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Diversification and Solvency II: the capital effect of portfolio swaps on non-life insurers

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Diversification plays a pivotal role under the risk-based capital regime of Solvency II. The new rules reward large and well-diversified insurance companies with relatively low capital requirements compared to those of small and specialised nature. To enhance diversification, insurance companies can adjust their strategy by engaging in mergers and acquisitions or new market entries. Alternatively, insurers can accept higher Solvency II capital requirements, displaying a competitive disadvantage and impeding future growth. This research proposes a Solvency II portfolio swap as a new diversification solution that allows small and specialised insurance companies to improve their diversification, and thus, mitigate their diversification disadvantage. The effect of such swaps is demonstrated through the use of two hypothetical insurance companies by swapping 20% of their portfolio over four different scenarios. The swap allowed for a 6% reduction in the Solvency Capital Requirement (SCR) and a maximum increase of the SCR coverage ratio of 17%. With Solvency II posited to stimulate further mergers and acquisitions within the European insurance market, this paper offers an alternative method for insurers to diversify their portfolio. Furthermore, it is suggested that the proposed alternative risk transfer method may improve insurance market competition within the EU by facilitating small and specialised insurers’ competitiveness.
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Vol.:(0123456789)
The Geneva Papers on Risk and Insurance - Issues and Practice
https://doi.org/10.1057/s41288-022-00269-3
Diversification andSolvency II: thecapital effect
ofportfolio swaps onnon‑life insurers
BarrySheehan1 · ChristianHumberg1· DarrenShannon1·
MichaelFortmann2· StefanMaterne2
Received: 17 May 2021 / Accepted: 7 March 2022
© The Author(s) 2022
Abstract
Diversification plays a pivotal role under the risk-based capital regime of Solvency
II. The new rules reward large and well-diversified insurance companies with rela-
tively low capital requirements compared to those of small and specialised nature.
To enhance diversification, insurance companies can adjust their strategy by engag-
ing in mergers and acquisitions or new market entries. Alternatively, insurers can
accept higher Solvency II capital requirements, displaying a competitive disadvan-
tage and impeding future growth. This research proposes a Solvency II portfolio
swap as a new diversification solution that allows small and specialised insurance
companies to improve their diversification, and thus, mitigate their diversification
disadvantage. The effect of such swaps is demonstrated through the use of two hypo-
thetical insurance companies by swapping 20% of their portfolio over four different
scenarios. The swap allowed for a 6% reduction in the Solvency Capital Require-
ment (SCR) and a maximum increase of the SCR coverage ratio of 17%. With Sol-
vency II posited to stimulate further mergers and acquisitions within the European
insurance market, this paper offers an alternative method for insurers to diversify
their portfolio. Furthermore, it is suggested that the proposed alternative risk trans-
fer method may improve insurance market competition within the EU by facilitating
small and specialised insurers’ competitiveness.
Keywords Solvency II· Insurance· Diversification· Alternative risk transfer·
Regulation
* Barry Sheehan
barry.sheehan@ul.ie
1 University ofLimerick, Limerick, Ireland
2 TH Köln University ofApplied Sciences, Köln, Germany
B.Sheehan et al.
Introduction
The implementation of Pan-European insurance regulations, Solvency II, has
changed the regulatory capital requirements regime for insurers from a volume-
based measure to a risk-based approach. The objective of this approach is to bet-
ter reflect the underlying risk profile of an insurer. However, the new rules could
also lead to higher capital requirements. Indeed, under the new rules of Solvency
II, the Quantitative Impact Study 4 (QIS 4) found that non-life insurers face three
to four times higher capital requirements in comparison to Solvency I (Timetric
2016). While diversification plays a pivotal role under the Solvency II regime,
the new rules reward large and well-diversified insurance companies with lower
capital requirements. On the other hand, small and specialised insurers may face
relatively high capital requirements, possibly due to limited or non-existent geo-
graphical or product diversification. Such a diversification disadvantage could
threaten the existenceof these companies. Along with the limitation of diversifi-
cation opportunities, they could become a vulnerable target amongst large insur-
ers looking for investment opportunities to foster growth. This research proposes
a Solvency II portfolio swap as an alternative diversification method allowing
insurers with a high degree of risk concentration to overcome their diversification
disadvantage under the current Solvency II regime. The swap benefits include a
reduction of the Solvency Capital Requirement (SCR), an increase of the Sol-
vency ratio, and a rise of the insurer’s own funds, while simultaneously retaining
the net premium income. Furthermore, through cost-effective diversification, this
research will help small and medium insurers to persist inand contribute to sus-
taining a competitive insurance market for the European Union (EU). The effect
of the Solvency II swap is illustrated using two hypothetical insurance companies
swapping 20% of their insurance risks. For both insurers, the impact on the SCR,
coverage ratio and Solvency II balance sheet is analysed.
The aim of Solvency II is to enhance the resilience of the insurance industry
and improve customer protection (Swain and Swallow 2015). To do so, Solvency
II pursues a holistic risk assessment approach based on three pillars: (1) quantita-
tive requirements, (2) governance and supervision requirements, and (3) disclo-
sure and transparency requirements (Lloyd’s 2010). Within the first pillar, insur-
ance companies are obliged to hold sufficient capital against their risks, which is
referred to as the SCR. The SCR calculation can be conducted through the Stand-
ard Formula or a (partial) internal model (Heep-Altiner etal. 2018). This paper
focuses on a portfolio swap for non-life insurers to enhance their diversification
benefits under the Standard Formula. A functional Microsoft Excel model is pro-
vided in the Supplementary Material presenting how insurers may benefit from
using a Solvency II portfolio swap. This model includes the relevant Solvency II
Standard Formula calculations and can be adapted freely by readers to create and
replicate swap scenarios.
The Standard Formula of Solvency II follows a modular approach in which
the overall risk exposure is divided into different risk modules, each comprised
of submodules (EIOPA 2014). Both the risk modules and submodules are
Diversification andSolvency II: thecapital effect ofportfolio…
aggregated using a correlation matrix. The Standard Formula’s risk modules con-
tain market risk, counterparty default risk, life underwriting risk, health under-
writing risk, non-life underwriting risk and intangible asset risk. For non-life
insurers, the most significant risk module is the non-life underwriting risk, which
amounts to 52.4% of the overall diversified solo Basic Solvency Requirement
(BSCR) (EIOPA 2011). Additionally, diversification effects reduce the non-life
underwriting SCR by 20% on average (EIOPA 2011). Insurers may also decide to
develop an internal model to better reflect the company’s unique risk profile, in
accordance with the European Commission (2015) Delegated Regulation (Arti-
cles 114–127). Partial or full internal models are significantly individualised to
the specific insurer for which it is created (Heep-Altiner etal. 2018). The realised
capital benefits derived from the Solvency II portfolio swap would vary depend-
ing on the methodology taken during internal model development. However, the
Solvency II Standard Formula (Articles 100–110) used in this research provides a
standardised method to measure the risk reduction benefits of the portfolio swaps
between two counterparties in an equivalent manner.
The non-life risk is further divided into premium and reserve risk, catastrophe
risk and lapse risk. The premium and reserve risk covers the risk arising “[…]
from fluctuations in the timing, frequency and severity of insured events” as well
as risk occurring from fluctuations “[…] in the timing and amount of claim set-
tlements” (European Commisson 2009, Article 105a) and has the highest pro-
portion of the risk charge for the non-life module (EIOPA 2011). The non-life
catastrophe risk contains “the risk of loss, or of adverse change in the value of
insurance liabilities, resulting from significant uncertainty of pricing and provi-
sioning assumptions related to extreme or exceptional events” (European Com-
misson 2009, Article 105b). Last, the lapse risk covers risks stemming from the
policyholder’s opportunity to exercise contractually agreed options inter alia pre-
mature contract termination and contract renewal to previously agreed conditions
(European Commisson 2010). However, the lapse risk can be seen as insignificant
as its contribution to overall non-life risk capital charge is less than 1% (EIOPA
2011). Both the catastrophe and the premium and reserve risk are seen as the pri-
mary drivers of the non-life SCR.
