Net retention oss reserves Net capacity et premiums Gross capacity Net capacity approx. 1% < 10% Gross capacity Gross premiums 10 25 Gross premium volume Capital plus loss reserves N t retention > CHF 150000 Net retention GNPI GNPI Capital plus loss reserves 12.5 50% approx. 200% Net retention Retention Net retention Liquid funds approx. 2% Facultative premiums Gross premiums app approx. 5% 25 approx. Designing property reinsurance programmes The pragmatic approach UM3UM3
Designing property reinsurance programmes The pragmatic approach
Table of contents Page Foreword 3 1 Introduction 4 Interests and criteria when designing reinsurance programmes 4 Focus of this text 6 2 Setting retentions 8 Retention per risk 8 Retention per accumulation loss potential 17 Retention per annual loss potential 20 3 Designing programmes 23 Designing per-risk reinsurance programmes 23 Designing per-event reinsurance programmes 29 Designing annual reinsurance programmes 34 4 Special types of cover 38 Multi-year treaties 38 Multi-line treaties 40 Non-traditional solutions 41 Reinsurance for common account 42 Facultative reinsurance prior to treaty cessions 44 Reinsurance of policies with first-loss or layer features 45 5 Terms and abbreviations 46 2
Foreword When designing a reinsurance programme for a given portfolio, various factors come into play, for example: statutory regulations; risk theory considerations; risk aversion of the persons involved; tradition; situation in the reinsurance market. There is no recipe for the best reinsurance programme. Different solutions will be obtained depending on the weight given to the factors influencing the decision. The purpose of this brochure is to support the process of designing a programme by giving pointers and food for thought to clients and brokers, as well as to Swiss Re employees whose jobs involve advising clients. The publication takes a pragmatic approach. Risk theory and mathematical aspects are not considered in detail, although the most important results or conclusions are incorporated into the methods presented here. New products are progressively taking their place alongside the more common reinsurance solutions. This brochure concentrates on the traditional products while at the same time making reference to the possible use of ART (Alternative Risk Transfer). In the first section, we present various factors which can influence the design of programmes. Against this background, we define which criteria serve as the basis for this brochure. The second section is concerned with setting the retention as a cornerstone in programme design. The third section shows how the overall programme is structured on the basis of the retention. Finally, in the fourth chapter, a number of non-standard reinsurance solutions are discussed. Markus Schmutz, August 1999 3
1 Introduction Interests and criteria when designing reinsurance programmes A reinsurance programme consists of treaties between two parties: the insurance company and the reinsurer. Both have their own interests, and therefore their own requirements of the programme. These interests do not always coincide. The most important criteria for both parties are: Insurance company Goals of underwriting performance Protection against large fluctuations in the underwriting result, thus reducing the amount of capital needed and protecting capital and the balance sheet. These fluctuations can be caused by: Random variations in the claims burden compared to the long-term average. These variations can be caused by exceptionally large individual losses or an exceptionally high number of losses. Technological, legal and other changes which result in an unforeseen increase in the claims burden. Incorrect assessment of the risk and therefore insufficient premium. Goals of financial security Meeting the solvency requirements by reducing the amount of capital needed. These requirements can be statutory or issued by the insurance company s management for individual branches. Nowadays, rating agencies also pay more attention to a company s reinsurance protection. Ability to budget for results and thus stability of income. This increases shareholders confidence and makes it easier for the insurance company to acquire new capital. Liquidity. Prompt payment by the reinsurer can ensure the insurance company s liquidity in the event of a loss. Goals of profit and growth Tax savings. In many countries there are limits on the tax-free creation of reserves in years when business is good. Reinsurance premiums, however, are normally tax-free. Reinsurance capital is cheaper than other sources of capital. This is particularly important when building up a portfolio, introducing a new product or increasing underwriting capacity. Reduction of operating costs for own account (gearing effect of reinsurance commissions). Cross-subsidisation. Optical improvement of results in badly performing lines of business. Non-economic goals Services provided by the reinsurer; Tradition; Personal relations. 4
Reinsurer As a service provider, the reinsurer obviously wants to be in a position to cover the insurance company s requirements as best it can. Nevertheless, a few points need to be borne in mind: Moral hazard If the insurance company cedes virtually all the risk to the reinsurer, there is a danger that it will lose interest in the original policies performance. The reinsurer therefore aims to spread the risk reasonably across both parties in a programme. Administration expenses The reinsurer wants to work in a cost-effective manner and keep administration expenses to a minimum. It therefore prefers programme structures in which only as much risk as necessary is ceded. Accumulation In the area of perils without accumulation potential, the reinsurer wants to write as much business as possible, since each additional treaty reduces the relative fluctuation within its portfolio. The opposite is the case with catastrophic perils. For those perils in particular where the reinsurer already has high exposure (eg earthquake in California or Japan), the need for capital quickly increases with additional business. The reinsurer should therefore monitor and restrict its exposure to perils of this kind. Price Generally speaking, almost any underwriting risk can be reinsured in return for commensurate remuneration. Market practice Some risks are not covered because of industry-wide agreements. One example of this is war risk, which can bring about damage on an unforeseeable scale. In 1937, the War and Civil War Exclusion Agreement was concluded, whereby the signatories (among them Swiss Re) undertook not to write any war risks. External factors Situation in the reinsurance market The current state of the reinsurance market has a considerable influence on programme design. Examples of factors are capacity available for specific risks; price level of various products (eg proportional vs non-proportional business). 5
