metadata: authors: 0: author: Gurenko,Eugene Nikolay
1: author: Itigin,Alexander
count: Europe and Central Asia
docna: 0: docna: Reinsurance as capital optimization tool
            under Solvency II
docty: Policy Research Working Paper
subtopic: Climate Change Mitigation and Green House Gases,Capital Markets and Capital Flows,Capital Flows,Airports and Air Services,Transport Services,Natural Disasters
teratopic: Law and Development,Urban Development,Finance and Financial Sector Development
abstracts: cdata!: This paper compares solvency capital
            requirements under Solvency I and Solvency II for a sample
            mid-size insurance portfolio. According to the results of a
            study, changing the solvency capital regime from Solvency I
            to Solvency II will lead to a substantial additional
            solvency capital requirement that might represent a heavy
            burden for the company's shareholders. One way to
            reduce the capital requirement under Solvency II is to
            increase reinsurance protection, which will reduce the net
            retained risk exposure and hence also the solvency capital
            requirement. Therefore, this paper proposes an extended
            reinsurance structure that, under Solvency II, brings the
            capital requirement back to the level of that required under
            Solvency I. In a step-by-step approach, the paper
            demonstrates the extent of solvency relief attained by the
            insurer by applying different possible adjustments in the
            reinsurance structure. To evaluate the efficiency of
            reinsurance as the solvency capital relief instrument, the
            authors introduce a cost-of-capital based approach, which
            puts the achieved capital relief in relation to the costs of
            extending the reinsurance protection. This approach allows a
            direct comparison of reinsurance as a capital relief
            instrument with debt instruments available in the capital
            market. With the help of the introduced approach, the
            authors show that the best capital relief efficiency under
            all examined reinsurance alternatives is achieved when a
            financial quota share contract is chosen for proportional reinsurance.
repnme: repnme: Reinsurance as capital optimization tool
            under Solvency II
display_title: Reinsurance as capital optimization
            tool under Solvency II
listing_relative_url: /research/2013/01/17151391/reinsurance-capital-optimization-tool-under-solvency-ii
topicv3: Air Transport m1326010 165,Transport m1326661 135,Capital Markets m1326967 332,Climate Change Mitigation m1327079 579,Earthquake m1503308 3154
publishtoextweb_dt: 2013-01-01T00:00:00Z
historic_topic: Law and Development,Urban Development,Finance and Financial Sector Development
no_of_pages: 40
author_keys: 0: author_key: 87409
1: author_key: 942405
model_extractions: WPS6306 Policy Research Working Paper 6306 Reinsurance as Capital Optimization Tool under Solvency II _Eugene N. Gurenko Alexander Itigin_ The World Bank Finance and Private Sector Development Non-Banking Financial Institutions January 2013
Policy Research Working Paper 6306

# **Abstract**

This paper compares solvency capital requirements under Solvency I and Solvency II for a sample mid-size insurance portfolio. According to the results of a study, changing the solvency capital regime from Solvency I to Solvency II will lead to a substantial additional solvency capital requirement that might represent a heavy burden for the company’s shareholders.

One way to reduce the capital requirement under Solvency II is to increase reinsurance protection, which will reduce the net retained risk exposure and hence also the solvency capital requirement. Therefore, this paper proposes an extended reinsurance structure that, under Solvency II, brings the capital requirement back to the level of that required under Solvency I. In a step-by-step approach, the paper demonstrates the extent of solvency relief attained by the insurer by applying different possible adjustments in the reinsurance structure. To evaluate the efficiency of reinsurance as the solvency capital relief instrument, the authors introduce a costof-capital based approach, which puts the achieved capital relief in relation to the costs of extending the reinsurance protection. This approach allows a direct comparison of reinsurance as a capital relief instrument with debt instruments available in the capital market. With the help of the introduced approach, the authors show that the best capital relief efficiency under all examined reinsurance alternatives is achieved when a financial quota share contract is chosen for proportional reinsurance.

