70136
Working Paper
Assessing the Impact of Reinsurance on Insurers’
Solvency under Different Regulatory Regimes
Eugene N. Gurenko, Lead Insurance Specialist
Alexander Itigin, Actuarial Consultant
Draft
GCMNB
June 9, 2010
Background
This paper aims to identify discrepancies between an economic risk-based view of insurers’
solvency net of reinsurance and the regulatory treatment of reinsurance under three most
common regulatory solvency regimes: Solvency I, Solvency II and Swiss Solvency Test (SST).
The main rationale behind this comparison is to pinpoint potential shortfalls in the regulatory
treatment of reinsurance for the purposes of solvency calculations. The paper also makes
practical recommendations on how to best utilize reinsurance for the purposes of risk
management and increasing profitability which may be of interest for insurers and insurance
regulators.
To build the argument, the paper utilizes numerous reinsurance scenarios in which we test the
effects of most common forms of reinsurance (e.g. Quota Share (QS), and Excess of Loss (XL))
on the solvency position of a hypothetical insurance company specialized in writing catastrophe
risk under different regulatory regimes compared to the risk-based economic view of solvency.
The selection of a specialized catastrophe risk insurer has been driven mainly by a more
pronounced discrepancy arising from a comparison of the regulatory and economic views of
solvency net of reinsurance for portfolios of catastrophe risk.
The proposed work builds on the previous research by the authors on the accuracy and reliability
of risk-based solvency measures in approximating the level of risk retained by insurance and
reinsurance entities specialized in writing catastrophe risk.
Methodological Approach
To demonstrate the differences between the regulatory and economic views of minimum riskbased capital required for a given portfolio of insurance risk for different levels of risk retention,
we subject the modeled portfolio of catastrophe risk to a series of reinsurance scenarios that vary
by the extent and type of risk transfer. For each test, we then compute the solvency margin
required under Solvency I, Solvency II and SST and for an economic risk-based view of
solvency.
The portfolio of insurance risk subjected to the solvency tests consists of stand-alone catastrophe
insurance policies covering earthquake related property damages of residential dwellings in four
countries of South-Eastern Europe. For simplification purposes, we assumed that the company
has no investment risk (i.e. invests all its surplus and reserves into cash and short-term highly
rated government paper) – hence the risk capital requirements for the assets were set at zero.
Again, for simplification reasons, we also assumed away the operational risk, whose
quantification is required under Solvency II.
Event data set
To carry out our analyses, we used a stochastic data set of insured property losses in South East
Europe. The data was provided by RMSI (2008), a risk modeling consultancy. The data set
approximates losses that would be sustained by an insurance portfolio consisting exclusively of
earthquake risk related liabilities, e.g. a portfolio of stand-alone earthquake insurance policies for
residential property in four countries – Croatia, Bosnia and Herzegovina, Macedonia and
Albania. A deductible of 3 percent was assumed for each insured risk. For each country, the
RMSI provided an estimate of insured residential loss in the capital city and in the rest of
country. Insurance penetration was assumed to be 8 percent in capital cities and 6 percent
outside. The probability of occurrence for each loss event and its severity were estimated by
RMSI based on the underlying physical hazard and building vulnerability data.
We assumed that the event frequency is distributed according to the Poisson distribution. From
the original event data set described above, we derived the expected frequency (Poisson lambda)
of 1.79. A customized distribution for loss severity results directly from the original event data
set. Through a Monte-Carlo simulation for these frequency-severity parameters, we produced
100,000 data records of annual residential earthquake insured losses. Our sensitivity analysis was
based on this derived data set. The data set specifies both (i) the total annual loss for the total
residential portfolio in four countries and (ii) the total annual loss for each country separately.
Further, for each country the loss in the capital city and outside is specified. Each of the 100,000
annual insured losses can occur with the entry probability of 1/100,000 = 0.001 percent.
Measures of required solvency capital net of reinsurance
For the above described portfolio of insurance risk we calculated the insurer’s solvency margin
capital required under Solvency I, Solvency II and the SST regimes. The mathematical formulas
used for these calculations are described below.
