Insurance and Reinsurance In the Modelled World – A Personal History

1. Insurance and Reinsurance In the Modelled World – A Personal History David Simmons, Managing Director Analytics, Willis Re

2. A personal history of modelling in reinsurance • I started in reinsurance in 1985 • Reputedly first mathematician to work for a London reinsurance broker • The aim, to use the new IBM PC and sexy new Lotus Symphony software to model reinsurance risk • The first models were deterministic • If this happens • …to this portfolio • …with this reinsurance • …then what’s the impact • Or pricing models • Burning cost • Exposure curve • Programme consistent pricing • Market consistent pricing But how do we advise what a client should do?

3. The lost years • For a long time I really didn’t get it • What reinsurance people bought seemed to be based upon: • Simple rules of thumb, eg buy 5% of agg for cat risk (where did these come from?) • Or by comparison with what peers bought (why is that appropriate – and how do you compare?) • A key value of the broker was to bring this intelligence • Yes there was appreciation of capital requirements • Quota share often described as a capital protection product given simple premium volume linked capital rules then applying • Care taken to limit net PMLs to acceptable amounts (however both terms defined) • And yes, much reinsurance was also bought for shorter term aims • Earnings (and bonus) protection • Well priced opportunistic purchases (hard sold by broker) • Bu there was no framework, let alone a rigorous one, to: • Assess whether a particular strategy was appropriate • Assess whether a particular purchase was appropriate • To look at reinsurance strategy across an operation for consistency

4. The birth • Stochastic theory for insurance modelling had been around for some time • eg Risk Theory : The Stochastic Basis of Insurance; Beard, Pentikainen and Pesonen, 1984 • But take up limited by hardware and software limitations • Similarly, the theory for catastophe modelling was becoming formalised • eg Natural Hazard Risk Assessment for an Insurance Program, Don Friedman, 1984 • In 1987 Karen Clark, later to found AIR, built first Hurricane model funded by reinsurance broker Blanch (but smartly she kept the IPR) • 1991: the key year • I build my first stochastic reinsurance model in Excel with Excel macros • My colleague Andrew Mitchell (now also at Willis) built the first stochastic UK windstorm model • These early models were, in retrospect, poor, and ran incredibly slowly but the die was cast • The fundamentals were there • Hardware and software improving • Theory in place • Market was receptive • Working models had been created

5. Childhood • Our new toys were creating a stir in a market that was stressed by a chain of losses • Eg European storms 87J and 90A/Daria, Piper Alpha, Hurricane Andrew • Adverse comparisons were made between the London market and “professional reinsurers” in Europe • This lead to a flight to modelling in the London market • Stochastic Modelling • Guy Carpenter’s Instrat lead the way, with thought leadership from Rodney Kreps and Gary Venter • In 1990 , Kreps published Reinsurer Risk Loads from Marginal Surplus Requirements, laying out the basis for the standard deviation load XL pricing methodology still widely used (and abused) today • @Risk and Crystal Ball emerged, stochastic add-ins for Excel • MetaRisk from Guy Carpenter was the first dedicated broker tool for reinsurance optimisation, followed by ReMetrica from Greig Fester (initially a near copy of MetaRisk) • Catastrophe Modelling • At first catastrophe modelling was pioneered by reinsurance brokers but as the 1990s continued we saw the emergence of the three now dominate modelling companies: RMS. EQECAT and AIR • Storm models were followed first flood models (eg UK storm surge in 1992) and earthquake models • By end of decade most major perils for major markets were modelled • Scientific/industry engagement increased with launch of Greig Fester Hazard Research Centre at UCL and the Risk Prediction Initiative in Bermuda

6. Growing pains • The new models seemed to offer the panacea to the industries problems • A technical basis to replace the now discredited ”underwriters born not made” attitude and the naïve subscription market that arguably pertained before • For me the answer at last, now there was a story, Risk vs Return • At last “cost” could be compared to a consistent measure of benefit • Typically mean reduction in underwriting profit was compared to a percentile value as a proxy for capital, or probability of missing a particular target • Reinsurance pricing seemed to have more logic; Kreps formula separated • Expected Loss cost • Expenses • Cost of Capital BUT we had that perfect storm • Demand from people wanted a certainty that didn’t exist • Lack of transparency, and indeed understanding, around models and techniques • There were a few people who did understand, but they were learning on the job The days of the computer says no (or, more perhaps more dangerously, yes)