This paper is a product of the Non-Banking Financial Institutions, Finance and Private Sector Development. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org. The author may be contacted at egurenko@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# **Reinsurance as Capital Optimization Tool under Solvency II**

Eugene N. Gurenko<sup>1</sup> Alexander Itigin<sup>2</sup> Keywords: Solvency I, Solvency II, Reinsurance, Insurance Portfolio, Non-Life, Capital Requirement, Risk Management JEL code: G22 Sector Board: Financial Sector

> 1 **Eugene N. Gurenko** is a Lead Insurance specialist at the World Bank Capital Markets and Non-Bank Finance Practice. Email: egurenko@worldbank.org 2 **Alexander Itigin** is a World Bank Consultant and a senior actuary at a leading global and a member of the German Society of Certified Actuaries.

> We are very grateful for useful comments provided by our colleagues Serap Gonulal, Senior Insurance Specialist, World Bank and Craig Thorburn, Lead Insurance Specialist, World Bank.
|Line of business|A.<br>Gross Premium|<br>2011|B.<br> <br>[96] Ultimate<br>Loss Ratio 2011|C=A*B<br>Ultimate gross<br>Loss 2011|
|---|---|---|---|
|Motorvehicle liability insurance|20,000|70%|14,000|
|Other motor insurance|5,000|60%|3,000|
|Marine, aviation and transport insurance|5,000|80%|4,000|
|Fire and otherdamage to property insurance|15,000|70%|10,500|
|Generalliabilityinsurance|5,000|60%|3,000|
||D.<br>cession|E=A*D<br>2011 (prop. RI}|F=A-E<br>2011 (prop. Ri}|
|---|---|---|---|
|Motor vehicle liability insurance|0%|0|20,000|
|Marine, aviation and transport insurance|50%|2,500|2,500|
|Fire and otherdamage to property insurance|30%|4,500|10,500|
|Generalliabilityinsurance|0%|0|5,000|

|Line of business|G.<br>PMLgross|H=G*(1- A)<br>PML net retained <br>after prop. RI|I.<br>| Non-prop XL RI<br>2011|
|---|---|---|---|
|Motor vehicle liability insurance|10,000|10,000|9,500xs 500|
|Other motor insurance|10,000|10,000|9,500xs 500|
|Marine, aviation and transport insurance|50,000|25,000|24,500 xs 500|
|Fire and other damage to property insurance||||
|Fire non natural catastrophe per risk|30,000|21,000|20,500xs 500|
|Fire natural catastrophe per event (EQ)|100,000|70,000|69,500xs 500|
|Generalliabilityinsurance|5,000|5,000|4,500xs500|
<!-- Start of picture text --> K=3*C L=K*(1-D) M N=L-M<br>Ultimate Ultimate Ultimate Ultimate<br>Line of business gross loss 2009- | netloss retained | loss covered by | net loss retained<br>2011 under prop. RI non-prop. RI under prop. & non-<br>2009-2011 2009-2011 prop RI 2009-2011<br>Motor vehicle liability insurance 42,000 42,000 500 41,500<br>Other motor insurance 9,000 9,000 500 8,500<br>Marine, aviation and transport insurance 12,000: 6,000 500 5,500<br>Fire and other damage to property insurance 31,500 22,050 1,000 21,050<br>General liability insurance 9,000 9,000 500 8,500<br><!-- End of picture text -->

<!-- Start of picture text --> A. B. C=B/A<br>Total gross loss | Total net loss of | Retention ratio<br>of last three last three years<br>103,500 85,050<br><!-- End of picture text -->

<!-- Start of picture text --> D. E. F. G=C*(0.18*E<br>Adjusted gross | Adjusted gross | Adjusted gross + 0.16 * F)<br>premium 2011 | premium under€| premium above €| Premium Index<br>52,500 s25005/7.5m | oo 5/7.5m | 7,765<br><!-- End of picture text -->