Brokers As business intermediaries, brokers have an important role in many markets. This can, for instance, lead to standard solutions becoming widespread in certain markets. Brokers remuneration is usually proportional to the reinsurance premium. They therefore tend to have an interest in placing treaties with higher premium (and hence a high degree of risk transfer). Economic factors economic situation; inflation; capital market interest rates, performance of the stockmarkets. There is generally a greater need for reinsurance when the economy is experiencing a difficult phase. Focus of this text Programme design obviously depends on many factors. As we have seen, the interests of the insurance company and the reinsurer are not always the same. Some of these factors can be quantified, others are rather irrational. Theoretical approaches Most of the approaches using models for designing programmes and setting retentions aim at protecting capital against the risk of random fluctuations. They are based on mathematical models of the fluctuation potential of the business and on assumptions about the management s risk aversion as regards capital and the probability of ruin. 1 In practice, however, the problem which often arises is that there is not enough data available to actually implement the mathematical models. Moreover, these are always simplifications of reality and cannot reflect in detail the complex relationships between the various influencing factors. 1 See also: Swiss Re brochure no. 98-104: Setting retentions. Fundamental considerations. Swiss Re brochure no. 96-66: Insurance and risk capital: Swiss Re s value proposition. 6
Our approach In contrast to the theoretical models, the aim of this publication is to show an approach to designing programmes which is based on simple, practical implementation. No mathematical knowledge is necessary. The scope of the information required is relatively modest which makes the procedure easier. Per-risk reinsurance cover is designed on the basis of so-called rules of thumb. These are empirical values for various key figures in a reinsurance programme. The rules of thumb have been established by Swiss Re by analysing insurance companies and their reinsurance programmes. We are not, therefore, talking about hard and fast rules but rather about empirical values which have stood the test of time. The rules of thumb ensure that the liability (and therefore also the potential for fluctuation) within the insurance company s retention is appropriate compared to premiums and capital. They also take account of the reinsurer s interest in having a fair distribution of risk between the parties. As regards the design of the per-event cover for a portfolio, we mainly rely on information about the return periods of major loss events. In the area of natural hazards, these figures are determined by reinsurers, brokers or consultants using scientific methods and software packages applied to the insurance company s portfolio. 7
2 Setting retentions The key when designing a programme is setting the retention. By retention we mean the maximum amount of a loss potential that an insurance company is willing to pay. A loss potential can be a loss on an individual risk, an accumulation loss across an entire portfolio (eg caused by an earthquake) or the total claims burden of a portfolio within a year. The purpose of setting retentions in property insurance is to recognise and quantify all important loss potentials and then to decide on this basis what maximum amount an insurer is prepared to pay in respect of each potential. The factors which influence this decision have been mentioned in the previous chapter. Retention per risk In practice, it is recommended that the retention first be determined per loss on the individual risk. This is because the size of this retention also influences the accumulation losses to the net portfolio as a whole as well as the total annual claims burden. Rules of thumb As mentioned earlier in the introduction, not all rules of thumb have to be complied with all the time. On the contrary, for a given portfolio, it is practically impossible to find a reinsurance programme that complies with all the rules. Even if such a programme could be put together, it would certainly not be an optimum solution. Equally, complying with all the rules does not protect an insurer against being ruined. If one rule is not complied with, this should be seen as a reason for reviewing the programme to see whether changes are appropriate. If more than one rule is not complied with, and the deviations point to the same problem (eg that the retention is too low), this is then a strong indication that the problem really exists. The following terms are used for the rules of thumb: Capacity Facultative Volume (premiums) Underwriting capacity = gross capacity Surplus Gross premiums Obligatory capacity = treaty capacity Net capacity = retention WXL per risk Deductible = net retention Net premiums = GNPI Figure 1: Terminology used in the rules of thumb 8
