median 1,451 4,70025.0% quartile 401 93,00010.0% 130 99,9000.5% 19 924,700
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R²#=#0.976
0
50,000
100,000
150,000
200,000Fit$of$Exponential$distribution
Series1 Expon.#(Series1)observed< exponenDal<fit<
PercentilesObserved Exponential
100.0% maximum 194,897 53,90099.5% 54,340 24,80090.0% 11,514 10,78275.0% quartile 4,150 6,50050.0% median 1,451 3,20025.0% quartile 401 1,30010.0% 130 5000.5% 19 25
exponential&distribution,&the&same...&
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Vilfredo&Pareto&1848N1923&
&Generalized&Pareto&Distribution&
k&&=!!shape!
three&variables:&
σ!!=!!scale!µ!!=!!location!
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Extreme&value&distributions:&flexible&enough&to&fit&a&variety&of&data&
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&peaksNoverNthreshold&(PoT):&&&&&&all&records&above&a&threshold&
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Maurice!Fréchet!Emil!Gumbel! Weibull!
Generalized!Extreme!Value!Distribution!
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!block!maxima:!!!!!!!largest!per!block!of!records!
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h"p://www.r3bloggers.com/playing3with3quanDles3part31/<
•"No"assump*ons"are"made"about"the""""non2extreme"observa*ons"
Key&idea:&the&tail&has&its&own&“child”&distribution&
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EVA&in&pracBce,&part&I&&&quanBfying&exposure&&&&&&&&&&&probability&
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EVA&in&pracBce,&part&I&
& &&&&•&Is&EVA&suitable&for&the&data?&
&&&&&&&&&&•&What&threshold&is&best?&
•&What&values&for&location,&scale,&shape?&
•&What&losses&for&range&of&probabilities?&
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Threshold&selection:&
Scale&
Shape&
LocaBon&
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0.0 0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
1.0
Probability plot
empirical
model
3 4 5 6 7 8 9
34
56
78
9
Quantile Plot
model
empirical
Diagnose&fit:&
h"p://www.sldinfo.com/wp3content/uploads/2011/09/bigstock_Black_Swan_63382.jpg<
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BestNfit&results:&
&>¤t1&<O&pp.fit(current,&2375,&npy&=&153)&
&&&threshold &2,375&
&&&nexc & &181&
&&&nllh& & &2,733.23&
&&&mle& &71,115.9&&&&&44,033.9&&&&&0.574&
&&&se & &3,017.5&&&&1,775.6&&&&0.025&
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EVA&in&pracBce,&Part&II&
Compute&exposure&x&probability:&
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EVA&in&pracBce,&Part&II&&&&&&&&&&risk&miBgaBon&
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Annual&reserve&funding:&
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p&≥&100%&funded&from&general&fund&
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580<
100%&selfNinsured&
Mitigation&(nonNfinancial)&
PreNaudit&risk&management:&
general&fund&budget&
Exposure&
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selfNinsure&
reserve& insurance&
Mitigation&(nonNfinancial)&
Tiered&risk&management:&
general&fund&budget&
transfer&
$580k& $195kO$240k& >$320k&
Black&Swans&Exposure&
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How&well&did&it&work?&
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…compared&to&what?&
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Import&data&file:&"working5filename&<O&scan(file&=&”filename.ext",&sep&=&",")&
Test&whether&EVA&is&suited&for&the&data:&&lmomplot(working5filename,&idenBfy&=&TRUE)&
Test&fit&over&a&range&of&thresholds:&&pp.fitrange(working5filename,&2,&5,&npy&=&192.6,&nint&=&100)&
EsBmate¶meters&for&the&selected&threshold:&"results5file&<O&pp.fit(working5filename,&2.7878,&npy&=&192.6)&
DiagnosBc&plot&of&fit:&&pp.diag(results5file)&
Determine&exposure&for&a&given&probability:&&qgpd(q,&μ,&σ,&ξ)&
only&six&“r”&commands&required!
