reinsurance - example

7/23/2019 Reinsurance - Example

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ReinsurancePresentation Example

2003 CAS Research Working Party:

Executive Level Decision Making using DFA

Raju Bohra, FCAS, ARe


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2003 CAS ResearchWorking Party

2

Backgroun

!ynamic "inancial Analysis #!"A$ Systems %oel theEntire &perations #'ia(ilities an Assets$ o) an*nsurance Company

Statistical Simulation +echni,ues are use to %oelnot only Point Estimates- (ut also the !istri(ution o)&utcomes

+his Pro.ies Ans/ers Con.entional Analysis cannot What Is The Chance Of A Given Financial Result?

o! Often Is A Given Alte"native #ette"?

To What Deg"ee?

$n%e" What Ci"cu&stances?


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3

&utline o) Process

*enti)y Companys 1ees an &(ecti.es Return What is 'ou" &easu"e of success?

4sually state in accounting terms Risk Wh' %o 'ou (u' "einsu"ance?

%easure o) .olatility o) return- usually o/nsie

%oel 4nerlying 5ross 'ia(ilities (y 'ine o) Business Select Reinsurance &ptions to Compare

6o/ oes changing retentions impact net results7 What com(ination o) excess an pro8rata /ork (est7 What is impact o) changing co.ers or inuring structure7 6o/ o loss sensiti.e an commission terms impact results7 What is e))ect o) com(ining programs across operating units7

Run %oel Se.eral +imes /ith 9arying Structures Create Statistics an Charts to E.aluate &ptions


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&utline o) Process

Simulate

Results

Define Reins

Structure

Model Insurance

and Asset

Portfolio

Gross,

Ceded, and

Net Results,

in FinancialAccountin

Frame!ork

"oss distri#utions

Premiums

Balance Sheet

"imits

Retentions

Ceded Rates


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;

Bene)its o) Process

6elp you Better E.aluate your Reinsurance Program 4nerstan the impact o) reinsurance Align reinsurance /ith your strategy

Analy o) Reinsurance +ransaction 5o (eyon only seeing )cost * ce%e% +"e&iu&, See risk reuction impact o) reinsurance ?uanti)y risk8return traeo)) #)a++les to a++les,measurement$

Analysis is +ailore to Companys Risk Appetite +olerance )or risk Current )inancial conition

)What is the #est Reinsu"ance -"og"a&,


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@

Scope an 'imitations

Comprehensi.ely- *nsurance Companies )ace manySources o) Risk )rom their &perations: Asset risk value of invest&ents Creit risk +"e&iu& an% "einsu"ance "eceiva(les 'ia(ility risk f"e.uenc' an% seve"it' of losses

Pricing risk Catastrophes Reser.ing risk 'arge 'osses

+o o a Reinsurance Analysis /e "ocus our %oelingE))orts 5ross prospecti.e losses )or lines o) (usiness Cee reinsurance terms )or se.eral reinsurance programs

iels a Solution /ith Regar to Reinsurance Strategy Relati.ely ,uick moel set up 1o ata =noise> )rom generally unrelate issues- eg asset mix


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D

%oel Setup an &ptions

'ia(ility %oeling 5ross Business Core losses /ere moele aggregate istri(utions 'arge losses /ere moele using se.erity an )re,uency istri(utions Catastrophes /ere moele using output )rom a catastrophe moel

Reinsurance &ptions 1et Business &' attaching at FG0m an up Pro Rata 2;H ?S /ith )lat 20H ceing comm

Stop loss attaching at I;H loss an 'AE- G0 pts o) limit

%oele !etail 1eee to Support !ecision %aking Accounting- asset .alues- reser.e (alances- an cash )lo/ parameters

/ere entere using most recent pu(lic )inancial statements Jept less rele.ant sources o) .ariation static

Economic .aria(les Reser.e e.elopment


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I

%oel Results

+hree +ypes o) Charts /ere Prouce !istri(ution graphs

/ho!s "ange of outco&es fo" va"ious o+tions

!istri(ution statistics ta(le/ho!s outco&e ave"ages an% "isk &easu"es

Risk Return graph/ho!s "isk 0 "etu"n t"a%e1off

+he "ollo/ing Criteria /ere Assume Return %aximi


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K

!istri(ution 5raphs

!istri(ution 5raphs Chart sho/s pro(a(ility o) return outcomes )or each option Bene)it o) reinsurance is less .olatility #narro/er cur.e$ an less

pro(a(ility o) extreme .alues #smaller tail$ Cost o) reinsurance is sho/n as shi)ting o) a.erage .alue to the le)t-

more a.erage total cost "ormal statistics are e.elope later to ,uanti)y risk- )or example:

Analytic: 9arianceLSt !e.- Ruin- EP!- 9aR- +ail 9aR Business: Pro(a(ility key accounting .alue )alls (elo/ threshol

!istri(ution 5raphs Cumulati.e

Chart sho/s cumulati.e pro(a(ility o) total cost o" less)or each retentionoption Can rea o)) percentile .alues )rom chart 'o/er cur.e is (etter at that le.el Can ,uanti)y ho/ o)ten an option is (etter than another


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G0

Projected Net Income $%&&&' under Reinsurance

0%

5%

10%

15%

20%

25%

30%

35%

40%

-300 -275 -250 -225 - 200 -175 -150 -125 -100 -75 -50 -25 0 25 50 75 100 125 150 175

IncrementalPro#a#ilit

(

No Reinsurance Net of )*cess of "oss

9alue o) Reinsurance

Reinsurance Cost!rop in A.g *ncome

'oss o) *ncome4psie PotentialReuction o) *ncome

!o/nsie Potential


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GG



0%

5%

10%

15%

20%

25%

30%

35%

40%

- 300 - 275 - 250 - 225 - 200 - 175 - 150 - 125 - 100 - 75 - 50 - 25 0 25 50 75 100 125 150 175