<!-- Start of picture text --> H. I=H/3 J. K. L=C* (0.26 *J+0.23* kK)<br>Adjusted gross | Mean adjusted | Mean adjusted | Mean adjusted Claims Index<br>loss 2009-2011 gross loss of | gross loss under | gross loss above<br>2009-2011 €40.3m € 40.3m<br>108,000 | 36,000 | 36,000 S| 7,691<br><!-- End of picture text -->
<!-- Start of picture text --> A. B. Cc D=A*C E=A-D<br>. .<br>Line of business Retained Premium] Non-prop XLRI | Non-prop XLRI | XLRI premium Retained.<br>(prop RI) 2012 2012 Rate on GNPI 2012 Premium (prop &<br>XL} 2012<br>Motor vehicle liability insurance 20,000 9,500 xs 500 2.3% 460 19,540<br>Other motor insurance 5,000 9,500 xs 500 4.9% 247 4,753<br>Marine, aviation and transport insurance 2,500 24,500 xs 500 9.6% 240 2,260<br>Fire and other damage to property insurance 10,500 8,248<br>Fire non natural catastrophe per risk 20,500 xs 500 14.6% 1,530<br>Fire natural catastrophe per event (EQ) 69,500 xs 500 6.9% 722<br>General liability insurance 5,000 4,500 xs 500 AAM 222 4,778<br><!-- End of picture text -->

|.<br>.<br>Line of business|A.<br>Retained Premium]<br>(prop RI) 2012|B.<br>Non-propXLRI <br>2012|Cc<br>| Non-propXLRI <br>Rate on GNPI|D=A*C<br>|XLRI premium<br>2012|E=A-D<br>Retained<br>.<br>Premium (prop &<br>XL} 2012|
|---|---|---|---|---|---|
|Motor vehicle liability insurance|20,000|9,500xs 500|2.3%|460|19,540|
|Other motor insurance|5,000|9,500xs 500|4.9%|247|4,753|
|Marine, aviation and transport insurance|2,500|24,500xs 500|9.6%|240|2,260|
|Fire and otherdamage to property insurance|10,500||||8,248|
|Fire non natural catastrophe per risk||20,500xs 500|14.6%|1,530||
|Fire natural catastrophe per event (EQ)||69,500xs 500|6.9%|722||
|General liability insurance<br><br>|5,000<br><br>|4,500xs 500<br>|AAM<br>|222<br> <br>|4,778<br> <br><br>|
|[total<br>z|o<br>—_|P||<br>|e<br>|<br>39,579|
|Line of business|F.<br>Gross provisions for|G.<br>Net retained provisions|
|---|---|---|
|Motor vehicle liability insurance|15,000|13,000|
|Marine, aviation and transport insurance|1,000|400|
|Fire and otherdamage to property insurance|1,000|500|
|Generalliabilityinsurance|3,000|2,700|

||H=A<br>Volume measure<br>premium|l=G6<br>Volume measure<br>reserves|J=H+1<br>Volume measure<br>V_lob|
|---|---|---|---|
|Motor vehicle liability insurance|19,540|13,000|37,540|
|Other motor insurance|4,753|1,500|6,253|
|Marine, aviation and transport insurance|2,260|400|2,660|
|Fire and otherdamage to property insurance|8,248|500|8,748|
|Generalliabilityinsurance|4,778|2,700|7,478|

||__|| <br>StdDev_prem<br>without NP Factors|orton <br>NP Factors||sane] <br>StdDev with NP<br>Factors|soho |<br>StdDev_res|acta<br>StdDev_lob|
|---|---|---|---|---|---|
|Other motor insurance|7.0%|72.1%|5.0%|10.0%|5.4%|
|Marine, aviation and transport insurance|17.0%|60.3%|10.3%|14.0%|9.9%|
|Fire and other damage to property insurance|10.0%|60.6%|6.1%|11.0%|6.1%|
|Generalliabilityinsurance|15.0%|77.4%|11.6%|11.0%|10.0%|
Q = total of J R. 5. T=Q*5 Total volume measure Total StdDev rho (std_dev) Capital requirement Vv prem & reserve risk NL_pr <!-- Start of picture text --> A. B. c D. E=B+C-D F=A-E G = totalFF<br>Windstorm[Earthquake[Earthquake |PPpropPPpropprop RI RI premium XL RI RI Mitigation SCR<br>Flood | 100,000 | 30,000 || 9,500 | 722s|p||p| tz22 |<br>al |<br>subsidence|||||<br>E822<br>rotal Ft<br><!-- End of picture text -->