Solvency I
Required Solvency Capital = max (Premium Index, Claims Index)
Premium Index =
Retention Rate * (0.18 * min (Gross Premium, €50m) + 0.16 * max (Gross Premium - €50m, 0))
Claims Index =
Retention Rate * (+ 0.26 * min (Mean Gross Loss last 3 yrs, €35m)+ 0.23 * max (Mean Gross Loss last 3
yrs - €35m, 0))
Where
Retention Rate = Total Retained Loss for last 3 yrs / Total Gross Loss for last 3 yrs
As we assume that there hasn't been any loss and the retention rate was held steady over the
last 3 years, the above formula for the Retention Rate has been substituted with the one below:
Retention Rate = Total Retained Premium / Total Gross Premium
Solvency II
2
Required Solvency Capital = + Scenario per occurrence loss with return period 200 yrs – Expected Annual
Net Retained Loss - RI Recoverables
where Scenario per occurrence loss with a return period 200 yrs denotes the event loss which can
be expected not to be exceeded more often than once in 200 years. This value can be estimated
directly from the annual per occurrence probability loss exceedence curve for the modeled
portfolio of risk provided in Table I below.
RI Recoverables stands for reinsurance recoverables that will be received from reinsurers under a
company’s reinsurance program.
Please notice that in our definition of Required Solvency Capital (RSC), we follow the Standard
Model approach rather than the Internal Model approach. According to the Internal Model
philosophy, RSC is calculated based on the Annual Net Retained Loss VaR (99.5%) instead of a
scenario loss with return period 200 yrs.
Table 1. Occurrence Exceedence Probability Curve (€)
Severity
OEP REP
Conf level
315,397,951
1000
99.90%
262,694,164
500
99.80%
221,425,527
300
99.67%
196,232,960
200
99.50%
150,292,092
100
99.00%
97,640,148
50
98.00%
86,330,234
40
97.50%
70,192,679
30
96.67%
53,958,412
20
95.00%
27,387,517
10
90.00%
9,501,341
5
80.00%
Swiss Solvency Test
Required Solvency Capital = + Annual Net Retained Loss TVaR(99.0%)
- Expected Annual Net Retained Loss
where Annual Net Retained Loss TVaR (99.0%) denotes the Annual Net Retained Loss Tail
Value at Risk (also often called the Expected Shortfall) at the confidence level of 99.0
percent. This is the average annual aggregate net retained loss calculated from the data set
values that exceed those in excess of 99.0 percentile of the annual aggregate net retained loss
distribution. As opposed to VaR which looks at losses up to a predefined percentile (thus
disregarding distributions’ tails), TVaR approximates the average value of the tails. Table 2
below presents the comparison of the VaR and TVAR values of the annual aggregate loss
exceedence curve for the modeled risk portfolio.
3
Table 2. Annual Aggregate Net Retained Loss Exceedence Curve (€)
Conf level
99.00%
99.10%
99.20%
99.30%
99.40%
99.50%
99.60%
99.70%
99.80%
99.90%
Value at Risk
159,253,147
165,545,132
175,110,003
184,185,117
195,865,818
211,438,112
222,773,122
247,751,975
282,934,981
320,521,774
Tail Value at Risk
228,180,049
235,407,272
243,467,238
252,707,742
263,085,471
275,398,861
289,926,108
308,518,979
332,248,479
361,236,285
The differences between the VaR and TVAR approaches are further illustrated in Figure 1.
Figure 1
Simulations
In this Section we demonstrate that for the same portfolio of insurance risk protected by a given
reinsurance program insurers operating in three different jurisdictions (say, in EU countries in
2012, in Switzerland in 2011, and now in all EU countries) will end up with three very different
regulatory solvency requirements.
Each reinsurance scenario differs in some way from the previous one in terms of the type of
reinsurance treaties used (XL vs. QS) and the level of overall risk retention by the insurer. We
then calculate the required solvency capital for each of three regulatory solvency regimes and
compare them with an economic risk-based solvency requirement. The latter is defined as the
risk-based capital needed to support a portfolio of retained risk (e.g. net of reinsurance
recoverables) for loss scenarios with a return period of up to 500 years on a per occurrence basis
4
(e.g. VAR with 99.8% confidence level)1minus annual expected loss. The regulatory solvency
margin requirements are then expressed as a percentage of the minimum risk-based economic
capital.
