Principles of traditional
non-life reinsurance
A study aid
Richard R. Doerr, Heinz Fischer
Module 1
Introduction to the
reinsurer's business
Module 2
Module 3
Proportional
reinsurance
Non-proportional
reinsurance
Module 4
Combinations of proportional
and non-proportional
reinsurance
© 2002
Swiss Reinsurance Company
Zurich
Title:
Principles of traditional
non-life reinsurance
A study aid
Authors:
Richard R. Doerr
Fritz Eugster
Heinz Fischer
Peter Gasser
Emil Landolt
Heinz Stettler
Editing and production:
Thomas Hirt
Compendio Bildungsmedien AG
Lehrmittelentwicklung der
AKAD-KS Gruppe
Niklaus Müntener; Gérard Wicht
Technical Training
Division Reinsurance & Risk;
Corporate Communications
Division Reinsurance & Risk
Swiss Re
Mythenquai 50/60
P.O. Box
CH-8022 Zürich
Telephone +41 43 285 21 21
Fax
+41 43 285 20 23
R&R, 01/03, 60 en
Table of contents
Contents and learning objectives of Module 4
1. Why do we combine proportional and non-proportional
reinsurance treaty types?
A brief summary of the previous modules
1.1 Key factors for the success of the primary insurer
1.2 Recap of the types of reinsurance and treaty types available
1
2. The most common combinations of proportional and
non-proportional reinsurance treaty types
2.1 Combination of a quota share and a WXL on the retention
2.1.1 Quota share with a WXL/R on the quota share retention
2.1.2 Quota share with a WXL/E on the quota share retention
2.2 Combination of a surplus and a WXL on the retention
2.2.1 Surplus with a WXL/R on the retention
2.2.2 Surplus with a WXL/E on the retention
2.3 Combination of a quota share or surplus and a CatXL on the retention
2.3.1 Quota share with a CatXL on the quota share retention
2.3.2 Surplus with a CatXL on the retention under the surplus
8
1
3
9
9
16
20
20
24
26
26
28
3. Interactions between proportional and non-proportional reinsurance
treaty types
32
4. Graphical representation of reinsurance programmes
4.1 Per-risk covers
4.2 Event covers next to per-risk covers
42
42
45
The learning steps you should have completed after working
through the module
48
Summary
50
Revision questions and exercises on the module as a whole
54
Answers to the revision questions
56
List of working examples
62
List of figures
63
Contents and learning objectives of Module 4
Welcome to the “Combination of proportional and
non-proportional reinsurance” module. Before
beginning this module, you should have already
worked through Module 1, “Introduction to
the reinsurer’s business”, Module 2, “Proportional
reinsurance” and Module 3, “Non-proportional
reinsurance”, as we are assuming that you have the
knowledge imparted in these modules. It will be
difficult for you to understand why we combine
different types of reinsurance and treaty types if
you are not aware of the prerequisites that must
be met by a primary insurer if it is to be successful
and develop its business further, or you do not
know the forms and types of reinsurance and treaty
types that can make a significant contribution to
achieving these conditions.
Learning objectives
The core topic of this module is the combination
of proportional and non-proportional reinsurance
treaties in a reinsurance programme. The module
will essentially provide you with insight beyond
the basic mechanics involved: Which functions
do these types of combinations fulfil? What are
the reasons why they are used and what are the
problems inherent to them?
We would, however, like to stress that an in-depth
analysis of various combinations of reinsurance
treaty types would far exceed the limitations of
this introduction. Our aim is to present key problem issues in reinsurance programmes and thereby
provide you with a basis on which you can build –
in future training courses and naturally on the job.
In particular, we will pursue the following learning
objectives:
1. Why do we combine proportional and
non-proportional reinsurance treaty types?
A brief summary of the previous modules
(pages 1–7)
The aim of this section is to filter out the information of relevance to this topic from modules 1–3
and refresh your memory as a basis for the other
sections. After working through this section, you
will be able to
– describe the (four) key success factors for insurance business, which can be influenced positively by suitable reinsurance cover;
– explain which treaty types are, depending on
the type of constellation, well suited, less suited
or totally unsuitable to positively impact specific
key success factors for the primary insurer, and
derive therefrom the combinations quota share
or surplus with a WXL/R, WXL/E and CatXL
as the most common combinations of proportional and non-proportional reinsurance treaty
types.
Relevant technical terms:
Risk of change, catastrophe accumulation, accumulation per risk.
2. The most common combinations of
proportional and non-proportional
reinsurance treaty types (pages 8–31)
Section 2 is the main section of this module. It
describes how combinations of proportional and
non-proportional reinsurance treaty types work
and what impact they have on the development
of an insurance portfolio.
After working through this section, you will be
able to describe, using examples, how the
following combinations work and how losses
are apportioned:
– quota share and a WXL/R or WXL/E on the
quota share retention;
– surplus and a WXL/R or WXL/E on the retention;
– quota share and a CatXL on the quota share
retention;
– surplus and a CatXL on the retention.
Relevant technical terms:
CatXL, facultative reinsurance, fac-oblig reinsurance, quota share, loss burden, surplus, WXL/R,
WXL/E.
3. Interactions between proportional and
non-proportional reinsurance treaty types
(pages 32–40)
Reinsurance treaties that are combined in a reinsurance programme can have interactive effects on
each other. This section deals with this phenomenon. After working through this section, you will
be able to
– describe, using typical examples, what the interactive effects between proportional and non-proportional reinsurance are and how they originate.
Explanations of the pictograms
E
= Working examples
R
= Revision questions with answers at the end of the
module
S
= Summary
4. Graphical representation of reinsurance
programmes (pages 42–47)
A number of ways of illustrating the combination
of reinsurance treaty types have emerged. A common and clear method is the graphical representation of reinsurance programmes. After working
through this section, you will be able to
– draw accurate graphical representations of perrisk covers and event covers in a reinsurance
programme.
1. Why do we combine proportional and non-proportional reinsurance
treaty types? A brief summary of the previous modules
1.1 Key factors for the success of the primary insurer
Module 1 (Section2 Reinsurance is insurance for insurers) sets out the prerequisites which a
primary insurer must fulfil in order to be successful.
Stabilising the claims experience
One of these prerequisites is that the insurance portfolio which the insurer retains for its
own account must be as balanced as possible in order to stabilise the claims experience,
ie to avoid excessive fluctuations in the annual loss burden. This includes:
– the reinsurance of insurances with liabilities above the portfolio average: ceding the peak
risks (see also Module 1, Sect. 2.2.3);
– the reinsurance of directly accumulating policies (so-called per-risk accumulation); for a
solution using proportional reinsurance to be feasible, it must be possible to detect, preassess and estimate potential accumulations. If this is not possible, or is too time-consuming,
non-proportional reinsurance may be a help (see also Module 1, Sect. 2.2.4);
– in the case of a catastrophe accumulation, the reinsurance of a portfolio against loss
events with accumulation of many policies which are normally independent of each
other (CatXL, see also Module 1, Sect. 2.2.5).
Sufficient automatic treaty capacity
The primary insurer must also have sufficient automatic underwriting capacity at its disposal
if it wishes to be successful. In order to be competitive in the marketplace, the insurer must
be in a position to assume amounts of liabilities that exceed its own financial capabilities
(see also Module 1, Sect. 1.2). Here again, reinsurance can provide assistance, as it is easier
and more economical to obtain than additional risk capital.
Strong portfolio growth
The strong growth of the portfolio or parts thereof may cause the insurer financial problems
if, as a result, it is no longer able to meet legal or operational capital requirements (eg if
the existing capital level is no longer sufficient to meet the solvency margin prescribed by EU
law). A suitable reinsurance programme can prevent such developments in the original
portfolio from impacting on the primary insurer’s retained portfolio, and thus on its annual
financial results.
Persistently bad results
Annually recurring losses in an insurance portfolio can also pose a threat for the primary
insurer (persistently bad results). The actual cause is always the same: the premiums are
not sufficient to cover the loss burden and the operating costs. The main reason for this are
inadequate insurance conditions, in other words insufficient pricing in relation to the
insured risks and the cost structure in the form of low premium rates and/or the lack of
or insufficient deductibles (policyholders’ excesses). The following circumstances could
produce such a negative development:
1 Combination of proportional and non-proportional treaty types – Module 4
1. Why do we combine proportional and non-proportional reinsurance treaty types?
A brief summary of the previous modules
– Inaccurate assessment of the insured risks when a new insurance product is launched or a
new class of business written for which the primary insurer does not have the requisite
claims experience (lack of claims experience). The costs of a start-up or forced acquisition
may also mean that the premium which remains is no longer enough to finance the loss
burden.
– Change in the portfolio’s characteristics, whether this be a change in the risk situation (without the possibility of a short-term adjustment in the insurance conditions) or the actual
or supposed need to adjust to market conditions, ie the competitive environment may
lead the primary insurer to relax its existing insurance conditions, eg by including new,
additional risks in the insurance cover, by reducing or dispensing with policyholders’
excesses, or by lowering premium rates without the cost or risk situation having improved
(risk of change).
S
Key factors for the success of the primary insurer
Stabilising the claims
experience
(curtail fluctuations
in the annual loss
burden)
Sufficient automatic
treaty capacity
Strong portfolio
growth
(financial bottlenecks)
– Peak risks
in the portfolio
– Per-risk
accumulations
– Catastrophe risk
– Additional capacity
– solvency
requirements
Persistently
bad results
– Inaccurate risk
assessment
(lack of claims
experience)
– Change in the
portfolio's
characteristics
(risk of change)
2 Combination of proportional and non-proportional treaty types – Module 4
1.2 Recap of the types of reinsurance and treaty types available
In traditional reinsurance, the reinsurer provides support to the primary insurer in managing
the four key success factors by means of the following instruments:
Figure 1/1:
Forms and types of reinsurance,
treaty types
(taken from Module 1, Sect. 4)
Reinsurance
Forms of
reinsurance
Facultative reinsurance
Types of
Proportional
reinsurance
Nonproportional
Treaty reinsurance
Proportional
Non-proportional
Distinguishing criterion
The way business is
allocated to the treaty
Reinsurance
treaty types
Quota
share
Surplus
facoblig
Distinguishing criterion
Unit of loss
XL/R
XL/E
SL
In modules 2 and 3 we described what the different areas of application for the various types
of reinsurance and treaty types are, what their advantages and disadvantages for the primary
insurer and the reinsurer are, and how they affect the losses remaining in the insurer’s retention. The table on the following page summarises this information:
3 Combination of proportional and non-proportional treaty types – Module 4
–
–
– Reduces fluctuations caused by large
losses on individual risks
– Protection against high losses arising
from loss accumulation events
– Cover designed to protect results,
as it stops the annual aggregate
loss burden at a given point
– Property insurance
– Unbalanced portfolios
– Additional capacity
– Relief for underlying treaties
– Mainly property insurance (fire and allied
perils)
– Only if a unit of risk can be defined beforehand
– Classes of insurance covering loss events
which may affect more than one unit of risk
or several policies
– Rarely granted on account of the stringent
prerequisites which must be met
Fac-oblig
reinsurance
WXL/R
WXL/E
CatXL
SL
– Automatic cover for risks which
would otherwise have to be reinsured
on a facultative basis
– Homogenisation of the retained
portfolio
– Requires very specific prerequisites
both of an objective and subjective
nature
– Volatile reinsurance cover, tends to be
short-lived
– Increased risk of fortuitous loss occurrences and risk of change
– Increased catastrophe accumulation risk
– No reduction in the relative risk of
fluctuation
– No homogenisation of the retained
portfolio
Surplus
– Limiting the risk of fortuitous loss
occurrences and risk of change
– Proportionate reduction of the catastrophe accumulation risk
– Reduction of fluctuations in absolute
terms
– Homogeneous insurance portfolios
– New insurance companies
– Lack of claims experience
– Guaranteeing the solvency margin (instead
of obtaining additional equity capital)
– Financing quota share to cover costs and
losses from forced acquisition or new product
launches
– Compensation or supporting quota share
for high-risk or loss-prone business
Disadvantages for the primary insurer
Quota share
Advantages for the primary insurer
Area of application
Figure 1/2:
Summary of the areas where
proportional and non-proportional reinsurance treaty
types are used and their advantages and disadvantages
for the primary insurer
Treaty type
1. Why do we combine proportional and non-proportional reinsurance treaty types?
A brief summary of the previous modules
4 Combination of proportional and non-proportional treaty types – Module 4
An analysis of this table shows which treaty types are better suited to each specific portfolio
and to the primary insurer’s objectives, and which are not so appropriate or are not at all
appropriate:
Fluctuations in the annual loss burden
– Peak risks in the portfolio. The effects of individual large losses on the primary insurer’s
retained portfolio can be limited to the desired per case amount by means of specific proportional reinsurance. Depending on the circumstances and class of insurance, this can be
achieved by means of facultative reinsurance, surplus reinsurance or fac-oblig reinsurance.
In certain classes, non-proportional reinsurance in the form of a WXL/R can be applied.
In addition to purely proportional combinations, such as quota share/surplus, this can also
mean combinations of a quota share and a WXL/R or a surplus and a WXL/R in classes of
insurance where this is appropriate (mainly fire and allied lines).
– Per-risk accumulation. What we said about the peak risks in the portfolio also applies to
per-risk accumulations that can be clearly ascertained, defined and assessed in advance.
If this is not the case, the primary insurer may instead use a combination of a quota share
and a WXL/E or a surplus and a WXL/E.
– Catastrophe risk. Although in quota share reinsurance the catastrophe risk is automatically
passed on to the reinsurer to the extent of the cession under the treaty, the share which
remains in the insurer’s retention is still exposed to the same degree of catastrophe accumulation risk. The insurer can obtain effective cover in the form of a CatXL, resulting in
the combination quota share and a CatXL on the quota share retention.
In surplus reinsurance, only a very small amount of the catastrophe risk is passed on to the
reinsurer. All small and medium-sized risks which remain partially or fully in the primary
insurer’s retention expose the insurer to the full catastrophe accumulation risk. Here again,
a CatXL is the best option, resulting in the combination surplus reinsurance and a CatXL
on the surplus retention.
Additional capacity
The surplus offers supplementary automatic reinsurance cover – in addition to the quota share
– resulting in the proportional combination of a quota share/surplus. This combination, or
simply the surplus treaty alone, may be topped up with overlying surplus or fac-oblig reinsurance covers. Likewise, additional capacity can be procured by an excess of loss per risk
(WXL/R) in the classes of insurance where this is appropriate (mainly fire and allied lines).
5 Combination of proportional and non-proportional treaty types – Module 4
1. Why do we combine proportional and non-proportional reinsurance treaty types?
A brief summary of the previous modules
Strong portfolio growth and persistently bad results (lack of claims experience and
risk of change)
The effects of these two factors on the primary insurer’s retention cannot be eliminated totally,
but they can be reduced at least to the extent of the proportional cession by means of quota
share reinsurance, possibly in combination with a surplus.