As can be seen from Figure 1, the rules of thumb refer to a standard reinsurance programme. 2 The largest risks are reduced by means of proportional facultative reinsurance. The surplus treaty homogenises the remaining portfolio, and finally a per-risk excess of loss protects the proportional retention against major losses. The rules of thumb should be applied similarly to programme structures which do not correspond to this pattern: If, in addition, there is a quota share on the retention of the surplus treaty, net capacity and net premiums are reduced by the amount of the quota share cession. On the other hand, liability and premiums under the quota share are added to those of the surplus. In the case of a purely proportional programme (without a WXL), the retention becomes the net retention. Rule of thumb regarding the gross property portfolio Gross premium volume Capital plus loss reserves approx. 200% (Rule of thumb 1) In order to keep the amount of reinsurance bought at a reasonable level, the insurer should adapt its capital resources to the gross business (or conversely, keep its financial capacity in mind when writing business). Its financial security must not be too heavily dependent on reinsurers. The denominator in the above fraction is open to interpretation. What is meant by capital? Is it the equity capital as published? Do hidden reserves count as well? What reserves should be included? (Equalisation reserves? Other reserves?) These questions must be answered before applying the rule of thumb. All rules of thumb which contain capital and reserves thus say something about an insurance company s aversion to risk: the fewer the number of items on the liabilities side of the balance sheet which are interpreted as capital, the more averse the company is to taking risks. Possible measures if this rule is not complied with: write more/less business; adjust premium level; adjust capital resources. Rules of thumb for setting the proportional retention (net capacity) GNPI Capital plus loss reserves approx. 50% (Rule of thumb 2) 2 See also Chapter 3: Designing programmes 9
This rule is similar to the traditional definition of solvency (capital divided by premium volume). The target figure appears very low compared to the European solvency regulations (approx. 500%). Apart from the freedom in defining the denominator (see previous rule), it must also be remembered that in the rule of thumb, only the fire premium volume is compared to the insurer s total assets. Under the European solvency guidelines, the total premium volume from all lines of business is included. Possible measures if this rule is not complied with: adjust retention and/or reinsurance programme; adjust premium level; write more/less business; adjust capital resources. Net premiums Gross premiums > 15% (Rule of thumb 3) The aim here is to make sure the insurance company keeps a certain minimum involvement in its own business. Possible measures if this rule is not complied with: increase retention; introduce or extend co-reinsurance (by the ceding company); switch to XL reinsurance. Net capacity Net premiums < 10% (Rule of thumb 4) The insurance company s retention should show a minimum degree of balance. The company should be able to pay 10 total losses from the premiums. Possible measures if this rule is not complied with: reduce retention; increase premium level; write more business (especially small risks). Rules of thumb for setting the net retention (deductible) Net retention GNPI approx. 2% (Rule of thumb 5) This rule reduces the impact of a single maximum loss on the results as a whole. An individual loss should not increase the loss ratio by more than 1% to 3%. Possible measures if this rule is not complied with: adjust retention and protect it with a WXL/R; adjust net retention; adjust premium level; acquire more/less business. 10
Net retention Liquid funds approx. 5% (Rule of thumb 6) It should not be possible for a single loss to bring an insurer into payment difficulties. In general, property damage losses have to be paid at short notice. The insurer should not be forced to sell securities from its investment portfolio at unfavourable terms. Possible measures if this rule is not complied with: adjust retention and introduce WXL/R; adjust net retention; adjust liquid funds. Net retention Capital plus loss reserves approx. 1% (Rule of thumb 7) There are various interpretations of the denominator in this rule (compare rules of thumb above which contain the capital). This percentage can be higher or lower depending on the definition (what is and is not part of it?). Possible measures if this rule is not complied with: adjust net retention; adjust capital resources. Net retention Retention approx. 5% 25% (Rule of thumb 8) An insurer should keep an interest in the performance of its own business by retaining a reasonable proportion of such business. If, however, its deductible is set too high, the reinsurance purchased will do little to reduce fluctuations in results any further. Possible measures if this rule is not complied with: adjust net retention; adjust retention. Net retention > CHF 150000 (Rule of thumb 9) For cost reasons, the reinsurer should not and does not want to pay frequent, minor losses. Tables of limits In practice, we frequently come across more than just one retention amount. According to different criteria, individual retentions are set out for different risks in tables of limits. For an experienced underwriter, it is obvious that the same capacity should not be used for each risk. Nevertheless, it is extremely difficult to draw up a reasonable set of rules. The main criteria should be the anticipated profit and the anticipated fluctuation. The higher the profit, the higher the retention. And the greater the fluctuation, the lower the retention. 11
Both figures are unknown, however, and can at best only be estimated by the underwriter. The main criteria are thus subjectively influenced figures and so not very suitable for a fixed set of rules. Measurable criteria often used for the grading of retentions are: type of risk; quality of construction; fire protection; premium rate (although frequently used, the premium rate is not really suitable as a grading criterion as is it subject to market forces and does not, therefore, represent an objective measurement of the risk). An insurer s intention when using a table of limits is to reduce the portion retained in undesirable risks. This usually increases the premium volume of the surplus treaty, but often the expected profit for the reinsurer is reduced as a result. Recheck Recheck is a computer-aided model for property fire reinsurance. This software can be used to investigate the effects of various reinsurance structures, eg regarding the distribution of premiums among the individual reinsurance covers, or compliance with the rules of thumb. The software also shows the effects of important factors such as inflation, changes in the premium level, the effects of individual major losses etc. on the portfolio as a whole. A risk profile (and if possible also a loss profile) of the portfolio to be investigated is a prerequisite for using Recheck. Upon request, Swiss Re will gladly carry out a Recheck-supported analysis of a client portfolio to look for alternative programme designs. Example 1 The information supplied by the company is corrected for inflation and anticipated portfolio growth so as to reflect the portfolio in the year of cover as accurately as possible. This is why the band limits in the risk profile are not round figures. Capital plus loss reserves 180 000 000 Liquid funds 320 000 000 Gross premiums 115 032 000 Gross capacity 120 400 000 Table 1: Key data 12