Base Case Scenario
Under the base case scenario the insurer assumes all the risk, i.e. transfers no risk to reinsurers.
As a result the insurers keeps the entire premium - €45 mm, see Table 3.
Table 3. Reinsurance Premium vs. Retained Premium
Total Reinsurance Premium
Total Retained Premium
0
45,069,552
The estimates of the required regulatory solvency capital (RSC) under three different solvency
regulations are presented in Table 5, which also compares how these amounts correspond to the
economic capital required by the S&P for an AA rated company, which for the purposes of this
paper has been defined as follows:
EC = OEP 500 year loss – RI Recoverable – Annual Net Retained Expected Loss=€ 252,286,069
Where OEP 500 year loss is defined as a loss with the exceedence probability of (100%99.8%=0.2%) per individual occurrence for a given portfolio of catastrophic risk. The values of
OEP Loss Exceedence Costs can be obtained from Table 1.
RI Recoverable stands for reinsurance recoverables, e.g. the maximum amount that can be
recovered from reinsurers in case of a catastrophic loss covered by the insurer. In the case of the
Base Scenario no risk is transferred to reinsurers, hence this value is set at zero.
Annual Net Retained Expected Loss (ANREL) is the annual long-term average expected payout
covered out of the insurer’s own financial resources (e.g. not covered by reinsurers). The
ANREL value can be found in Table 4 below.
Table 4. Annual Net Retained Loss
Annual Net Retained Expected Loss
10,408,093.63
To compare how the regulatory treatment of reinsurance (for the purposes of solvency
calculation) differs from the economic effect of reinsurance on the required minimum economic
risk capital (EC) we introduced the ratio of required Regulatory Solvency Capital (RSC) to
Economic Capital (EC) for three different solvency regimes. As can be seen from Table 5, the
values of the ratio significantly vary from one regulatory solvency measure to another. The
RSC/EC ratio for Solvency I is the lowest of all, which demonstrates how inadequate the
measure of Solvency I is for mono-line insurers involved in writing volatile types of risk (e.g.
catastrophe, aviation, credit risk insurance). Although the ratios for two other measures of risk1
While we acknowledge a certain degree of arbitrariness in the selection of the return period for our definition of economic solvency capital, we
would like to point out that in its definition of a minimum risk-based capital for a AA rated insurer, the S&P proposes a similar definition. The
readers however are invited to reset the return period to either a higher or lower number, based on their own views of what constitutes a prudent
level of financial resilience for an insurance/reinsurance entity.
5
based solvency – Solvency II and SST – are different as well, they are considerably closer to the
economic risk capital required for the utilized portfolio of risk. The difference between the two
ratios can be attributed to the mathematical definitions of risk chosen – 99.5% VAR on a per
occurrence basis for Solvency II and TVAR for a 99.0% VAR on an aggregate annual risk basis
for SST.
Table 5. Regulatory Solvency Capital Requirements vs. Economic Capital
EC*
Solvency Capital
Solvency I
Solvency II
Swiss Solvency Test
RSC/EC
252,286,069
8,112,519.27
185,824,866.33
217,771,955.77
3.2%
73.7%
86.3%
252,286,069
252,286,069
As can be seen from Table 5, standing at 86.3% the RSC/EC ratio for the SST demonstrates that
it is the most stringent of three solvency measures due to the use of the 99% TVAR approach to
risk measurement. The RSC/EC ratio for the SST is closely followed by that of Solvency II
(73.7%), which by definition disregards all risk scenarios beyond a 200 year return period on a
per occurrence basis.
Scenario 1: Reinsurance - 20% Cession to a Quota Share Reinsurance Treaty
Under this scenario, the insurer cedes 20% of the risk and premium to a reinsurer on a
proportional quota-share basis. See Table 6 below.
Table 6. Retained and Reinsured Premium
Total Reinsurance Premium
Total Retained Premium
9,013,910
36,055,641
We assume that the treaty has no aggregate reinsured limit and thus provides for a complete risk
transfer regardless of the ultimate size of insured loss. In Table 7 below we provide the outcomes
of this simulation.