A. B. c D. E=B+C-D F=A-E G = totalFF Windstorm[Earthquake[Earthquake |PPpropPPpropprop RI RI premium XL RI RI Mitigation SCR Flood | 100,000 | 30,000 || 9,500 | 722s|p||p| tz22 | al | subsidence||||| E822 rotal Ft
|Cn|NLSCR|
|---|---|
|A. NL premium & reserve||
|B. NL Natural catastrophe|1,222|
|C=A+ B: Simple total|10,266|
|D. Diversification effect<br>||
|E=C-D:TotalSCR|a|

= max((1 — RR) - (Recoverables ); 0) = (SCR )-
<!-- Start of picture text --> A. B. C. D=A* BFC<br>Line. of business; ExpectedPremium Gross2012 [%]UltimateExpected |Proportionalcession RI] 2012Expectedcededlossto<br>Loss Ratio 2012 prop RI<br>Motor vehicle liability insurance 20,000 70% 0% 0<br>Other motor insurance 5,000 60% 0% 0<br>Marine, aviation and transport insurance 5,000 80% 50% 2,000<br>Fire and other damage to property insurance 15,000 70% 30% 3,150<br>General liability insurance 5,000 60% 0% 0<br>ftoalooo<br><!-- End of picture text -->

<!-- Start of picture text --> E. F. G. H=E*G 1=D+H<br>Premium (prop 2012 Net rate on GNPI |2012 ceded to XL} 2012 ceded to<br>RI) 2012 RI prop & XLRI<br>Motor vehicle liability insurance 20,000 9,500 xs 500 1.5% 306 306<br>Other motor insurance 5,000 9,500 xs 500 3.3% 165 165<br>Marine, aviation and transport insurance 2,500 24,500 xs 500 6.4% 160 2,160<br>Fire non natural catastrophe per risk 20,500 xs 500 9.7% 1,020<br>Fire natural catastrophe per event (EQ) 69,500 xs 500 3.4% 361<br>General liability insurance 5,000 4,500 xs 500 3.0% 148 148<br>[toa E00 SPOtc7320<br><!-- End of picture text -->

<!-- Start of picture text --> J. K. L=J-K M=lI4L<br>Gross provisions for Net retained Reinsurance share Reinsurance<br>Line of business outstanding claims provisions for on provisions far recoverables<br>outstanding claims outst. claims<br>Motor vehicle liability insurance 15,000 13,000 7,000 7,306<br>Other motor insurance 2,000 1,500 500 665<br>Marine, aviation and transport insurance 1,000 400 600 2,760<br>Fire and other damage to property insurance 1,000 500 500 5,031<br>General liability insurance 3,000 2,700 300 448<br><!-- End of picture text -->
<!-- Start of picture text --> N. O. P=0O-N<br>NL capital requirement with NL capital requirement without Risk mitigation<br>reinsurance reinsurance<br>9,424 104,179 94,755<br><!-- End of picture text --> <!-- Start of picture text --> Q=M/4 R=P*Q/ total O S. T=(1-5) * (Q+R)<br>Counterparty Reinsurance recoverables Risk mitigation Recovery rate Loss Given Default<br>Reinsurance company 1 2,803 23,689 506 13,246<br>Reinsurance company 2 2,803 23,689 50% 13,246<br>Reinsurance company 3 2,803 23,689 5036 13,246<br>Reinsurance company 4 2,803 23,689 50% 13,246<br>11,210 94,755 | 52,983<br><!-- End of picture text -->

<!-- Start of picture text --> PR<br>Default 2,635<br><!-- End of picture text --> <!-- Start of picture text --> PR<br>A. NL underwriting risk 9,424<br>B. Deatfult 2,635<br>C=A+B: Simple total 12,059<br>D. Diversification effect 1,078<br>E=C-D: Total SCR 10,981<br><!-- End of picture text -->
|Line of business|A<br>Expected gross<br>premium 2012|B.<br>Proportional RI<br>cession|C=A*B<br>Ceded Premium <br>2012 (prop. RI)|D=A-C<br>| Retained Premium<br>2012 (prop. RI)|
|---|---|---|---|---|
|Motorvehicle liability insurance|20,000|50%|10,000|10,000|
|Other motor insurance|5,000|50%|2,500|2,500|
|Marine, aviation and transport insurance|5,000|50%|2,500|2,500|
|Fire and other damage to property insurance|15,000|50%|7,500|7,500|
|Generalliabilityinsurance|5,000|50%|2,500|2,500|