Previous research has investigated the determinants of insurer insolvency risk,
methods of efficient insurance portfolio risk allocation and the impact of risk trans-
fer methods on capital requirements. Caporale etal. (2017) highlight that the lines
of business underwritten by general insurance companies and their reinsurance lev-
els are key determinants of insolvency in the U.K. Similarly, Gestel et al. (2007)
investigated the relationship between financial ratios and credit ratings for different
types of insurers. The authors found that different credit rating models were needed
for different insurer business types (non-life, life, composite, reinsurance, financial
guarantors). Nguyen and Vo (2020) also show that European insurers who concen-
trate on insurance as their core business and operate in more mature markets have
a higher solvency level. With risk concentration identified as a key determinant of
insurer insolvency risk, this research article proposes a novel swap innovation for
insurance counterparties to diversify their portfolios, geographically and by business
line.
B.Sheehan et al.
Kim and Hardy (2009) propose a capital allocation methodology based on a
solvency exchange option. Similar to the Solvency II Standard Formula outlined
in European Commisson (2015) Articles 100–110, the proposed method seeks to
adjust capital allocation using a risk-based approach at a line-of-business level.
Specifically, the property insurance line of business was shown to better diversify
with Energy Efficiency Insurances than other financial market instruments such
as weather derivatives (Baltuttis etal. 2020). For large insurance conglomorates,
intra-group transfers of insurance underwriting risk have been shown to be an effec-
tive risk management tool for optimising capital requirements (Asimit etal. 2016).
From a risk transfer perspective, Asimit etal. (2015) describe how to structure an
optimal non-life reinsurance contract under the Solvency II regulatory framework.
The authors find similar optimal reinsurance structures derived from two different
calculation methods of the risk margin. While previous literature has investigated
the potential to optimise insurance portfolio risk under the Solvency II framework,
no previous research has considered insurance portfolio swaps as a mechanism to
achieve this. This is the first paper to evaluate the diversification, risk reduction and
solvency capital effect of two insurance counterparties mutually benefitting from
portfolio swap under the Solvency II regime.
Many practitioners and researchers have predicted that Solvency II could foster
merger and acquisition (M&A) activities across the insurance sector. Stoyanova and
Gründl (2014) provide empirical evidence that Solvency II could evoke a wave of
M&As within the European non-life insurance sector. The authors applied a theoret-
ical model to assess an insurer’s decision to consolidate based on input factors such
as the costs associated with the M&A, the SCR calculation method post-merger,
the riskiness of an insurer’s business, and the size of the merging insurers. Their
findings suggest that through cross-border consolidation, insurance companies could
take advantage of geographic diversification, resulting in an enhanced cost effi-
ciency due to reduced capital requirements. Furthermore, Conning and Company
(1995) (as cited in Cummins and Xie 2008) noted that upon the implementation of
the risk-based capital (RBC) standard in 1994 (a major regulatory change in U.S.
property-liability insurance), the number of M&As spurred due to well-capitalised
insurers acquiring financially vulnerable companies. Likewise, Cummins and Xie
(2008) and Cummins etal. (1999) found that financially vulnerable companies are
more likely to be acquired than insurers with a strong financial recordfor the U.S.
property-liability insurancesectorand U.S. life insurance industry, respectively.
For example, the leading global insurer AXA received approval to acquire the
Bermuda-based specialist insurer, XL Group. According to AXA (2018), the acqui-
sition of XL is expected to reduce XL Group’s SCR by approximately 30%, benefit-
ting AXA Group’s solvency ratio by about 5 to 10 points. Other effects resulting
from the acquisition were cost synergies, revenue synergies and reinsurance syn-
ergies, altogether amounting to approximately USD 400 million pre-tax earnings
per annum. In contrast, a wave of M&A activities in the wake of Solvency II could
be disadvantageous for the European insurance market. Particularly, the disappear-
ance of small and specialised insurers could encourage the formation of only a few
large market participants who thendominate the market and determine prices. Fur-
thermore, these large, well-diversified companies may have a financially stronger
Diversification andSolvency II: thecapital effect ofportfolio…
position but also increase risk, which could promote a higher risk concentration and
ultimately enable the emergence of systemic risk.
Currently, the two leading theories in the literature on the impact of M&As on a
firm’s functioning are the conglomeration hypothesis and the strategic focus hypoth-
esis. Advocates of the conglomeration hypothesis claim diversified firms that oper-
ate in several business lines, or offer a broad product variety, can profit from cost
and revenues scope economies, and therefore achieve better efficiency than spe-
cialised firms (Berger etal. 2000; Liebenberg and Sommer 2008; Cummins etal.
2010; Biener etal. 2016). Cost scope economies can arise from reduced production
costs through the utilisation of shared resources, whereas revenue scope economies
result from ‘one-stop shopping’ customer preferences (Cummins and Xie 2008). In
contrast to the conglomeration hypothesis, advocates of the strategic focus hypoth-
esis emphasise the benefits of specialisation (Berger etal. 2000; Cummins and Nini
2002; Liebenberg and Sommer 2008; Cummins etal. 2010). According to this the-
ory, concentrating on the main business and core competencies is value-maximising
for firms.
Utilising the concept of profit scope economies, Berger etal. (2000) sought to
contrast the relative efficiency between diversified and specialised insurers in the
U.S. during the period between 1988 and 1992. Their work defined insurers con-
ducting business in both property-liability (P–L) and life-health (L–H) insurance as
diversified, while those operating in only one segment were labelled as specialists.
The results were mixed and dependent on the type of firm. For large insurers that
specialised in offering personal lines, the conglomeration hypothesis dominated.
In contrast, forsmall insurers specialised in offering commercial lines, the strate-
gic focus hypothesis is deemed more appropriate. Similarly, Cummins etal. (2010),
analysed the economies of scope for the U.S. insurance sector between 1993 and
2006. Their research compared insurers providing both P–L and L–H insurance with
those specialising in either one of these segments (P–L or L–H). Opposite to Berger
etal. (2000), their findings suggest no robust support for scope economies. Hence,
Cummins etal. (2010) conclude that insurers specialising in only one insurance seg-
ment (P–L or L–H) are superior to companies pursuing a strategy of diversification,
which is consistent with the strategic focus hypothesis.
While the aforementioned studies of Berger etal. (2000) and Cummins et al.
(2010) investigated the difference between P–L and L–H insurers, several stud-
ies have focused specifically on diversification effects within the property-liability
insurance market. Using a sample of 914 property-liability insurers between 1995
and 2004, Liebenberg and Sommer (2008) examined the impact of line-of-business
diversification on insurers’ performance. Their results demonstrated a diversification
penalty of 1% of return on assets (ROA), or 2% of return on equity (ROE), indicat-
ing that non-diversified insurers outperform those of adiversified nature. Further-
more, using a sample of 718 U.S. property-liability insurers between 1994 and 2002,
Elango etal. (2008) found that geographic diversification affected the relationship
between product diversification and firm performance. Their results indicated that
inefficiencies tend to outweigh any prospect synergies; thus, high levels of diversi-
fication across both geography and products is disadvantageous with respect to the
B.Sheehan et al.
insurer’s performance. Firms showed the best performance results with high product
diversification and modest geographical diversification.
In agreement with Elango et al. (2008), Shim (2011) found that higher prod-
uct diversification for insurers seems to be associated with lower financial perfor-
mance, indicating that additional diversification costs outweigh any possible syn-
ergy effects. Using a sample of U.S. property-liability insurers over a 15-year period
(1989–2004), Shim (2011) provided empirical evidence that the financial perfor-
mance of the acquiring insurer decreased while its earnings volatility increased dur-
ing the post-merger integration time. With respect to cost efficiency, Luhnen (2009)
analysed the productivity of 295 companies intheGerman property-liability insur-
ance industry between 1995 and 2006. They labelled specialised insurers as those
gaining more than twothirds of their annual premium income in one line of busi-
ness. Their results indicated that specialised insurers were superior to diversified
insurers that spread their business across various lines of business. Furthermore,
Luhnen’s (2009) results revealed that, in Germany, 90% of the large and 75% of the
medium-sized property-liability insurers operate under decreasing returns to scale
(DRS). This indicated that further growth (e.g. through M&As) would not improve
these insurers’ efficiency.