Table 7. Regulatory Solvency Capital vs. Economic Capital
Regulatory
Solvency Capital
Solvency I
6,490,015.42
Solvency II
148,659,893.07
Swiss Solvency Test
174,217,564.62
Notes: *ANREL = €8,326,474.
EC
201,828,856
201,828,856
201,828,856
Delta to base
case scenario
-20.00%
-20.00%
-20.00%
RSC/EC
3.2%
73.7%
86.3%
As expected, a 20% cession of the risk across the whole portfolio results in a 20% reduction for
both RSC and EC, which can be observed by comparing the values of RSC/EC ratio to those
obtained under the Base Case Scenario – the ratios stayed the same. Since the values of the
RSC/EC ratio changed proportionately by 20%, one can see that in this specific case the
regulatory treatment of reinsurance for the purpose of providing solvency relief fully corresponds
to the economic reality –a 20% risk reduction in the required risk capital achieved through a risk
transfer to a third party.
6
Scenario 2. Reinsurance – 80% to a Quota Share Reinsurance Treaty
In this scenario, we continue to test the impact of a proportional reinsurance treaty on the
changes in the regulatory measures of the required solvency capital compared to those for the
required economic capital. In this case, the insurer transfers 80% of risk and premium to a
reinsurer. As shown in Table 8 below, although one would expect the risk transfer to result in an
80% reduction for all three measures of RSC, this is not the case for Solvency I, where only a
50% reduction is achieved. This less than expected drop in the RSC under Solvency I can be
explained by the fact that insurers cannot realize a solvency relief when their risk retention drops
below the minimum prescribed by the Solvency I formula. While in the previous simulation this
was not a constraint due to a very insignificant amount of risk transfer, in this case the constraint
became binding resulting in a disproportionate reduction in the required solvency margin. We
must point out that this discrepancy between economic and regulatory outcomes of risk transfer
in the case of Solvency I solvency regulations can be viewed as distortionary as it creates strong
incentives for companies to retain more risk, which in the case of mono-line writers can be
highly counterproductive from the risk management perspective.
However, as shown by the RSC/EC ratio the two other RSC measurers dropped proportionately
to the risk transfer, e.g. by 80%. Similarly, we can observe a proportional drop in the amount of
premium retained by the insurer – see Table 9.
Table 8. Regulatory Solvency Capital Requirements vs. Economic Capital
Solvency Capital
Delta to base
case scenario
EC*
RSC/EC
Solvency I
4,056,259.64
-50.00%
50,457,214
8.0%
Solvency II
37,164,973.27
-80.00%
50,457,214
73.7%
43,554,391.15
-80.00%
50,457,214
86.3%
Swiss Solvency Test
Notes: *ANREL = €2,081,618
Table 9. Reinsurance vs. Retained Premium
Total Reinsurance Premium
Total Retained Premium
36,055,641
9,013,910
Scenario 3. Reinsurance: 40% cession to QS; CAT XL: €85m xs. €5m (up to REP 100 yrs)
In this simulation we introduce a more complex reinsurance program whereby an insurer
transfers 40% of total risk to a proportional Quota Share treaty while capping the remaining 60%
of the risk with an €85 million Excess of Loss Catastrophe Risk reinsurance treaty (CAT XL),
which attaches at €5million – the insurer’s own minimum risk retention. The overall effects of
this risk transfer are summarized below.
7
Table 10. Regulatory Solvency Capital Requirements vs. Economic Capital
Solvency Capital
Delta to gross
portf.