Band limits (sum insured) (000s) Band midpoint No. of risks Gross premiums lower upper (000s) (000s) 0 181 90 122 681 42 066 181 301 241 30 954 18 329 301 482 391 11 256 7 957 482 722 602 5 393 5 767 722 963 843 2 837 4 204 963 1 204 1 084 932 1 768 1 204 1 505 1 355 621 1 471 1 505 1 806 1 656 288 859 1 806 2 107 1 957 213 771 2 107 2 408 2 258 165 697 2 408 3 010 2 709 170 881 3 010 3 612 3 311 109 695 3 612 4 816 4 214 183 1 502 4 816 6 622 5 719 164 1 875 6 622 10 836 8 729 287 5 255 10 836 15 050 12 943 169 4 438 15 050 21 672 18 361 102 4 088 21 672 28 896 25 284 63 3 412 28 896 43 344 36 120 40 3 256 43 344 57 792 50 568 25 2 501 57 792 86 688 72 240 5 827 86 688 120 400 103 544 11 2 413 Table 2: Risk profile 176 670 115 032 Rule of thumb regarding the gross portfolio Gross premium volume Capital plus loss reserves = 115032000 = 64% (Rule of thumb 1) = 180000000 This figure should be around 200%. In other words, the company is comfortably capitalised for its portfolio. Setting the proportional retention The table below shows the effects of various retentions on rules of thumb 2 to 4. The net premiums here were calculated on the basis of the risk profile. 13
Net capacity 1 000 2 000 3 000 4 000 5 000 6 000 7 000 8 000 9 000 10 000 11 000 12 000 Rules of thumb (000s) min. max. Net premiums 84 958 89 202 91 883 94 109 95 990 97 703 99 179 100 656 101 970 102 845 103 720 104 594 (000s) Rule of thumb 2: 47.2% 49.6% 51.0% 52.3% 53.3% 54.3% 55.1% 55.9% 56.7% 57.1% 57.6% 58.1% approx. 50% GNPI/ Capital Rule of thumb 3: 73.9% 77.5% 79.9% 81.8% 83.4% 84.9% 86.2% 87.5% 88.6% 89.4% 90.2% 90.9% 15% Net premiums/ Gross premiums Rule of thumb 4: 1.2% 2.2% 3.3% 4.3% 5.2% 6.1% 7.1% 7.9% 8.8% 9.7% 10.6% 11.5% 10% Net capacity/ Net premiums Table 3: Rules of thumb relating to the proportional retention Rule 2 allows a certain degree of room for manoeuvre. How far can you deviate from the 50%? A look at the risk profile shows that with a retention of 1000 000, a large number of risks would be ceded to the surplus treaty. In order to keep administrative expenses under control, the retention in our example should not, therefore, be less than 3 to 4 million. Neither of the other two rules restricts our choice. We proceed using a somewhat aggressive retention of 6 000 000. To avoid being too exposed on a per-risk basis compared to capital, we will protect the retention with an XL treaty (see next section). Setting the deductible The table below shows the effects of various deductibles on rules of thumb 5 to 8, assuming a proportional retention of 6 000 000 (according to the above table, the GNPI is then 97 703 000). Net retention 500 750 1 000 1 250 1 500 1 750 2 000 2 250 2 500 2 750 Rules of thumb (000s) min. max. Rule of thumb 5: 0.5% 0.8% 1.0% 1.3% 1.5% 1.8% 2.0% 2.3% 2.6% 2.8% approx. 2% Net retention/ GNPI Rule of thumb 6: 0.2% 0.2% 0.3% 0.4% 0.5% 0.5% 0.6% 0.7% 0.8% 0.9% approx. 5% Net retention/ Liquid funds Rule of thumb 7: 0.3% 0.4% 0.6% 0.7% 0.8% 1.0% 1.1% 1.3% 1.4% 1.5% approx. 1% Net retention/ Capital Rule of thumb 8: 8.3% 12.5% 16.7% 20.8% 25.0% 29.2% 33.3% 37.5% 41.7% 45.8% 5% 25% Net retention/ Retention Table 4: Rules of thumb regarding the net retention 14
Using the table, we decide on a deductible of 1500 000. Therefore, compliance with rules 5 to 7 is achieved more or less, although the insurer retains relatively little risk compared to net premiums, liquidity and capital. Obviously, this is not necessarily in the reinsurer s interest. For a primary insurer, however, it may well be worthwhile when prices in the reinsurance market are low. Example 2 A company protects its fire portfolio per risk by means of the following reinsurance programme: Source of business 2 Source of business 1 Surplus: 2.25 lines 39 000 000 20 000 000 40% Quota share ceded 10 000 000 xs 2 000 000 12 000 000 10 000 000 xs 2 000 000 12 000 000 2 000 000 2 000 000 Figure 2: Programme structure Source of business 1: Gross capacity 20 000 000 of which the company retains a quota share retention of 60% (12 000 000) Source of business 2: Gross capacity 39 000 000 of which the company retains a maximum of 12 000 000 under a surplus treaty with a graded retention. The retentions of 12 000 000 from sources of business 1 and 2 are protected by a joint per-risk WXL of 10 000 000 xs 2 000 000. 15
The premiums are distributed as follows: Gross premiums 330 000 000 Proportional treaties 25 000 000 Facultative reinsurance 5 000 000 Net premiums 300 000 000 Table 5: Premium distribution No details are available of equity capital and liquidity. However, the company can be described as financially very sound. How should the retentions be judged in this programme, using the rules of thumb? Retention Net premiums 300000000 = = 91% (> 15%) (Rule of thumb 3) Gross premiums 330000000 A large proportion of the business is retained by the insurance company. Net capacity 12000000 = = 4% (< 10%) (Rule of thumb 4) Net premiums 300000000 There is no need to reduce the retention as it is very well balanced. Net retention Net retention = 2000000 = 0.67% (approx. 2%) (Rule of thumb 5) GNPI 300000000 This good balance in the net retention suggests that it is too low. Net retention = 2000000 = 16.7% (5% 25%) (Rule of thumb 8) Retention 12000000 Compared to the retention, the net retention is not too low. Net retention = 2000000 (> CHF 150000) (Rule of thumb 9) Minor losses are not covered by the XL. 16