IncrementalPro#a#ilit(

No Reinsurance Net of +uota Share


Reuction o) *ncome!o/nsie Potential

'oss o) *ncome4psie Potential


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G2



0%

5%

10%

15%

20%

25%

30%

35%

40%

- 300 - 275 - 250 - 225 - 200 - 175 - 150 - 125 - 100 - 75 - 50 - 25 0 25 50 75 100 125 150 175

IncrementalPro#a#ilit(

No Reinsurance Net of Sto, "oss


Reuction o) *ncome!o/nsie Potential

'oss o) *ncome4psie Potential


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G3



0%

5%

10%

15%

20%

25%

30%

35%

40%

- 300 - 275 - 250 - 225 - 200 - 175 -150 - 125 - 100 - 75 - 50 - 25 0 25 50 75 100 125 150 175

Cumulati-ePro#a#ilit

No Reinsurance Net of )*cess Co-er

Reinsurance Bene)itSa.ings at K;thPercentile

Worse o)) /ithReinsurance @DH o)time #2 out 3 yrs$

Better o)) /ithReinsurance 33H o)time #G out 3 yrs$


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G



0%

5%

10%

15%

20%

25%

30%

35%

40%

- 300 - 275 - 250 - 225 - 200 - 175 -150 - 125 - 100 - 75 - 50 - 25 0 25 50 75 100 125 150 175

Cumulati-ePro#a#ilit

No Reinsurance Net of +uota Share

Reinsurance Bene)itSa.ings at K;thPercentile

Worse o)) /ithReinsurance DIH o)time #D out K yrs$

Better o)) /ithReinsurance 22H o)time #2 out K yrs$


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G;



0%

5%

10%

15%

20%

25%

30%

35%

40%

- 300 -275 - 250 -225 - 200 - 175 -150 - 125 - 100 - 75 - 50 - 25 0 25 50 75 100 125 150 175

Cumulati-ePro#a#ilit(

No Re ins ur ance Ne t of Sto, "os s

Bene)it o) ReinsuranceSa.ings at K;thPercentile

Worse o)) /ithReinsurance I@H o)time #@ out D yrs$

Better o)) /ith

Reinsurance GH o)time #G out D yrs$


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G@

!istri(ution Statistics +a(le

Summari


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GD

!istri(ution Statistics +a(le

Distri#ution Statistics

Risk and Return Calculations

No Rein )*cess Pro Rata Sto, "oss

Return MeasureExpecte SAP 1et *ncome 3:-3@3 2D-2;: G@-I23 2K-IKG

Risk . Percentile Return Period0CGH G in G000 years #2:2-GK2$ #G2K-K@K$ #G2G-;DK$ #G@G-3K2$

0C;H G in 200 years #GI@-;@@$ #G0:-@:G$ #K3-D@@$ #G0;-D@@$

GC0H G in G00 years #G@0-:2@$ #K0-@2@$ #I0-@K@$ #DK-@2D$

;C0H G in 20 years #K2-I0:$ #:K-;;K$ #:@-II;$ #2;-D:@$

G0C0H G in G0 years #;:-K0I$ #2I-:0D$ #2D-K3D$ #2;-D:;$

2;C0H G in : years 2-K;G @-2K; G-G;@ #G@-0@2$

%eian G in 2 years :3-D@2 3G-I:D 2G-;@2 30-2GG

D;C0H I0-0D3 ;;-I0G 3K-DGI @@-;22

K0C0H G0;-;:0 D3-K32 ;2-:;G KG-KIKK;C0H G20-K3I I3-I:@ @0-G;0 G0D-3I@

KKC0H G:@-22; G0G-0D; D2-DK: G32-@D3

KKC;H G;3-K@: G0;-I;0 D@-@@3 G:0-:G2

KKCKH GDG-0;K GGI-3I2 I;-2GG G;D-;0D

Risk . /olatilit( StatisticsStanar !e.iation @:-II@ :0-:K: 32-:KI :I-202


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GI

Risk Return 5raph

5raphs Risk an Return Statistics )or each &ption

5enerally- *ncrease Return Re,uires Aitional Risk

Running %ultiple &ptions /ill trace out E))icient "rontier *enti)ies ine))icient options that pro.ie a lo/er le.el o) return )or the

same or more risk as another option

*enti)ies un)a.ora(le options that pro.ie insu))icient return )or le.el o)risk #con.ex points on cur.e$

*enti)ies options that ha.e most attracti.e risk return trae8o))s

Chart is the *ntersection o) three Jey 9ie/s o) Risk 4nerlying risk in port)olio Reinsurers risk appetite #re)lecte in cee premiums$

Companys measure an tolerance )or risk


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GK

Risk Return 5raph

Risk Return 0radeoff Chart

G0-000

G;-000

20-000

2;-000

30-000

3;-000

:0-000

30-000 3;-000 :0-000 :;-000 ;0-000 ;;-000 @0-000 @;-000 D0-000

Risk . Standard De-iation of Net Income $after.ta*'

Return

.)*,ected

SAPN

etInc

om

e$

PR1 RA0A

)2C)SS

S01P "1SS

N1 R)IN


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&(ser.ations

All &ptions are E))icient (ase on a 'inear RiskPre)erence 1o option pro.ies less return )or the same or greater risk than

another option

*) a lines /as ra/n through the points- no option is clearly on acon.ex point

Ranking may Change gi.en an Alternate RiskPre)erence "unction #use Alexs iso8line 5raphics$

Ranking may also Change using an Alternate Risk%easure +he Stop 'oss option /ill pro(a(ly per)orm .ery /ell using a risk

measure that re)lects o/nsie risk only

reinsurance - example

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