EC*
RSC/EC
Solvency I
4,056,259.64
-50.00%
70,470,612
5.8%
Solvency II
30,593,890.25
-83.54%
70,470,612
43.4%
Swiss Solvency Test
45,146,579.55
-79.27%
70,470,612
64.1%
Notes: *ANREL = €2,145,885
The main finding of this simulation is a considerable deterioration in the ratio of the required
regulatory capital to the economic capital relative to the previous case scenario. Despite the fact
that the economic capital requirements increase from $50.4 million in the previous case to $70.4
in this scenario (due to a lesser amount of economic risk transfer provided by this program), we
can observe that Solvency I capital requirements remain the same, while those under Solvency II
even drop from $37.16 million to $30.6 million. This is due to the fact that the Solvency II
measure of RSC by design does not account for any risk in excess of a 200 year return period on
an annual per occurrence basis. Hence, even though the $85 million layer of reinsurance in
excess of $5 million in addition to a 40% proportional cession (e.g. $104.8 m) did a better job
reducing the risk from an annual event with a 200 year return, it did not transfer any risk beyond
that point. The SST was only solvency measure that captured the lack of risk transfer beyond that
point by increasing the amount of regulatory capital required from $43.5 to $45.1 million – see
Figure 2. With the RSC/EC ratios being 5.8% and 43.4%, respectively, Solvency I and Solvency
II measures of RSC clearly fall short of approximating the true economic effect of this risk
transfer on the solvency requirements – e.g. while the economic quality of this risk transfer is
inferior to that in the previous scenario, the Solvency I and Solvency II minimum capital
requirements remained the same or dropped.
Another interesting observation is a considerable increase in the retained premium for the insurer
from $9 million in the previous case to $21.7 million in this scenario due to the reduced amount
of available reinsurance protection – see Table 11. An insurer operating under the Solvency II
regulations in a competitive market is likely to have no other choice but to structure its
reinsurance coverage in a way which would enable to achieve the minimum reinsurance cost
while meeting the regulatory solvency requirements.
Table 11. Reinsurance vs. Retained Premium
Total Reinsurance Premium
Total Retained Premium
23,336,734
21,732,818
8
Figure II. Economic vs. Regulatory Capital
500 OEP REP
$262 m
QS
$196 m
40%
X
200 OEP REP
$85 m
XL
$5 m
Scenario 4. Reinsurance: 40% cession to QS;€112 m xs. €5m (up to REP 200yrs) to CAT XL
In this Scenario, similarly to Scenario 3, the insurer employs a combination of proportional and
non-proportional (excess of loss reinsurance). Keeping the percentage of risk/premium ceded to
the QS treaty at 40%, the insurer increases the overall amount of coverage provided by the CAT
XL treaty from €85 to €112 million – a net increase of €27 million in reinsurance coverage. The
results of the simulation are summarized below.
Table 12. Solvency Capital vs. Economic Capital
Solvency Capital
Delta to base case
Solvency I
4,056,259.64
Solvency II
3,791,638.08
Swiss Solvency Test
28,394,947.48
Notes: *ANREL = €1,948,137
-50.00%
-97.96%
-86.96%
EC*
43,668,360
43,668,360
43,668,360
SC/EC
9.3%
8.7%
65.0%
Table 13. Reinsurance vs. Retained Premium
Total Reinsurance Premium
Total Retained Premium
23,631,259
21,438,292
9
Several interesting observations can be made based on the results of this simulation. First, the
amount of solvency capital required under Solvency II is below that required under Solvency I.
The outcome can be attributed to the fact that while the solvency margin under Solvency I
remains the same until a certain minimum risk retention level has been reached, the RSC under
Solvency II is phased out to zero as the amount of reinsurance protection approaches the
expected probable loss from a 200 year event - the maximum amount of risk capital required at
this confidence level. The effect is clearly demonstrated in Table 12 which presents the values of
the RSC/EC ratio. The biggest discrepancy between the economic capital and that required by
the regulators arises for Solvency I and Solvency II measures, 9.3% and 8.7%, respectively. This
case is of particular interest as it shows that a risk-based measure of solvency such as Solvency II
can result in a larger discrepancy with the economic measure of solvency than Solvency I, a nonrisk based measure of solvency.
Another important finding is the almost negligible additional premium cost required to obtain a
very considerable solvency relief achieved under Solvency II compared to the previous scenario.
If in Scenario 3, an insurer would retain €21.74 million in premium and would be required to put
up €30.6 million in solvency margin requirements; under the current scenario, an insurer would
keep €21.44 million in premium but would be required to set aside only €3.8 million in solvency
capital. A simple calculation demonstrates that by forgoing only €0.3 mm the insurer would be
realizing a capital cost saving of €4.02 million2 - quite a stellar return on the investment! This
discovery strongly underscores the cost effectiveness of XL type coverage for insurers operating
under Solvency II. While being inferior in quality to proportional reinsurance treaties (with no
aggregate limits) XL coverage allows insurers to achieve regulatory solvency capital relief at a
much lower reinsurance cost.
