ILS Market-Derived Metrics; Finding the Market Transform

Transcription

1 ILS Market-Derved Metrcs; Fndng the Market Transform Morton Lane Ph D Lane Fnancal LLC and Unversty of Illnos and Jerome Kreuser Ph D RsKontroller Gmbh Jont AFIR/ERM PBSS LIFFE Colloquum Lyon, France June

2 Outlne 1) Motvaton and Prelmnary Results seven scenaros 2) Expanson to Full (10,000) scenaro set 3) Approprate Models and ther Duals 4) Transforms 5) Comparatve Prcng 6) Underwrtng and Prcng mplcatons 7) Other Questons Dates/tme/models/measures 2

3 Sample Set of ILS Embarcadero Re Ltd. Seres 2012-I Class A Kbou Ltd. Seres Class A Multcat Mexco 2009 Ltd Class D Queen Street V Ltd. Res Re 2010 Clas 4 Vega Captal Ltd. Seres I Class C At Issue Par Value - Issue Sze 150,000, ,000,000 50,000,000 75,000, ,500, ,000,000 Issue Spread 7.25% 5.25% 10.25% 8.50% 13.00% 5.65% Maturty Date 2/13/2015 2/16/ /19/2012 4/9/2015 6/6/ /30/2013 Orgnal PPM Expected Loss 1.96% 0.95% 2.39% 1.77% 2.42% 1.30% 3/15/2012 Remanng Term (months) Secondary Market Prce Outstandng Market Value $150,322,500 $299,820,000 $50,105,000 $75,090,000 $119,062,750 $151,770,000 Secondary Market Yeld 7.17% 5.26% 9.79% 8.45% 11.81% 4.96% Remodeled* Expected Loss 2.21% 0.85% 2.93% 2.42% 2.00% 2.86% * As remodeled by AIR 3

4 Rankng of Scenaros for the Market and Tranchng nto Buckets Market Value Weghted ILS Portfolo* Embarcade ro Re Ltd. Seres 2012-I Class A Kbou Ltd. Seres Class A Queen Street V Ltd. # of Scenaros Tranche Probablty Expected Loss by Tranche EL In Tranche EL In Tranche EL In Tranche Frst Tranche B-T-W 1-5,000 5, Second Tranche B-T-W 5,001-8,000 3, Thrd Tranche B-T-W 8,001-9,000 1, Fourth Tranche B-T-W 9,001-9, Ffth Tranche B-T-W 9,501-9, Sxth Tranche B-T-W 9,901-9, Seventh Tranche B-T-W 9,961-10, ,000 1 a pror Expected Loss ** 2.02% 2.21% 0.85% 2.42% Secondary Market Yeld*** 8.37% 7.17% 5.26% 8.45% Excess Return 6.35% 4.96% 4.41% 6.03% * 92 of the outstandng ILS market portfolo are chosen - certan deals are elmnated to avod dstortons of maturty or mparment. ** a pror Expected Loss n ths Table s calculated as the sumproduct of the the expected loss n each tranche multpled by the probablty of each tranche. *** The portfolo yeld s the market value w eghted yeld of all the ndvdual deals. 4

5 Optmzed Soluton Probabltes - The Market Transform Market Value Weghted ILS Portfolo* Embarcade ro Re Ltd. Seres 2012-I Class A Kbou Ltd. Seres Class A Queen Street V Ltd. Indvdual Scenaros Probablty Tranche Probablty Expected Loss by Tranche EL In Tranche EL In Tranche EL In Tranche Frst Tranche B-T-W 1-5, Second Tranche B-T-W 5,001-8, Thrd Tranche B-T-W 8,001-9, Fourth Tranche B-T-W 9,001-9, Ffth Tranche B-T-W 9,501-9, Sxth Tranche B-T-W 9,901-9, Seventh Tranche B-T-W 9,961-10, Rsk Adusted Expected Loss ** 4.62% 2.74% 0.87% 7.03% Secondary Market Yeld*** 8.37% 7.17% 5.26% 8.45% Excess Rsk Adusted Return 3.74% 4.42% 4.38% 1.42% * 92 of the outstandng ILS market portfolo are chosen - certan deals are elmnated to avod dstortons of maturty or mparment. ** Rsk-Adusted Expected Loss n ths Table s calculated as the sumproduct of the the expected loss n each tranche multpled by the derved probabltes. *** The portfolo yeld s the market value w eghted yeld of all the ndvdual deals. 5

