Risk comments including some Re-insurance issues (Socio-Economic Security)

1. Risk comments including some Re-insurance issues (Socio-Economic Security) Jorge A. Prieto, PhD. PEng. Natural Resources Canada, Geological Survey of Canada, Geo-Risks Group 1 May 2013

2. World economic losses 1980 to 2012, left 2010, below 2012 Topics Geo, Munich Re 2011, 2013

3. After 1,000 Earthquakes or “scenarios” or “years”. Simulations using @Risk software for a set of properties

4. Cumulative: probability of a loss less than Area of each yellow rectangle = frequency x loss = probability x loss = fi x Li = pi x Li for a set of properties

5. 1-Cumulative: probability of a loss more than Area of each yellow rectangle = frequency x loss = probability x loss = fi x Li = pi x Li Risk curve, Risk profile curve for a set of properties

6. 6 After 1,000 Earthquakes or “scenarios” or “years” Note: that the frequency of a loss is different from the frequency of an earthquake, and from the frequency of ground motions, because uncertainty in ground motions and uncertainty in buildings damage given ground motions, increase the number of possibilities or outcomes. So the same earthquake produces different frequencies of losses. for a set of properties

7. 7 Loss 1 Ground motion 1 Loss 2 Loss 3 Loss 4 Earthquake Loss 1 Ground motion 2 Loss 2 Loss 3 Loss 4 1 property Each outcome has a possible frequency or probability

8. 8 Loss 1 Ground motion 1 Loss 2 Loss 3 Loss 4 Earthquake Loss 1 Ground motion 2 Loss 2 Loss 3 Loss 4 1 property Each outcome has a possible frequency or probability Geo-risks: more complexity because more number of possible outcomes Geo-hazards

9. After 1,000 Earthquakes or “scenarios” or “years” Area = Sum (fi x Li) = total loss during those years Average loss during those years = Sum(fi x Li)/Sum(fi) = Area/1,000 = Annual loss Annual insurance rate, ratio = (Annual loss)/(Properties value) for a set of properties

10. We noted before that the frequency of a loss is different from the frequency of an earthquake, and from the frequency of ground motions. In the case of 1 property (e.g. 1 building), it is possible to agregate the frequencies of damage given ground motions, and of ground motions given an earthquake. However, when there is more than 1 property, it is not possible to aggregate the frequencies, unless the relation between the frequencies of the properties are known. That is to say, when there is more than 1 property, it is essential to include the “correlation” between the losses. After 1,000 Earthquakes or “scenarios” or “years” for a set of properties

11. 11 Loss 1b Loss 1 Ground motion 1 Ground motion 1 Loss 2b Loss 2 Loss 3 Loss 3b Loss 4b Loss 4 Earthquake Earthquake Loss 1b Loss 1 Ground motion 2 Ground motion 2 Loss 2b Loss 2 Loss 3 Loss 3b Loss 4 Loss 4b 2 properties Losses have to be aggregated, e.g: Loss 1 + Loss 1b What is the frequency of the joint loss? The frequency of the aggregated losses depends on the “correlations” between losses

12. 12 • Losses occurred to 2 buildings are correlated if given that some • level of damage occurred in 1 building it is likely that it also occurres • in the 2nd building. • Correlation in losses to buildings happens because: • Buildings are located nearby: Because of similar Geology, similar • levels of shaken are expected. • -Buildings were designed and built similarly (Same engineering design, • year of construction, materials). • Examples: • -Losses in Townhouses should have high level of correlation because they are • located nearby and also because similar design and possible year of construction • -Losses in the Vancouver new convention center, have maybe no that high correlation • with losses suffered by the Burnaby City Hall, during a natural disaster.

13. 13 Simulations using 20 real buildings, total asset value = CA 12 million No correlation, uncertainty due just to buildings, no ground motions. As the mean loss is 1.38 million (area under the curve), the loss ratio is 1.38/12 = 0.115 = 11.5%. This loss has a aprobability of 0.46 of being exceeded. Assuming that each trial is a year with same probability, the annual loss ratio would be 0.115/1000.

14. Simulations using 20 real buildings, total asset value = CA 12 million Assuming high correlation among losses.

15. 15 Effect of correlation of losses No correlated losses Correlated losses Note that although the mean loss does not change, the probability of exceeding a loss of 3.25 million increases from 0.9% (0.8+0.1) to 2.7% (1.7+1) because including the “correlations”. That is probabilities of high losses increases by a factor of 3 because the correlations!.

16. 16 Effect of larger window time considered (e.g increase from 1000 to 10,000 years) No correlated losses Correlated losses Note that when we increase the period of observation (number of trials or scenarios), the Maximum Loss Observed, for the case of correlation, increases from 4.6 million (previous slide, 1,000 scenarios or years) to 5.05 million when we simulate 10,000 years. We are simulating just the Holocene! within Earth’s history!

17. 17 • From the 2 preceding slides is clear that: • - Correlations among assets, properties, buildings increase • the probabilities of high losses. • As we increase the period of observation (for example, considering • more of the Geological history or the Earth), the maximum losses • increases.