We also observe that the solvency relief provided under the SST in response to a €27 million
increase in XL coverage amounts to only €16.75 million, which raises interesting questions
about the adequacy of this risk-based solvency measure when it comes to estimating the
economic effects of XL reinsurance coverage on insurers’ capital position. We are going to
explore this specific issue in more detail in the next three simulations.
Scenario 5. No Proportional Cession to QS; XL - 190m xs 5m (up to REP 200yrs)
In this simulation we explore the effects of an XL reinsurance program – €190 million in excess
of €5 million on the regulatory solvency requirements as well as the economic capital of the
insurer. The results of the simulation are summarized below.
Table 14. Regulatory Solvency Capital vs. Economic Capital Requirements
Solvency Capital
EC
RSC/EC
Solvency I
6,258,894
-22.85%
70,260,344
8.9%
Solvency II
3,799,140
-97.96%
70,260,344
5.4%
42,005,395
-80.71%
70,260,344
59.8%
Swiss Solvency Test
2
Delta to base
case scenario
The calculation assumes the insurer’s cost of capital of 15%.
10
Notes: *ANREL = €2,433,819
Table 15. Reinsurance vs. Retained Premium
Total Reinsurance Premium
Total Retained Premium
10,297,915
34,771,637
The first most obvious finding of this simulation is that compared to the previous simulations the
insurer achieves the lowest required RSC under Solvency II at the lowest reinsurance cost which
presents a tempting opportunity for the regulatory arbitrage. At the same time, while achieving
the maximum regulatory capital relief at the lowest cost possible, the insurer is compromising on
the quality of its reinsurance protection as shown by a very low RSC/EC ratio of 5.4%. Hence,
the finding demonstrates considerable economic benefits for the insurer of strictly complying
with the Solvency II capital requirements without considering the impact of the reinsurance
program on its economic capital – the company can now retain €34.8 of the premium out of the
total €45.1 written while, at the same time, obtaining an almost complete capital relief.
As opposed to the previous scenario, by substituting a 40% of QS3 reinsurance coverage with the
additional €78 million of XL coverage, the insurer sees its RSC requirements under the SST
increased from €28.4 million to about €40 million, which demonstrates a strong regulatory bias
for QS coverage rather than CAT XL for the purposes of solvency relief.
Scenario 6. No Proportional Cession to QS; XL – €225 m xs €5m (up to TVAR of gross
portfolio)
In this and the following simulation (Scenario 7) we will focus our attention exclusively on the
effect of XL reinsurance on the regulatory solvency requirements under SST. We demonstrate
that the marginal impact of additional layers of XL reinsurance on the company’s regulatory
solvency requirements gets less and less pronounced as we move out over and above the level of
protection required for a 200 year event.
We also show that despite this effect the insurer is considerably economically better off
employing the XL reinsurance coverage rather than QS type treaties or its own capital for
meeting the minimum SST requirements.
As can be seen from Table 16, compared to Scenario 5, in this case the insurer bought €35
million more of XL protection, which results in the reduction of the regulatory solvency capital
under the SST by only about €13 million – clearly a highly disproportionate solvency capital
relief.
Table 16. Regulatory Solvency vs. Economic Capital
Solvency
Capital
Solvency I
Solvency II
6,219,385
2,708,235
Delta to base case
-23.34%
-98.54%
3
EC
35,402,399
RSC/EC
17.6%
7.6%
Depending upon the definition of the event return period, the amount of reinsurance coverage to be afforded under
a 40% QS treaty may vary from €80 million (for a 200 year loss) to €200 million for a 500 year loss.
11
35,402,399
Swiss Solvency Test
Notes: *ANREL=€2,291,764
28,970,896
-86.70%
35,402,399
81.8%
Table 17. Reinsurance Premium vs. Retained Premium
Total Reinsurance Premium
Total Retained Premium
10,517,411
34,552,141
The marginal cost of this capital relief however is rather small – €0.22 million- which compares
rather favorably with the insurer’s own opportunity cost of financing €13 million in regulatory
capital requirements in the absence of the XL risk transfer. Assuming the expected return on
equity of 15%, the insurer would be spending €1.95 million in capital financing costs, which
demonstrates the benefits of substituting the insurer’s own risk capital with reinsurance in the
upper layers of the risk transfer program.