<!-- Start of picture text --> E. F=E *(1-B) G. H. 1=D*H<br>Line of business PML gross PML net retained | Non-prop XL RI Non-prop XL RI XL RI premium<br>after prop. RI 2012 Rate on GNPI 2012<br>Motor vehicle liability insurance 10,000 5,000 4,500 xs 500 1.0% 102<br>Other motor insurance 10,000 5,000 4,500 xs 500 2.5% 62<br>Marine, aviation and transport insurance 50,000 25,000 24,500 xs 500 9.6% 240<br>Fire and other damage to property insurance 0<br>Fire non natural catastrophe per risk 30,000 15,000 14,500 xs 500 11.4% 852<br>Fire natural catastrophe per event (EQ) 100,000 50,000 49,500 xs 500 5.9% 439<br>General liability insurance 5,000 2,500 2,000 xs 500 2.1% 52<br>tot<br><!-- End of picture text -->

|Line of business|E.<br>PML gross|F=E *(1-B)<br>PML net retained | <br>after prop. RI|G.<br> Non-prop XL RI<br>2012|H.<br>Non-prop XL RI<br>Rate on GNPI|1=D*H<br>XL RI premium<br>2012|
|---|---|---|---|---|---|
|Motorvehicle liability insurance|10,000|5,000|4,500 xs 500|1.0%|102|
|Othermotor insurance|10,000|5,000|4,500 xs 500|2.5%|62|
|Marine, aviation and transport insurance|50,000|25,000|24,500 xs 500|9.6%|240|
|Fire and other damage to property insurance|||||0|
|Fire non natural catastrophe per risk|30,000|15,000|14,500 xs 500|11.4%|852|
|Fire natural catastrophe per event (EQ)<br>|100,000<br>|50,000<br>|49,500 xs 500<br>|5.9%<br>|439<br>|
|General liability insurance<br>|5,000<br>|2,500<br>|2,000 xs 500<br>|2.1%<br><br>|52<br><br>|
|t|||||ts|
<!-- Start of picture text --> eeA. NL underwriting risk eo7,410<br>B. Deafult 2,959<br>C. Diversification effect 1,118<br>E = C- D: Total SCR [| 9252 |<br><!-- End of picture text -->

|e<br>A.|e<br>eo|
|---|---|
|NL underwriting risk|7,410|
|B. Deafult|2,959|
|C. Diversification effect<br>|1,118<br>|
|E=C-D:TotalSCR|[|<sup>9252</sup>||

|Lineofbusiness|E.<br>PMLgross|F=E*(1-B)<br>PMLnet retained |<br>after prop. RI|G.<br> Non-prop XL RI<br>2012|H.<br>Non-prop XLRI<br>Rate on Premium|1=D*H<br>XL RI premium<br>2012|
|---|---|---|---|---|---|
|Motorvehicle liability insurance|10,000|5,000|4,750 xs 250|2.3%|230|
|Othermotor insurance|10,000|5,000|4,750 xs 250|4.9%|124|
|Marine, aviation and transport insurance|50,000|25,000|24,750 xs 250|16.4%|410|
|Fire and other damage to property insurance||||||
|Fire non natural catastrophe per risk|30,000|15,000|14,750 xs 250|18.9%|1,417|
|Fire natural catastrophe perevent (EQ)|100,000|50,000|49,750 xs 250|8.1%|609|
|General liability insurance<br>|5,000<br>|2,500<br>|2,250 xs 250<br>|4.4%<br>|111<br>|
|[t||t|h|e|2.801|