18. 18 Economic security: How much and how we can pay for future losses? A first problem is that first we need a Risk Curve. As we have seen a proper risk curve has to include the effects of correlations (specially at the right side or “tail” of a loss distribution. There are good advances in understanding correlations in ground motions. However, correlations among buildings are less understood. The problem of including the distance between buildings is not well solved yet. Accurate Correlations due to same code vintage, structural type, etc, are not very advanced Yet. Very simplified models have to be used.

19. 19 Economic security: How much and how we can pay for future losses? Knowing a Risk Curve and selecting some value, automatically provides a limit to the loss, and the area below the curve and up to the value selected provides the “average annual loss”. Then the average annual loss can be collected in advance (premium) to accumulate to pay but only up to the loss value selected. Losses larger than the value selected can not be paid.

20. 20 Economic security: How much and how we can pay for future losses? • How much? • Reinsurers use a concept: Probable Maximum Loss, PML • The problem is that as we have seen, the PML can be any value • that we decide to select from a Risk Curve, each with some probability • of being exceeded, and each provide a different annual loss to be collected.

21. 21 Economic security: How much and how we can pay for future losses? There is not a value with a near “0” probability of being exceeded If there is enough window time, the maximum loss increases, as we have seen. Therefore, even the probability of having a loss similar to the total value of a set or portfolio of properties is not “0”. There is also some probability of having more than 1 loss in 1 year. The PML can be extremely large!

22. 22 The PML calculated by a “normal” fire re-insurance underwriter for the WTC twin towers in New York was the value of 1 tower. However, that PML estimation was exceeded by a factor of 2! Had the towers were rebuilt, there would be some probability of being destroyed again. Photograph downloaded from Wikipedia

23. 23 To cover, protect, 100% of the value of a portfolio, would be necessary to have a long time accumulating the expected, average annual loss (premiums) without suffering any losses during that long time. For example: If the average annual loss ratio is 1/1000 to cover up to 100% = 1 (this could come from some risk curve, or can be a ratio fixed, decided, to charge) we will need 1/(1/1000) = 1000 years collecting 1/1000*(value of the portfolio) each year, and hoping the catastrophic event do not happen within those years. The pro bability of losing 100% can be for example 1/500. Even if the probability of losing a value near to 100% is far lower than 1/1000, the catastrophe can occur. Off course, one can decide to charge 1/100 as an annual rate, and wait 100 years to accumulate to be prepared, but the event can occur any way, apart than a 1% rate per year is a high value to charge. Similarly, one can charge 10% per year, an extremely high value (not many people is going to pay that)!, and the event can occur any way within those 10 years. Therefore, just a fraction of a portfolio is protected (covered).

24. 24 Examples: In Mexico and in Colombia, following recent regulation, each insurance company has to be Re-Insured against Earthquake (their earthquake portfolios has to be covered) up to the loss corresponding to an annual exceedance probability of 1/1,500. The loss corresponding to that probability varies according to each insurance company, following their Risk Curves. So, a direct property owner (e.g. home owner) is covered up to 100 % of the value of his/her property, as far as, the aggregated loss for the Insurance company does not exceed the 1/1,500 loss. If the aggregated loss for the insurance company exceeds that value, it is verly likely that the company goes to default, and the property owners are not paid. Previously, in Colombia the maximum value re-insured was 15% of the earthquake portfolio. The situation is similar for any country in the World (changing, percentages)

25. 25 Examples 2: Larger Re-Insurers increase their capital in a way, that for example, they are able to pay up to 2 losses with an annual probability of 1/100 each loss occurring the same year, from their risk curves. This means, that they are using an annual probability of exceedance of 1/100*1/100 = 1/10,000. Should the losses in a year exceed the one corresponding to that probability, the Re-insurer could go to default with the Insurance Companies. They use 2 losses of 1/100 instead of 1 loss with probability of 1/10,000 because as we shown here, low probabilities occur at the tail of the risk Curves, which are difficult to estimate because of the Correlation Problem!

26. 26 A subtle issue: Note that although the maximum loss can be selected from a riks curve by fixing a probability as a target for economic security, in practice, an affordable average annual rate is fixed (not too different from 1/1000 over asset values) and the maximum loss corresponding to that ratio and a given probability of exceedence are obtained from the risk curve.

27. 27 As our economic, finance, system has a limited capacity, to deal with earthquake and other type of risks, it is essential that we continue our efforts to use other mechanisms to help mitigating them, e.g. regulation, advanced risk based building codes, and in my opinion, Education.

28. Topics Geo, Munich Re, 2013 These are Losses. A significant part due to the Increase in Exposure. What about Loss Ratios? If the loss ratios are increasing, that means that the current economic system is not been able to create enough wealth to balance losses (no Resiliency capacity). Therefore, a potential increase in loss ratios would be one of the largest challenges, not just the Re-Insurers and insurers, but for the we the whole society have in the current and future Times.

29. 29 Thanks