Apart from the impact of M&As on the efficiency of insurers, another area of
concern is their effect on the financial stability of the insurance market. A wave of
M&As could lead to an increase in insurance market concentration and leadtowards
a market with only a few large insurers. Among the existing literature, two contra-
dicting hypotheses regarding the effect of market concentration have evolved: the
concentration-stability view and the concentration-fragility view (Beck etal. 2006;
Uhde and Heimeshoff 2009; Shim 2017). The concentration-stability view empha-
sises the benefits of market concentration, arguing that higher market concentration
is allied with enhanced financial stability (Shim 2017). On the other hand, the con-
centration-fragility view suggests that market concentration is negatively related to
financial stability (Shim 2017). Most of the literature focuses on the banking sector,
however, withstudies explicitly targeting the insurance industry being limited.
Shim (2017) scrutinises the relationship between market concentration and finan-
cial stability of insurance companies and argues in agreement with the concentra-
tion-fragility view. Using a sample of U.S. property-liability insurers between 1992
and 2010, Shim (2017) applied a Z-score as a proxy measure for financial stabil-
ity and the industry Herfindahl index to replicate market concentration. The results
demonstrated a negative relationship between market concentration and financial
stability or, in other words, higher market concentration was linked to lower finan-
cial stability. The results of Shim (2017) are in line with the findings of Altuntas
and Rauch (2017), who investigated the impact of concentration on an insurer’s
financial stability using regression analysis. Their sample comprised 14,402 firm-
years of property-liability insurers in 29 countries between 2004 and 2012. Altun-
tas and Rauch (2017) provided empirical evidence for the concentration-fragility
view. In contrast to Shim (2017) and Altuntas and Rauch (2017), who focused on
the relationship between risk concentration and financial stability on a broader
scale, Mühlnickel and Weiß (2015) examine the contribution of consolidation in the
insurance industry, specifically to systemic risk. Their study comprised 394M&As
Diversification andSolvency II: thecapital effect ofportfolio…
with transaction volumes of at least USD50 million, or purchased stakes of 50%
or higher. Their results indicated a strong positive relationship between consolida-
tion and moderate systemic risk, and they conclude that insurance mergers can cause
destabilisation in the insurance and banking industries.
Past research, as demonstrated above, explores the potential effects of M&As on
the insurance industry, as well as emphasises the benefits of specialised insurers for
the industry. Insurers seek to use their capital in the most efficient way; however,
with the current Solvency II regime in place, small and specialised insurers are at a
disadvantage. These companies are being penalised by capital charges due to miss-
ing or limited diversification. To manage their capital, insurers can use special forms
of reinsurance, such as structured reinsurance, or engage in M&As. Swaps can also
bean effective alternative to reinsurance or M&As. Swaps are an agreement between
two counterparties to exchange cash flows of an underlying asset (Liebwein 2009).
Since the first swap agreement between IBM and the World Bank in 1981 (Smith
etal. 1988), financial swaps have grown in popularity as a tool for market partici-
pants to manage financial market turbulence and increasing volatility (Takeda 2002).
In addition to financial swaps, there is also the opportunity to exchange insurance
risks through so-called risk swaps – a financial instrument enabling the exchange
of two (one-on-one risk swap) or more insurance risks (multi-risk-swap) (Takeda
2002). In a risk swap, two insurers agree to exchange the cash flows of an insurance
portfolio serving as the underlying asset (Liebwein 2009). For example, two insur-
ance companies, one located in Ireland and one located in Germany, can agree to
exchange 20% of each other’s motor insurance portfolio (including premiums and
future claims). In principle, such an exchange is comparable to the concept of reci-
procity (Swiss Re 1996; Kielholz and Durrer 1997), which dates back to 1881 when
reciprocal reinsurance arrangements were first used (Norgaard 1964). In reciprocal
reinsurance agreements, the cedent obtains insurance risk (usually a similar propor-
tion) from its reinsurer in return for its cession (Carter etal. 2000).
With risk swaps, both entities can swap their overexposure (or at least a part of
it) against another risk class not contained in their portfolio prior to the swap. This
allows diversification effects of multi-dimensional scope, and thus enables a more
efficient portfolio of insurance risks (Grandi and Müller 1999). According to Takeda
(2002), risk swaps must be clearly defined and quantified to be on a parity condition,
meaning both sides of the swap have the same expected loss. Although they do not
necessarily have to be designed on a parity basis, it is advantageous as no exchange
of money is required (Cummins 2008; Njegomir and Maksimović 2009). In the past,
risk swaps were mainly associated with catastrophe exposures. For example, in 2010
Tokio Marine and State Farm exchanged Tokyo earthquake exposure against Madrid
earthquake exposure, each worth USD200 million (Takeda 2002). At an insurance
group level, intra-group transfers have been shown to optimise the risk position
while reducing the technical provisions and capital requirements for the entire con-
glomerate (Asimit etal. 2016). Similar to the proposed portfolio swaps, these intra-
group transfers utilise proportional risk transfers. However, to achieve optimal insur-
ance risk diversification, the risk management tool is shown to be most beneficial to
large insurance groups. This research article extends this concept to small insurers
B.Sheehan et al.
who may achieve risk diversification through Solvency II portfolio swaps with an
insurance counterparty.
Currently, under the Solvency II regime, risk swaps have the potential to serve
as an effective instrument for small and specialised insurers in managing their risk
capital. As specialised insurance companies tend to outperform insurers of a more
diversified nature, the Solvency II swap provides a useful diversification solution
for such insurers. By exchanging a specific amount of insurance risks, specialised
insurers could enhance their risk diversification while avoiding an acquisition or a
new market entry. In theory, the swap enables them to synthesise the efficiency of
specialised insurers with the lower capital requirements of adiversified insurance
company.
This research proposes Solvency II portfolio swaps as an alternative diversifica-
tion method for small and specialised insurance companies. These Solvency II port-
folio swaps would enable these companies to benefit from geographical or product
diversification under the Standard Formula of Solvency II and, as a consequence,
reduce their SCR. Furthermore, such a swap will contribute to sustaining a com-
petitive insurance market for the EU. A key differentiator between M&As and Sol-
vency II portfolio swaps as a tool for non-life insurance portfolio diversification is
the exchange of equity. Portfolio swaps do not involve real equity transfer between
insurers. The swaps represent a strategic alliance between two insurance counterpar-
ties who may mutually benefit from exchanging insurance risks.
The remainder of the paper is organised as follows. First, we introduce the meth-
odology, including the structure of the Solvency II portfolio swap, the different sce-
narios conducted, and the data used. The subsequent section presents the results of
the Solvency II portfolio swap. The Discussion and Conclusion sections outline the
swap’s impact and implications for the European insurance industry, and provide a
proposal for future research.
Research methodology
This research proposes a Solvency II portfolio swap to optimise primary insurers’
capital efficiency through enhanced diversification. The purpose of the swap is to
provide primary insurers with a tool to diversify their portfolio and reduce their
SCR, while also maintaining their net premium earned. The Solvency II swap was
constructed as a reciprocal exchange of insurance risk between two insurance com-
panies (see Fig.1).
Fig. 1 Solvency II swap
Diversification andSolvency II: thecapital effect ofportfolio…
To analyse the swap effect, we established two hypothetical insurance companies
that swapped a predefined proportion of their insurance portfolio in four different
scenarios. In order to broaden the generality of the resulting portfolio swap benefits,
this research details four scenarios, which reflect all methods an insurer may use to
diversify their non-life insurance risk and optimise their portfolio through geograph-
ical diversification and line-of-business diversification. The four scenarios illustrate
the diversification benefits of portfolio swaps on single-line/multi-line insurers in
thesame/different geographical regions.
The first scenario comprises an Irish and German insurer in which the Irish insur-
er’s exposure consisted of property insurance only (referring to line of business no.4
in Annex I, European Commisson 2015), while the portfolio of the German insurer
solely comprised motor insurance risks (referring to line of business no.7 in Annex
I, European Commisson 2015) (see Table1). The proportion swapped between the
two counterparties amounted to 20% of their portfolio. This threshold was chosen
based on the ‘80/20’ rule, limiting inwards reinsurance to 20% of gross net pre-
miums for Irish insurers. Although the Central Bank of Ireland removed the 20%
limitation on inwards reinsurance, insurers that seek to exceed the 20% threshold
are obliged to submit a business plan that requires approval from the central bank
(Central Bank of Ireland 2010). Furthermore, we assumed the swap to be set up
on a funds-witheld basis to mitigate the counterparty default risk (Bank of England
2016). In a funds-withheld agreement, all or a specified share of the ceded premium
remains at the cedent as collateral against future obligations against the reinsurer
(Hayes etal. 2011). In this swap, the collateral is equal to the exposure for the coun-
terparty default calculation; therefore, there is no increase in the capital requirement
for the counterparty default risk. In order to assess the impact of the swap on the two
insurers under the current Solvency II regime, the Standard Formula was modelled
in Excel. To gain a clearer understanding of the effect of the Solvency II swap, we
also illustrated its impact for the premium and reserve risk module as well as the
catastrophe risk module hereinafter.