7. The Panacea?Risk vs Return Less Cost Target Less Risk More Risk More Cost

8. Nobody understands me Some common problems in the early days of modelling: • Modelling too simplistically applied • Confusion of single portfolio VAR points with real capital requirements • Over-simplistic adoption of Kreps pricing formula for XL business • Lack of understanding of inherent complexity of models • Management demanded a number to manage to, not a probability range • Peril models particularly were over sold and over bought • Vendors focussed on model sophistication and robustness, what buyers wanted to hear, not uncertainty, definitely what they didn’t want to hear • Difficult for market to absorb new thinking • Early science/industry collaborations largely failed • People too busy with the day job to try/absorb new ideas • Silo mentality • Models were single purpose, no real joined up thinking • Often there was a conflict between the underwriter (salesman) and modeller (policeman) All of these problems persist today

9. Example 1Overstated capital benefit • For practical reasons, only one portfolio or element of a portfolio was modelled • eg only storm element of property catastrophe • “Capital benefit” modelled by change in by 1 in 200 of that portfolio/peril • OK often said to be a proxy, but then confused by spurious “economic value” calculations • Example : UK client in 1999 with a early Internal Capital Model • Broker : This deal saves you £200m of capital (meaning 1 in 100 for UK storm is reduced by £200m) • Client: But if I add in rest of my cat risks the 1 in 100 only drops by £150m after this cover • Client again: Indeed if I add in rest of my property book risks the 1 in 100 is only £120m off • And again: If I add in the rest of my active underwriting risk the benefit is only £80m • And more: If I also add in reserving risk the benefit is only £50m • And the coup de grace: If we add in asset risk, then then my company 1 in 100 is only down £20m • Suddenly the “Economic Benefit “ is not looking so rosy, exit broker wounded • An example of naivety/loose language not an attempt to mislead (I was that broker) • But an example of interpretation running ahead of model ability • Broker did not have the data, knowledge or time to build a full ECM and so assess capital benefit • To be honest neither did client, they later acknowledged that their model was useless

10. Example 2Kreps Formula • Still widely used for XL reinsurance pricing but how many have read the theory • Price is a function of expected loss cost plus expenses plus capital charge • Capital charge is “reluctance factor” times standard deviation of result • Reluctance factor, per paper, depends upon the risk aversion and the return expectation of reinsurer, coupled with correlation of new risk with the rest of their book • But how many people using the formula are aware of the theory? 5%? • Assumptions behind Kreps formula • XL losses are normally distributed - clearly wrong, tail is far fatter • In examples in paper, a 1 in 1,000 capital measure is assumed. Now given distribution is normal this is arguably consistent with a real lower return period, but looks a conservative assumption • Paper gives “reluctance factors”, ie percentages applied to standard deviation , of • 33% if 12% desired return on capital and risk is 100% correlated with rest of book • 52% if 20% desired return on capital and risk is 100% correlated with rest of book • Arguably (perhaps indisputably) current factors are way outside of these guidelines • By theory if low correlation with rest of book, reluctance factor should be near zero • Factor should never be greater than 55% even for mono-line Florida writer • But factor is often higher as confused by non-explicit cat model uncertainty loads and expenses

11. Example 3Marginal Capital Models • Rather than use a crude approximation for capital usage as per Kreps formula, why not compute actual marginal capital requirements for each deal? • Because its hard, but peril models seemed to open the door to this approach for catastrophe risks • Seminal paper published by Lowe and Stanard in 2003 • “An Integrated Dynamic Financial Analysis and Decision Support System for a Property Catastrophe Reinsurer” • Process copied by many, but as always devil in detail • But Model dependent • What if chosen model is wrong – frequency, severity, regional correlations • How can different models be melded (eg some US Hurricane on RMS, some on AIR) • What if no model exists for a particular territory/peril? • And Portfolio dependent • Capital is marginal to what? Renewed book, held book, budgeted book, forecast book? • How to react to portfolio developing/opportunities offered different from plan • Models typically are order dependent, ie first risk have lower charge than later ones, is this good to encourage early responses or poor as randomly skews optimal portfolio • What about non-cat risks (as per example 1)?