6 ILS Securtes used n optmzaton SINGLE-PERIL USW USQ EUW EUQ JPW JPQ OTH Potental Coverage % of Lmt USW % USQ % EUW % EUQ JPW JPQ % OTH % MULTI-PERIL 0% USW, USQ % EUW, JPQ USW, EUW USW,EUW, USQ,JPQ % USW,EUW, JPW, USQ, JPQ % USW,EUW,USQ % Exhaustable Lmt $18,436 % Exposure by Perl 72% 58% 19% 3% 14% 3% 100% TOTAL LIMIT $10, % 6

7 % tle Prob 1010 bps 1000 Probabltes Dstrbutons of Portfolo Outcomes 900 A Pro (.e. model or random) Probabltes vs Rsk Adusted Probaltes [Probabltes shown as 100* bass ponts - Densty Dstrbutons] Not to scale- for llustratve purposes only 99%-tle Prob 465 bps Hundreds of Bass Ponts bps bps Ordered Probabltes (Worst 10%) 7

8 Sx Sample Deals wth Expected Loss and Excess Return [Ordered Hghest XS Return to Lowest ] [Orgnal Spread noted as Secondary Yeld =EL+XS] 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% Secondary Market Yeld 3/15/2012 RESIDENTIAL RE (13:00%): Gulf and East Coast Wnd; US EQ; Others US 2.00% 9.82% 11.82% Premum, or Secondary Market Yld MULTICAT MEXICO 2009 LTD (10.25%): Mex, Pacfc Wnd 2.93% 6.86% QUEEN STREET V LTD (8.50%): US Wnd, Euro Wnd 2.42% 6.03% EMBARCADERO RE LTD SERIES 2012-I (7.25%): CA EQ 2.21% 4.96% KIBOU LTD. SERIES (5.25%): Japan EQ 0.85% 4.41% Orgnal Expected Loss XS Return VEGA CAPITAL LTD 2010-I (5.65%): US/Euro Wnd, CA/JP EQ, JP Wnd 2.86% 2.10% 8

9 Fg 4 Sx Sample Deals wth Expected Loss and Rsk Adusted Excess Return [Ordered Hghest XS Return to Lowest ] [Orgnal Spread Noted on Left Axs ; Secondary Yeld =EL+XS] -2.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% Secondary Market Yeld 3/15/2012 RESIDENTIAL RE (13:00%): Gulf and East Coast Wnd; US EQ; Others US 2.00% 3.30% 6.51% 11.82% MULTICAT MEXICO 2009 LTD (10.25%): Mex, Pacfc Wnd 2.93% 6.86% QUEEN STREET V LTD (8.50%): US Wnd, Euro Wnd 2.42% 4.61% 1.42% EMBARCADERO RE LTD SERIES 2012-I (7.25%): CA EQ 2.21% 0.54% 4.42% Expected Loss Rsk Adustment KIBOU LTD. SERIES (5.25%): Japan EQ 0.85% 0.02% 4.38% XS Returns after Rsk Adustment VEGA CAPITAL LTD 2010-I (5.65%): US/Euro Wnd, CA/JP EQ, JP Wnd 2.86% 2.10% 9

10 Premum Components 0.00% WHOLE PORTFOLIO 4.00% 8.00% 12.00% 16.00% 20.00% Indvdual Deals arranged by EL Components of Premum on 3/15 ILS Portfolo [Ordered by Expected Loss, Largest to Smallest] Expected Loss Rsk Adustment XS Return after Rsk Adustment 10

11 0.00% 4.00% 8.00% 12.00% 16.00% 20.00% WHOLE PORTFOLIO Sngle Perl Deals US Wnd US Quake EU Wnd Japan Quake Components of Premum, 3/15/2012 ILS Portfolo [Grouped by Type/Perl then Ordered by Expected Loss] Other - MultCatMex Mult-Perl Deals US Wnd and US Quake Expected Loss Rsk Adustment US/EUWnd and US/J Quake XS Return after Rsk Adustment US/EU/J Wnd and US/J Quake US/EU Wnd and J Quake 11