According to the European Commisson (2015), the capital charge for the pre-
mium and reserve risk is calculated as follows:
where
𝜎nl
refers to the combined standard deviation for the non-life premium and
reserve risk and
Vnl
refers to the volume measure for the non-life premium and
reserve risk. The volume measure Vnl is calculated as the sum of the volume meas-
ures for each line of business Vs with
DIVs displays the factor for geographical diversification within each line of business
and allows for a diversification effect up to 25%. In order to quantify the diversifica-
tion effect, the Herfindahl index is used (European Commisson 2015, Annex III).
This is defined as the sum of the squared volume measures for the premium and
reserve risk for each geographical region relative to the squared sum of the overall
line of business volume measure (Hürlimann 2009). Within Europe, the Standard
SCRpre
&
res =3
𝜎
nl Vnl
Vs=(Vprem
,
s+Vres
,
s)×(0.75 +0.25 ×DIVs).
B.Sheehan et al.
Table 1 Input data scenario 1
Counterparty details Counterparty 1 Counterparty 2
Name of Entity Irish property insurer German motor insurer
Geographic exposurecountry Ireland Germany
Geographic exposureregion Northern Europe Western Europe
Loss ratio 80% 80%
Combined ratio 95% 95%
SCR ratio as reported 165% 165%
Non-life premium & reserve risk submodule V prem V res V prem V res
Motor liability insurance** 0 0 200,000 200,000
Other motor insurance and proportional reinsurance** 0 0 0 0
Marine, aviation and transport insurance** 0 0 0 0
Fire and other damage to property insurance** 200,000 200.000 0 0
Sum 200,000 200.000 200,000 200,000
Non-Life catastrophe risk submodule
SCR Cat 55,000 55,000
Non-life lapse risk submodule
SCR lapse 1000 1000
Market risk submodule
SCR market 45,000 45,000
Life risk submodule
SCR life 0 0
Health risk submodule
SCR health 0 0
Intangible assets risk submodule
SCR intangible asset 1000 1000
Operational risk submodule
SCR operational risk 6000 6000
Diversification andSolvency II: thecapital effect ofportfolio…
Table 1 (continued)
Counterparty details Counterparty 1 Counterparty 2
Adjustment submodule
SCR adjustments 38,000 38,000
*All figures in EURthousand
**And proportional reinsurance
B.Sheehan et al.
Formula allows insurers to diversify their business across four geographic regions:
Northern, Western, Eastern and Southern Europe (European Commisson 2015,
Annex III). The combined standard deviation (
𝜎nl
) for the premium and reserve
risk follows a two-stepprocedure. For each line of business, the Standard Formula
defines one standard deviation for the premium risk (
𝜎prem
) and one for the reserve
risk (
𝜎res
), which are then aggregated to a combined standard deviation per insur-
ance segment. Using a given correlation matrix, all line of business standard devia-
tions are aggregated to the overall standard deviation (
𝜎nl
) for the non-life premium
and reserve risk (European Commisson 2015, Annex IV), which allows for diversifi-
cation across business lines.
In scenario one, the volume measure for the premium and reserve risk was
equally weighted for both insurers and consisted of EUR200 million for boththe
premium risk and reserve risk, respectively (see Table1). The Solvency II swap
enabled both insurers to exchange 20% of their premium exposure while their
reserve volume was not affected. Prior to the swap, the Irish insurer had EUR200
million Northern European property exposure, whereas the German insurer held
EUR200 million Western European motor exposure. As the swap was set as 20%
of the premium exposure, the notional amount swapped consisted of EUR 40
million. After the swap, the Irish insurer’s Northern European property expo-
sure reduced to EUR160 million and itsimultaneously received EUR40 million
Western European motor exposure. The German insurer held EUR160 million
Western European motor exposure and EUR40 million property exposure post-
swap. Regarding the volume of the premium and reserve risk, both counterparties
had the same exposure pre- and post-swap; however, the swap allowed the insur-
ers to diversify their exposure through different lines of business. Geographical
diversification only occurs at the line-of-business level (i.e. swapped portfolios
must be the same line of business originating in different regions), making geo-
graphical diversification benefits unachievable in this scenario.
The catastrophe risk module for non-life insurers comprises natural catastro-
phes and man-made catastrophes (European Commisson 2015). The Standard For-
mula provides a scenario-based and a factor-based approach to calculate the capital
charge. This research uses the scenario-based calculation. Furthermore, man-made
catastrophe risk is excluded from our calculation. This simplification allowed for a
better illustration, as the non-life underwriting risk module and especially the catas-
trophe risk submodule was subject to criticism due to its high complexity (EIOPA
2011).
Natural catastrophe risk contains five perils: windstorm risk, earthquake risk,
flood risk, hail risk and subsidence risk (only for France) (European Commisson
2015). For each of these perils, a capital charge is calculated at the country level
(Ehrlich and Kuschel 2011). Thereby, the sums insured serve as a volume measure,
which are multiplied with a given risk factor. Additionally, the Standard Formula
defines specific scenarios in which the capital requirement equals the larger of the
sequence of two events. Using a correlation matrix, the countries’ capital require-
ments are aggregated to the overall capital charge for each peril. Finally, the natu-
ral catastrophe risk submodule is determined as the root of the sum of each peril’s
squared capital requirements (European Commisson 2015).
Diversification andSolvency II: thecapital effect ofportfolio…
Due to the nature of the catastrophe risk module, the Irish insurer was exposed to
windstorm risk in Ireland, while the German insurer was subject to exposure for flood
and hail risk in Germany. Following a 20% swap, the Irish and German insurer reduced
their windstorm risk and flood and hail risk, respectively, to 80% of their initial expo-
sure and simultaneously assumed 20% of their counterparty’s risk. Consequently, both
insurers were exposed to windstorm, flood and hail risk, with the Irish insurer’s major
exposure being windstorm and the German insurer’s flood and hail risk. The swap
allowed for diversification via different perils because, under the Standard Formula,
both property (windstorm for Ireland) and motor (flood and hail for Germany) business
cover different perils. In order to additionally diversify across geographic areas within
the catastrophe risk module, both counterparties needed to hold exposure of the same
peril (e.g. a German and Irish insurer with windstorm exposure).
Apart from scenario one, we conducted three additional scenarios, all of which
followed the aforementioned methodology. For the second scenario, we conducted
a swap between an Irish property and a German property insurer (Table4, Appen-
dix A), controlling for geographical diversification. Scenario three examined Irish
and German diversified insurers, with both holding an equally weighted portfolio of
insurance risks (Table7, Appendix B). Within this scenario, business line and geo-
graphical diversification benefits can be achieved. Last, scenario four investigated
the impact of the swap between two German insurance companies, one only with
property and one only with motor exposure (Table10, Appendix C). The under-
writing risks investigated in the study are derived from the non-life line of business
segments as defined in Annex I to Delegated Regulation (E.U.) 2015/35. The inclu-
sion of other segments, for example marine, aviation and transport insurance, would
change the standard deviations included for non-life premium and reserve risk used
to calculate the SCR, resulting in alternative risk-based SCR reductions (European
Commisson 2015).
The data used to calculate the SCR ratio was based on the QIS 5 (EIOPA
2011). According to this study, the average insurer has an SCR ratio of 165%,
which served as the pre-swap SCR in this research. Furthermore, to assess the
swap’s impact on each counterparty’s Solvency II balance sheets, we compiled
a balance sheet based on the average QIS 5 solo insurer. Overall, the QIS 5
study comprised data of 2,520 insurance companies, of which 1,284 were non-
life insurers. Of the non-life insurers, only 72 were classified as large compa-
nies (> EUR 1 billion gross written premiums), 378 were considered medium
(EUR0.1billion – 1 billion gross written premiums), and 834 were labelled as
small (< EUR 0.1billion gross written premiums) (EIOPA 2011). As small and
medium-sized insurers were our target group, the QIS 5 served as a comprehen-
sive data set for our research.
