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

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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

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Topics Geo, Munich Re 2011, 2013

World economic losses 1980 to 2012,left 2010, below 2012

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9.5% 85.5% 5.0%

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Curve #1

Minimum1.140E-005Maximum 1.3433Mean 0.1112Std Dev 0.1251Values 1000

After 1,000Earthquakes or“scenarios” or “years”.

Simulations using@Risk software

for a set of properties

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9.5% 85.5% 5.0%

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Cumulative:probability of a loss less than

Area of each yellow rectangle = frequency x loss = probability x loss = fi x Li = pi x Li

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9.5% 85.5% 5.0%

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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

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9.5% 85.5% 5.0%

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After 1,000Earthquakes or“scenarios” or “years”


Note: that the frequency of a lossis different from the frequency ofan earthquake, and from the frequencyof ground motions, becauseuncertainty in ground motionsand uncertainty in buildings damagegiven ground motions, increasethe number of possibilitiesor outcomes. So the same earthquakeproduces different frequenciesof losses.

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Earthquake

Ground motion 1

Ground motion 2

Loss 1

Loss 2

Loss 3

Loss 4

Loss 1

Loss 2

Loss 3

Loss 4

1 property

Each outcome has a possible frequency orprobability

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Earthquake

Ground motion 1

Ground motion 2

Loss 1

Loss 2

Loss 3

Loss 4

Loss 1

Loss 2

Loss 3

Loss 4

1 property

Each outcome has a possible frequency orprobability

Geo-hazards Geo-risks: more complexity becausemore number of possible outcomes

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9.5% 85.5% 5.0%

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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)

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9.5% 85.5% 5.0%

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We noted before that the frequency of a lossis different from the frequency ofan earthquake, and from the frequencyof 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 givenan earthquake.However, when there is more than 1 property, it is notpossible to aggregate the frequencies, unless the relationbetween the frequencies of the properties are known. That is to say, when there is more than 1 property, it isessential to include the “correlation” between the losses.

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2 properties

Earthquake

Ground motion 1

Ground motion 2

Loss 1

Loss 2

Loss 3

Loss 4

Loss 1

Loss 2

Loss 3

Loss 4

Losses have to be aggregated, e.g:

Loss 1 + Loss 1bWhat is the frequency of the jointloss?

The frequency of the aggregatedlosses depends on the “correlations”between losses

Earthquake

Ground motion 1

Ground motion 2

Loss 1b

Loss 2b

Loss 3b

Loss 4b

Loss 1b

Loss 2b

Loss 3b

Loss 4b

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Losses occurred to 2 buildings are correlated if given that somelevel of damage occurred in 1 building it is likely that it also occurresin the 2nd building.

Correlation in losses to buildings happens because:

-Buildings are located nearby: Because of similar Geology, similarlevels 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 arelocated nearby and also because similar design and possible year of construction

-Losses in the Vancouver new convention center, have maybe no that high correlationwith losses suffered by the Burnaby City Hall, during a natural disaster.

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99.1% 0.8% 0.1%

3.250 3.850

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Minimum 262,533.60Maximum4,457,984.88Mean 1,375,017.96Std Dev 680,090.60Values 1000

Simulations using 20 real buildings, total asset value = CA 12 millionNo 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%. Thisloss 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.

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99.1% 0.8% 0.1%

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

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99.1% 0.8% 0.1%97.3% 1.7% 1.0%

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Curve #2


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!.

Effect of correlation of losses

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99.1% 0.8% 0.1%97.2% 2.0% 0.8%

3.250 3.850

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Curve #2


No correlated losses

Correlated losses

Effect of larger window time considered (e.g increase from 1000 to 10,000 years)

Note that when we increase the period of observation (number of trials or scenarios), the Maximum LossObserved, for the case of correlation, increases from 4.6 million (previous slide, 1,000 scenarios or years) to5.05 million when we simulate 10,000 years. We are simulating just the Holocene! within Earth’s history!

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From the 2 preceding slides is clear that:

- Correlations among assets, properties, buildings increasethe probabilities of high losses.

-As we increase the period of observation (for example, consideringmore of the Geological history or the Earth), the maximum lossesincreases.

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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 haveseen 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 ofincluding the distance between buildings is not well solved yet. Accurate Correlations due to same code vintage, structural type, etc, are not very advancedYet.Very simplified models have to be used.

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Knowing a Risk Curve and selecting some value, automaticallyprovides a limit to the loss, and the area below the curve and up to the valueselected 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 largerthan the value selected can not be paid.

99.1% 0.8% 0.1%

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1. How much?

Reinsurers use a concept: Probable Maximum Loss, PML

The problem is that as we have seen, the PML can be any valuethat we decide to select from a Risk Curve, each with some probabilityof being exceeded, and each provide a different annual loss to be collected.

99.1% 0.8% 0.1%

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There is not a value with a near “0” probability of being exceededIf 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 probabilityof having more than 1 loss in 1 year.The PML can be extremely large!

99.1% 0.8% 0.1%

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The PML calculatedby a “normal” fire re-insuranceunderwriter for the WTC twin towers in New York was the value of 1 tower.

However, that PMLestimation was exceeded bya factor of 2!

Had the towers were rebuilt,there would be some probabilityof being destroyed again.

Photograph downloaded from Wikipedia

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To cover, protect, 100% of the value of a portfolio, would be necessary to havea 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 comefrom 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) eachyear, and hoping the catastrophic event do not happen within those years. The probability of losing 100% can be for example 1/500. Even if the probability of losinga 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% rateper 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 occurany way within those 10 years.

Therefore, just a fraction of a portfolio is protected (covered).

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Examples:

In Mexico and in Colombia, following recent regulation,each insurance company has to be Re-Insured againstEarthquake (their earthquake portfolios has to be covered)up to the loss corresponding to an annual exceedanceprobability 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 coveredup to 100 % of the value of his/her property, as far as, theaggregated loss for the Insurance company does not exceed the 1/1,500loss. If the aggregated loss for the insurance company exceedsthat value, it is verly likely that the company goes to default,and the property owners are not paid. Previously, in Colombia the maximumvalue re-insured was 15% of the earthquake portfolio.

The situation is similar for any country in the World (changing, percentages)

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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 1/100each 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 1/10,000because as we shown here, low probabilities occur at the tail of the riskCurves, which are difficult to estimate because of the Correlation Problem!

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A subtle issue:

Note that although the maximum loss can beselected from a riks curve by fixing a probability as a target for economic security, in practice, an affordable average annualrate is fixed (not too different from 1/1000 over asset values) and the maximum loss corresponding to that ratio and a given probabilityof exceedence are obtained from the risk curve.

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As our economic, finance, system has a limited capacity,to deal with earthquake and other type of risks, it is essentialthat 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.

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Topics Geo, Munich Re, 2013

These are Losses. A significant part due to theIncrease in Exposure.

What about Loss Ratios?

If the loss ratios are increasing, that means that the current economic system is not been able to createenough wealth to balance losses (no Resiliency capacity).

Therefore, a potential increase in loss ratios would be oneof the largest challenges, not just the Re-Insurers and insurers,but for the we the whole society have in the current and futureTimes.

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Thanks

Documents

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