12 -16.00% % -8.00% -4.00% 0.00% 4.00% 8.00% 12.00% 16.00% 20.00% Market Weghted Whole Portfolo US WIND (Sngle perls) DEALS IN THE PORTFOLIO Components of Premum, 3/15/2012 ILS Portfolo [Grouped by Type/Perl then Ordered by Expected Loss] Successor X Seres Class V-F4 GlobeCat Ltd. Seres USW Class A-I US W Ibs Re II Ltd. Seres Class B US B- Successor X Seres Class V-D3 US W East Lane Re V LTD. Seres 2012 Class B US W, ST BB Montana Re Ltd. Seres Class A US B East Lane Re V LTD. Seres 2012 Class A US W, ST BB Ibs Re Ltd. Seres Class B US B Ibs Re II Ltd. Seres Class A US BB- EOS Wnd Ltd. Class A US Shore Re Ltd. Seres Class A MA BB Johnston Re Ltd. Seres Class A NC BB- Johnston Re Ltd. Seres Class A NC BB- Johnston Re Ltd. Seres Class B NC BB- Johnston Re Ltd. Seres Class B NC BB- Longpont Re II Ltd. Class A Northeast BB+ Longpont Re II Ltd. Class B Northeast BB+ Foundaton Re III Ltd. Seres Class A US BB+ Ibs Re Ltd. Seres Class A US BB- Foundaton Re III Ltd. Seres Class A US BB+ US Expected Loss Rsk Adustment XS Return after Rsk Adustment 12

13 Consder the Market to be solvng the collectve Optmzaton Model PRIME MAX w subect to w p rl, * (, ) (, ) w l p w l p : λ w w : q w * w 1 : ω 0 : µ 13

14 DUAL to PRIME MIN λ, q, ωµ, subect to w l p qw λ (, ) + ω+ * * ( ) λ l p + ω µ + q = p rl,, λ, q, ωµ, 0 You can wrte the constrant as: ( ) λ l p + ω µ + q = p rl,, p 1+ λ ( r + λ ) l = ω µ + q or, ( r ) or + λ ω µ + q p l, = 1+ λ 1+ λ 14

15 An Alternatve Vew of the Market; No Bounds, No Montoncty Requrement PRIME subect to * (, ) (, ), : λ w w : q * MAX w w l p w l p w p rl w 1 : ω w 0 : µ DUAL to PRIME MIN λωµ,, subect to ( ) λ l p + ω µ = p rl,, λ, ωµ, 0 λ w ( l, p ) + ω * Orgnal wthout bounds Then we can wrte the prce equaton as: p ( r ) + λ ω µ l, = 1+ λ 1+ λ 15

16 % 100% % % Impled Probabltes vs. Scenaro Loss for the Market Portfolo 3/15/ % 60% Impled Probabltes vs. Scenaro Loss for the Market Portfolo 3/15/2012 (wth Monotoncty Requrement) % 40% Dual Impled Probabltes Dual Impled Probabltes % Impled Probabtes (Scaled) n Upper Half Loss 20% Impled Probabtes (Scaled) n Upper Half Loss % 0% Percentage Loss Lower Half % 10,000 Scenaros organsed by Loss B-T-W rght to left Percentage Loss Lower Half -20% 10,000 Scenaros organsed by Loss B-T-W rght to left % -40% % -60% % -80% 16

17 100% 100% 80% 60% Impled Probabltes vs. Scenaro Loss for the Market Portfolo 3/15/2012 (worst 25%) 80% 60% Impled Probabltes vs. Scenaro Loss for the Market Portfolo 3/15/2012 (wth Monotoncty Requrement) Worst 25% Dual Impled Probabltes Loss 40% 40% 20% Impled Probabtes (Scaled) n Upper Half Dual Impled Probabltes Loss 20% Impled Probabtes (Scaled) n Upper Half 0% Percentage Loss Lower Half -20% 10,000 Scenaros organsed by Loss B-T-W rght to left 0% Percentage Loss Lower Half -20% 10,000 Scenaros organsed by Loss B-T-W rght to left -40% -40% -60% -60% -80% -80% 17

18 Detaled Model Examned MIN λ, q, ωµ, subect to w l p qw λ ( ), + ω+ * * ( ) λ l p + ω µ + q = p rl,, λ, q, ωµ, 0 The prevous model wth the addton of:. + 1 λ λ 18

19 40% 20% Impled Probabltes vs. Scenaro Loss for the Market Portfolo 3/15/2012 (wth Monotoncty Requrement) Worst 25% Dual Impled Probabltes Loss 0% Impled Probabtes (Scaled) n -20% Upper Half Percentage Loss Lower Half -40% 10,000 Scenaros organsed by Loss B-T-W rght to left -60% -80% 19