Results
Table 2 summarises the Solvency II portfolio swap results for scenario one in
which Irish property risk was exchanged against German motor risk. Prior to the
swap, the combined ratio for both counterparties was set at 95%. Consequently,
B.Sheehan et al.
there was no change in the combined ratio post-swap. A capital reduction of 4.2%
is observed for the Irish property insurer and 6.0% for the German motor insurer,
resulting in a total amount of EUR8 million and EUR11 million, respectively.
Figure2 illustrates the capital relief decomposed into the various risk modules
of the Standard Formula. For each module, the capital requirement pre- and post-
swap and the percentage share of the capital relief are highlighted. A functional
Microsoft Excel model is provided in the Supplementary Material illustrating the
portfolio swap scenario one. This model includes the relevant Solvency II Stand-
ard Formula calculations and can be adapted freely by readers to replicate each
swap scenario. Furthermore, the detailed calculation of the impact of the Sol-
vency II portfolio swap on the premium and reserve underwriting risk for both
insurance counterparties in scenario 1 is provided in Appendix D. For a detailed
Table 2 Swap summary scenario 1
Company name Counterparty 1 Counterparty 2
Irish property insurer German motor insurer
Geographic region Northern Europe Western Europe
Life / non-life Non-life Non-life
Line of business Property Motor
Premium volume 200m 200m
Reserve volume 200m 200m
Combined ratio % 95% 95%
SCR (pre-swap) 183m 185m
Combined ratio % (post-swap) 95% 95%
SCR (post-swap) 176m 174M
Capital relief from swap 8m 11m
Portfolio swap % 20% 20%
Portfolio swap notional EUR 40m 40m
20%
20%
40MM
183176 €40MM185174
660311418383662319318383
-32-31 -3 2-31
171163 173161
45 45 12 12 00 00113105 11 45 45 12 12 00 00115103 11
-29-26 -2 9-25
142131 144128
85,9 82,8 55 47 11 88,4 82,7 55 45 11
Swap Details
Module Title
SCR Pre-Swap
(€MM)
SCR Post-
Swap (€MM)
0% 0%
SCR_op
rerusnI rotoM namreGrerusnI ytreporP hsirI
Swap Details
SCR_intangibleSCR_market SCR_default
SCR
% Change
SCR Pre-
Swap (€MM)
SCR Post-
Swap (€MM)
Module Title
% Change
-6%-19
%-4%-15% egnahC %%0
% Change
-6%-8%-7%
-10%
SCR_health SCR_nonlife
SCR_op
Key
RCSBjdA
Key
SCR_intangibleSCR_market SCR_defaultSCR_life
Adj
Diversificaon
Sum of SCRs
SCR_life
-11%
Diversificaon
-4%-5%-5%
-8%
SCR_nonlife
Diversificaon
Sum of SCRs
-7%
SCR_health
SCR
BSCR
Diversificaon
Sum of SCRs
Sum of SCRs
Premium & Reserve
CatLap se
Premium & Reserve
Ca
apse
Fig. 2 Capital relief decomposed by risk modules for scenario 1
Diversification andSolvency II: thecapital effect ofportfolio…
description of SCR calculation using the Standard Formula, readers are referred
to European Commission (2015) Delegated Regulation (Articles 100–110).
The swap reduced the Irish insurer’s capital requirement by 3.6% for premium
and reserve risk (85.9 million to 82.8 million) and by 14.8% for catastrophe risk
(55.0 million to 47.0 million). In contrast, for the German insurer, the premium and
reserve risk decreased by 6.5% (88.4 million to 82.7 million) and catastrophe risk
decreased by 18.8% (55.0 million to 45.0 million) through the swap. Both coun-
terparties experienced no change in lapse risk. The non-life SCR results from the
aggregation of premium and reserve risk, catastrophe risk and lapse under consider-
ation of predefined correlations (European Commisson 2015). Regarding theswap’s
impact on the non-life SCR, a 7.2% decrease is observed for the Irish insurer and
a 10.3% reduction for the German insurer. With respect to the Solvency II balance
sheet, own funds increased by 4.4% and 3.5% for the Irish property insurer and Ger-
man motor insurer, respectively, while the Solvency ratio rose by 15% and 17%,
respectively (Fig.3, Table3).
The results for scenario two (Irish property and German property insurer) showed
a capital reduction of 4.6% for the Irish property insurer and 4.8% for the Germany
property insurer and an increase in the Solvency ratio of 14% and 15%, respectively
(Appendix A). Scenario three (Irish diversified vs. German diversified insurer) illus-
trates a reduced capital requirement of 3.7% for the Irish diversified insurer and
5.3% for the German diversified insurer, while the coverage ratio increased, respec-
tively, by 12% and 17% (Appendix B). In scenario four (German property vs. Ger-
man motor insurer) the Germany property insurer’s capital reduced by 1.8% and its
solvency ratio increased by 7%, while the German motor insurer experienced a 3.9%
lower capital requirement and 10% higher coverage ratio (Appendix C). Detailed
information for scenarios two to four, such as the decomposed capital relief per risk
module and the balance sheet impact, are illustrated in their respective appendices.
Table 3 Solvency II balance sheet impact (pre- and post-swap) for scenario 1
*Excluding liabilities subordinates
Company name Counterparty 1 Counterparty 2
Irish property
insurer
Swap estimated
impact
German motor
insurer
Swap
estimated
impact
Total assets 2,387m 2,387m 2,415m 2,415m
Best estimate (non-life) 1,606m -4M 1,624M 4M
Risk margin (non-life) 136m -9.8m 138m -14.2m
Other liabilities* 343m 347m
Total liabilities 2,085m 2,072m 2,109m 2,098m
Assets less éiabilities 302m 316m 306m 316m
Subordinated liabilities 0m 0m 0m 0m
Total basic own funds 302m 316m 306m 316m
Solvency Capital Requirement 183m 176m 185m 174M
Solvency ratio 165% 180% 165% 182%
B.Sheehan et al.
Discussion
This research provides an alternative diversification method that allows insurers
to improve their capital efficiency under the current Solvency II regulation, par-
ticularly those of small and specialised nature. The operation and effect of the
swap using two hypothetical insurance companies is demonstrated by swapping
20% of their insurance portfolio. The swap’s impact on various Solvency II risk
modules, the SCR, coverage ratio and balance sheet is illustrated for four differ-
ent scenarios. In this section, the key findings of this research are summarised,
implications for the insurance market are explored, and limitations are discussed.
Furthermore, directions for future research are suggested.
The ex-ante diversification benefits derived from the portfolio swap are dem-
onstrated through the relative reduction in SCR using the Solvency II predefined
Standard Formula. This risk-based computation provides a standardised, equiva-
lent and industry-endorsed method for comparing the relative risk reductions of
two insurance counterparties resulting from a portfolio swap. Indeed, insurance
companies may use full or partial internal models to determine their specific
SCR. These alternative models may enhance or weaken the capital effect of the
diversification benefits from portfolio swaps, depending on the approach (Heep-
Altiner etal. 2018). However, QIS5 showed that SCR results derived from an
internal model were very close to the SCR calculated using the Standard Formula
at the individual insurer level (EIOPA 2011).
Overall, the results show that for all scenarios conducted, both insurers
improved their capital efficiency through the utilisation of geographic or business
line diversification, or through a combination of both. The reduction of the capi-
tal requirement ranged from 3.7% and 6.0% over all scenarios, with the exception
of scenario four (German property vs German motor insurer), in which one coun-
terparty only achieved a 1.8% decrease. The study finds that the swap achieves
the best economic results for single line insurers operating in different Solvency
II regions (e.g. Northern and Western Europe (scenarios two and three). Further-
more, the swap results indicate that for insurers diversified through various busi-
ness lines, the economic benefit is slightly less than for non-diversified insurers.
The increase in basic own funds varied between 1.7% and 4.5%, whereas the SCR
coverage ratios increasedby between 7% and 17% post-swap across all scenarios.
Additionally, for both scenarios one (Irish property and German motor insurer)
and four (German property and German motor insurer), the swap was more ben-
eficial for the motor insurer due to the lower volatility of the property business.