12. OK enough history, where are we now? • Demand coming from 3 places: • Regulation: insurance regulators reflecting Basle II/III risk adjusted capital regimes • Rating Agency: Responding to same zeitgeist • Best practice: “me to” response plus parental pressure • Solvency II not an even playing-field yet • UK: ICAS regime in 2005 encouraged capital model development: 60 + companies in pre-approval • Ireland: Home to many (re)insurance groups: 40+ companies in pre-approval • Germany: A handful of companies in pre-approval • Similar to Germany in most of rest of Europe • Core to many/most internal models is cat risk • Insurers encouraged to develop “own view of risk” • Cannot hide behind 3rd party models or 3rd party advice • As with ICAS, logical end point of Solvency II is a transparent model • Identify risk • Manage risk • Quantify risk?

13. Are there any technical barriers? • I would argue no • There are a number of software choices available In the market • Processing power is cheap • But it is true that many models are hampered by poor performance • One example, reinsurance department only allowed three runs a year as model is so slow! • Why? Poor and perhaps over ambitious design? • Better a simple model with known flaws than a complex one nobody understands • But do regulators buy that message? • The drag will be people and money • Not enough actuaries in the world • Not enough money within insurers • Certainly not enough expertise within most regulators • But biggest issue is the cultural shift that full adoption of a capital model entails But I fully expect that, like in the UK after ICAS, it will be the rare exception for all but the smallest companies not to have an internal capital model in place, partial at least, within 5 years

14. Current position • “Chief Scientific Officers” are emerging in the London Insurance Market • Most have catastrophe modelling backgrounds • Clearly influenced by need to deliver “own view of risk” • Open access model platforms are being postulated • Eg OASIS backed with UK research council funding • Circa 20 companies now signed up including all three big brokers, more progressive Lloyd’s syndicates (eg Hiscox, Catlin) and big reinsurers like Renaissance Re and SCOR. • RMS has “mea culpa” moment • Acknowledges that uncertainty in models was underplayed in the past • Developing a new open platform (though on their terms) • All three modellers embrace need for own view of risk (liability reduction?) • But companies still need some certainty • Where do companies “hang their hat” • Regulators and shareholders won’t want to hear huge uncertainty margins • Knowledge may not bring power but paralysis

15. The essential problem • There is much more good news that bad • Catastrophe modelling has immeasurably improved how insurers view catastrophe risk • The importance of science, often seen as peripheral, is now fundamental • The concept of “own view of risk” is a grown-up response to the real world • There are many more catastrophe science aware people in the industry now than even 5 years ago • Greater interaction between science and the insurance industry (eg Willis Research Network) • But there are many problems • Most insurers still do not have the wherewithal to form their own view of risk • Regulators don’t really know what they want and expect • Insurers are still expected to come up with a single 1 in 200 number: regulators and management • How uncertainty around that number is captured, represented or acted upon is far from clear • CROs and CSOs often seen as barriers to business rather than conduits to profitable buisness • Legal challenge to scientific community: eg Italian scientists, UK libel laws • Backlash against perceived model failures • Katrina • NZ earthquakes • Japanese earthquake/Tsunami • Copenhagen extreme rain

16. Conclusions • We have come a hell of a long way in 20 years • But we have a lot further to go • Capital models allow real, transparent management of insurers • Specific to clients portfolio and risk appetite • Centrality of peril models/peril science never more important • But still uncertainty about where we should be heading • Companies must now develop their “own view of risk” • Rise of the Chief Scientific Officer • Models advise, models do not decide • What the model says is right is not necessarily the right thing to do • Make sure inherent uncertainty is understood • But in context that faith in modelling is not undermined • Science needs to answer questions insurers want to understand • And present its results in ways insurers can use