In this instance, non-proportional reinsurance treaty types are totally unsuitable for the following reasons: when dealing with the risk of change or lack of claims experience (new product,
new class of insurance, new insurance company), it has to be taken into account that the
premiums originally fixed may not be sufficient to cover the changes in the risk situation.
In other words, the annual premium income cannot fully finance the annual loss burden.
Regardless of any individual large losses or catastrophe losses which may occur, financial
losses will be incurred both in the gross portfolio and the insurer’s retained portfolio.
A changing cost structure can also contribute to such financial losses, particularly in the case
of a forced acquisition. Furthermore, a portfolio with strong growth can cause financial
bottlenecks in financing reserves and providing additional equity capital to ensure solvency
requirements are met.
The difficulties caused by a premium level that is not sufficient to cope with a changing risk
or cost situation cannot be overcome by means of excess of loss reinsurance. On the contrary,
in addition to the annual financial losses incurred on the retained portfolio, the primary
insurer’s overall loss is increased by the cost of the excess of loss reinsurance. The exception
here is stop loss reinsurance; however, we will refrain from discussing this in detail here as it
has only a very restricted area of application. Returning to the difficulties mentioned above,
it can be concluded that, in this case, even a combination of proportional and non-proportional reinsurance would not provide any extra relief for the retained portfolio.
We therefore have the following most common types of combination, which we will look
at in the next section:
– Combination of quota share and excess of loss reinsurance: a quota share with a WXL/R
or WXL/E and CatXL on the quota share retention (or the entire quota share);
– Combination of surplus and excess of loss reinsurance: a surplus with a WXL/R or WXL/E
and CatXL on the surplus retention.
6 Combination of proportional and non-proportional treaty types – Module 4
S
Problems in the
gross insurance portfolio
(or parts thereof)
Solutions provided by reinsurance (RI)
for the primary insurer's retained portfolio
with proportional RI
Risk of fluctuation:
– Individual large losses
(peak risks)
with non-prop RI
with a combination
of prop/non-prop RI
– fac. RI
– surplus
– fac-oblig RI
– quota share/surplus
WXL/R
– quota share with
WXL/R
– surplus with WXL/R
– Per-risk accumulation
– quota share
(only partially)
– to a larger extent
with quota share/
surplus, fac-oblig RI,
fac RI (requires prior
accumulation control)
WXL/R or
WXL/E
– quota share with
WXL/R or WXL/E
– surplus with WXL/R
or WXL/E
– Catastrophe
accumulation
(catastrophe risk)
– quota share
(only partial relief)
Cat XL
– quota share with CatXL
– surplus with CatXL
Additional capacity
(automatic capacity)
– surplus
– fac-oblig RI
WXL/R (partially)
–
Strong growth
(Solvability)
– quota share
not suitable
–
– quota share
– surplus (less suitable)
not suitable
–
–
– quota share
not suitable
–
Persistently bad results
– risk of change
– lack of claims
experience
7 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional
and non-proportional reinsurance treaty types
On the basis of what we have seen in the last section, it is obvious that the primary insurer
often has more than one problem to deal with in its portfolio. In cases where it is not possible to find an optimal solution to the primary insurer’s specific problems with just one treaty
type, there is the option of combining various treaty types. Frequently, such combinations
are also the result of specific goals which the primary insurer wishes to achieve with its reinsurance programme.
Many reinsurance programmes therefore comprise more than one type of treaty. As we have
already described the purely proportional (quota share/surplus) and purely non-proportional
(eg WXL/R and CatXL) combinations, here we will limit ourselves to five common combinations of two treaties, where one is proportional and one non-proportional. More complex
combinations, in other words, actual reinsurance programmes, will be dealt with in later
training modules.
In this section, we will deal individually with the following combinations:
Figure 2/1:
The most common combinations
of a proportional and a nonproportional reinsurance treaty
Combinations of reinsurance treaty types (selection)
WXL/R
Combinations of proportional treaty types and WXL covers
(WXL/R or WXL/E)
Combinations
with CatXL
Quota share
Surplus
and
and
Quota share or
surplus
and
WXL/E
WXL/R
WXL/E
8 Combination of proportional and non-proportional treaty types – Module 4
CatXL
2.1 Combination of a quota share and a WXL on the retention
2.1.1 Quota share with a WXL/R on the quota share retention
As we have already seen, one of the disadvantages of quota share reinsurance lies in the fact
that it has no homogenising effect on the primary insurer’s retained portfolio (see also
Module 2, Sec. 3.2.2). It is possible to partially alleviate this deficiency by adding a WXL/R
on the quota share retention. This stabilises the claims experience of an unbalanced quota
share retention portfolio by spreading sporadic individual, relatively high losses over several
years.
Figure 2/2:
Combination of quota share
reinsurance and a WXL/R on
the quota share retention
Quota share retention
Quota share
cession
WXL/R cover
Deductible
Note
In practice, the WXL/R is often arranged to cover the
100 % quota share rather than the quota share retention.
In these instances, it is not only the primary insurer who
benefits in its quota share retention from the WXL/R
cover, but also the reinsurer of the quota share cession.
In other words, the reinsurer who underwrites the
WXL/R cover is reinsuring both the primary insurer
and the reinsurer who has accepted the quota share
cession.
In this section, we will proceed as follows:
– First of all, we will show, using Example 2/1 how the losses are apportioned to the quota
share and the WXL/R.
– Then we will look at the effects of the WXL/R on the quota share retention in Example 2/2.
– Finally, we will describe two characteristics which make the combination of quota share
and WXL/R on the retention a very interesting tool in certain situations.
9 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
2/1
E
Apportionment of losses under the quota share and WXL/R on the quota share retention
An insurance portfolio is reinsured as follows:
Quota share reinsurance
Quota share 100 % treaty limit
Quota share retention 60 %
Quote share cession 40 %
4 000 000
2 400 000
1 600 000
WXL/R on the quota share retention of 60 %
2 000 000 per risk xs 400 000 per risk
Facultative proportional reinsurance
for risks which exceed the treaty limit of 4 000 000
Note
Combining proportional treaties with non-proportional
facultative agreements for peaks in the portfolio causes
problems which are beyond the scope of this module.
For further details, refer to the Swiss Re publication
“Facultative non-proportional reinsurance and obligatory
treaties; Caution: faulty design”
In order to understand how the reinsurance combination works, let us take a look at risks nos. 1–5 in the
portfolio. These have the following gross sums insured and gross losses (figures in thousands):
Risk no.
1
2
3
4
5
Gross sums insured
1 200
3 500
5 000
1 000
8 000
Gross losses
600
3 000
2 500
667
1 200
The quota share’s treaty limit is 4 000 000. Risks nos. 1, 2 and 4 are therefore fully
reinsured, whilst risks nos. 3 and 5 exceed the quota share reinsurance. Both risks
are reinsured under a facultative proportional reinsurance agreement for the portion
that exceeds the treaty limit (risk no. 3 for 1 000 000 and risk no. 5 for 4 000 000).
The losses incurred are apportioned to the facultative proportional reinsurance, the
quota share and the WXL/R in the usual way, as follows:
1. Share of loss to fac prop reinsurance for risks 3 and 5, which exceed the quota
share’s treaty limit (figures in thousands).
Risk 3:
Liability 5000
Claims 2500
Risk 5:
Liability 8000
Claims 1200
of which 4000 to quota share (4/5);
1000 fac prop (1/5)
of which fac prop 1/5=500;
quota share 4/5 = 2000
of which 4000 to quota share (1/2);
4000 fac prop (1/2)
of which fak. prop. 1/2 = 600;
quota share 1/2 = 600
10 Combination of proportional and non-proportional treaty types – Module 4
2. Apportionment of losses to the quota share cession (40 %) and the quota share
retention (60 %) (figures in thousands).
Risk 1:
Risk 2:
Risk 3:
Risk 4:
Risk 5:
Losses
Losses
Losses
Losses
Losses
600
3000
2000
667
600
Cession
Cession
Cession
Cession
Cession
240
1200
800
267
240
Retention
Retention
Retention
Retention
Retention
360
1800
1200
400
360
3. Apportionment to the WXL/R cover of those losses which exceed 400 000 in the
quota share retention (figures in thousands).
Risk 1:
Risk 2:
Risk 3:
Risk 4:
Risk 5:
Loss in retention 360
Loss in retention 1800
Loss in retention 1200
Loss in retention 400
Loss in retention 360
Deductible 400
Deductible 400
Deductible 400
Deductible 400
Deductible 400
Loss to
Loss to
Loss to
Loss to
Loss to
WXL/R cover =
0
WXL/R cover = 1400
WXL/R cover = 800
WXL/R cover =
0
WXL/R cover =
0
In table form, this gives the following picture:
Risk/loss no.
Gross
loss
fac prop
Quota share treaty limit
4 000 000
100 %
Cession 40 %
WXL/R
2 000 000 xs 400 000
Retention 60 %
Cover
Deduc-
—
360
400
tible
1
600
—
600
240
360
2
3000
—
3000
1200
1800
1400
3
2500
2000
800
1200
800
4
667
667
267
400
5
1200
600
600
240
360
Total
7967
1100
6867
2747
4120
500
—
400
—
400
—
360
2200
1920
Step 1
Step 2
Step 3
Apportionment
Apportionment
Apportionment
Fac prop – quota share
Cession – retention
Cover– deductible
So much on the question of how losses are apportioned for the combination of quota share
reinsurance and a WXL/R on the retention.
11 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
Effect of the WXL/R on the quota share retention
As we have already seen, the WXL/R smoothes out individual large losses in the quota share
retention by spreading them over several years. We will look at this effect in more detail in
the following example.
2/2
E
Balancing effect of the WXL/R on the quota share retention
We have the following details for a quota share treaty:
Quota share RI
Quota share retention
Quota share cession
100 %
60 %
40 %
Treaty limit
(sum insured)
2 000 000 per risk
1 200 000 per risk
800 000 per risk
Premium income
(remains stable)
9 000 000
5 400 000
3 600 000
In this example, the quota share retention portfolio is still unbalanced. The ratio of
treaty limit to premium income is more than 22 % (1 200 000 : 5 400 000 = 0.222).
A single loss can therefore consume over 22 % of the annual premium income. In order
to stabilise the claims experience in the quota share retention, we apply a WXL/R:
WXL/R cover on the quota share retention (1 200 000)
990 000 per risk xs 210 000 per risk
Thanks to the WXL/R cover, an individual loss can now only use up just under 3.9 %
of the annual premium income (210 000 : 5 400 000 = 0.388), but no longer as
a maximum limit but as a deductible, ie an amount the insurer has to bear in every
loss event exceeding 210 000 for the 60 % quota share retention.
To demonstrate the effect of the WXL/R on the quota share retention, let us now
take a look at the claims experience over a period of 5 years. For this, we assume
the following:
– 57.5 % of annual premium income is used to cover individual losses of less than
350 000 apiece. The loss burden over 5 years under the 100 % quota share from
these small losses is therefore 25 875 000 (5 x 9 000 000 x 0.575).
60 % = 15 525 000 of this is borne by the quota share retention.
– 30 % of premium income is used to cover the primary insurer’s administration and
acquisition costs. These are proportionally offset by the reinsurance commission.
Overall, 87.5 % of premium income is therefore used to cover losses of less than
350 000 each and administration/acquisition costs. Thus, 12.5 % of premium income is left to cover losses of more than 350 000 each or represents profit. During
the observation period of 5 years, a total of 6 individual large losses occur with
loss amounts of 350 000 or more. These are given in the table that follows.
Note
It is no coincidence that we have set the border between
“small” and “large” individual losses at 350 000. The
reason we have chosen this amount is that the WXL/R
on the quota share retention with a loss retention of
210 000 has the same effect as a WXL/R with a loss
retention of 350 000 on a gross basis. A more detailed
explanation of this relationship will be given later.
12 Combination of proportional and non-proportional treaty types – Module 4
Let us now take a look at how the claims experience would affect the quota share’s
result without the WXL/R.
Loss total over 5 years
100 % QS
Individual losses < 350 000
Individual losses > 350 000
year
loss no.
1
1
2
2
3
3
4
4
5
5
6
25 875 000
350 000
1 800 000
350 000
500 000
900 000
400 000
QS retention
(60 %)
15 525 000
210 000
1 080 000
210 000
300 000
540 000
240 000
As we have already seen, the 100 % quota share can bear a loss ratio from large
losses of 12.5% of annual premium income, or 1 125 000, before it goes into the red.
This limit of 12.5 % also applies to the quota share retention. The retention’s annual
premium income is 5 400 000, which means that the quota share retention shows a
financial loss in those years in which the large losses exceed 675 000 (=12.5 %).
This is the case in year 2 and year 4:
– In year 2 (large loss no. 2), the QS will suffer a financial loss as this individual loss
on its own is 1 080 000, or 20 % of the annual premium income of 5 400 000.
– In year 4 (large losses nos. 4 and 5), the QS will also suffer – an albeit smaller –
annual financial loss. These two large losses together will use up 840 000 or
15.6 % of the annual premium income.
Let us now look at the losses incurred by the WXL/R:
Losses retained > 210 000
Loss no.
Amount
1
210 000
2
1 080 000
3
210 000
4
300 000
5
540 000
6
240 000
Deductible
WXL/R
210 000
210 000
210 000
210 000
210 000
210 000
0
870 000
0
90 000
330 000
30 000
1 320 000
Total
This shows that the WXL/R bears a loss burden over 5 years of 1 320 000 with an
underlying premium income of 27 000 000 (5 x 5 400 000), or 4.9 % (1 320 000/
27 000 000 = 0.049). The primary insurer should be able to obtain this WXL/R
for clearly less than 12.5 %. In return, the WXL/R ensures that the annual loss
burden borne by the primary insurer is less likely to exceed the critical value of
12.5 % as a result of losses >350 000 or >210 000 for the 60 % QS retention.
The WXL/R helps to smooth the results of the portfolio by spreading the loss
peaks over several years.
So much on how the WXL/R affects the quota share retention. Let us now look at the two
peculiarities of quota share reinsurance with a WXL/R on the retention.
13 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
WXL/R on the quota share retention on a gross basis (1st peculiarity)
On a gross basis, the WXL/R kicks in from a higher deductible, because it only applies to
the quota share retention and not to the quota share cession. The primary insurer can therefore obtain the WXL/R for a lower reinsurance premium than if it had to cover 100 % quota
share with the same deductible amount of 210 000 (see the note that follows the example).
2/3
E
Effect of the quota share cession on the limits of the WXL/R (gross)
For this example we will use the same figures as in Example 2/2:
Maximum liability for 100 % QS
Maximum liability for 60 % QS retention
WXL/R
2 000 000 per risk
1 200 000 per risk
990 000 per risk xs 210 000 per risk
Question: Which WXL/R cover is the same on a gross basis (100 % limit of liability
= 2 000 000 per risk) as the WXL/R cover 990 000 xs 210 000 for a
60 % limit of liability (=1 200 000 per risk)?