Within the Standard Formula, the adjusted standard deviation for the premium
risk is 6.4% for property business and 8% for motor business (European Commis-
son 2015, Annex II). Similar differences can be seen when looking at the differ-
ent perils within the natural catastrophe risk module. For flood and hail risk, the
initial motor exposure is adjusted by a factor of1.5 and 5, respectively, whereas
there is no adjustment for the initial property exposure (European Commisson
2015). Therefore, by swapping motor exposure for property exposure, the motor
insurer cedes a certain proportion of risk requiring a higher capital charge while
Diversification andSolvency II: thecapital effect ofportfolio…
simultaneously assuming the same proportion of risk requiring a lower capital
charge. However, the capital efficiency also improved for the property insurer
post-swap as enhanced diversification outweighed the slightly higher capital
charge for the assumed motor exposure. Additionally, it should be noted that both
portfolios were equally profitable with a combined ratio of 95%.
The results of the Solvency II swap indicate a performance-enhancing effect on
insurers’ solvency, especially the SCR, coverage ratio and own funds. Insurance
companies with a high degree of risk concentration could use our swap to enhance
their diversification under the Standard Formula and thus reduce their solvency cap-
ital requirements. Although diversification is not the only factor driving an insurer’s
capital requirements, the British insurer Esure is an exemplar of the critical role of
diversification. In 2015, under Solvency I, the coverage ratio for Esure was 390%,
but it declined to 123% under Solvency II (Esure 2016). According to Fitch (2016),
this was mainly driven by Esure’s low diversified business profile (83% of its premi-
ums came from itsU.K. motor insurance portfolio) and only in part from their credit
risk (approximately 10% investments in non-investment grade bonds).
The proposed portfolio swaps reflect, in principle, the diversification benefits
derived from long-established reciprocal insurance (Carter et al. 2000) and risk
swaps (Takeda 2002). Previously, insurers who engage in these exchanges seek to
benefit, ex-post, from gaining a more efficient portfolio of insurance risks. However,
this diversified risk allocation is now also reflected in lower risk-based Solvency II
capital requirements. Therefore, the benefits of insurance portfolio diversification
may be determined ex-ante, showcasing the potential for portfolio swaps and other
risk exchange mechanisms to spread risk concentration and, thereby improve market
competition and stability.
Alternatively, insurers could diversify their portfolios by entering new markets
or even by acquiring another insurer. While both alternatives aredeemed appropri-
ate for large insurance companies, they may not be feasible for small and special-
ised insurers. Reasons for this may include a lack of knowledge that hinders entry
into new and unknown markets, the high costs of an acquisition, and the uncertainty
aroundas well as the long-term impact of such a decision. Furthermore, a wave of
M&As within the European insurance sector could be negative as such a develop-
ment, in which smaller insurers are acquired by large insurers, would ultimately
strengthen large insurers’ market power and reduce competition. As noted by Takeda
(2002), the great advantage of risk swaps is that they reduce risk while keeping its
cost at a minimum. Thus, the Solvency II swap provides an alternative diversifica-
tion method that allows small and specialised insurance companies to overcome
their diversification disadvantage at relatively low costs and enable them to prosper.
By doing so, the swap also promotes a competitive EU insurance market.
Theoretically, the swap works; however, a disadvantage of such reciprocal rein-
surance agreements is the possibility that the insurance risks ceded between the
counterparties are different in their profitability. This research took the assumption
that the risks ceded were equally profitable with a combined ratio of 95%, meaning
both counterparties had the same expected loss. In practice, it is most likely that two
insurers that are willing to conduct such a swap hold portfolios of different prof-
itability, e.g. one portfolio has a combined ratio of 96% and the other portfolio’s
B.Sheehan et al.
combined ratio is 98%. In such a scenario, one company would benefit more than
the other. Carter etal. (2000) argue that in such a case the agreement is highly likely
to be terminated within a short time. Further, if the economic results of one portfolio
are negative and the other positive, one counterparty would worsen their economic
result. In the worst case, this could even turn a profit into a loss, which might hinder
insurers from engaging in such swap activities. Other difficulties can be seen in find-
ing an appropriate counterparty that also holds a low diversified portfolio and the
uncertainty of the counterparty’s underwriting quality. While the Solvency II swap
provides an attractive diversification method, it also contains a certain degree of risk
and uncertainty, which needs to be addressed.
Given the nature of the proposed Solvency II portfolio swap, the insurance risk
reduction on each counterparty’s portfolio is reflected in a lower SCR. This innova-
tion is derived from the European regulatory capital requirements regime for insur-
ers changing from a volume-based measure to a risk-based framework. Indeed, the
portfolio swap benefits from the risk-based SCR computation, but it does not benefit
from capital arbitrage in the structure presented. Capital arbitrage opportunities have
been demonstrated with tail risk transfers between lighter (value-at-risk-based) and
stricter (expected-shortfall-based) regulatory regimes (Asimit et al., 2013). How-
ever, the proposed portfolio swap does not exploit mispricing since the common
Standard Formula is used to determine the SCR before and after the swap to deter-
mine the risk reduction. Furthermore, the portfolio swap does not benefit from regu-
latory arbitrage as the explicit capital and risk reductions are only clear for insurers
within the Solvency II regulatory framework.
The implementation of a profit-based commission could help to overcome the
hindrance of unequally profitable portfolios. In such a case, the counterparty with
the lower profitability would compensate the other through the payment of an
appropriate amount of money. The appropriate compensation would be the amount
of money at which both insurers have the same profitability in their portfolios. In
order to calculate the commission, the combined ratios of both counterparties, the
notional amount swapped, and the current interest rate should be considered. By
doing this, insurance portfolios with different profitability would be aligned, so
that both insurers are at parity. This paper did not demonstrate this in the swap,
as we had attempted to keep the swap at its most basic level to truly understand its
impact. Future studies should consider the complexities that might be included in
the model.
Conclusion
This research proposes a diversification method that can be used by primary insurers
to improve their portfolio diversification and enhance their capital efficiency. While
risk swaps have been used within the insurance industry, mainly for catastrophe risk,
we showed how the concept of swaps could be used by insurers as a capital manage-
ment tool under the Solvency II regime. Using two hypothetical insurance compa-
nies swapping 20% of their insurance risk, the impact of the Solvency II swap is
Diversification andSolvency II: thecapital effect ofportfolio…
illustrated across four different scenarios. The scenarios included separate diversifi-
cation through geographical area or business line, as well as a combination of both.
The results showed a positive impact on insurers’ financial performance for all four
scenarios conducted, including an SCR reduction ofup to 6%. Furthermore, all sce-
narios showed an increase in insurers’ solvency coverage and own funds.
With the presented research, insurers can use the swap to enhance their diversi-
fication under the Standard Formula. By exchanging a specific amount of insurance
risks, insurers could enhance their risk diversification while avoiding an acquisi-
tion or a new market entry. More predominantly, small organisations could use it
as a new method to offset diversification disadvantages that exist for them under
Solvency II at relatively low cost. Specialised insurance companies tend to outper-
form insurers of a more diversified nature. In theory, the swap enables the synthesis
ofthe benefits of a specialised insurer with those ofa diversified company. However,
companies should consider their organisational strategy and choose a diversification
method that aligns with their business model. To fully understand the benefits, com-
panies could use internal data and examine the impact specific to their company, and
then compare the results to their current reinsurance solution.
The research findings indicate that the swap is an effective method for smaller
insurance companies to avoid the diversification disadvantages of Solvency II.
Although some limitations exist and additional features are needed for the swap
to be more efficient, it provides a new diversification solution. It is clear that the
Solvency II portfolio swap and other methods of diversification need to be further
explored within the Solvency II literature. The initiation of Solvency II regulations
allows space for financial innovation by allowing insurers to alleviate their geo-
graphical or product offering concentrations through the use of a Solvency II portfo-
lio swap (Fig.4).
Appendix A: Irish property insurer vs. German property insurer
See Tables4, 5, 6, and Fig.4 and 5.
B.Sheehan et al.