Thus, the company retains a large proportion of the business. The excellent balance in both the retention and the deductible would even permit an increase in the proportional retention. In terms of volume, however, the proportional treaties are already very small and would become virtually meaningless if the retention were to be increased. In a case like this, therefore, an XL on the gross portfolio is a good solution. Another advantage of this method is that it results in a considerable reduction in administrative expenses. Retention per accumulation loss potential Various perils covered in the primary policies of a portfolio can lead to accumulation losses as one event can affect several policies or risks at the same time. An insurance company s per-risk retention should therefore also be protected against any accumulation loss potential, such as natural hazards or conflagration. The issue of adequate cover per event should be analysed separately for different perils since, for example, the loss potentials from an earthquake or a conflagration can assume very different dimensions. Required amount of cover against natural hazards EML for catastrophe perils A natural catastrophe is characterised by a large area being affected at the same time and a correspondingly high number of individual losses (not only from the property line of business), which can add up to an enormous event loss. The size of the fire EML becomes meaningless in this context the risk is all the insured property in a given region. What is adequate event cover for a regional portfolio which contains policies offering natural hazards cover? The answer to this question is influenced by many factors, the most important being the estimate of how often the portfolio is expected to be affected by event losses of a certain size. It is not normally enough to analyse the effects of past losses on the portfolio, as the return periods of the catastrophe losses in question may be 100 years or more, and representative loss experience is therefore not available in most cases. Instead, we must look at exposure. We have to consider how different earthquakes, storms or floods could affect the values currently insured and how high the corresponding event losses could be. Obviously, major events occur less frequently than smaller ones. From this spectrum of event losses, which scenario should be the basis for deciding the extent of catastrophe cover? This depends on what probability of occurrence is acceptable to a company. One would probably like to have reinsurance cover for an event expected once in a hundred years. In the case of a catastrophe expected only once every 1000 years, the answer is no longer so clear. 17
These considerations are mainly influenced by an insurance company s risk aversion and financial strength. Many companies, however, also go by the cover which their competitors are buying. One goal might be to be better reinsured than the competition in the event of a major catastrophe. Conversely, it makes no sense to buy much more cover than the other market players, since the government would very probably step in after a loss so great that it threatened the whole industry. Requirements under supervisory law, current market practice or quite simply the cost of cover often play an important role as well. The influence of rating agencies, which have begun to include a company s catastrophe exposure in their assessments, is also gaining in significance. The result of these reflections is often summarised in the form of a natural perils EML (Estimated Maximum Loss). This describes the losses expected from a natural disaster as a percentage of the values insured in a defined area. The underlying return period or probability of occurrence is typically in the range of 100 to 1000 years, or between 1% and 1 per annum. This figure is in fact dependent on the company s reinsurance strategy. Often, however, figures such as these are bandied about without the necessary background information. Computer programs for analysing natural hazards A systematic analysis of a portfolio s catastrophe exposure can only be carried out with the help of a computer. The insurance industry and specialist consultants have recognised this in recent years. Natural hazards software for many of the more important insurance markets is already available, or else corresponding services are on offer. However, without careful application and critical checks of the results, and particularly unless common sense is exercised when introducing them into insurance practice, the benefit of such tools is questionable. Services offered by Swiss Re to its clients in the field of natural perils EMLs Swiss Re s specialists are happy to provide clients with support in setting or confirming their natural perils EMLs (whether calculated themselves or by consultants). Example 3 Calculations using Swiss Re s earthquake analysis program have come up with the following relationship between losses and return periods for an insurance company s portfolio: Return period (years) 25 50 100 250 500 1 000 10 000 Event loss (as a percentage 0.01% 0.1% 0.3% 1.0% 1.8% 3.0% 8.5% of the total EQ sums insured) which is exceeded every 25, 50, 100, 250, 1000 and 10 000 years on average. Table 6: Loss frequency relationship 18
Market studies show that, on average, insurance companies in the country in question purchase catastrophe cover up to about 1.2% of the total earthquake sums insured. There are no regulatory requirements. So what is a reasonable EML or catastrophe cover for this company? Market standard For the sake of simplicity, let us assume that the company has an average portfolio and capitalisation usual in that market. The most obvious solution is to keep to the market average, which in this country generally lies between a 250-year and a 500-year loss. EML/worst case comparison It is a feature of the catastrophe loss potential in this example that only a small event loss can be expected every 100 years, but an enormous event loss (along the lines of the worst case scenario ) can be expected every 1000 or 10 000 years. Loss potentials of this kind are also known as low frequency high severity potentials. The worst case here is therefore many times greater than the EML; in contrast to the case where an extreme event can be expected on average every 100 to 200 years and also where the worst case cannot be much larger (see Figure 3 below). Losses as a percentage of insured values 10% Worst case much greater than hundred-year loss (eg EQ Israel) 1% Worst case barely any greater than hundred-year loss (eg EQ Japan) 0.1% 0.0001 10 000 0.001 1 000 0.01 100 0.1 10 Frequency Return period Figure 3: Loss potentials with different EML to worst case ratios 19