Scenario 7. No Proportional Cession to QS; XL – 455 m xs 5m
In this final simulation, we aim to further emphasize the inherent limitation of the SST which
manifests itself in the unattainable full solvency relief no matter how much of XL reinsurance
one can buy. In this case, the insurer more than doubles the limit of reinsurance protection
acquired under the previous scenario by going from €225 to €455 million of XL protection. With
this level of reinsurance protection, the insurer can comfortably cover itself against any loss that
falls within a 1000 plus return period, e.g. well beyond the probable maximum loss chosen for
our definition of the economic capital (a 500 year event – or €262.7 million loss).
Yet, compared with the previous scenario, under the SST the additional reinsurance €230 million
of reinsurance coverage bought by the company yields it a regulatory capital relief of only
€17.19 million – see Table 18 below. This effect can be attributed to the TVAR measure utilized
by the SST which produces the effect of an ever evading full solvency relief, e.g. the effect of a
cat chasing its own tail. We also observe that since our definition of the economic risk capital has
capped the maximum required at the level of the loss equivalent to a 1 in 500 year event, our EC
and Solvency II RSC requirements have been more than fully satisfied.4
Nevertheless, despite the disproportionately small marginal effect of the additional XL coverage
on the solvency relief under the SST, the insurer may still find it beneficial to buy extra layers of
XL reinsurance coverage at a relatively low cost. For instance, the additional 230 million of
reinsurance coverage would cost the insurer only €0.310 million extra vs. the opportunity cost of
€2.685 million in own risk financing costs to achieve the same relief in solvency margin. Hence,
the practical implication of the above described drawback of the SST measure are rather limited.
Table 18. Required Solvency Capital vs. Economic Capital
Solvency I
Solvency II
Solvency Capital
Delta to base case
EC*
6,163,560.29
2,895,968.98
-24.02%
-98.44%
5.0
5.0
4
SC/EC
123.3%
57.8%
Our calculation of required economic risk returns zero (rather than negative numbers) when the set capital limit is
exceeded.
12
Swiss Solvency Test
11,778,223.45
*Notes: *ANREL = €2,104,031
-94.59%
5.0
235.6%
An interesting paradox is also observed in the change of the solvency margin required under
Solvency II – despite the fact that compared to the previous scenario the insurer now has more
than €200 million of additional reinsurance protection its solvency margin requirement goes up
from €2.708 million to €2.895 million.
Table 19. Reinsurance Premium vs. Retained Premium
Total Reinsurance Premium
Total Retained Premium
10,827,550
34,242,002
Estimating the Impact of Counterparty Credit Risk on Reinsurer’s Solvency
In this Section we consider the impact of counterparty credit risk on the solvency requirements
under the SST and the Solvency II regulations. There are no such requirements under the
Solvency I regulations. The counterparty risk in this case is defined as the risk of reinsurers’
default on their obligations – i.e. a failure to pay reinsurance claims in full to reinsured parties.
Obviously, in case of such a default, the reinsured parties will be faced with reduced reinsurance
recoverables and additional incremental increases in the required risk-based solvency margin –
both of which will lead to the immediate need for more capital. To provide for such adverse
scenarios, the SST and the draft Solvency II regulations5 require insurers to set aside additional
capital related to the credit quality of reinsurers. A brief description of the methodologies used
for computing these credit-risk related charges can be found in Annex I. In this Section we
provide only the outcomes of credit-risk related calculations.
Swiss Solvency Test
Under the SST, the Required Capital for credit-risk related charges varies with the credit rating
of reinsurers in accordance with the following formula:
Required Capital = Exposure * Weighting Factor * 8%
Where
Exposure = Expected annual loss ceded to RI
and the weighting factors for different ratings are presented in Table 20.
Table 20. Reinsurance Credit Risk Weighting Factors
S & P Rating
AAA
AA
5
Weighting Factor
20%
20%
See Technical Specifications for QIS 5 – draft.