Answer:
We have to convert the WXL/R cover for a 60 % limit of liability to a
100 % limit of liability, using the following method:
WXL/R cover for
a 60 % limit of liability
990 000
xs
210 000
→
: 0.6 =
: 0.6 =
or in general
WXL/R cover on retention
: QS retention
as a fraction =
WXL/R deductible on retention : QS retention
as a fraction =
WXL/R cover for
a 100 % limit of liability
1 650 000
xs
350 000
100 % WXL/R cover
100 % WXL/R deductible
Note for the non-mathematically minded: If you are having problems following these calculations,
try doing them in reverse. Assume that you know the WXL/R cover for a 100 % treaty limit and have
to work out the 60 % treaty limit. The calculations would then look like this:
60 % of 1 650 000, or 1 650 000 x 0.6 = 990 000 and
60 % of 350 000, or 350 000 x 0.6 = 210 000
As dividing is the opposite of multiplying you should now be able to see why we have to divide by the
QS retention as a fraction if we want to calculate the WXL/R on the 100 % quota share from the WXL/R
on the quota share retention.
The WXL/R on the 100% quota share with the same deductible amount of 210 000
requires a higher WXL/R reinsurance premium rate than the WXL/R on the quota
share retention of 990 000 per risk xs 210 000 per risk. This results alone from the
fact that an additional layer of 140 000 per risk xs 210 000 per risk would be necessary to provide protection up to the deductible of 350 000 per risk of the WXL/R cover of 1 650 000 per risk on a gross basis.
14 Combination of proportional and non-proportional treaty types – Module 4
Easy adaptation of the WXL/R to changes in the quota share cession percentage
(2nd peculiarity)
The cession percentage of a quota share cession is often changed; for example, the primary
insurer and reinsurer may agree that the quota share cession (eg a solvency relief quota
share) is reduced successively each year until it reaches 0.
To avoid having to adjust the WXL/R each year, the primary insurer places a WXL/R for
100 % treaty limit at the outset and then buys only the percentage rate of this WXL/R
that it actually needs for its retention. Instead of adjusting the WXL/R each year to changes
in the quota share cession, only the percentage placed has to be adjusted to the relevant
quota share retention.
2/4
E
Adjusting a WXL/R on a 100 % treaty limit to the percentage of the quota share retention
We will use the figures from the previous example and assume that the primary
insurer wishes to reduce the quota share cession from 40 % to 0 within 5 years by
increasing the quota share retention by 10 % each year.
The primary insurer buys a WXL/R of 1 650 000 per risk xs 350 000 per risk from
the outset.
However: in the first year, the primary insurer only places the 60 % it needs for its
quota share retention, or 990 000 (=1650 000 x 0.6) xs 210 000 (= 350 000 x 0.6).
If the quota share retention is increased to 70 % in the second year, it will place
1650 000 x 0.7 = 1155 000 xs 350 000 x 0.7= 245 000, etc. In other words,
it increases the percentage placed from 60 % to 70 %.
This brings us almost to the end of this section on the combination of a quota share and
a WXL/R on the quota share retention. It should be clear to you now that this is quite a
common combination:
1. in classes of insurance which are not particularly suited to surplus reinsurance (eg motor
own damage insurance);
2. in cases where the reinsurer is reluctant to underwrite a pure WXL/R and where the
prospect of a quota share cession (supporting quota share) makes a participation in
the WXL/R more attractive; and
3. in cases where the primary insurer also has an interest in this combination, namely when
a pure WXL/R would be too expensive and the primary insurer would rather cede part
of its business in the form of a quota share in order to obtain a better premium rate for
the WXL/R by granting the parallel quota share.
15 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
2.1.2 Quota share with a WXL/E on the quota share retention
This combination works in exactly the same way as the quota share with a WXL/R on the
quota share retention as long as there are only losses affecting individual independent risks.
However, if several losses are caused by the same event, the situation looks totally different.
2/5
E
Quota share with a WXL/E on the quota share retention
We will use the same figures as in Example 2/2 (pages 12 - 14), with the following
changes:
– The quota share retention is protected by a WXL/E instead of a WXL/R.
– The losses incurred by risks 2 and 4 are caused in the same year by the same
event.
As we already know how the quota share works, we can limit ourselves here to
analysing the effect on the apportionment of losses to the retention and the WXL,
now a WXL/E.
Apportionment of losses under the new reinsurance programme (figures in thousands):
Risk no.
Retained loss
before WXL/E
1
2 and 4
3
5
6
210
1380
210
540
240
WXL/E on QS
retention 990 000
xs 210 000
0
990
0
330
30
Total
2580
1350
Retention
after WXL/E
210
210
210
210
210
1050
180
1230
Not covered
by WXL/E
180
|
|
|
|
|
————————
We can see that, by aggregating losses to several risks because they were caused by
the same event, the burden on the WXL is increased. In this case, however, the increase is only small as there is a gap in cover of 180 000, which the primary insurer
has to bear.
The moral of the story is: whoever buys protection in the form of a WXL/E instead of a
WXL/R needs more cover, in other words, more than up to the highest retention per risk.
Just how much more depends on the accumulation potential per event. Refer to the digression on the next page for further thoughts on this dilemma.
First, however, we would like to point out that the combination of a quota share and a WXL/E
on the retention offers additional protection for the primary insurer for the accumulation
and catastrophe accumulation risks which are only partially ceded under the quota share
cession, but only to the extent of the WXL cover that exists.
16 Combination of proportional and non-proportional treaty types – Module 4
Digression: WXL/E or WXL/R?
To begin with, we would like to stress that the WXL is considered to be an XL which can
be affected by a loss on one individual insured risk, in other words, by a loss that is limited
to the area of insurance policies which are normally considered to be one risk and are combined and treated as such in practice.
There is usually considerable probability of such a loss occurring in the lower WXL layers
or the lower areas of WXL cover.
A WXL can be affected by an individual loss affecting one insured risk or one event which
affects several insured risks at the same time.
If the WXL is applied per event (WXL/E), all losses from the same event are aggregated to
form one ultimate net loss and the deductible and the WXL cover are applied only once per
event to this ultimate net loss.
In the case of an individual loss affecting one insured risk only, the WXL/R works in exactly
the same way as the WXL/E. The situation is different, however, if losses affecting several
insured risks are triggered by one and the same event. With the WXL/R, each individual risk
loss represents a separate ultimate net loss, to which the deductible and WXL cover are
applied separately. The deductible and WXL cover can therefore be triggered by the event
as many times as there are losses affecting single insured risks (insofar as each of these
losses exceeds the deductible and lies within the cover limit of the WXL). If none of the
losses exceeds the deductible, the WXL/R is not affected.
The question of whether a WXL/E or a WXL/R should be chosen has long been the cause
of controversy and depends largely on the class of insurance involved. In some classes, the
definition of what exactly is “one risk” has become more and more difficult or even unrealisable as insurance has developed. In order to avoid the problems that this has caused, it is
usual in these classes of insurance for WXL cover to be taken out per event.
Admittedly it is also not easy to define what one event is, and experience has shown that the
definitions finally chosen do not always fit every event encountered in practice. We must
remember, however, that one of the purposes of the event definition is to get the primary
insurer to reflect on the loss potential of an accumulation event, whatever its definition, as
then there is less danger of the primary insurer being misled into buying far too little event
coverage.
The WXL/E has significant disadvantages: for the same deductible and cover it protects against
two fundamentally different exposures: those per risk and those per event. These two types
of exposure are driven by fundamentally different forces of development. This explains the
tendency such covers have to fall apart over the course of time. The duality of the exposures
of the WXL/E can also cause unexpected gaps in cover, in which the sum total of the losses
per event is higher than the deductible plus cover, so that no more cover is available for losses from the same event affecting individual independent risks.
17 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
In property insurance in particular, attempts are therefore being made to overcome this
duality by splitting the reinsurance protection into WXL/R and CatXL cover per event.
Although this separates the two types of exposure, it still remains difficult, even in property
insurance, to define what is one risk.
Also in property insurance, cedents often prefer a solution involving WXL/E cover, since this
allows the seamless addition of further layers by using the same definition for the ultimate net
loss for all covers. The reinsurer does not like the duality of the WXL/E in property insurance,
preferring instead the combined WXL/R and CatXL solution. This eliminates a large part of
the disadvantages of the WXL/E and also makes it possible to take into account individually
the diversity of the per-risk and per-event exposures when setting the deductible and structuring cover as part of a tailor-made programme.
When concluding WXL/E and WXL/R covers, particular importance should be placed on
setting practical and effective (ie correspondingly defined) original underwriting limits to
which the primary insurer has to be bound in the WXL reinsurance treaty. These limits are
key to determining the extent to which the WXL cover will be exposed to losses affecting
individual independent risks.
Depending on the level of the deductible – in particular with effective definition and limitation of the original underwriting limits – the high WXL/E layers or upper parts of WXL/E
single layers can take on an almost CatXL character (ie they are almost only hit by events
affecting several insured risks at the same time).
18 Combination of proportional and non-proportional treaty types – Module 4
S
Combination of quota share reinsurance and a WXL/R on the quota share retention
The WXL/R serves to stabilise the claims experience of an unbalanced quota share retention
portfolio by spreading individual, relatively high losses over several years.
This combination is used
– in classes of insurance which are not particularly suited to surplus reinsurance (eg motor
own damage insurance);
– in cases where the reinsurer is reluctant to underwrite a pure WXL/R and where the
prospect of a quota share cession makes a participation in the WXL/R more attractive;
– in cases where the pure WXL/R would be too expensive and the primary insurer would
rather cede part of its business to a quota share in order to obtain a better premium rate
for the WXL/R by virtue of the parallel quota share cession.
Combination of quota share reinsurance and a WXL/E on the quota share retention
The WXL/E also serves to stabilise an unbalanced quota share retention portfolio by
spreading over several years the sum of the losses caused by one and the same event and
affecting one or more insured.
This combination is used when it is difficult or impossible to limit and define precisely
what one risk is.
The duality of the exposures – per risk and per event – can cause unexpected gaps in cover
in cases where the ultimate net loss per event is higher than the deductible plus cover,
so that the reinsurance protection cannot cover the sum of all losses from the same event
affecting individual independent risks.
19 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
2.2 Combination of a surplus and a WXL on the retention
2.2.1 Surplus with a WXL on the retention
The surplus treaty is used to procure sufficient capacity per risk. In many cases it is possible
to satisfy the primary insurer’s capacity requirements with its chosen retention and a reasonable number of lines under the surplus. However, for the retained portfolio, the ratio of
treaty limit per risk to annual premium income often remains relatively poor. In other
words, the homogenising effect of the surplus on the retained portfolio is not yet sufficient.
In order to avoid a situation whereby the primary insurer has to choose a lower retention in
order to achieve a better balance in the retained portfolio, increase the number of surplus
lines and cede even more premium, or is even forced to reduce its reinsurance capacity, the
primary insurer can opt to protect its retention with a WXL/R. Although this does not improve the balance of the retention per se, it does enable the primary insurer to smooth the
effect of individual losses which correspond to or approach the maximum retention by means of
the non-proportional WXL/R, ie to spread these over several years.
Figure 2/3:
Combination of surplus and a
WXL/R on the retention
Surplus
Retention (1 line)
WXL/R cover
Deductible
20 Combination of proportional and non-proportional treaty types – Module 4
2/6
E
Surplus with a WXL/R on the retention
An insurance portfolio is reinsured as follows (figures in thousands):
Surplus
Premium income
(remains stable)
Treaty limit/
sum insured
Retention (1 line)
Surplus with 9 lines
8 000
10 000
1 000 per risk
9 000 per risk
WXL/R on the retention
750 per risk xs 250 per risk
Facultative proportional reinsurance
for all portions of liability above
10 000 per risk
The following losses are incurred over a period of 5 years:
Risk no.
1
2
3
4
5
6
7
8
9
Sum insured
900
500
3 000
(fac RI 2 000!) 12 000
400
2500
800
4 000
1 500
Loss (gross)
600
450
750
2 400
350
500
750
1 000
450
The losses incurred are apportioned to the facultative reinsurance, the surplus and
the WXL/R as follows:
1. Losses apportioned to fac prop reinsurance for risks which exceed the surplus
treaty limit
Risk no.
4
Liability
12 000
loss
2 400
fac
prop
2 000
(2/12)
Shares of liability
Surplus Surplus
retention
9 000
1 000
(9/12)
(1/12)
Shares of loss
fac
Surplus Surplus
prop
retention
400 1 800
200
2. Apportionment of losses to the surplus and the surplus retention
Risk no.
Liability
Loss
1, 2, 5, 7
3
6
8
9
< 1 000
3 000
2 500
4 000
1 500
various
750
500
1 000
450
Shares of liability
Surplus
Surplus
retention
0
all liabilities
(2/3) 2 000 (1/3) 1 000
(3/5) 1 500 (2/5) 1 000
(3/4) 3 000 (1/4) 1 000
(1/3) 500 (2/3) 1 000
Shares of loss
Surplus
Surplus
retention
0
all losses
(2/3) 500
(1/3) 250
(3/5) 300
(2/5) 200
(3/4) 750
(1/4) 250
(1/3) 150
(2/3) 300
21 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
3. Apportionment of losses to the WXL/R and the deductible
Risk no.
Loss to surplus
retention
600
450
250
200
350
200
750
250
300
1
2
3
4
5
6
7
8
9
Deductible
Net retained loss
250
250
250
250
250
250
250
250
250
250
250
250
200
250
200
250
250
250
Share of loss
to WXL/R
350
200
0
0
100
0
500
0
50
Losses affecting the WXL/R occur relatively seldom. The absolute frequency is therefore low. This is a prerequisite to prevent the WXL/R from becoming overloaded.
(Here, the frequency is 5 losses in 5 years, ie 1 loss per year.)
Note
In our example, the frequency, seen in relation to the
total number of losses is relatively high because we did
Risk/
loss no.
Gross
loss
fac prop RI
not want to overload the example with numerous losses that do not affect the WXL.
Surplus
WXL/R on retention
9 lines of 1 000
750 xs 250
Loss to
Loss to retensurplus
tion before
WXL/R
Retention
after WXL/R
1
600
0
600
350
250
2
450
0
450
200
250
3
750
250
0
250
(1/12) 200
0
200
350
100
250
4
(2/3)
500
2 400 (2/12) 400 (9/12) 1800
(1/3)
5
350
6
500
7
750
8
1 000
(3/4)
750
(1/4)
250
0
250
9
450
(1/3)
150
(2/3)
300
50
250
3 350
1 200
2 150
Total
7 250
0
(3/5)
300
(2/5)
0
400
3 500
200
0
200
750
500
250
Note on Example 2/6
The balance of the surplus retention before the WXL/R
is equal to the ratio of the limit of liability per risk to the
annual premium income = 1 000 000 : 8 000 000 =0.125.