Table 4 Input data scenario 2
Counterparty details Counterparty 1 Counterparty 2
Name of entity Irish property insurer German property insurer
Geographic exposure – country Ireland Germany
Geographic Exposure – region Northern Europe Western Europe
Loss ratio 80% 80%
Combined ratio 95% 95%
SCR ratio as reported 165% 165%
Non-life premium & reserve risk submodule V prem V res V prem V res
Motor liability insurance** 0 0 0 0
Other motor insurance and proportional reinsurance** 0 0 0 0
Marine, aviation and transport insurance** 0 0 0 0
Fire and other damage to property insurance** 200,000 200,000 200,000 200,000
Sum 200,000 200,000 200,000 200,000
Non-life catastrophe risk submodule
SCR Cat 55,000 55,000
Non-life lapse risk submodule
SCR lapse 1000 1000
Market risk submodule
SCR market 45,000 45,000
Life risk submodule
SCR life 0 0
Health risk submodule
SCR health 0 0
Intangible asets risk submodule
SCR intangible asset 1000 1000
Operational risk submodule
SCR operational risk 6000 6000
Diversification andSolvency II: thecapital effect ofportfolio…
Table 4 (continued)
Counterparty details Counterparty 1 Counterparty 2
Adjustment submodule
SCR adjustments 38,000 38,000
*All figures in EURthousand
**And proportional reinsurance
B.Sheehan et al.
Table 5 Swap summary scenario 2
Company name Counterparty 1 Counterparty 2
Irish property insurer German property insurer
Geographic region Northern Europe Western Europe
Life / non-life Non-life Non-life
Line of business Property Property
Premium volume 200m 200m
Reserve volume 200m 200m
Combined ratio % 95% 95%
SCR (pre-swap) 183m 183m
Combined ratio % (post-swap) 95% 95%
SCR (post-swap) 175m 174M
Capital relief from swap 8m 9m
Portfolio swap % 20% 20%
Portfolio swap notional EUR 40m 40m
Table 6 Solvency II balance sheet impact (pre- and post-swap) for
scenario 2
*Excluding liabilities subordinates
Company name Counterparty 1 Counterparty 2
Irish property
insurer
Swap estimated
impact
German property
insurer
Swap
estimated
impact
Total assets 2,387m 2,387m 2,387m 2,387m
Best estimate (non-life) 1,606m 0m 1,606m 0m
Risk margin (non-life) 136m -10.9m 136m -11.3m
Other liabilities* 343m 343m
Total liabilities 2,085m 2,074M 2,085m 2,074M
Assets less liabilities 302m 313m 302m 314M
Subordinated liabilities 0m 0m 0m 0m
Total basic own funds 302m 313m 302m 314M
Solvency Capital Requirement 183m 175m 183m 174M
Solvency ratio 165% 179% 165% 180%
Diversification andSolvency II: thecapital effect ofportfolio…
Fig. 3 Swap impact on the Solvency II balance sheet for scenario 1
Fig. 4 Capital relief decomposed by risk modules for scenario 2
B.Sheehan et al.
Appendix B: Irish diversied insurer vs. German diversied insurer
See Tables7, 8, 9 and Figs.6 and 7.
0%
20%
40%
60%
80%
100%
Assets (Pre-Swap) Liab ility (Pre-Swap) Assets (Post-Swap)Liability (Post-Swap)
Best Esmate of Liabilies Risk Margin Own FundsMarket Value of Assets
Solvency Ratio = 165% Solvency Ratio = 179%
0%
20%
40%
60%
80%
100%
Assets (Pre-Swap) Liab ility (Pre-Swap) Assets (Post-Swap)Liability (Post-Swap)
German Property Insurer
Solvency Ratio = 165% Solvency Ratio = 180%
Fig. 5 Swap impact on the Solvency II balance sheet for scenario 2
Diversification andSolvency II: thecapital effect ofportfolio…
Table 7 Input data scenario 3
*All figures in EURthousand
**And proportional reinsurance
Counterparty details Counterparty 1 Counterparty 2
Name of entity Irish div. insurer German div. insurer
Geographic exposure – country Ireland Germany
Geographic exposure – region Northern Europe Western Europe
Loss ratio 80% 80%
Combined ratio 95% 95%
SCR ratio as reported 165% 165%
Non-life premium & reserve risk submod-
ule
V prem V res V prem V res
Motor liability insurance** 50,000 50,000 50,000 50,000
Other motor insurance and proportional
reinsurance**
20,000 20,000 20,000 20,000
Marine, aviation and transport insurance** 50,000 50,000 50,000 50,000
Fire and other damage to property insur-
ance**
80,000 80,000 80,000 80,000
Sum 200,000 200,000 200,000 200,000
Non-life catastrophe risk submodule
SCR Cat 55,000 55,000
Non-life lapse risk submodule
SCR éapse 1000 1000
Market risk submodule
SCR market 45,000 45,000
Life risk submodule
SCR life 0 0
Health risk submodule
SCR health 0 0
Intangible assets risk submodule
SCR intangible asset 1000 1000
Operational risk submodule
SCR operational risk 6000 6000
Adjustment submodule
SCR adjustments 38,000 38,000
B.Sheehan et al.
Table 8 Swap summary scenario 3
Company name Counterparty 1 Counterparty 2
Irish diversified insurer German diversified insurer
Geographic region Northern Europe Western Europe
Life / non-life Non-life Non-life
Line of business Multi-line Multi-line
Premium volume 200m 200m
Reserve volume 200m 200m
Combined ratio % 95% 95%
SCR (pre-swap) 171m 171m
Combined ratio % (post-swap) 95% 95%
SCR (post-swap) 165m 162m
Capital relief from swap 6m 9m
Portfolio swap % 20% 20%
Portfolio wap otional EUR 40m 40m
Table 9 Solvency II balance sheet impact (pre- and post-swap) for
scenario 3
*Excluding liabilities subordinates
Company Name Counter party 1 Counterparty 2
Irish Diversified
Insurer
Swap Estimated
Impact
German Diversi-
fied Insurer
Swap
Estimated
Impact
Total Assets 2,232m 2,232m 2,232m 2,232m
Best Estimate (Non-Life) 1,501m 0m 1,501m 0m
Risk Margin (Non-Life) 128m -8.8m 128m -12.7m
Other liabilities* 321m 321m
Total Liabilities 1,949m 1,941m 1,949m 1,937m
Assets less Liabilities 283m 291m 283m 295m
Subordinated Liabilities 0m 0m 0m 0m
Total Basic Own Funds 283m 291m 283m 295m
Solvency Capital Requirement 171m 165m 171m 162m
Solvency Ratio 165% 177% 165% 182%
Diversification andSolvency II: thecapital effect ofportfolio…
Appendix C: German property insurer vs. German motor insurer
See Tables10, 11, 12 and Figs.8 and 9.
20%
20%
€40MM
171 165 €40MM171162
668117218383661217218383
-31-30 -31-30
158151 158148
45 45 12 12 00 00100 93 11 45 45 12 12 00 001009011
-27-25 -27-23
127 118127 114
71,2 68,0 55 49 11 71,2 68,0 55 45 11
Swap Details
Module Title
SCR Pre-Swap
(€MM)
SCR Post-
Swap (€MM)
0% 0%
SCR_op
rerusnIdeifisreviDnamreGrerusnIdeifisreviDhsirI
Swap Details
SCR_intangibleSCR_market SCR_default
SCR
% Change
SCR Pre-
Swap (€MM)
SCR Post-
Swap (€MM)
Module Title
% Change
-5%-19
%
-5%-11% egnahC%%0
% Change
-5%-7%-6 %
-10%
SCR_health SCR_nonlife
SCR_op
Key
RCSBjdA
Key
SCR_intangibleSCR_market SCR_defaultSCR_life
Adj
Diversificaon
Sum of SCRs
SCR_life
-11%
Diversificaon
-4%-5%-4 %
-7%
SCR_nonlife
Diversificaon
Sum of SCRs
-7%
SCR_health
SCR
BSCR
Diversificaon
Sum of SCRs
Sum of SCRs
Premium & Reserve
CatLapse
Premium & Reserve
Ca
apse
Fig. 6 Capital relief decomposed by risk modules for scenario 3
0%
20%
40%
60%
80%
100%
Assets (Pre-Swap) Liab ility (Pre-Swap) Assets (Post-Sw ap )Liability (Post-Swap)
Best Esmate of Liabilies Risk Margin Own FundsMarket Value of Assets
Solvency Ratio = 165% Solvency Ratio = 177%
0%
20%
40%
60%
80%
100%
Assets (Pre-Swap) Liab ility (Pre-Swap) Assets (Post-Sw ap )Liability (Post-Swap)
German Diversified Insurer
Solvency Ratio = 165% Solvency Ratio = 182%
Fig. 7 Swap impact on the Solvency II balance sheet for scenario 3
B.Sheehan et al.