<!-- Start of picture text --> eeA. NL underwriting risk eo6,970<br>B. Deatult 2,989<br>C. Diversification effect 1,107<br>E=C- D: Total SCR 8,351<br><!-- End of picture text -->
<!-- Start of picture text --> E. F=E*(1-B) G. H. 1=D*H<br>Line of business PML gross PML net retained | Non-prop XL RI Non-prop XLRI XL RI premium<br>after prop. RI 2012 Rate on Premium 2012<br>Motor vehicle liability insurance 10,000 3,000 4,750 xs 250 2.5% 253<br>Other motor insurance 10,000 3,000 4,750 xs 250 5.4% 136<br>Marine, aviation and transport insurance 50,000 25,000 24,750 xs 250 18.1% 452<br>Fire and other damage to property insurance<br>Fire non natural catastrophe per risk 30,000 15,000 14,750 xs 250 20.8% 1,559<br>Fire natural catastrophe per event (EQ) 100,000 50,000 49,750 xs 250 8.9% 670<br>General liability insurance 5,000 2,500 2,250 xs 250 4.9% 122<br>Ptoral t1<br><!-- End of picture text -->

|Line ofbusiness|E.<br>PMLgross|F=E*(1-B)<br>PMLnet retained |<br>after prop. RI|G.<br> Non-prop XL RI<br>2012|H.<br>Non-prop XLRI<br>Rate on Premium|1=D*H<br>XL RI premium<br>2012|
|---|---|---|---|---|---|
|Motorvehicle liability insurance|10,000|3,000|4,750 xs 250|2.5%|253|
|Other motor insurance|10,000|3,000|4,750 xs 250|5.4%|136|
|Marine, aviation and transport insurance|50,000|25,000|24,750 xs 250|18.1%|452|
|Fire and other damage to property insurance||||||
|Fire non natural catastrophe per risk|30,000|15,000|14,750 xs 250|20.8%|1,559|
|Fire natural catastrophe perevent (EQ)|100,000|50,000|49,750 xs 250|8.9%|670|
|General liability insurance<br>|5,000|2,500<br>|2,250 xs 250<br>|4.9%<br>|122<br>|
|Ptoral|||t|||

|e<br>A.|e<br>>|
|---|---|
|NL underwriting risk|6,968|
|B. Deafult||
|C. Diversification effect||
|E=C-D:TotalSCR|7,794|
<!-- Start of picture text --> A. B. C=A+B D. E. F=D+E<br>Reinsurance Reinsurance Total reinsurance Reinsurance Reinsurance _ | Total reinsurance<br>original portf. original portf. portf. updated portf. updated portf. updated portf.<br>Motor vehicle liability insurance 0 460 460 10,000 253 10,253<br>Other motor insurance 0 247 247 2,500 136 2,636<br>Marine, aviation and transport insurance 2,500 240 2,740 2,500 452 2,952<br>Fire and other damage to property insurance 4,500 4,500 7,500 0 7,500<br>Fire non natural catastrophe per risk 1,530 1,530 1,559 1,559<br>Fire natural catastrophe per event (EQ) 722 722 670 670<br>General liability insurance 0 222 222 2,500 122 2,622<br><!-- End of picture text -->

||A.<br>Reinsurance<br>original portf.|B.<br>Reinsurance<br>original portf.|C=A+B<br>Total reinsurance<br>portf.|D.<br>Reinsurance<br>updated portf.|E.<br>Reinsurance_ <br>updated portf.|F=D+E<br>| Total reinsurance<br>updated portf.|
|---|---|---|---|---|---|---|
|Motorvehicle liability insurance|0|460|460|10,000|253|10,253|
|Othermotor insurance|0|247|247|2,500|136|2,636|
|Marine, aviation and transport insurance|2,500|240|2,740|2,500|452|2,952|
|Fire and otherdamage to property insurance|4,500||4,500|7,500|0|7,500|
|Fire non natural catastrophe per risk||1,530|1,530||1,559|1,559|
|Fire natural catastrophe per event (EQ)<br>||722<br>|722<br>||670<br>|670<br>|
|General liability insurance<br><br>|0<br><br>|222<br>|222<br>|2,500<br><br><br>|122<br><br>|2,622<br>|
|[Tota<br>CT|oo—|en|taza=~|]<br>25000<br>|sat|2atga|