In other words, a single maximum loss per risk can use
up a full 12.5 % of the annual premium income – that
is too much for a retention. The WXL/R improves this
ratio to 250 000 : 8 000 000. This means that the maximum amount that the primary insurer retains for own
account on an individual loss per risk cannot exceed
3.125 % of premium income. However, it is now no
longer a maximum limit per risk, but a deductible or a
loss limit which the primary insurer must bear itself in
full in the event of a loss. Over 5 years, the retained
premium income amounts to 40 000 000 (5 x 8 000 000),
compared to a loss burden under the WXL/R of
1 200 000, or 3 % of the underlying premium income.
22 Combination of proportional and non-proportional treaty types – Module 4
From the figures presented, we can draw two interesting inferences:
– First observation: The WXL/R is affected in particular when the risk loss ratio,
ie the ratio of the risk loss to sum insured, is relatively high. This is particularly
true for smaller risks, which is not surprising given that the WXL/R only starts to
operate when the deductible has been reached. Even with a maximum retention
of 1 000 000, the risk loss ratio must exceed 25 % to trigger the WXL/R (25 % of
1 000 000 = 250 000).
Examples are risks 1, 3, 4, and 5:
Risk 1
Loss 600 000; retention 900 000
Loss ratio 66 2/3 % (600 000 : 900 000 = 0.6666)
WXL/R pays 350 000
Risk 3
Loss 250 000; retention 1 000 000
Loss ratio 25 % (250 000 : 1000 000 = 0.25)
WXL/R pays 0
Risk 4
Loss 200 000; retention 1000 000
Loss ratio 20 % (200 000 : 1000 000 = 0.2)
WXL/R pays 0
Risk 5
Loss 350 000; retention 400 000
Loss ratio 87,5 % (350 000 : 400 000 = 0.875)
WXL/R pays 100 000
– Second observation: Large losses often correspond to relatively large sums insured.
The siphon effect of the prior proportional surplus cession means, however, that
the WXL/R is only used when the risk loss ratio exceeds 25 % (see also Section 3).
Examples are risks 3, 8, and 9:
Risk 3
Gross loss 750 000; gross sum insured 3 000 000
Share of retention 250 000; retention 1 000 000
Loss ratio 25 % (250 000 :1000 000 = 0.25)
WXL/R pays 0
Risk 8
Gross loss 1000 000; gross sum insured 4 000 000
Share of retention 250 000; retention 1000 000
Loss ratio 25 % (250 000 : 1000 000 = 0.25)
WXL/R pays 0
Risk 9
Gross loss 450 000; gross sum insured 1500 000
Share of retention 300 000; retention 1000 000
Loss ratio 30 % (300 000 : 1000 000 = 0.3)
WXL/R pays 50 000
23 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
The WXL/R is primarily a cover for major risks in the portfolio and for higher risk loss
ratios. This is no secret, but it is worthwhile remembering it in practice.
In our example, nothing can happen to our WXL/R if the gross liability is less than
250 000. The same applies if the primary insurer reduces the surplus retention to
250 000 for major gross liabilities.
Likewise, the risk loss ratio for the maximum retention must be above 25 % in order
to trigger the WXL/R; or already as much as 40 % for a retention of 625 000.
2.2.2 Surplus with a WXL/E on the retention
This combination works in exactly the same way as the surplus with a WXL/R on the retention
as long as there are only losses affecting individual independent risks. However, if several losses
are caused by the same event, the situation looks totally different.
2/7
E
Surplus with a WXL/E on the retention
We will use the same figures as in Example 2/6 (pages 21–23), with the following
changes:
– The surplus retention is protected by a WXL/E instead of a WXL/R.
– The losses incurred by risks 1 and 7 are caused by the same event.
As we already know how the surplus works, we can limit ourselves here to analysing
the effect on the apportionment of losses to the retention and the WXL, now a WXL/E.
Apportionment of losses under the new reinsurance programme:
Risk no
Retained loss
before WXL/E
1 and 7
2
3
4
5
6
8
9
600 + 750 = 1 350
450
250
200
350
200
250
300
Total
3 350
WXL/E
on retention
750 xs 250
750
200
0
0
100
0
0
50
1 100
Retention
after WXL/E
Not covered
by WXL/E
250
250
250
200
250
200
250
250
1 900
350
2 250
350
|
|
|
|
|
|
|
|
|
——————————
24 Combination of proportional and non-proportional treaty types – Module 4
We can see that, as with the quota share, the burden on the WXL is increased by
aggregating losses to several risks caused by the same event.
In this case, however, the increase is only small as there is a gap in cover of
350 000, which falls back to the primary insurer’s retention!
At this point it is perhaps useful to remember that the combination of a surplus and a WXL/E
on the retention provides protection for the retained portfolio against accumulation risks
(and, insofar as the cover is sufficient, catastrophe accumulation risks), which would not be
the case with surplus reinsurance alone.
S
The combination surplus and a WXL/R on the retention
The surplus is used to procure sufficient capacity per risk and level out the risks in the
retained portfolio.
The WXL/R is added to stabilise the annual loss burden of the retained portfolio by enabling
the primary insurer to smooth the effect of individual losses which correspond to or
approach the maximum retention by means of the non-proportional WXL/R, ie to spread
these over several years.
The combination surplus and a WXL/E on the retention
The surplus works in exactly the same way in this combination.
The WXL/E ensures that the annual loss experience on the retained portfolio is stabilised
by spreading the sum of the losses caused by one and the same event and affecting one
or more insured risks over several years, insofar as they remain in the primary insurer’s
retention.
This combination is used when it is difficult or impossible to limit and define precisely
what one risk is.
What we have previously mentioned regarding the combination of quota share and a
WXL/E also applies here: the duality of the WXL/E exposures – per risk and per event –
can cause unexpected gaps in cover in cases where the total loss per event is higher
than the deductible plus cover, so that the reinsurance protection is not sufficient to
cover losses from the same event affecting individual independent risks.
25 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional
reinsurance treaty types
2.3 Combination of a quota share or surplus and a CatXL on the retention
2.3.1 Quota share with a CatXL on the quota share retention
In Module 2 we saw that one of the advantages of quota share reinsurance is that the primary
insurer is able to pass on to the reinsurer a uniform proportional quota share cession from
the reinsured portfolio including the corresponding portion of the catastrophe accumulation
risk.
As a result, only the quota share retention – comprising the primary insurer’s uniform percentage share in all risks ceded to the quota share, whether small or large – is still exposed
to catastrophe risks. Depending on the constellation, a natural disaster may affect not only
large risks, but also a host of small risks, thereby creating a large catastrophe accumulation.
To protect itself against this catastrophe accumulation, which may threaten the company’s
existence, the primary insurer can take out a CatXL on the quota share retention. As we
know, the CatXL is an XL/E which is normally only triggered when one and the same loss
event affects more than one risk.
Figure 2/4:
Combination of quota share
and a CatXL
CatXL cover
Quota share retention 75%
Quota share
cession
25%
Deductible
Claims in the quota share retention
per event
26 Combination of proportional and non-proportional treaty types – Module 4
2/8
E
Combination of quota share and a CatXL on the quota share retention
Reinsurance cover
Quota share retention
Quota share cession
Quota share limit (automatic underwriting capacity)
75 %
25 %
100 %
1 200 000 per risk
400 000 per risk
1 600 000 per risk
Facultative proportional reinsurance for peak risks above 1 600 000 per risk.
CatXL for 1 500 000 per event xs 1 500 000 per event
Losses: 7 losses occur, caused by one and the same event, as follows:
Loss no.
1
2
3
4
5
6
7
Sum insured
2 100 000
1 400 000
600 000
840 000
6 400 000
320 000
720 000
Shares of loss
1 680 000
280 000
400 000
756 000
1 120 000
320 000
360 000
Total
4 916 000
Apportionment of losses (in thousands)
No.
1
2
3
4
5
6
7
fac
prop
500 = 24 %
0
0
0
4 800 = 75 %
0
0
Shares of liability
QS cession
QS retention
fac
prop
400 = 19 % 1 200 = 57 %
400
350 = 25 % 1 050 = 75 %
0
150 = 25 %
450 = 75 %
0
210 = 25 %
630 = 75 %
0
400 = 6 1⁄4 % 1 200 = 18 3⁄4 %
840
80 = 25 %
240 = 75 %
0
180 = 25 %
540 = 75 %
0
Total
1 240
Shares of loss
QS
QS recession tention
320
960
70
210
100
300
189
567
70
210
80
240
90
270
919
2 757
Calculation for CatXL:
Ultimate net loss = sum of risk losses falling to the quota share retention = 2 757 000.
Share of CatXL, ie amount reimbursed by CatXL reinsurer to primary insurer: ultimate
net loss (2 757 000) – deductible (1 500 000) = 1 257 000.
It is clear that the CatXL cover would have soon been exhausted if a few more risks
had been affected by the same catastrophic event. The quota share cession assumed
a share of 919 000 = 25 % of the sum of losses affecting the 100 % QS of 3 676 000.
27 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional reinsurance treaty types
2.3.2 Surplus with a CatXL on the retention under the surplus
The surplus provides the necessary capacity per risk and improves the balance in the retained
portfolio.
However, all small and minor risks remain in the retention. If a catastrophe event were
to affect these risks, such an event could result in an extremely large accumulated loss.
The primary insurer can protect itself against this by means of a CatXL.
2/9
E
The combination of surplus and CatXL
Figure 2/5:
Combination of surplus and
a CatXL
CatXL cover
Surplus
Deductible
Retention (1 line)
Claims in the retention per event
A surplus covers a portfolio of individual risks which exceed the retention of 500 000
per risk. If only losses affecting individual risks were to occur, this would be sufficient cover for the portfolio, as the premium volume on the retention is 25 000 000.
As a result, an individual loss cannot account for more than 2 % of premium income.
However, several parts of the portfolio are exposed to heavy explosion risks (eg fireworks factories). The explosions expert estimates, after an assessment of the various
areas on the spot, that in the worst case 8 risks would be completely destroyed and
25 others partly affected.
28 Combination of proportional and non-proportional treaty types – Module 4
He calculates: 8 x 500 000 = 4 000 000 and 25 x 200 000 = 5 000 000,
together perhaps 9 –10 000 000.
The primary insurer is not able to bear such a large amount in its retention, so it purchases a CatXL of say 9 000 000 per event with a deductible of 1 000 000 per event.
S
Combination of quota share and CatXL
The quota share provides additional automatic capacity and absorbs a portion of the
catastrophe accumulation risk as part of the quota share cession.
The CatXL offers additional protection for the remaining catastrophe accumulation risk
that is retained in the quota share retention.
Combination of surplus and CatXL
The surplus provides the necessary capacity per risk and levels out the risks in the retained
portfolio.
The CatXL offers protection against catastrophe accumulations in the otherwise unprotected surplus retention.
29 Combination of proportional and non-proportional treaty types – Module 4
2. The most common combinations of proportional and non-proportional reinsurance treaty types
R
1. Situation: A primary insurer wants to obtain underwriting capacity by taking out a
surplus treaty. To minimise administration, the level of the primary insurer’s retention
under the surplus is set quite high. This retention is then reduced by means of a quota
share and protected against claims fluctuations by a WXL/R on the quota share retention.
Surplus
Retention (1 line)
Surplus with 4 gross lines
Premium income
8 000 000
not relevant
Maximum liability
2 000 000
8 000 000
Quota share on the surplus retention
Quota share cession (60 %)
Quota share retention (40 %)
4 800 000
3 200 000
1 200 000
800 000
WXL/R on the quota share retention
700 000 per risk xs 100 000 per risk
Facultative proportional reinsurance
For all shares of liability > 10 000 000
a) During the treaty negotiations, discussion also dwells on whether, given the conditions
(maximum deductible 100 000; no decrease in underwriting capacity), it would also
make sense to have a solution combining a surplus and a WXL/R on the retention.
What would the terms of this WXL/R have to be?
b) The additional quota share increases the loss amount which has to be reached before
the WXL/R operates on a gross basis. Which deductible would have to be set on the
gross business in order for it to correspond to the deductible of 100 000 under the
quota share retention?
c) “A WXL/R with the same deductible on the surplus retention that would correspond
to a limit of 100 % quota share (= 2 000 000) requires additional cover.” Explain why
this statement is true.
d) In addition to the losses with loss amounts of less than 250 000, a further 5 individual large losses occur within a period of 5 years (cf table on page 31).
Complete the table on the following page by calculating the apportionment of losses.
2. a) When would a WXL/E on the relevant retention be advisable in the case of combinations involving quota share reinsurance and surplus reinsurance?
b) In the case of the WXL/E, what do you understand by duality of exposures and
to what should particular attention be paid when combining other treaties with a
WXL/E?
30 Combination of proportional and non-proportional treaty types – Module 4
31 Combination of proportional and non-proportional treaty types – Module 4
900 000
4 000 000
5
600 000
1 500 000 1 200 000
4
600 000
3 000 000
12 000 000 9 000 000
1800 000
Gross loss
3
2
1
No. Liability
fac prop
Figure to revision question 1d) on page 30
Surplus RI
4 lines of 2 000 000
Cession
Retention
Quota share RI
Maximum liability 2 000 000
Cession 60%
Retention 40%
Apportionment of losses
WXL/R
700 000 xs 100 000
Cover
Deductible
3. Interactions between proportional and non-proportional reinsurance
treaty types
We have already seen that a reinsurance treaty has an effect on the reinsured portfolio. For
example, how it is possible to balance or homogenise the portfolio retained by the primary
insurer (retained portfolio) by means of a surplus treaty. We have also shown, using simple
examples, how various reinsurance treaties impact on one another when used in combination on the same reinsured portfolio.
These interactions stem from the difference in nature of the units of reference to which the
limits are applied. They are of particular importance in the combination of proportional and
non-proportional reinsurance:
– In proportional reinsurance, claims (and premiums) are apportioned in the same ratio as
the liability. Once a risk has been ceded to the reinsurance treaty, the reinsurer has to bear
its share also of minor and small claims.
Note
For the sake of completeness, we would like to remind
you that, in the case of quota share, all insurance
contracts in the portfolio are ceded up to the treaty
limit; for surplus reinsurance, all insurance contracts
which exceed the line or chosen retention are ceded
up to the treaty limit.
– In non-proportional reinsurance, in contrast, the crucial factor is the loss amount which
falls to that portion of the risk protected by the non-proportional cover. Only insofar as
this loss amount exceeds the deductible does the reinsurer participate in the loss up to the
extent of the cover granted.