13
A
BBB
BB
B
CCC or lower
50%
100%
100%
150%
150%
Based on the above formula and the weighting factors we have obtained the following results –
see Table 21 below.
Table 21. Reinsurers’ Credit Risk Related Solvency Requirements under Solvency II
RI Scenario
1
2
3
4
5
6
7
Exp loss ceded to RI
2,081,619
8,326,475
8,262,208
8,459,956
7,974,274
8,116,330
8,304,063
Required Capital
AA RI
33,306
133,224
132,195
135,359
127,588
129,861
132,865
Required Capital
A RI
83,265
333,059
330,488
338,398
318,971
324,653
332,163
Required
Capital
BBB RI
166,529
666,118
660,977
676,796
637,942
649,306
664,325
As can be seen from the table, in case Scenario 1, the credit risk charges under the SST can add
€0.033 in additional RSC requirements for an AA rated reinsurer to €0.166 million for and BB
rated reinsurer, respectively – a 500% difference! However, if expressed as a percentage of the
total solvency margin required net of credit risk charges, these amounts appear to be rather trivial
– well under 1%.
Solvency II:
Table 22. Reinsurance Credit Risk Related Solvency Requirements (€)
RI Scenario
1
2
3
4
5
6
7
RSC_Crdt,
AA
438,762
1,755,050
1,827,794
2,129,644
2,124,130
2,137,914
2,137,914
RSC_Crdt AA/
RSC_UW
0.30%
4.72%
5.97%
5.17%
55.91%
78.94%
73.82%
RSC_Crdt,
A
980,854
3,923,416
4,086,035
4,760,821
4,748,496
4,779,310
4,779,310
RSC_Crdt, A
/RSC_UW
0.66%
10.56%
13.36%
125.56%
124.99%
176.47%
165.03%
RSC_Credit,
BBB
2,146,356
8,585,422
8,941,273
10,417,875
10,390,904
10,458,333
10,458,333
RSC_Credit,
AA/RSC_UW
1.44%
23.10%
29.23%
274.76%
273.51%
386.17%
361.13%
Table 22 shows that in the case of Solvency II reinsurance related credit risk solvency
requirements can be many times the solvency margin computed without the counterparty credit
risk. For instance, in the case of Scenario 6, we notice that even for an AA rated reinsurer in case
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of a small retention, an insurer would have to put up the additional 79% of original solvency
capital in the form of credit quality related charges. This number goes to 386% in case of a nonrated reinsurer! Such a stringent approach to the counterparty credit risk is likely to considerably
raise the capital costs of insurers seeking reinsurance protection hence pushing them to increase
their own risk retentions or co-insure the risk with their own reinsurance captives located in the
offshore zones.
Conclusions
Based on the presented simulations of reinsurance protection for a given portfolio of catastrophe
risk under three different solvency regimes, we would like to draw the following conclusions:
1. Depending upon a regulatory framework, the same reinsurance protection can result in
very different solvency margin requirements, which creates ample possibilities for
regulatory arbitrage.
2. The upcoming Solvency II regulations appear to significantly underestimate the risk of
extreme events by assuming away all potential losses which fall beyond the 99.5%
confidence level.
3. The Swiss Solvency Test produces more conservative measures of solvency for monoline writers involved in highly volatile lines of business (such as catastrophe risk,
aviation, etc.).
4. At the same time, for portfolios of risk with low frequency high severity characteristics,
the SST does not provide adequate credit for XL reinsurance as it suffers from the ever
diminishing effect of non-proportional reinsurance on the required solvency margin. In
the extreme the SST produces a paradoxical situation for the insurer when the RSC can
no longer be materially reduced by purchasing additional reinsurance.
5. The counterparty credit risk charges contemplated by the draft Solvency II regulations
seem to make reinsurance protection uneconomical if purchased from below investment
grade reinsurers and when the amount of risk transfer many times exceeds the risk
retention. The effect is likely to favor larger insurers capable of retaining more risk and
while co-insuring the rest of the risk with the group captives established in offshore
zones. The latter can in turn reinsure the way they see fit without being penalized with
additional credit risk related charges for risk transfer to third parties.
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