<!-- Start of picture text --> G. H. I. J=A*(1-G-H) |K=D*(1-G-1)<br>[%] Expected Reinsurance Reinsurance P &Lstatement | P & L statement<br>Line of business ultimate loss ratio commission commission costs of prop RI | costs of prop RI<br>original portf. updated portf. original portf. updated portf.<br>Motor vehicle liability insurance 70% nil. 18% 0 1,200<br>Other motor insurance 60% mil. 27% 0 325<br>Marine, aviation and transport insurance 80% 10% 9% 250 275<br>Fire and other damage to property insurance 70% 20% 18% 450 900<br>General liability insurance 60% nil. 27% 0 325<br>tot 080s<br><!-- End of picture text -->
<!-- Start of picture text --> L=J+B6 M=K+E<br>Line of business total P & L statement costs | total P & L statement costs<br>of RI, original port. of RI, updated portf.<br>Motor vehicle liability insurance 460 1,453<br>Other motor insurance 247 461<br>Marine, aviation and transport insurance 490 fof<br>Fire and other damage to property insurance 2,702 3,129<br>General liability insurance 222 4A7<br>[Totaltt| tt<br><!-- End of picture text -->

|Line of business|L=J+B6<br>total P & L statement costs|<br>of RI, original port.|M=K+E<br> total P & L statement costs<br>of RI, updated portf.|
|---|---|---|
|Motor vehicle liability insurance|460|1,453|
|Other motor insurance|247|461|
|Marine, aviation and transport insurance|490|fof|
|Fire and other damage to property insurance|2,702|3,129|
|General liability insurance<br>|222<br><br>|4A7<br><br><br>|
|[Totalt||tt|
<!-- Start of picture text --> RI comm<br>ata! tt {{TT4<br>40% INENITELR+ RI Comm= 95%<br>LINE20% TTT<br> re ae<br>Of<br>0% 20% 40% 60% 80% 100% 120% 140% 1606<br>LR<br>Loss Ratio (LR)<= 50% Reinsurance commission (Rl) =45%<br>Loss Ratio (LR) >= 85% = Reinsurance commission (Rl) = 10%<br>For LRs between 50% and 85%, RI commission drops by 1% for any LR increase of 1%.<br><!-- End of picture text --> <!-- Start of picture text --> G. H. I. J=A*(1-G-H) K =TotalD * 5%<br>. . [%] Expected ultimate Reinsurance Reinsurance P & L statement P & L statement<br>Line of business<br>loss ratio. commissionaoe originala commissionsoos costs of prop RI costs of prop RI<br>portf. updated portf. original portf. updated portf.<br>Motor vehicle liability insurance 70% nil. Whole account 0<br>Other motor insurance 60% mil. oa . 0<br>. —— . sliding scale with<br>Marine, aviation and transport insurance 80% 10% . : . 250<br>. .<br>Fire reinsurer's margin<br> and other damage to property insurance 70% 20% of 5% 450<br>General liability insurance 60% nil. 0<br>[tot00s<br><!-- End of picture text --> <!-- Start of picture text --> L=J+B M=K+E<br>Line of business total P & L statement costs of RI, | total P & L statement costs of RI,<br>original portt. updated portt.<br>[totalTt<br><!-- End of picture text -->
Now, the additional reinsurance costs for the updated reinsurance structure amount to only € 4.4m – 4.1m = 0.3m. With the achieved capital requirement relief of € 7.8m we calculate the relative cost of capital as 0.3/3.2 = 9.4%. Hence, by introducing the financial quota share reinsurance we have achieved a substantial reduction in the cost of capital. Most likely, the resulting cost of capital will compare favorably with the borrowing costs for an emerging market mid-size insurance company. Reinsurance has proven to be a competitive capital relief instrument!

We must point out however that to make good use of financial quota share contracts for achieving cost efficient solvency relief, one needs to ensure that such contracts must fulfill certain requirements to qualify as reinsurance for regulatory purposes and hence achieve the desired solvency relief effect. In many cases, the ceding company will be required by law to prove to the market regulator that the contract transfers a substantial amount of risk and hence can be considered a reinsurance contract. If this cannot be proved, the contract will be considered not as reinsurance but as a purely financial instrument and therefore no solvency capital relief effect will be granted. Please refer to the paper _“Insurance Risk Transfer and Categorization of Reinsurance Contracts”_ by the same authors.