As soon as a proportional reinsurance treaty is placed on top of a non-proportional one,
the proportional treaty exerts a type of siphon effect in favour of the non-proportional one.
And as soon as a reinsurance combination of this type is changed, the apportionment of
losses is also affected.
We do not want to go into too much detail at this stage, as this will lead us too far into the
area of programme structuring, which is beyond the scope of this introduction. Instead
we will use three working examples to highlight the interactive effects that proportional and
non-proportional reinsurance covers exert on each other.
32 Combination of proportional and non-proportional treaty types – Module 4
3/1
E
Interactions between a quota share and a WXL/R on the quota share retention
A primary insurer has taken out a WXL/R to protect its quota share retention. The
liabilities which exceed the limit of the quota share are protected by proportional
facultative reinsurance.
The primary insurer later decides to reduce the quota share cession (leaving
the treaty limit unchanged) but forgets to adjust the WXL/R cover in line with
the increased quota share retention.
Let us now take a look at how this affects the apportionment of losses:
Original reinsurance cover
QS retention
protected by a WXL/R of
900 000 xs 300 000 per risk
QS cession
QS treaty limit (automatic underwriting capacity)
66 2⁄3 %
1 200 000 per risk
33 1⁄3 %
100 %
600 000 per risk
1 800 000 per risk
Peak risks which exceed 1 800 000 are covered by
facultative proportional reinsurance.
Reinsurance cover later changed to
QS retention
QS cession
QS treaty limit (automatic underwriting capacity)
80 %
20 %
100 %
1 440 000 per risk
360 000 per risk
1 800 000 per risk
Losses: The following 8 losses are incurred:
Loss no.
1
2
3
4
5
6
7
8
Sum insured
900 000
4 500 000
1 500 000
630 000
720 000
3 000 000
570 000
1 290 000
Loss amount
450 000
900 000
780 000
126 000
660 000
3 000 000
300 000
510 000
Total
6 726 000
33 Combination of proportional and non-proportional treaty types – Module 4
3. Interactions between proportional and non-proportional reinsurance
treaty types
Apportionment of losses under original reinsurance cover (in thousands)
No.
Liability Loss
1
2
3
4
5
6
7
8
Total
900
4 500
1 500
630
720
3 000
570
1 290
450
900
780
126
660
3 000
300
510
6 726
Shares of liability
Shares of loss
fac
QS
QS
fac
QS
WXL/R QS retenprop
cession
retention
prop cession
tion/deduc.
0
300 =331⁄3% 600 =662⁄3%
0
150
0 300 =16 2⁄3 %
2 700 = 60 % 600 =131⁄3% 1 200 =262⁄3%
540
120
0 240=26 2⁄3 %
1
2
0
500 =33 ⁄3% 1 000 =66 ⁄3%
0
260
220 300=ded.
0
210 =331⁄3% 420 =662⁄3%
0
42
0 84=66 2⁄3 %
0
240 =331⁄3% 480 =662⁄3%
0
220
140 300=ded.
1 200= 40 % 600 = 20% 1 200 = 40 % 1 200
600
900 300=ded.
0
190 = 331⁄3% 380 = 662⁄3%
0
100
0 200=66 2⁄3 %
1
2
0
430 = 33 ⁄3% 860 = 66 ⁄3%
0
170
40 300=ded.
1 740 1 662 1 300 2 024
Apportionment of losses after reduction in quota share cession (in thousands)
No.
Liability Loss
1
2
3
4
5
6
900
4 500
1 500
630
720
3 000
450
900
780
126
660
3 000
7
8
Total
570
1 290
300
510
6 726
Shares of liability
fac
QS
QS
prop
cession
retention
0
180 = 20 % 720 = 80 %
2 700 = 60 % 360 = 8 % 1 440 = 32 %
0
300 = 20 % 1 200 = 80 %
0
126 = 20 % 504 = 80 %
0
144 = 20 % 576 = 80 %
1 200 = 40 % 360 = 12 % 1 440 = 48 %
0
0
114 = 20 % 456 = 80 %
258 = 20 % 1 032 = 80 %
Shares of loss
fac
QS
WXL/R QS retenprop cession
tion/deduc.
0
90
60 300 = ded.
540
72
0 288 = 32 %
0
156
324 300 =ded.
0
25
0 101 = 80 %
0
132
228 300 = ded.
1 200
360
900 300 ded.
+240*
0
60
0 240 = 80 %
0
102
108 300 = ded.
1 740 997 1 620 2 369
* Note on loss no. 6: the portion of the loss that remains in the quota share retention of 1 440 000
(48 % of 3 000 000) exceeds the ceiling of the WXL/R (deductible plus cover) by 240 000, which
thus falls back to the primary insurer’s net retention.
Result: A significantly heavier burden is placed on the WXL/R by the increase in the
quota share retention from 66 2⁄3 % to 80 %, namely 1 620 000 instead of 1 300 000,
a difference of 320 000 or almost 25 % more. Through the primary insurer’s carelessness, a gap in cover of 240 000 has emerged for loss no. 6 as a result of insufficient
cover under the WXL/R. In order to absorb a total loss of this kind under the treaty limit, the WXL/R limits on the quota share retention should have been adapted as follows:
34 Combination of proportional and non-proportional treaty types – Module 4
Previous quota share retention 66 2⁄3 %, WXL/R cover 900000, deductible 300000,
corresponding to a ceiling of 1 200 000.
New quota share retention 80 %, ie
WXL/R cover 900 000 : 66 2⁄3 x 80 =
1 080 000 and deductible 300 000 : 66 2⁄3 x
80 = 360 000 corresponding to a new ceiling of 1 440 000 (ie plus 240 000).
Of course, the WXL/R reinsurer would object to an increase in the quota share retention protected by the WXL/R without the corresponding adjustment to the WXL/R
limits.
3/2
E
Interactions between a surplus and a WXL/R
A primary insurer reinsures its portfolio by means of a surplus treaty and wants to
additionally protect its retention with a WXL/R.
The primary insurer later decides to increase its retention and protect this increased
retention with an additional WXL/R (2nd layer or 2nd WXL/R).
We maintain that this change will have a decisive impact on the exposure of the
existing WXL/R (now the 1st WXL/R). In order to substantiate this statement,
let us take a look at the constellation we have described using the following figures:
Original reinsurance cover
Retention = 1 line
protected by a WXL/R of 300 000 xs 100 000 per risk
Surplus (2.5 lines @ 400 000)
Underwriting capacity
400 000 per risk
1 000 000 per risk
1 400 000 per risk
Reinsurance cover later changed to
Retention = 1 line
protected by
1st WXL/R of 300 000 xs 100 000 per risk
and 2nd WXL/R of 300 000 xs 400 000 per risk
Surplus (1 line @ 700 000)
Underwriting capacity
700 000 per risk
700 000 per risk
1 400 000 per risk
Losses: The following 5 losses are incurred:
Loss No.
1
2
3
4
5
6
Sum insured
300 000
80 000
1 200 000
600 000
900 000
700 000
Total
Loss amount
270 000
50 000
900 000
300 000
630 000
140 000
2 290 000
35 Combination of proportional and non-proportional treaty types – Module 4
3. Interactions between proportional and non-proportional reinsurance treaty types
Apportionment of losses under original reinsurance cover (in thousands)
No. Liability
Loss
Shares of loss
Comments
Surplus
WXL/R
Reten2.5 lines @ 400
300 xs 100 tion
0
170
100
Surplus not affected.
0
0
50
Surplus and WXL/R
1
2
300
80
270
50
3
1 200
900
600
200
100
Surplus cession of 800
with loss apportionment
2/3 RI, 1/3 primary insurer.
4
600
300
100
100
100
Surplus cession of 200
with loss apportionment
1/3 RI, 2/3 primary insurer.
5
900
630
350
180
100
Surplus cession of 500
with loss apportionment
5/9 RI, 4/9 primary insurer.
6
700
140
60
0
80
Surplus cession of 300
with loss apportionment
3/7 RI, 4/7 primary insurer.
WXL/R not affected.
2 290
1 110
650
530
not affected.
Total
Apportionment of losses under new reinsurance cover (in thousands)
No. Liability
Loss
Surplus
1 line
@ 700
Shares of loss
2nd
1st
WXL/R
WXL/R
300 xs
300 xs
400
100
0
170
0
0
Comments
100
50
Surplus not affected.
Retention
1
2
300
80
270
50
0
0
3
1 200
900
375
125
300
100
Risk triggers surplus cession
of 500. Loss apportionment
5/12 RI, 7/12 primary insurer.
4
5
600
900
300
630
0
140
0
90
200
300
100
100
Surplus not affected.
6
700
Total
140
2 290
0
515
0
215
40
1 010
100
550
Surplus and WXL/R not
affected.
Risk triggers surplus cession
of 200. Loss apportionment
2/9 RI, 7/9 primary insurer.
Surplus not affected.
Result: Under the original reinsurance cover, the portion of the risks exceeding
400 000 would be reinsured proportionally under the surplus treaty. With the new
reinsurance cover, the proportional surplus reinsurance is set to start only at 700 000,
and the difference is covered non-proportionally by a 2nd WXL/R. This means that
the siphon effect of the proportional reinsurance treaty does not work for losses 4
and 6, while for losses 3 and 5 it is reduced. The result: the 1st WXL/R has to bear
a portion of 1 010 000 of the losses, instead of the 650 000 borne by the original
WXL/R. In other words, the loss burden for the unchanged WXL/R 300 000 xs 100 000
is increased significantly simply because the reinsurance cover above the ceiling of
400 000 has been changed from a proportional (surplus) treaty to a non-proportional
(2nd WXL/R) one.
It is thus clear that whether the liabilities on top of the 1st WXL/R are reinsured on
a proportional or non-proportional basis has a significant impact on the risk borne by
this cover.
36 Combination of proportional and non-proportional treaty types – Module 4
3/3
E
Interactions between a surplus, WXL/R and CatXL
A primary insurer has reinsured its portfolio with a surplus treaty. The retention is
covered by a CatXL per event against catastrophe risks.
The primary insurer later quadruples its retention and takes out a WXL/R to protect
it. In other words, the net retention is still the same as the previous retention but is
no longer a line but a loss limit or deductible. Similar to the retention under the original reinsurance, the net retention (WXL/R deductible) is protected by the CatXL per
event against catastrophe losses.
We maintain that this change will significantly increase the burden on the CatXL. Here
is the illustration in figures:
Original reinsurance cover
Retention = 1 line
Surplus (9 lines @ 100 000 per risk)
Underwriting capacity
CatXL per event
100 000 per risk
900 000 per risk
1 000 000 per risk
750 000 xs 250 000 per event
Reinsurance cover later changed to
Retention = 1 line
protected by WXL/R of
300 000 per risk xs 100 000 per risk
400 000 per risk
Surplus (1.5 lines @ 400 000 per risk)
Underwriting capacity
CatXL per event
600 000 per risk
1 000 000 per risk
750 000 xs 250 000 per event
Losses: The following 4 losses are caused by the same event:
Loss no.
1
2
3
4
Sum insured
90 000
600 000
800 000
300 000
Loss amount
70 000
480 000
560 000
240 000
Total
1 350 000
37 Combination of proportional and non-proportional treaty types – Module 4
3. Interactions between proportional and non-proportional reinsurance
treaty types
Apportionment of losses under original reinsurance cover (in thousands)
No. Liability
Loss
Shares of loss
Comments
Surplus
Retention
9 lines @ 100
1 line @ 100
—
70
Surplus not affected.
400
80
Surplus cession of 500. Loss appor-
1
2
90
600
70
480
3
800
560
490
70
Surplus cession of 700. Loss apportionment 7/8 RI, 1/8 primary insurer.
4
300
240
160
80
Surplus cession of 200. Loss apportionment 2/3 RI, 1/3 primary insurer.
1 350
1 050
300
tionment 5/6 RI, 1/6 primary insurer.
Total
CatXL 750 xs 250
RI cover
50
Deductible
250
Apportionment of losses under new reinsurance cover (in thousands)
No. Liability Loss
Surplus
1.5 lines
@ 400
0
Shares of loss
Comments
WXL/R
Retention
after WXL/R
300 xs 100 (net retention)
0
70
Surplus and WXL/R
1
90
70
2
600
480
160
220
100
Surplus cession of 200 with
loss apportionment 1/3 RI,
2/3 primary insurer.
3
800
560
280
180
100
Surplus cession of 400 with
loss apportionment 1/2 RI,
1/2 primary insurer.
4 300
Total
240
1 350
0
440
140
540
100
370
Surplus not affected.
not affected.
CatXL 750 xs 250
RI cover
120
Deductible
250
Result: The previous retention was quadrupled to 400 000 per risk, and a WXL/R of
300 000 xs 100 000 taken out to protect it. The net retention per risk thus remains
the same at 100 000 per risk, only that under the previous cover this was a limit of
liability, and under the new cover it is a loss limit = deductible. In other words, under
the original cover, the liability exceeding the retention of 100 000 per risk was covered
by a proportional reinsurance (surplus). Under the new programme, the liability
exceeding the same net retention of 100 000 is protected for the next 300 000 per
risk by non-proportional reinsurance (WXL/R). In other words, part of the previous
surplus has been replaced by a WXL/R. This means that the loss burden for the
CatXL increases from 50 000 to 120 000. It is clear that the unchanged CatXL is
sensitive to whether the liabilities exceeding the (net) retention are reinsured on
a proportional or non-proportional basis.
The significantly increased catastrophe risk for the (net) retention means a largely
increased loss burden under the CatXL, which reaches the cover limit per event a lot
sooner or may even exceed it. Primary insurers who decide to change their retentions
from a liability to a loss basis are well advised to make sure they have sufficient
catastrophe cover.
38 Combination of proportional and non-proportional treaty types – Module 4
So much on the interactive effects between proportional and non-proportional treaties. Let
us summarise what we have learned:
S
When various types of reinsurance treaties are combined, they exert interactive effects
on each other which could be key in assessing the risk under the individual reinsurance
treaties in a programme. Even if the reinsurer is only participating in one treaty of a reinsurance programme, it must know the entire programme in order to be able to adequately assess the individual treaty it is being offered.
The siphon effect of proportional reinsurance means that the interactive effects are particularly noticeable when combining proportional and non-proportional treaty types.
proportional RI
siphon effect – partial relief
for underlying RI
non-proportional or proportional RI
R
3. An insurance portfolio is reinsured as follows:
Quota share reinsurance
Quota share 100 % treaty limit
Quota share retention (60 %)
Quota share cession (40 %)
4 000 000
2 400 000
1 600 000
WXL/R on the quota share retention
2 000 000 per risk xs 400 000 per risk
Facultative reinsurance
for risks which exceed the treaty limit of 4 000 000
The following losses are incurred:
Risk No.