Ability to pay If an insurance company includes natural perils in its original policies, it should also be reasonably certain of being able to meet these obligations in the event of a loss. In this case, we would therefore recommend an EML in the range between the 500-year and the 1000-year loss. Ratio of original prices to reinsurance prices The price which the company has to pay for the cover in the reinsurance market is obviously also a factor in its decision. If original premiums are inadequate, reinsurance cover may in certain circumstances cost more than the primary business brings in. Retention per annual loss potential By setting a retention for each loss on an individual risk and for each accumulation loss potential, an insurer protects itself against major losses and loss events. However, an accumulation of such losses in a single year can still have a considerable effect on an insurer s annual results and indeed even threaten its existence. A significant increase in the frequency of small and mediumsized loss events can have the same effect. A cautious insurer will therefore also check the risk of such frequency fluctuations. There are no detailed criteria for setting a retention on the annual loss burden. However, the reinsurer will have to take care that it does not, through its reinsurance cover, assume all of the insurer s entrepreneurial risk. The annual net retention must therefore be set in such a way that the insurer itself suffers a reasonable loss before an annual loss cover cuts in. This is normally the case when the net retention is greater than the GNPI and the risk premium of the net portfolio. In case of substantial prior, non-proportional reinsurance, the retention level should take into account the resulting reduction of exposure. As a rule of thumb, the cedent s net retention should be fixed in such a way that it takes at least one but no more than five average years profits to level out a bad year under the net retention. From a risk theory point of view, the insurer s management should consider what fluctuations in results the company is prepared to bear (eg the loss which will be exceeded once every 25 years). In order to do this, the distribution function of the annual loss for the net retention must be known, in other words, the probability of certain loss amounts being reached or exceeded in a given year. If the loss experience is insufficient, the distribution functions of the annual loss for all contributory loss potentials must be estimated individually and then combined. 20
When considering the annual retention and retentions across several lines of business, Swiss Re can offer support as part of its value proposition with tools especially developed for this purpose. 3 Example 4 An insurance company wants to protect its hail portfolio by means of a stop loss treaty. Historically, the business has produced the following loss ratios: Year Loss ratio 1983 63.40% 1984 82.00% 1985 62.00% 1986 126.00% 1987 56.10% 1988 77.30% 1989 106.60% 1990 36.70% 1991 49.60% 1992 58.90% 1993 65.50% 1994 119.00% 1995 95.00% 1996 94.70% Average 78.06% Table 7: Loss ratios The company s expense ratio for this business is 22%, the estimated GNPI for 1998 is 14 000 000. The following is known about the reinsurance costs at various deductibles: Deductible (% GNPI) RI premium rate 60% 23.3% 70% 16.8% 80% 11.4% 90% 7.5% 100% 5.0% 110% 3.4% Table 8: Reinsurance costs 3 Cf. Swiss Re brochure no. 96-66: Insurance and risk capital: Swiss Re s value proposition 21
What is a sensible retention for this business? With all of the various deductible options shown, the insurance company itself suffers a loss before the reinsurance cover comes into play: Deductible (% GNPI) Losses + internal costs + RI premium 60% 60% + 22% + 23.3% = 105.3% 70% 70% + 22% + 16.8% = 108.8% 80% 80% + 22% + 11.4% = 113.4% 90% 90% + 22% + 7.5% = 119.5% 100% 100% + 22% + 5.0% = 127.0% 110% 110% + 22% + 3.4% = 135.4% Table 9: Net result at various deductibles A further criterion is the frequency with which the cover would be affected by a loss. (For reasons of simplicity, frequency is estimated in the following table based on past loss statistics. Obviously, for higher loss levels in particular, the observation period of 14 years is not necessarily representative). Deductible (% GNPI) Loss frequency 60% 10/14 = 71% 70% 7/14 = 50% 80% 6/14 = 43% 90% 5/14 = 36% 100% 3/14 = 21% 110% 2/14 = 14% Table 10: Loss frequencies at various deductibles Frequencies higher than 20% to 30% should be avoided. The insurance company should be able to pay itself a loss occurring once every 4 years, not least in order to avoid excessive administration costs. It is reasonable, therefore, to set the retention at above 95%. 22
3 Designing programmes Designing per-risk reinsurance programmes For the per-risk cover of a portfolio, proportional and non-proportional types of treaty are generally used. General remarks The most common is a combination of proportional facultative reinsurance, a surplus treaty and a per-risk WXL. Here, the purpose of the surplus treaty is to homogenise the insurance company s retention by proportionally reducing risks which exceed the retention. The facultative cessions cap risks which are too large to fully fit into the surplus treaty. Finally, the WXL protects the proportional retention against major losses. The combination of proportional and non-proportional types of cover is also advantageous since the cycles in proportional and non-proportional reinsurance markets do not run completely in parallel. For the proportional reduction of individual risks, hybrid forms of reinsurance exist in addition to strictly facultative or strictly obligatory reinsurance: Fac./Oblig.: Here the insurance company is free to choose whether or not it wants to cede a risk. The reinsurer is obliged to accept it. The extent of the cession is limited by specifying a maximum retention and a number of lines. Open cover: Similar to Fac./Oblig. but differing in that the insurance company can decide what percentage of the risk it wants to cede. Semi-automatic cover: The risks are accepted by the reinsurer individually and then ceded to the relevant treaty. In this way, the reinsurer has better control over the original risks, while the insurance company has lower administration costs (compared to strictly facultative cessions) and a provisional cover note until the reinsurer has made a final decision. Oblig./Fac.: The reverse of Fac./Oblig. For large, financially sound companies or for companies with a well-balanced portfolio, an XL on the gross capacity is another possible variant. With this method only the largest risks are truncated by means of facultative (proportional or non-proportional) reinsurance. A per-risk WXL protects the remainder of the portfolio in the company s retention after any facultative cessions. Quota share treaties can be used instead of surplus treaties or also to provide further protection for the retention under a surplus treaty. Quota shares do not improve the balance of the retention. They take an equal proportion of premiums and liability across all sizes of risk. Reasons for using quota share treaties may be: 23