# 4. <u>Conclusions</u>

In this paper, we have compared solvency capital requirements under Solvency I and Solvency II for a sample mid-size insurance portfolio. We have shown that the capital requirement under the Solvency II regime is substantially higher than under the Solvency I regime. Hence, according to our result, changing the solvency capital regime from Solvency I to Solvency II will lead to a substantial additional solvency capital requirement which might represent a heavy burden for the company’s shareholders.

One way to reduce the capital requirement under Solvency II is to increase reinsurance protection, which will reduce the net retained risk exposure and hence also the solvency capital requirement. Therefore, we proposed an extended reinsurance structure which under Solvency II brings the capital requirement back to the level of that required under Solvency I. In a step-by-step approach we demonstrate the extent of solvency relief attained by the insurer by applying different possible adjustments in the reinsurance structure: increasing the cession to proportional reinsurance, reducing the retention of nonproportional reinsurance, and selecting better rated reinsurers for its reinsurance program.

To evaluate the efficiency of reinsurance as the solvency capital relief instrument, we have introduced a cost-of-capital based approach which puts the achieved capital relief in relation to the costs of extending the reinsurance protection. This approach allows a direct comparison of reinsurance as capital relief instrument with debt instruments available in the capital market. With the help of the introduced approach, we have shown that the best capital relief efficiency under all examined reinsurance alternatives is achieved when a financial quota share contract is chosen for proportional reinsurance. For the sample insurance portfolio and the proposed reinsurance structure, we achieved the cost of capital required for the capital relief of less than 10% - a highly competitive rate in comparison with the cost of corporate borrowing in the capital market.

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# **Annex A1**

# **Solvency Capital Requirements according to Solvency I**

In order to calculate Solvency Capital Requirements, first one needs to calculate the Retention Ratio Retention Ratio = ( + retained loss report yr.

+ retained loss 1<sup>st</sup> yr. before report yr.

+ retained loss 2<sup>nd</sup> yr. before report yr. ) / ( + gross loss report yr. + gross loss 1<sup>st</sup> yr. before report yr. + gross loss 2<sup>nd</sup> yr. before report yr. ).

Then the Premium Index and the Claims Index can be calculated. The Premium Index is calculated as follows Premium Index = Retention Ratio * ( + 0.18 * min (adjusted gross premium for report yr., € 57.5 M) + 0.16 * max (adjusted gross premium for report yr. – € 57.5 M, 0) ), The expression in brackets in the above formula for the Premium Index is equal to the adjusted gross premium for the report year up to the limit of € 57.4 M multiplied by 0.18 plus the premium in excess of € 57.5 M, if any, multiplied by 0.16. Adjusted gross premium is equal to the gross premium plus 50% of the premium from the lines Aviation Liability, Water Transport Liability and General Liability (if any).

Claims Index is calculated as follows Claims Index = Retention Ratio * ( + 0.26 * min (mean gross loss of last three yrs., € 40.3 M) + 0.23 * max (mean gross loss of last three yrs. – € 40.3 M, 0) ), where mean gross loss of last three years is calculated as mean gross loss of last three yrs = ( + adjusted gross loss report yr. + adjusted gross loss 1<sup>st</sup> yr. before report yr. + adjusted gross loss 2<sup>nd</sup> yr. before report yr. ) / 3 The expression in brackets in the above formula for the Claims Index is equal to the mean gross loss of last three years up to the limit of € 40.3 M multiplied by 0.26 plus the mean gross loss of last three years in excess of € 40.3 M if any multiplied by 0.23. Adjusted gross loss is equal to the gross loss plus 50% of the gross loss from the lines Aviation Liability, Water Transport Liability and General Liability (if any).

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Finally, the Solvency Capital Requirement is calculated as maximum of both Premium Index and Claims Index Solvency Capital Requirement = max (Premium Index, Claims Index) If the resulting Solvency Capital Requirement for the report year is lower than for the previous year, the following further calculation needs to be carried out.

Loss reserve ratio = max (1, loss reserves at the end of report yr. / loss reserves at the beginning of report yr.) Solvency Capital Requirement = max (max (Premium Index, Claims Index), Loss reserve ratio * Solvency Capital Requirement previous yr.) 19