1
2
3
4
5
6
Sum insured
1 200 000
3 500 000
5 000 000
1 000 000
8 000 000
6 000 000
Loss (gross)
600 000
3 000 000
2 500 000
667 000
1 200 000
5 700 000
39 Combination of proportional and non-proportional treaty types – Module 4
3. Interactions between proportional and non-proportional reinsurance treaty types
Assuming that the primary insurer chooses proportional facultative reinsurance cover
for risks which exceed the quota share treaty limit, what portion of losses incurred by
risks 1–6 must be borne by the facultative reinsurance, the quota share cession, the
WXL/R cover and the insurer’s retention?
Risk/loss Gross
No.
loss
1
2
3
4
5
6
Total
fac prop
Quota share reinsurance
Treaty limit 4 000 000
100 %
Cession
Retention
40 %
60 %
WXL/R
2 000 000 xs 400 000
Cover
Retention
after WXL/R
600
3 000
2 500
667
1 200
5 700
13 667
40 Combination of proportional and non-proportional treaty types – Module 4
41 Combination of proportional and non-proportional treaty types – Module 4
4. Graphical representation of reinsurance programmes
4.1 Per-risk covers
Reinsurance programmes can be represented graphically using a coordinate system.
We proceed as follows:
– On the vertical axis, we enter the sums insured or the limits of the successive reinsurance
covers in the given proportion.
– On the horizontal axis, we show the parallel quota shares, also in the given proportion
and using the same scale, with the quota share retention on the left and the quota share
cession on the right. A 100 % quota share is thus always represented as a square.
4/1
E
Representing quota share/surplus reinsurance with a WXL/R on the quota share
retention
The primary insurer needs automatic underwriting capacity of 3 000 000 per risk
and is able to bear a retention of 150 000 per risk. The reinsurance programme
is structured as follows:
Surplus
2 lines @ 1 000 000
2 000 000 per risk
Quota share reinsurance on the surplus retention
Treaty limit
1 000 000 per risk
Quota share cession 25 % equal to a maximum liability of 250 000 per risk
Quota share retention 75 % equal to a maximum liability of 750 000 per risk
WXL/R on the quota share retention
510 000 per risk xs 240 000 per risk
42 Combination of proportional and non-proportional treaty types – Module 4
Figure 4/1:
Graphical representation of
a reinsurance programme
for the combination of quota
share/surplus reinsurance
and a WXL/R on the quota
share retention.
3 000 000
–
2000 000
–
1000 000
900 000
800 000
700 000
600 000
500 000
400 000
300 000
200 000
100 000
0
–
QS retention (75 %)
QS
–
cession
–
(25 %)
– WXL/R
(510 000 : 0.75 = 680 000)
–
–
–
– Deductible
– (240 000 : 0.75 = 320 000)
–
–
Surplus
Treaty limit 2 000 000
Remember
This figure shows the “gross business”. For this reason, the limits of the WXL/R,
which only comes to bear on the quota share retention, must first be converted to
a gross basis (100 % quota share = surplus retention).
On a gross basis, the WXL/R 510 000 per risk xs 240 000 per risk on the quota
share retention (=net) corresponds to the following WXL/R on a 100 % quota
share (a 100 % quota share is equal to the surplus retention):
WXL/R cover for
75 % maximum liability
(= net)
510 000
xs
240 000
→
: 0.75 =
: 0.75 =
WXL/R cover for
100 % maximum liability
(= gross)
680 000
xs
320 000
43 Combination of proportional and non-proportional treaty types – Module 4
4. Graphical representation of reinsurance programmes
We can represent this graphically provided that we use the same scale on the x and
y axes (in this case the 100 % quota share is always represented as a square!).
Surplus
800 000
A
Upper limit of
WXL/R cover
for protected
QS retention
700 000
.1
600 000
lin
e
no
500 000
300 000
200 000
100 000
X
ht
400 000
.3
o
en
lin
ht
aig
no. 2
r
t
S
line
ight
a
r
t
S
B
WXL/R deductible
on a gross basis
WXL/R deductible
on QS retention
= net retention
75%
0
00 % 10 % 20 % 30% 40 % 50 % 60 % 70% 80 % 90 % 100 %
A
B
X
Deductible
on QS reten- WXL/R share
tion = net
of loss = under
retention
QS retention
900 000
Upper limit of cover
WXL/R
on a gross basis
Loss on QS retention
Quota share
cession
(25%)
Loss under surplus retention
(here 500 000)
Quota share retention (75 %)
WXL/R cover on 75 %
1 000 000
St
ra
ig
Figure 4/2:
Graphical interpretation of
the WXL/R on the quota share
retention
From this figure, we can deduce the following:
– The point 0 on both axes is joined by straight line no.1 to the top-right corner of
the “100 % quota share” square. On the vertical line which borders this square
on the right, we carry through the gross deductible from 0 upwards and join this
point by straight line no. 2 to the point 0 on both axis.
– This gives us a representation of the WXL/R for any quota share covered by this
WXL/R. In our case this is the quota share retention of 75 %. On the vertical line
which borders the QS retention on the right, we can read off the upper limit of
cover and the deductible for the WXL/R for 75 % from the intersections A and B,
and the cover as the difference in between.
– And there’s more: We enter a loss (in our figure, the loss is 500 000) under the 100 %
quota share (after the proportional prior reinsurance, in our example the surplus) on
the vertical line which borders the 100 % quota share to the right and join this point
with straight line no. 3 to the point 0 on both axes. At intersection X of this straight
line no. 3 with the vertical which borders the quota share retention of 75 % to the
right we can read off how much the loss for the 75 % quota share is and to what
extent the WXL/R on the quota share retention is affected (between X and B).
44 Combination of proportional and non-proportional treaty types – Module 4
4.2 Event covers next to per-risk covers
This type of graphical representation is particularly suited for covers on a per-risk basis.
If we also want to draw the per-event covers of a programme, we use a trick that we have
already seen in Module 3: we represent the event cover separately next to the per-risk
covers as a column to be filled in, drawn to the same scale as the per-risk cover.
4/2
E
Graphical representation of event covers next to per-risk covers
We shall expand Example 4/1 by assuming that the primary insurer has also taken
out a CatXL to protect its retention against accumulated losses per event.
CatXL
Figure 4/3:
Graphical representation of
event covers next to per-risk
covers
2 000 000 per event xs 500 000 per event
3 000 000
–
2 500 000
–
2000 000
–
1 500 000
–
1000 000
900 000
800 000
700 000
600 000
500 000
400 000
300 000
200 000
100 000
0
Surplus
Limit of cover 2 000 000
CatXL
Ceiling of cover
(here 2,5 m)
–
Quota share retention
–
(75 %)
–
–
WXL/R
– (510 000 : 0.75 = 680 000)
–
–
–
Deductible
– (240 000 : 0.75 = 320 000)
–
–
Quota
share
cession
(25 %)
Z = sum of
retained losses
from the
same event
(here 1.5 m)
CatXL pays
Z minus
deductible
(here 1 m)
Deductible
(here 500 000)
Sum of all losses in the quota share retention from the event that are
smaller than 240 000 (deductible), + number of all losses from the event
larger than 240 000 (deductible) multiplied by the deductible.
45 Combination of proportional and non-proportional treaty types – Module 4
4. Graphical representation of reinsurance programmes
Explanation:
The simple rule for filling in the net retention losses (net of surplus, quota share cession and XL/R) in the respective
CatXL column is as follows:
The loss relevant to the CatXL comprises
the sum of all losses from the event that are smaller than the WXL/R deductible on the quota share retention
(240 000),
plus
the number of all losses from the event that are larger than the WXL/R deductible on the quota share retention
(240 000), multiplied by the amount of this deductible.
If we have drawn the diagram of the CatXL column true to scale, we can now fill in the loss amount in the said
CatXL column from 0 upwards (to point Z). It is then possible to read off the CatXL loss as the section between
point Z and the CatXL deductible.
This brings us to the end of Module 4 and also the end of the “Principles of traditional
non-life reinsurance” study aid. We congratulate you on having borne with us to the end
and hope that
– we have provided effective support for you in your learning process
– we have stimulated your interest in learning more about the fascinating world of reinsurance beyond the learning objectives.
But before we conclude, do you know your stuff? Have you just read the module, or have
you learned the material as well? To enable you to reliably answer these questions for yourself, we will end the module with our usual three learning tools:
46 Combination of proportional and non-proportional treaty types – Module 4
– A list of the learning steps you should now have completed. The list refers to the learning
objectives that we mentioned at the start of the module. It shows you what knowledge
and skills we expect you to have learned – not least with regard to the training objective –
and gives you an opportunity to reflect on the transfer of knowledge through the learning
process.
– A summary of the module as a whole. This shows in graphical, summarised form the material we have looked at in this module and enables you to check that you have assimilated
the knowledge using key concepts through the factual connections.
– A representative selection of revision questions and exercises on the module as a whole.
These are for self-testing. You will find the answers in the “Answers to the revision
questions” section.
47 Combination of proportional and non-proportional treaty types – Module 4
The learning steps you should have completed
after working through the module
1. Why do we combine proportional and non-proportional reinsurance treaty types? A brief summary of the previous modules (pages 1–7)
Can you
– describe the (four) key success factors for insurance business, which can be influenced
positively by suitable reinsurance cover?
– explain which treaty types are, depending on the type of constellation, well suited, less
suited or totally unsuitable to positively impact specific key success factors for the primary
insurer, and derive therefrom the combinations quota share or surplus with a WXL/R,
WXL/E and CatXL as the most common combinations of proportional and non-proportional reinsurance treaty types?
Are you familiar with the relevant technical terms in this section?
Risk of change, catastrophe accumulation, accumulation per risk.
2. The most common combinations of proportional and non-proportional reinsurance treaty types (pages 8–31)
Can you describe, using examples, how the following combinations work and in particular
how losses are apportioned?
– quota share and a WXL/R or WXL/E on the quota share retention
– surplus and a WXL/R or WXL/E on the retention
– quota share and a CatXL on the quota share retention
– surplus and a CatXL on the retention
Are you familiar with the relevant technical terms in this section?
CatXL, facultative reinsurance, fac-oblig reinsurance, quota share, loss burden, surplus,
WXL/R, WXL/E.
3. Interactions between proportional and non-proportional reinsurance treaty types (pages 32–40)
Can you
– describe, using typical examples, what the interactive effects between proportional and
non-proportional reinsurance are and how they originate?
4. Graphical representation of reinsurance programmes (pages 42–47)
Can you
– draw accurate graphical representations of per-risk covers and event covers in a reinsurance
programme?
48 Combination of proportional and non-proportional treaty types – Module 4
49 Combination of proportional and non-proportional treaty types – Module 4
Summary
Section 1 Why do we combine proportional and non-proportional reinsurance treaty types?
A brief summary of the previous modules (pages 1–7)
Problems in the
gross insurance portfolio
(or parts thereof)
Solutions for the primary insurer's retained portfolio
provided by reinsurance (RI)
with proportional RI
Risk of fluctuation:
Individual large losses
(peak risks)
with non-prop RI
– fac RI
– surplus
– fac-oblig RI
– quota share/surplus
WXL/R
– quota share
(only partially)
– to a larger extent with
quota share/surplus,
fac-oblig RI, fac RI
(requires prior
accumulation control)
WXL/R or
WXL/E
Catastrophe
accumulation
(catastrophe risk)
– quota share
(only partial relief)
CatXL
Additional capacity
(automatic capacity)
– surplus
– fac-oblig RI
WXL/R partially
Strong growth (solvability)
– quota share
not suitable
Persistently bad results
risk of change
– quota share
– surplus (less suitable)
not suitable
lack of claims
experience
– quota share
not suitable
Per-risk accumulation
with a combination
of prop/non-prop RI
– quota share with
WXL/R
– surplus with WXL/R
– quota share with
WXL/R or WXL/E
– surplus with
WXL/R or WXL/E
– quota share with CatXL
– surplus with CatXL
50 Combination of proportional and non-proportional treaty types – Module 4
Section 2 The most common combinations of proportional and non-proportional
reinsurance treaty types (pages 8–31)
Combination
Description/purpose/area of application
The WXL/R is used to stabilise an unbalanced quota share retention.
Quota share
and
WXL/R
on the quota share retention
Area of application: classes of insurance which are not particularly suited to surplus reinsurance; pure
WXL/R cover is unattractive for the reinsurer and the quota share cession makes the participation in a
WXL/R more interesting; pure WXL/R is too expensive. Better price given for the WXL/R on account of
the quota share cession.
The WXL/E is used to stabilise an unbalanced quota share retention.
Quota share
and
WXL/E
on the quota share retention
Area of application: in all instances where it is difficult or impossible to limit and define precisely what
one risk is. The duality of the exposures – per risk and per event – can cause unexpected gaps in cover.
Surplus
and
WXL/R
on the retention
The surplus is used to procure sufficient capacity per risk and levels out the risks in the retention.
The WXL/R levels out the loss burden of the retained portfolio by making it possible for the
primary insurer to pass on part of individual losses which correspond to or approache the maximum
retention by means of the non-proportional WXL/R, ie to spread these over several years.
Surplus
and
WXL/E
on the
retention
The surplus is used to procure sufficient capacity per risk and levels out the risks in the retention.
The WXL/E levels out the loss burden of the retained portfolio by spreading the sum of the losses
caused by one and the same event and affecting one or more insured risks over several years,
insofar as they remain in the primary insurer’s retention.
Area of application: This combination is used where it is difficult or impossible to limit and define
precisely what one risk is. The duality of the exposures – per risk and per event – can cause unexpected gaps in cover.
Quota share
and
CatXL
The quota share provides automatic capacity. A portion of the catastrophe accumulation risk is passed
on to the reinsurer as part of the quota share cession. The CatXL offers additional protection for the
catastrophe accumulation risk that remains in the quota share retention.
Surplus
and
CatXL
The surplus provides the necessary capacity per risk and levels out the risks retained in the surplus
retention. The CatXL offers protection against catastrophe accumulations for the otherwise unprotected surplus retention.
51 Combination of proportional and non-proportional treaty types – Module 4
Summary
Section 3 Interactions between proportional and non-proportional reinsurance treaty types (pages 32–40)
When various types of reinsurance treaties are combined, they exert interactive effects on each other which could be key in assessing
the risk under the individual reinsurance treaties in a programme. Even if the reinsurer is only participating in one treaty of a reinsurance
programme, it must know the entire programme in order to be able to adequately assess the individual treaty it is being offered.
The siphon effect of proportional reinsurance means that the interactive effects are particularly noticeable when combining proportional
and non-proportional treaty types.
proportional RI
siphon effect – partial relief
for underlying RI
non-proportional or proportional RI
Section 4 Graphical representation of reinsurance programmes (pages 42–47)
See figures on pages 43 and 45.
52 Combination of proportional and non-proportional treaty types – Module 4
53 Combination of proportional and non-proportional treaty types – Module 4
Revision questions and exercises on the module as a whole
On page 55 you will find revision questions and exercises nos. 4–6 on the module as a whole.