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Diagnose&fit,&other&fit&examples:&
h"p://imgkid.com/black3swan3bird3wallpaper.shtml<
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Cueto<ORG,<Soto<NS,<Quintero<Núñez<MQ,<Benítez<SO,<Limón<NV<(2013)<Extreme<
temperature<scenarios<in<Mexicali,<Mexico<under<climate<change<condiDons.<Atmósfera<
26(4):5093520<doi:<10.1016/S018736236(13)7109230<<
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h"ps://www.flickr.com/photos/
stephcarter/254424283/<
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Outline:&
Accidensts,&safety,&complexity&
Nassim&Taleb’s&The&Black&Swan&
Extreme&Value&Analysis,&theory&
EVA&in&pracBce,&program&audiBng&I&
EVA&in&pracBce,&program&audiBng&II&
Wrap&and&Q&&&A&
6&
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•!The!numbers!only!tell!part!of!the!story!
•!Focus!on!the!confidence!interval!
•!Be!mindful!of!the!black!swans!
•!Don’t!overAextend!
•!Be!conservative!
•!Trust!the!method!
Tips:&
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Recommended&text:&
credit:<Sergis<V.<Duarte,<via<wikimedia.org<12/2006<
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References<
<
Bensalah<Y<(2000)<Steps"in"Applying"Extreme"Value"Theory"to"Finance:"A"Review.<Research<and<Risk<Management<SecDon,<Financial<Markets<Department,<Bank<of<Canada.<O"awa,<
Ontario,<Canada<p<9<
<
Brüggen<J<(2012)<The"global"voice"of"ATM"ICAO"European"Regional"Runway"Safety"Seminar"Amsterdam,<The<Netherlands<8<March<2012<h"p://slideplayer.com/slide/1448937/<
<
Cook<RI<(2000)<How"Complex"Systems"Fail,"a"Short"Trea*se.<CogniDve<Technologies<Laboratory,<University<of<Chicago<5<pps<
<
Dekker<S<(2011)<DriK"Into"Failure:"From"Hun*ng"Broken"Components"to"Understanding"Complex"Systems.<Ashgate<Publishing<Company<234<pps<
<
Dorner,<D<(1997)<The"Logic"of"Failure:"Recognizing"and"Avoiding"Errors"in"Complex"Situa*ons.<Basic<Books<240<pps<
<
Gall<J<(1977)<Syteman*cs:"How"Sytems"Work,"and"Especially"How"They"Fail.<Pocket<Books<111<pps<
<
Mohtadi<H,<Murshid<A<(2005)<Assessing"the"Risk"of"Terrorism"Using"Extreme"Value"Sta*s*cs.<Proceedings<of<the<InsDtute<of<Food<Technologists’<First<Annual<Food<ProtecDon<and<
Defense<Conference,<October<27,<2005<
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References<(cont’d)<
<
Perrow<C<(1999)<Normal"Accidents:"Living"with"High"Risk"Technologies.<Princeton<University<Press<464<pps<
Taleb<N<(2007)<The"Black"Swan:"The"Impact"of"the"Highly"Improbable.<Random<House,<NY<366<
pps<
Taleb<N<(2010)<The"Fourth"Quadrant:"A"Map"of"the"Limits"of"Sta*s*cs.<edge.org<<h"p://www.slideshare.net/MediaCorpInternaDonal/130221308503david3bond3thiess<
www.nyDmes.com/2007/04/22/books/chapters/042231st3tale.html<
www.thefullwiki.org/Black_swan_theory<
www.insead.edu/facultyresearch/faculty/documents/4_Quadrants3w.pdf<
www.nakedcapitalism.com<
www.coverclock.blogspot.com<
www.zoonek2.free.fr/UNIX/48_R/07.html<
www2.eo.com/publicaDons/journalofindexes/joi3arDcles/242303what3is3risk.html?
showall=&fullart=1<
<
Graphics:<
Unless<noted<otherwise,<all<<graphics<from<via<wikimedia.org<
Title<slide:<h"ps://www.flickr.com/photos/brucelee/4667973041/<
Camouflage:<h"p://www.demilked.com/animal3camouflage/<
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Outline:&
Q&&&A&
6&