20 0.00% 4.00% 8.00% 12.00% 16.00% 20.00% WHOLE PORTFOLIO Sngle Perl Deals US Wnd US Quake EU Wnd Japan Wnd Components of Premum, 3/15/2012 ILS Portfolo [Grouped by Type/Perl then Ordered by Expected Loss; Full Scenaro Set] Mult-Perl Deals US Wnd and US Quake US/EUWnd and US/J Quake Expected Loss Rsk Adustment XS Return after Rsk Adustment US/EU/J Wnd and US/J Quake US/EU Wnd and J Quake 20

21 Seven Scenaros Full Scenaro Set 0.00% 4.00% 8.00% 12.00% 16.00% 20.00% WHOLE PORTFOLIO 0.00% 4.00% 8.00% 12.00% 16.00% 20.00% WHOLE PORTFOLIO Sngle Perl Deals US Wnd Sngle Perl Deals US Wnd US Quake EU Wnd Japan Quake Other - MultCatMex Components of Premum, 3/15/2012 ILS Portfolo [Grouped by Type/Perl then Ordered by Expected Loss] US Quake EU Wnd Japan Wnd Components of Premum, 3/15/2012 ILS Portfolo [Grouped by Type/Perl then Ordered by Expected Loss; Full Scenaro Set] Mult-Perl Deals US Wnd and US Quake Mult-Perl Deals US Wnd and US Quake Expected Loss Expected Loss Rsk Adustment Rsk Adustment US/EUWnd and US/J Quake XS Return after Rsk Adustment US/EUWnd and US/J Quake XS Return after Rsk Adustment US/EU/J Wnd and US/J Quake US/EU/J Wnd and US/J Quake US/EU Wnd and J Quake US/EU Wnd and J Quake 21

22 -5.00% 0.00% 5.00% 10.00% 15.00% Selected Deals of Partcular Interest, 3/15/2012 ILS Portfolo [Grouped by Type/Perl then Ordered by Expected Loss; Full Scenaro Set] Atlas VI Captal Ltd Seres Class A -0.08% 6.94% Queen Street III Ltd % 3.90% Pylon II Captal Ltd. Class B -0.02% 2.98% Multcat Mexco 2009 Ltd Class D -0.04% 5.75% Expected Loss Rsk Adustment XS Return after Rsk Adustment Vega Captal Ltd. Seres 2010-I Class C 7.82% EOS Wnd Ltd. Class B 2.10% EOS Wnd Ltd. Class B 4.14% 22

23 A Very Rough Rule of Thumb for Underwrtng- - to establsh the threshold prce - 40% 20% Impled Probabltes vs. Scenaro Loss for the Market Portfolo 3/15/2012 (wth Monotoncty Requrement) Worst 25% Dual Impled Probabltes Loss Would be as follows 0% Impled Probabtes (Scaled) n -20% Upper Half RAEL (Threshold) Percentage Loss Lower Half -40% -60% 10,000 Scenaros organsed by Loss B-T-W rght to left -80% =.91*[Exp Loss] * CoTVaR 97.6 or = [Exp Loss] * CoTVaR 97.6 But there s consderable varablty 23

24 Chapter Graphs 24

25 Prcng Over tme (regresson) and at a pont n tme (Secondary Market) EL, RA and XS RAEL by Type* EL RA XSPrem Sgnfcant Elements of ILS Prcng Coeffcent of Multpler Investment Grade Yelds expressed as a rate (NBBI) Whole Portfolo 2.02% 2.61% % By Perl and Structure USW 1.44% 2.71% % USQ 1.08% 0.39% % EUW 1.02% 0.05% % JPQ 0.58% 0.09% % OTH 4.36% 0.09% % USW, USQ 2.04% 4.05% % USW,EUW, USQ,JPQ 3.71% 2.09% % W,EUW, JPW, USQ, JPQ 3.48% 3.60% % USW,EUW,USQ 2.47% 4.53% % * 90 Securtes Structure Indcator -Sngle Perl (0) Mult-Perl (100) Plus Expected Losses from; US Hurrcane US Wndstorm (Severe Thunderstorm, Wnter Storm) WSST Premum US Earthquake European Wnd Japanese Quake Some ntrgung smlartes Other CATs + European Quake and Japan Wnd Note that the lstng order and unts used may be dfferent from other statstcal tables. Ths s to enhance exposton. 25

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