A financially weak company which has to cede premiums in order to meet solvency criteria. Administrative problems: no possibility of ceding risks individually. Support quota shares: reinsurers who write lines on a poorly performing or unbalanced treaty are compensated for this with a quota share cession on a profitable and well-balanced business segment. Cheap catastrophe capacity (depending on the market situation). New business with very little loss experience: the insurance company wants to share the uncertainty with the reinsurer. If the surplus cover is very long, it may be divided up into a first and a second surplus for the following reasons: Advantages for the reinsurer: The reinsurer can pay a lower commission on the second surplus treaty, which only covers very large risks and is therefore not well balanced. The commission can be more closely adapted to the loss experience. Advantage for the insurance company: The markets for first and second surplus treaties are often different. In some circumstances, therefore, a split treaty can be placed more easily. Basis of cession If the insurance company cedes business to proportional treaties on the basis of an estimate of the maximum loss (eg MPL), it may want to protect the retention against an underestimation of the MPL. This is best done by means of a special MPL error cover which follows on above the per-risk WXL. If, for example, the minimum MPL is 30% and the proportional retention is 6 000 000, MPL error cover of up to 6 000 000/30% = 20 000 000 would be enough in each case. Another possibility is to cover the MPL error by means of the CatXL treaty. Depending on the faith it has in its own risk assessment and on financial strength and risk aversion, the company can bear all or part of the MPL error risk itself. A risk can encompass several policies (eg buildings, contents, business interruption) which are affected simultaneously in the event of a loss. A company which cedes these policies separately should have less capacity per insured interest than a company which cedes the risk as a whole. Conversely, a policy can also encompass several risks. If the cession is made on the basis of the top location, the company cedes many risks which, given their size, it could very well retain. 24
Rules of thumb The terms used in the rules of thumb are explained in Chapter 2. The rules below can be used only if the property portfolio as a whole is considered. They are not applicable to just part of the insured perils or risks. Rules of thumb for determining the gross capacity Gross capacity Gross premiums 12.5 50% (Rule of thumb 10) Already the gross portfolio should be reasonably balanced. Often this rule is in conflict with the insurance company s interest in placing as little facultative business as possible. Possible measures if the rule is not complied with: adjust premium level; write more/less business; adjust gross capacity; coinsurance. Gross capacity Net capacity 10 25 (Rule of thumb 11) The primary insurer and reinsurer should be reasonably involved in the risk, in particular, the primary insurer should retain a large enough proportion of it. This ensures that its interest in the performance of the gross business is maintained. Possible measures if the rule is not complied with: adjust gross capacity; adjust net capacity (retention); introduce co-reinsurance. Facultative premiums Gross premiums < 5% (Rule of thumb 12) Facultative cessions are expensive for the insurance company. They should therefore not be too numerous. Possible measures if the rule is not complied with: increase gross capacity; coinsurance; review underwriting policy for major risks. 25
Rule of thumb for surplus treaties Premiums Capacity 1 st surplus 1:2 (Rule of thumb 13) Until the end of the 1980s, a good balance was an important criterion for surplus treaties. At that time, business under reciprocity arrangements was relatively important and balanced treaties (with a balance of 1:1 or better) were considered to be particularly worth writing on a reciprocal basis. However, this type of balanced business barely needs any reinsurance against fluctuations. As the reinsurance market hardened in the early 1990s, reciprocal business (and with it these types of surplus treaties) virtually disappeared. First surpluses today have a balance of approximately 1:2. Smaller reinsurers are more interested in well-balanced surplus treaties. The lack of diversification in their portfolio means that they have to rely on their portfolios becoming balanced over time. For them, short-term treaties therefore have to be well balanced. With its highly diversified portfolio, Swiss Re is not dependent on a good balance within a treaty. When deciding to participate in a treaty, its main concern is that the commission is commensurate with the risk. For the sake of completeness, it should be noted that reducing the number of lines in the first surplus and at the same time increasing the number of lines in the second surplus improves the balance in both treaties. Premiums Capacity 2 nd surplus 1:10 (Rule of thumb 14) See comments on the previous rule of thumb. In the past, a balance of 1:5 was postulated for second surpluses. Rules of thumb for per-risk WXLs Deductible Cover 10% (Rule of thumb 15) Programmes with a longer XL cover should be divided up into several layers. If this is not done, the whole cover can be used up by just a few minor losses which barely exceed the deductible (in the case of a limited number of reinstatements). Moreover, smaller layers are easier to place because of reinsurers varying interests. 26