Table 10 Input data scenario 4
*All figures in EURthousand
**And proportional reinsurance
Counterparty details Counterparty 1 Counterparty 2
Name of entity German property insurer German motor insurer
Geographic exposure – country Germany Germany
Geographic exposure – region Western Europe Western Europe
Loss ratio 80% 80%
Combined ratio 95% 95%
SCR ratio as reported 165% 165%
Non-life premium & reserve risk submodule V prem V res V prem V res
Motor liability insurance** 0 0 200,000 200,000
Other motor insurance and proportional reinsur-
ance**
0 0 0 0
Marine, aviation and transport insurance** 0 0 0 0
Fire and other damage to property insurance** 200,000 200,000 0 0
Sum 200,000 200,000 200,000 200,000
Non-life catastrophe risk submodule
SCR Cat 55,000 55,000
Non-life lapse risk submodule
SCR lapse 1000 1000
Market risk submodule
SCR market 45,000 45,000
Life risk submodule
SCR life 0 0
Health risk submodule
SCR health 0 0
Intangible assets risk submodule
SCR intangible asset 1000 1000
Operational risk submodule
SCR operational risk 6000 6000
Adjustment submodule
SCR adjustments 38,000 38,000
Diversification andSolvency II: thecapital effect ofportfolio…
Table 11 Swap summary scenario 4
Company Name Counterparty 1 Counterparty 2
German property insurer German motor insurer
Geographic region Western Europe Western Europe
Life / non-life Non-life Non-life
Line of business Property Motor
Premium volume 200m 200m
Reserve volume 200m 200m
Combined ratio % 95% 95%
SCR (pre-swap) 183m 185m
Combined ratio % (post-swap) 95% 95%
SCR (post-swap) 180m 178m
Capital relief from swap 3m 7m
Portfolio swap % 20% 20%
Portfolio swap notional EUR 40m 40m
Table 12 Solvency II balance sheet impact (pre- and post-swap) for
scenario 4
*Excluding liabilities subordinates
Company name Counterparty 1 Counterparty 2
German property
insurer
Swap estimated
impact
German motor
insurer
Swap
estimated
impact
Total assets 2,387m 2,387m 2,415m 2,415m
Best estimate (non-life) 1,606m -4M 1,624M 0m
Risk margin (non-life) 136m -4.1m 138m -9.3m
Other liabilities* 343m 347m
Total liabilities 2,085m 2,077m 2,109m 2,103m
Assets less liabilities 302m 310m 306m 311m
Subordinated liabilities 0m 0m 0m 0m
Total basic own funds 302m 310m 306m 311m
Solvency Capital Requirement 183m 180m 185m 178m
Solvency ratio 165% 172% 165% 175%
B.Sheehan et al.
Appendix D: Non-life premium and reserve SCR calculation
pre- andpost-swap
See Fig.10.
20%
20%
€40MM
183180 €40MM185178
664311418383666319318383
-32-32 -32-31
171168 173165
45 45 12 12 00 00113110 11 45 45 12 12 00 00115107 11
-29-28 -29-27
142138 144135
85,9 82,8 55 54 11 88,4 82,7 55 51 11
Premium & Reserve
CatLapse
Premium & Reserve
Ca
apse
-7%
Diversificaon
-2%-2%-2 %
-3%
SCR_nonlife
Diversificaon
Sum of SCRs
-3%
SCR_health
SCR
BSCR
Diversificaon
Sum of SCRs
Sum of SCRs
Key
RCSBjdA
Key
SCR_intangibleSCR_market SCR_defaultSCR_life
Adj
Diversificaon
Sum of SCRs
SCR_life
-4%-5%-4 %
-7%
SCR_health SCR_nonlife
SCR_op
-6%-7% 0%
-4%-2%egnahC%%0
% Change
% Change
SCR Pre-
Swap (€MM)
SCR Post-
Swap (€MM)
Module Title
% Change
Swap Details
Module Title
SCR Pre-Swap
(€MM)
SCR Post-
Swap (€MM)
0% 0%
SCR_op
rerusnIrotoMnamreGrerusnIytreporPnamreG
Swap Details
SCR_intangibleSCR_market SCR_default
SCR
Fig. 8 Capital relief decomposed by risk modules for scenario 4
0%
20%
40%
60%
80%
100%
Assets (Pre-Swap) Liab ility (Pre-Swap) Assets (Post-Sw ap )Liability (Post-Swap)
Best Esmate of Liabilies Risk Margin Own FundsMarket Value of Assets
Solvency Ratio = 165% Solvency Ratio = 172%
0%
20%
40%
60%
80%
100%
Assets (Pre-Swap) Liab ility (Pre-Swap) Assets (Post-Sw ap )Liability (Post-Swap)
German Motor Insurer
Solvency Ratio = 165% Solvency Ratio = 175%
Fig. 9 Swap impact on the Solvency II balance sheet for scenario 4.
Diversification andSolvency II: thecapital effect ofportfolio…
Supplementary Information The online version contains supplementary material available at https:// doi.
org/ 10. 1057/ s41288- 022- 00269-3.
Acknowledgements We thank Kathrin Scherff, Gareth Matthews, Donna Ryan and Chris Lee for useful
discussions conceptualising this idea.
Funding Open Access funding provided by the IReL Consortium.
Declarations
Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of
interest.
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(DIVs)
Non-Life
Risk Capital
Charge (Vs)
Premium
Volume
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Volume
Premium
Standard
Deviaon
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About the authors
Dr. Barry Sheehan is a lecturer in risk and finance in the Kemmy Business School at the University
of Limerick. He is programme director for a cluster of award-winning inter-disciplinary programmes,
including the MSc in Machine Learning for Finance. With a professional background in actuarial science,
his research uses machine-learning techniques to estimate the changing risk profile produced by emerg-
ing technologies. He is a senior researcher of Emerging Risk Group (ERG) and Lero, which has long-
established expertise in insurance and risk management and has continued success within large research
consortia, including EU H2020 and Science Foundation Ireland research projects.
Mr. Christian Humberg is a reinsurance professional and graduate of the MSc in Risk Management and
Insurance at the University of Limerick. A designated Fellow of the Chartered Insurance Institute (FCII),
Christian engages in research advancing the current state-of-the-art in alternative risk transfer methods.
Dr. Darren Shannon is a lecturer in quantitative finance in the Department of Accounting and Finance,
University of Limerick, and a researcher in the ERG. Prior to receiving his PhD in Applied Statistics, he
completed an MSc in Computational Finance and a BSc in Mathematics. He has contributed heavily to
two EU H2020 research projects (VIDAS and Cloud-LSVA) that identified and addressed emerging risks
associated with conventional and highly-automated vehicles. Darren continues to be engaged with the
research community in facilitating the timely integration of advanced-tech vehicles onto public roads.
His research focus is split between developing high-impact outputs for emergent topics in finance (green
finance, application of ML/DL models) and for transportation safety and risk pricing (econometrics of
road collisions, the insurability of connected and autonomous vehicles).
Prof. Dr. Fortmann is a professor at the Institute of Insurance at the Technical University of Cologne. His
activities include teaching and research in insurance law and liability insurance. One focus is on D&O,
corporate liability, fidelity and cyber insurance. In addition, he heads the Master’s degree programme in
insurance law and is the academic director of the Automotive Insurance Manager and Cyber Insurance
Manager certificate programmes. He is also chairman of the examination board at the Institute of Insur-
ance Studies.
Prof. Stefan Materne (FCII) has held the Chair of Reinsurance at the Institute of Insurance at TH Köln
since 1998, focusing on the efficiency of reinsurance, industrial insurance and alternative risk transfer
(ART). Prof. Materne holds various international supervisory boards, board of directors and advisory
board mandates at insurance and reinsurance companies, captives, InsurTechs, the European Insurance
Supervisory Authority (EIOPA), and at insurance-scientific institutions. He also acts as an arbitrator and
party representative in arbitration proceedings.
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