They all relate to the information given below:
Information for questions 4–6
An insurance portfolio is reinsured as follows:
Quota share reinsurance
Quota share 100 %
Quota share retention 65 %
Quota share cession 35 %
Maximum liability
2 000 000 per risk
1 300 000 per risk
700 000 per risk
on top of which there is
Surplus reinsurance
2 gross lines
4 000 000 per risk
Amounts of liability that exceed 6 000 000 per risk are reinsured on a proportional facultative
basis.
The quota share retention of 65 % is protected by a WXL of 975 000 xs 325 000.
Case 1
The class of insurance is property; per-risk accumulation control is guaranteed,
so a WXL/R is possible.
Case 2
Here again, the class of insurance is property, but an accumulation control for
liabilities under 1 000 000 is not possible; the cedent therefore wants an WXL/E.
The cedent is convinced that in its property insurance portfolio unknown accumulations or accumulations that cannot be identified in advance between policies
with liability of up to 1 000 000 will not exceed the amount of 2 000 000 per
risk, as the portfolio only comprises residential buildings and contents and thus
a per-risk accumulation of more than two policies can be ruled out.
The 65 % quota share retention after the WXL is additionally protected by a CatXL of
3 000 000 per event xs 1 300 000 per event. The CatXL reinsurer is not the same as
the WXL reinsurer and does not know the details of the WXL treaty. The cedent has
provided the following information:
“The quota share retention is protected by a WXL cover with a deductible of 325 000 that comes
in before the CatXL cover. An event loss covered under the CatXL will therefore not contain any
individual losses per risk greater than 325 000.”
54 Combination of proportional and non-proportional treaty types – Module 4
4. Is there something in this information which is not quite right?
5. In case 1, one of the quota share reinsurers, with a share of 40 % of 35 % (= 14 % of 100 %),
wishes to extend the WXL/R cover to its share but only attaching from a deductible
corresponding to an amount of 350 000 per risk for the entire quota share cession of
35 % (and thus a deductible of 140 000 per risk for its share). How would you approach
this practically? Calculate the limits for the WXL cover on the gross retention of
100 % of the quota share and for the share of the quota share reinsurer of 40 % of 35 %.
6. The following losses are caused by one event:
Risk
1
2
3
4
5
6
7
Liability
1 500 000
2 500 000
1 000 000
1 900 000
4 000 000
2 000 000
5 000 000
Loss
1 000 000
350 000
800 000
250 000
500 000
1 800 000
190 000
Calculate the portions of losses borne by
a)
b)
c)
d)
e)
f)
g)
h)
the facultative proportional reinsurance
the surplus reinsurance
the gross retention of 100 % quota share
the quota share retention of 65 % before the WXL cover
the WXL/R on the quota share retention
the WXL/E on the quota share retention
the CatXL on the quota share retention of 65 % after the WXL/R
the CatXL on the quota share retention of 65 % after the WXL/E.
What problems do you envisage?
55 Combination of proportional and non-proportional treaty types – Module 4
Answers to the revision questions
1. a) In this case, the terms of the WXL/R would have to be: 1 900 000 per risk xs 100 000
per risk. The deductible amounts to only 5 % of the possible maximum liability in this
solution. This will probably overstretch the WXL/R.
(page 30)
b) WXL/R deductible on a gross basis: 100 000 : 0.4 = 250 000
(page 30)
c) If the primary insurer were to buy a WXL/R of 1 750 000 per risk xs 250 000 per risk
on the surplus retention, this WXL/R would have the same conditions as the WXL/R
700 000 per risk xs 100 000 per risk for the quota share retention.
As the primary insurer is only able to bear a deductible of 100 000, it must buy
additional WXL/R cover of 150 000 per risk xs 100 000 per risk.
It is also interesting to look at these interactive effects in a different way:
– Thanks to the quota share cession, the primary insurer can afford to buy a WXL/R
with a deductible of 12.5 % of the treaty limit (100 000 : 800 000 = 250 000 :
2 000 000 = 0.125 = 12.5 %)
– Without the quota share cession, the primary insurer would have to buy a WXL/R
with a deductible of just 5 % of the treaty limit (100 000 : 2 000 000 = 0.05 = 5%).
(page 30)
d) See table on page 57.
56 Combination of proportional and non-proportional treaty types – Module 4
900 000
4 000 000
5
600 000
1 500 000 1 200 000
4
600 000
3 000 000
12 000 000 9 000 000
1800 000
Gross
loss
3
2
1
No. Liability
300 000
0
(1/2)
0
200 000
0
(1/3)
(4/6) 6 000 000
(1/6) 1 500 000
0
0
900 000
Retention
(1/2) 300 000
1 200 000
(2/3) 400 000
(1/6) 1 500 000
Surplus RI
4 lines of 2 000 000
Cession
0
fac prop
180 000
720 000
240 000
900 000
540 000
120 000
480 000
160 000
600 000
360 000
Quota share RI
Maximum liability 2 000 000
Cession 60%
Retention 40%
Apportionment of losses
20 000
380 000
60 000
500 000
260 000
(page 30)
100 000
100 000
100 000
100 000
100 000
WXL/R
700 000 xs 100 000
Cover
Deductible
d)
57 Combination of proportional and non-proportional treaty types – Module 4
Answers to the revision questions
2. a) The WXL/E is used in all instances where it is difficult or impossible to limit and define precisely what one risk is.
b) We talk of duality of exposures in the case of the WXL/E as its cover is triggered
both per risk and per event. As a result, particular care should be taken to ensure
that a sufficiently high limit of cover is agreed in order to avoid gaps in cover.
(page 30)
3.
Risk/loss
No.
1
2
3
4
5
6
Total
Gross
loss
600
3 000
2 500
667
1 200
5 700
13 667
fac prop
0
0
500
0
600
1 900
3 000
Quota share reinsurance
Treaty limit 4 000 000
100 %
Cession
Retention
40 %
60 %
600
240
360
3 000
1 200
1 800
2 000
800
1 200
667
267
400
600
240
360
3 800
1 520
2 280
10 667
4 267
6 400
WXL/R
2 000 000 xs 400 000
Cover
Retention
after WXL/R
360
1 400
400
800
400
400
360
1 880
400
4 080
2 320
(page 40)
4. Case 1 does not entail any problems for the time being. The WXL/R cover of 975 000
per risk xs 325 000 per risk cannot be exceeded.
With case 2, however, we have the following problem: if an event occurs which causes
losses of more than 1 300 000 for the 65 % quota share retention, that portion of the
ultimate net loss per event which exceeds this amount falls back to the primary insurer’s
retention because the WXL/E cover of 975 000 per event xs 325 000 per event with its
ceiling of 1 300 000 is not enough to cover larger losses. The CatXL can therefore quite
well be hit by individual losses exceeding 325 000. If the CatXL reinsurer had worded
the CatXL reinsurance treaty precisely on the basis of the information provided by the
cedent, all loss amounts which exceeded the individual loss limit of 325 000 would remain excluded from the final event loss, at least to the extent that they exceed 325 000.
(page 55)
58 Combination of proportional and non-proportional treaty types – Module 4
5. The WXL cover should be placed in 2 layers with the following limits for the 100 %
quota share:
1st layer
500 000 per risk xs 500 000 per risk
2nd layer
1 000 000 per risk xs 1 000 000 per risk
Only the cedent needs the first layer for its quota share retention of 65 %:
Thus, it places 65 % of
500 000 per risk xs 500 000 per risk for 100 %, in other words,
325 000 per risk xs 325 000 per risk for the quota share retention of 65 %.
Both the cedent and the quota share reinsurer need the second layer. The cedent needs
the layer for its quota share retention of 65 % and the quota share reinsurer needs it for
its share of 40 % of 35 %. Placement, therefore of 65 % and 14 % – or a total of 79 % of
1 000 000 per risk xs 1 000 000 per risk for 100 %, in other words,
650 000 per risk xs 650 000 per risk for 65 % quota share retention
140 000 per risk xs 140 000 per risk for the 14% share of the quota share reinsurer.
This solution is the most practicable because changes to the covered QS shares do not
require changes to be made to the WXL treaty limit on a gross basis = 100 % quota
share. We merely have to adjust the percentage share placed.
(page 55)
6. a) prop fac RI 0, no liabilities in excess of 6 000 000
(page 55)
b) surplus
Risk
100 %
2
5
7
2 500 000
4 000 000
5 000 000
Liability
Quota share
(100 %)
2 000 000
2 000 000
2 000 000
Surplus
Losses
100 %
Surplus
500 000 = 1/5
2 000 000 = 1/2
3 000 000 = 3/5
350 000
500 000
190 000
1/5 = 70 000
1/2 = 250 000
3/5 = 114 000
(page 55)
59 Combination of proportional and non-proportional treaty types – Module 4
Answers to the revision questions
c) 100 % quota share (gross retention)
Risk
100 %
1
2
3
4
5
6
7
1 500 000
2 500 000
1 000 000
1 900 000
4 000 000
2 000 000
5 000 000
Liability
100 % quota share
(gross retention)
1 500 000 = 100 %
2 000 000 = 80 %
1 000 000 = 100 %
1 900 000 = 100 %
2 000 000 = 50 %
2 000 000 = 100 %
2 000 000 = 40 %
Losses
100 %
1 000 000
350 000
800 000
250 000
500 000
1 800 000
190 000
100 % quota share
(gross retention)
100% = 1 000 000
80% = 280 000
100% = 800 000
100% = 250 000
50% = 250 000
100% = 1 800 000
40% =
76 000
(page 55)
d) Quota share retention of 65% (before WXL)
Risk
1
2
3
4
5
6
7
Share of losses
100 % quota share
(gross retention)
1 000 000
280 000
800 000
250 000
250 000
1 800 000
76 000
65 % quota
share retention
650 000
182 000
520 000
162 500
162 500
1 170 000
49400
(page 55)
e) Apportionment of losses between 65 % quota share retention and WXL/R
Risk
1
2
3
4
5
6
7
65% quota
share retention
650 000
182 000
520 000
162 500
162 500
1 170 000
49 400
2nd layer
0
0
0
0
0
520 000
0
WXL/R on the quota share retention
1st layer
Net retention after WXL/R
325 000
325 000
0
182 000
195 000
325 000
0
162 500
0
162 500
325 000
325 000
0
49 400
(page 55)
f) Apportionment of losses between 65 % quota share retention and WXL/E
Risk
1
2
3
4
5
6
7
Total
./. deductible
./. 1st layer
./. 2nd layer
Remainder (retained)
Shares of losses for quota share retention
650 000
182 000
520 000
162 500
162 500
1 170 000
49 400
2 896 400
325 000
325 000
650 000
1 596 400
(page 55)
60 Combination of proportional and non-proportional treaty types – Module 4
g) CatXL on the 65 % quota share retention after WXL/R
Risk
1
2
3
4
5
6
7
Total
./. CatXL deductible
CatXL pays
Shares of losses for
65 % quota share
retention after WXL/R
325 000
182 000
325 000
162 500
162 500
325 000
49 400
1 531 400
1 300 000
231 400
Remember: all losses that form the ultimate net loss are for amounts under
325 000 (for the 65 % quota share retention after the WXL/R).
(page 55)
h) CatXL on the quota share retention of 65 % after WXL/E
Loss amount per event before WXL/E (see f)
WXL deductible
1st layer + 2nd layer WXL/E
Remainder
2 896 400
325 000
975 000
1 300 000
1 596 400
This contains losses to risks 1, 3 and 6, which all exceed 325 000 ! Are they nevertheless covered by the CatXL? ➠ A sticking point for the cedent and the CatXL
reinsurer?
(page 55)
61 Combination of proportional and non-proportional treaty types – Module 4
Appendix
List of working examples
Working example
Subject
page
2/1
Apportionment of losses under the quota share and WXL/R on the quota share retention 10
2/2
Balancing effect of the WXL/R on the quota share retention
12
2/3
Effect of the quota share cession on the limits of the WXL/R (gross)
14
2/4
Adjusting a WXL/R on a 100 % treaty limit to the percentage
of the quota share retention
15
2/5
Quota share with a WXL/E on the quota share retention
16
2/6
Surplus with a WXL/R on the retention
21
2/7
Surplus with a WXL/E on the retention
24
2/8
Combination of quota share and a CatXL on the quota share retention
27
2/9
Combination of surplus and a CatXL
28
3/1
Interactions between a quota share and a WXL/R on the quota share retention
33
3/2
Interactions between a surplus and a WXL/R
35
3/3
Interactions between a surplus, WXL/R and CatXL
37
4/1
Representing quota share/surplus reinsurance with a WXL/R on
the quota share retention
42
4/2
Graphical representation of event covers next to per-risk covers
45
62 Combination of proportional and non-proportional treaty types – Module 4
List of figures
The list below contains the figures which are of specific technical importance.
We have dispensed with references to the figures provided as learning aids.
Figure
Subject
page
1/1
Forms and types of reinsurance, treaty types
3
1/2
Summary of the areas where proportional and non-proportional
reinsurance treaty types are used and their advantages and
disadvantages for the primary insurer
4
2/1
The most common combinations of a proportional and a nonproportional reinsurance treaty
8
2/2
Combination of quota share reinsurance and a WXL/R on the
quota share retention
9
2/3
Combination of surplus and a WXL/R on the retention
20
2/4
Combination of quota share and a CatXL
26
2/5
Combination of surplus and a CatXL
28
4/1
Graphical representation of a reinsurance programme for the
combination of quota share/surplus reinsurance and a WXL/R
on the quota share retention
43
4/2
Graphical interpretation of the WXL/R on the quota share retention
44
4/3
Graphical representation of event covers next to per-risk covers
45
63 Combination of proportional and non-proportional treaty types – Module 4
Principles of traditional non-life reinsurance
A study aid
Overview and study tips for learners and trainers
Module 1
Introduction to the reinsurer's
business
Module 2
Module 3
Proportional reinsurance
Non-proportional reinsurance
Module 4
Combination of proportional
and non-proportional types
of treaty
© 2000
Swiss Reinsurance Company
Zurich
Title:
Principles of traditional
non-life reinsurance
A study aid
Authors:
Thomas Hirt
Gérard Wicht
Editing and production:
Thomas Hirt; AKAD Verlag
Teaching Materials Development,
AKAD Group
Niklaus Müntener; Gérard Wicht
Technical Training,
Reinsurance & Risk Division;
Corporate Communications,
Reinsurance & Risk Division
Translation by Swiss Re Language
Services
Swiss Re
Mythenquai 50/60
PO Box
CH-8022 Zurich
Telephone: +41 1 285 21 21
Fax:
+41 1 285 20 23
R&R, 02/01, 60 en
Table of contents
Welcome: To learners and trainers at Swiss Re
1. The content of the course – its structure and aims
1.1 The structure
1.2 The aim of the teaching material
1
1
1
2. How to make effective use of the teaching material
2.1 Our contribution to your learning success
2.2 Your contribution to your learning success: active learning
2.3 Different methods of using the teaching material
2.4 Time needed to work through the modules
3
3
5
6
6
3. Using the modules
3.1 Pure self-tuition or media mix?
3.2 Possible combinations of the modules
7
7
8
To learners and trainers at Swiss Re
Welcome
to the “Principles of traditional non-life reinsurance” course, which will provide you with an
introduction to the world of classic reinsurance business.