Rate on line 5% 100% (Rule of thumb 16) If the rate on line is lower, the treaty only protects the insurance company against very infrequent events. Pricing is therefore more difficult and reinsurers tend to ask for higher loadings on the risk premium. If, on the other hand, the rate on line is too high, there is the danger of money swapping : the company pays the reinsurer a high premium at the start of the year (or in instalments) which the reinsurer most probably pays back over the course of the year in the form of claims payments. This increases administration costs unnecessarily. In some cases, however, it may be that the insurance company does not have much in the way of liquid funds and therefore needs immediate payment from the reinsurer in order to pay losses. Possible measures if the rule is not complied with: increase deductible; introduce an annual aggregate deductible. Reinstatements It is in the reinsurer s interest to limit its liability whenever possible. One question with regard to per-risk WXLs is how many reinstatements should sensibly be agreed in the treaty. The following table may serve as an indication: 4,5 Risk ROL 5.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0% 90.0% 100.0% 1 st cover 4.9% 9.5% 18.1% 25.9% 33.0% 39.3% 45.1% 50.3% 55.1% 59.3% 63.2% 1 st reinstatement 0.1% 0.5% 1.8% 3.7% 6.2% 9.0% 12.2% 15.6% 19.1% 22.8% 26.4% 2 nd reinstatement 0.0% 0.0% 0.1% 0.4% 0.8% 1.4% 2.3% 3.4% 4.7% 6.3% 8.0% 3 rd reinstatement 0.0% 0.0% 0.0% 0.0% 0.1% 0.2% 0.3% 0.6% 0.9% 1.3% 1.9% 4 th reinstatement 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.1% 0.1% 0.2% 0.4% Table 11: Probability of the individual elements of cover being affected by losses in a given year For a treaty with a risk ROL of 60%, the probability that, in a given year, the third reinstatement will be affected by a loss is therefore 0.3%, ie this happens on average once every 333 years. Example 5 This example follows on from Example 1 in Chapter 2, where we fixed the proportional retention at 6 000 000 and the net retention at 1 500 000. We will now define the entire per-risk programme on the basis of the rules of thumb in this chapter. 4 0.0% in the table does not mean that the probability is zero, but only that it is less than 0.05% and has thus been rounded down in the table. 5 The table is based on the assumption that the number of losses follows a Poisson distribution. 27
Determining the gross capacity The following table shows the effect of various gross capacities on rules of thumb 10 to 12. Gross capacity 36 000 42 000 48 000 54 000 60 000 66 000 72 000 78 000 84 000 90 000 Rules of thumb (000s) min. max. Fac. premiums 2 720 2 204 1 699 1 363 1 155 946 738 595 455 316 (000s) Rule of thumb 10: 31.3% 36.5% 41.7% 46.9% 52.2% 57.4% 62.6% 67.8% 73.0% 78.2% 12.5% 50.0% Gross capacity/ Gross premiums Rule of thumb 11: 6 7 8 9 10 11 12 13 14 15 10 25 Gross capacity/ Net capacity Rule of thumb 12: 2.4% 1.9% 1.5% 1.2% 1.0% 0.8% 0.6% 0.5% 0.4% 0.3% 5.0% Fac. premiums/ Gross premiums Table 12: Rules of thumb for gross capacity Rule of thumb 12 does not restrict us here. On the basis of rules 10 and 11, we decide on a gross capacity of 54 000 000. The surplus cover therefore has 8 lines. Designing the surplus cover The surplus cover of 8 lines or 48 000 000 now has to be divided into a first and second surplus. The following table shows the effect of various divisions on rules of thumb 13 and 14 (the premiums for the various treaties have been calculated on the basis of the risk profile from Example 1): Number of lines 1 st surplus 1 2 3 4 5 6 7 8 Rules of thumb min. max. Premiums 1 st surplus 6 891 10 406 12 343 13 562 14 608 15 124 15 630 15 965 Capacity 1 st surplus 6 000 12 000 18 000 24 000 30 000 36 000 42 000 48 000 Rule of thumb 13: 1.15 0.87 0.69 0.57 0.49 0.42 0.37 0.33 1:2 Balance 1 st surplus Number of lines 2 nd surplus 7 6 5 4 3 2 1 0 Premiums 2 nd surplus 9 074 5 559 3 622 2 403 1 357 841 335 0 Capacity 2 nd surplus 42 000 36 000 30 000 24 000 18 000 12 000 6 000 0 Rule of thumb 14: 0.22 0.15 0.12 0.10 0.08 0.07 0.06 1:10 Balance 2 nd surplus Table 13: Rules of thumb for surplus treaties On the basis of the table, we decide on a first surplus of 4 lines and a second surplus of 4 lines. A division of 5 lines /3 lines would also be possible. In general, the number of lines in the second surplus should be less than or equal to that in the first surplus. However, in practice, the reverse is often true in order to meet the small reinsurers' requirements for a balanced treaty. 28
Designing the per-risk WXL on the retention In the previous chapter, we set the deductible at 1500 000. This certainly fulfils the first rule of thumb for WXLs. The table below shows the ROL of the per-risk WXL for various deductibles. In order to determine the ROLs we carried out an exposure rating 6 for the WXL in question on the basis of the risk profile. Cover 5 500 5 000 4 500 4 000 3 500 3 000 Rule of thumb min. max. Deductible 500 1 000 1 500 2 000 2 500 3 000 Rule of thumb 16 ROL 116% 64% 48% 39% 33% 29% 5% 100% Table 14: Rules of thumb for the per-risk WXL For deductibles under 1000 000, the ROL is too high (money swapping). However, so low a deductible could be chosen if there is also an annual aggregate deductible reducing the annual claims burden to the treaty. On the basis of this table, the deductible of 1500 000 chosen in Chapter 2 appears appropriate. The number of reinstatements can be determined with the aid of Table 11. Of course this number depends on the company's risk aversion. If we assume that the company wishes to insure itself against an annual loss which occurs roughly once every hundred years, 3 reinstatements should be sufficient. According to the table, the third reinstatement is affected by a loss with a probability of 0.2%, ie on average once in 500 years. Designing per-event reinsurance programmes WXL per event (WXL/E) Suitable products for protection against accumulation losses are non-proportional covers which are defined per event. For an insurer desiring protection against the consequences of large losses on individual risks and against accumulation losses, a WXL/E appears at first sight to be the most suitable solution: with just one treaty, the insurer can protect itself against two threats at the same time. Caution is required, however. It may be that the entire cover is used up by large individual losses, thus leaving insufficient cover for an accumulation loss (or vice versa). Moreover, in the case of an event involving several large individual losses (eg a major fire), the cover might not be sufficient. With this type of cover it is difficult for the reinsurer to reserve a large enough proportion of the treaty premium for accumulation losses since, when assessing the level of premium, many players in the reinsurance market often take into account only the relatively frequent losses affecting individual risks. 6 Upon request, Swiss Re will be happy to supply documentation on exposure rating. 29