Please take the time to read the next few pages, as these will show you how to make effective
use of the teaching material.
At the core of the course is a modular study aid which has been specially developed for you
as a (new) Swiss Re employee. It enables you to study on your own and therefore gives you
the greatest possible freedom in organising your own learning processes. In keeping with the
defined goals and objectives, you learn whenever you have the time and wherever you happen to be at that moment.
Educationalists are largely agreed that self-study is a very efficient method of learning. It is
particularly suited to the development of cognitive skills, ie to the acquisition of basic knowledge, which is what we want to impart in this course. Numerous studies have shown that
self-study fosters learning success at least as well as conventional classroom teaching, provided it is used correctly.
Apart from “suitable teaching material”, three key factors in particular are decisive for learning successfully through self-study: teaching material designed for self-study, an adequate working technique, and also (if necessary) accompanying measures to support learners.
To ensure that our study aid is suitable for self-study, we have involved teaching material
specialists from the publishing firm AKAD Verlag in its design and production. AKAD is
a leading adult education organisation in Switzerland which has always used independent
study as a component of its training courses.
We wish you an exciting and enriching learning experience!
Zurich, December 2000
Gérard Wicht
Swiss Re, Technical Training,
Reinsurance & Risk Division
Thomas Hirt
Editor-in-Chief, AKAD Verlag, Zurich
1. The content of the course –
its structure and aims
1.1. The structure
The whole training unit is divided into four modules (see also the diagram on page 2):
Module 1
Module 2
Module 3
Module 4
Introduction to the reinsurer’s business
Proportional reinsurance
Non-proportional reinsurance
Combination of proportional and non-proportional types of treaty
We recommend that you work through all four modules in order, though it is possible
to leave out individual ones. The table at the end of this overview provides a summary of
possible module combinations.
1.2. The aim of the teaching material
We realise that, as a (new) Swiss Re employee, you will want to get down to business as
quickly as possible. In other words, you will be wanting to get to grips as soon as possible
with the exciting topics associated with your job. Naturally, this is also our concern. However, those responsible for training at Swiss Re are convinced that, in the long term, successful generalist and specialist work can only be carried out on the basis of sound knowledge of
the basic principles. It is therefore the aim of this study aid to help you understand reinsurance business.
When completing the course, please bear in mind the following:
– The subject of this study aid is reinsurance. It is therefore assumed that you have a basic
knowledge of primary insurance.
Depending on your specific background and experience, your depth of knowledge in the
area of insurance will vary. We take this into account by dealing with the more basic insurance issues in greater detail in cases where we feel it is absolutely necessary to do so.
– The teaching material is concerned with traditional non-life reinsurance. The area of life
reinsurance is ignored. The same goes for the more recent developments in reinsurance
business which go under the name of “New Markets” or “Alternative Risk Transfer (ART)”.
– The teaching material is concerned with the basic mechanisms and concepts of reinsurance.
It is therefore kept neutral in terms of classes of business, branches of industry and countries.
We go into specific detail where it is necessary to do so in order to understand fundamental questions or where it seems appropriate to provide illustrative examples. Otherwise,
these issues are reserved for the more advanced training modules.
1
Overview and study tips
2
Overview and study tips
Combinations
Types of treaty:
Treaty structure:
Graphical representation of the combinations of various
types of treaty
Module 4
Combination of proportional and non-proportional types of treaty
Scope and other treaty
conditions
Quota share, surplus and
fac-obl reinsurance
Key events in Swiss Re’s
development
Brief history of Swiss Re
Scope and other treaty
conditions
Excess of loss reinsurance
and its various types; stop
loss reinsurance
Selected examples of combinations and their effects
Combinations
Types of treaty:
Treaty structure:
Obligatory non-proportional reinsurance
Module 3
Non-proportional reinsurance
Facultative and obligatory
reinsurance, proportional and
non-proportional reinsurance,
types of treaty
Forms and types of reinsurance,
treaty types
Facultative non-proportional
reinsurance
Safeguarding the reinsurer
Balancing the reinsurer’s
portfolio
Module 1
Introduction to the reinsurer’s business
Obligatory proportional reinsurance
The purpose of individual types of treaty in proportional and
non-proportional reinsurance
Facultative proportional
reinsurance
Unbalanced insurance portfolios and how they are balanced
by means of reinsurance
Actors in the insurance market;
coinsurance and reinsurance
Module 2
Proportional reinsurance
Reinsurance is insurance for
insurers
Overview of the insurance
industry
The teaching material at a glance
2. How to make effective use of the
teaching material
We have already said that our teaching material is no ordinary text book. This basically means
that we want to make the task of learning as easy as possible for you, so that you can use
your limited learning time as efficiently as possible. That is our contribution to your learning
success.
However, you have to remember that this can, in no way, be a substitute for your own efforts. Your learning success will essentially depend just as much on your own contribution.
2.1. Our contribution to your learning success
– The tables of contents. Each module contains a detailed table of contents which is visualised
graphically in the text. In this way, the train of thought linking the ideas becomes visible.
You can use the table of contents as a tool to help you determine whereabouts in the
material you are at any time. It will also enable you to visualise the material as a network of
associated concepts from the outset. In this way, you will create a workable basic knowledge
system, into which you will be able to integrate any detailed knowledge subsequently acquired, and to apply what you have learnt in a manner appropriate to the situation.
– Learning objectives. Each module contains a detailed list of learning objectives which
shows you what skills are expected of you. The full list of learning objectives is given again
at the end of each module as an aid to revision. Make use of this service to ascertain
whether you have not only read the material but also remembered it.
– Digestible, clearly structured units of material. The units of material are built up according
to a uniform pattern.
They start by setting out the position and giving a brief preview of the upcoming material.
This is followed by the actual learning text, in which we work through the material with
you, step by step.
– Summary. Each unit of material ends with a summary which repeats in condensed form
the essential points made in the section. These summaries of the sections are doubly useful
as a self-checking tool, allowing you to check whether you have taken in the immediately
preceding material, and enabling you to increase what you remember, since things that are
repeatedly ingrained are remembered.
S
The summaries are visually recognisable in two ways: by means of shading and through
the symbol “S” in the margin.
3
Overview and study tips
In this regard, we would like to point out why we have chosen this approach. If you are a
regular reader of technical literature, our texts may appear redundant to you from time to
time. This redundancy is quite intentional because, unlike a technical book, it is not only
essential that you understand the material, but also that you remember it. Even if this is
perhaps unpopular today: powers of retention increase considerably if material is revised at
regular intervals. You should therefore get to grips with the text and read it carefully even
if you already know something about the topic it deals with.
– Revision questions. At the end of each unit of material you will find revision questions.
These provide a test that will show you whether you have taken in and understood the
material. Most questions are formulated in such a way that hardly any time is needed to
answer them. Besides these, however, you will also find questions that are geared to practical applications and will therefore take more time to answer.
R
Revision questions are indicated visually by the symbol “R”. Specimen answers to all the
questions are to be found right at the end of each learning module. To ensure that, when
looking up the answer to a question, you do not automatically read the answer to the next
question, the revision questions in the text are not numbered consecutively.
We recommend that you always answer the questions immediately after working through
a learning unit – even in cases where you are pushed for time. Incidentally, the learning
benefit is greatest when you write down your answer on a sheet of paper and then compare it
with our specimen answer. If you have made a mistake, give some thought to where you
went wrong and then work through the relevant part of the text once again.
– Graphics. The texts contain numerous graphics. These give the optimum guidance, as they
provide visual links to the new information learnt. You should therefore remember to devote a sufficient amount of time to the graphics.
If you want to look up graphics – for revision purposes, for example – you will find a list
at the very end of each module.
– Examples and working examples. The whole text is interspersed with examples. These are
used primarily to illustrate and give a practical explanation of relationships. Working examples taken from real life are specially indicated by the letter “E”. You should pay particular attention to these, as they take up key problems referred to in the teaching material,
mostly using figures.
4
Overview and study tips
E
Given their importance, working examples are denoted in the margin by the letter “E”. A
list at the end of the module will make it easier for you to find these examples when you
come to revise.
– Summary of the whole module. At the end of each module (immediately before the revision questions and the exercises to the module), you will find a concise summary of all the
material in the module (keywords with explanations). The summaries are presented graphically in order to make the structure of the material easier to understand.
– Revision questions and exercises on the whole module. This section gives you the opportunity to check your learning success once again in a self-test. As with all questions, you will
find specimen answers with detailed comments in the section entitled “Answers to the revision questions”.
2.2. Your contribution to your learning success: active learning
Despite our contribution, your success is mainly dependent on you. You should therefore
approach the texts with an inquisitive mind. This is not always easy given the quantity of
material and the general pressure of time. Nevertheless, always try to be inquisitive about
what is to come. Learn actively!
– Keep track of things! At the start of each learning unit, consciously ask yourself the question as to where you currently are in the edifice of ideas, where you have come from and
where you are headed. To do this, make frequent use of the aids that we have built in: the
table of contents, the graphics showing the structure of the material, the guides indicating
whereabouts you are in the material, and the summaries.
– Divide up your learning time – don’t try to learn everything at once! Learning is strenuous
work, and our attention span is unfortunately more limited than we would often wish. You
won’t do yourself any favours by wanting to work through everything at one go. Be aware
of your personal concentration span and organise your learning time accordingly. The best
results are achieved through short, regular learning units with maximum concentration. You
should therefore create a learning environment in which you can actually work in a highly
concentrated way.
– Process the text. If we could remember everything we had ever read, learning would not be
a problem. Unfortunately, reading is not the same thing as learning! Something merely
read is soon forgotten – or can you remember exactly what you read in the newspaper this
morning? Therefore, process the text and – more important – revise!
How you decide to process the text depends on your individual capabilities and learning
preferences. Many work with underlining and marginal notes, others go for the ‘mindmapping’ technique, while yet others produce their own summaries in textual or graphic
form. Besides these methods, there are countless other techniques, some of which are very
individual.
If you already have tried-and-tested techniques, stick with them, as they are obviously in
line with your personal thought patterns.
5
Overview and study tips
2.3. Different methods of using the teaching material
Learning is something very individual. And there have been many attempts to define learning types from the large variety of individual learning patterns.
– If you are more of a systematic learner, you will prefer the step-by-step approach, in which
case you should let us guide you through the material page by page on our predetermined
route.
– If, on the other hand, you are one of those learners more geared to action or discovery,
you may possibly feel restricted by our step-by-step approach. You do, however, have the
option of working according to your own preferences: for example by beginning with the
revision questions and exercises to the whole module. Try and work out the relationships
by taking the working examples as the starting point for a topic. Alternatively, start with
the overall summary at the end of each module and launch into the texts from there.
If you choose to work like this though, you should make sure that you do not omit any
individual sections! The best way to do this is with the help of the learning objectives.
2.4. Time needed to work through the modules
It is extremely difficult to give any reasonably reliable indication of the time needed, because
reading and processing speeds are something very individual, and because your affinity to
individual topics will vary considerably.
The following estimates are therefore to be taken only as a rough guide:
Module 1
8–10 hours of study
Module 2
18–22 hours of study
Module 3
18–22 hours of study*
Module 4
8–10 hours of study
* Module 3 is slightly longer than Module 2. However, as quite a few of the basic considerations in both modules are
related, we assume that you will be able to progress more quickly in Module 3. This of course presupposes that you
work through Module 2 before going on to Module 3.
6
Overview and study tips
3. Using the modules
3.1. Pure self-tuition or media mix?
The teaching material is designed in such a way that the entire material can be worked
through, learnt, revised and practised in a self-study environment. If you are planning to
work through the entire course in self-study, you should ensure that the following criteria are
observed:
– People tend to forget that even self-study takes time. To ensure success, there should be
sufficient time available.
– The learning environment should be organised in such a way that concentrated study is
possible. People should not be disturbed while they are studying.
– Even experienced and very independent learners should have the possibility of access to a
contact person in order to clarify questions as they arise.
We realise that not everyone will be up to working through the whole material from start to
finish on their own. We therefore recommend that those responsible for training in Swiss
Re’s various divisions should, if necessary, supplement the uptake of knowledge through
self-study with the following measures:
– Attendance events. These can be integrated into the self-study programme, for example a
brief, half-day “kick-off” session at the beginning to introduce the teaching material and
clear up questions of an organisational nature; follow this up with one or two half- or
full-day seminars during the course of self-study and a refresher seminar at the end, at
which the material is repeated. The attendance events will serve primarily to consolidate
and practise the material together with an expert with the help of working examples.
– Regular or occasional, individual coaching by experts from Swiss Re. This enables learners
to adapt their learning schedule to their individual needs, thereby offering a high degree
of flexibility. Experts may be physically present or, if nothing else is feasible, able to be
“called up” virtually via individuals’ PCs.
– Supportive learning in a group. The formation of networks is extremely desirable. If more
than one learner is studying at a particular location, they can pair up or form a study
group. Where different locations are involved, such work groups can also be organised via
a virtual learning platform within Swiss Re.
Those responsible for training should be aware of the fact that study groups often do not
come into being by themselves. We recommend actively encouraging such study groups
and networks (at a kick-off session, for example) and also ensuring that the necessary time
and, if possible, a suitable place for study is made available to them. Ideally, a study group
will be overseen by a coach, who will serve as the contact for any problems encountered.
For virtual groups, it is possible that they might get to know each other via videoconferencing.
7
Overview and study tips
3.2. Possible combinations of the modules
We recommend working through Modules 1 to 4 in order, since this will ensure that a broad
overview is obtained. If required, however, it is possible to work through individual modules
on their own. In such cases, we still recommend that all four modules be handed out, with
the task being to really learn only the desired modules and just to read through the others.
Module 1
Introduction to
the reinsurer’s
business
Route 1
The systematic, comprehensive
route recommended by us.
Route 2
You already have elementary
knowledge of insurance and
reinsurance.
Route 3
You want to acquire knowledge of
proportional reinsurance in a short
time.
Route 4
You want to acquire knowledge of
non-proportional reinsurance in a
short time.
Route 5
You only want to get an overview of
the reinsurer’s business and the
most important technical terms.
8
Overview and study tips
X
(X)
(X)
X
Module 2
Proportional
reinsurance
Module 3
Nonproportional
reinsurance
Module 4
Combination of
proportional and
non-proportional
types of treaty
X
X
X
X
X
X
X
X