Tag Archives: aggregate exceedance probability

Arthur opens the US Hurricane Season

After Hurricane Arthur briefly made landfall in North Carolina on Thursday night, a weakened storm is now heading north. I thought this would be good time to have a look at the probable maximum losses (PMLs) published as at the Q1 2014 results by a sample of specialist (re)insurers, first presented in a post in June 2013. That post went into some detail on the uncertainties surrounding the published PMLs and should be read as relevant background to the figures presented here.

Despite predictions of an above average 2013 Atlantic hurricane season, the number of named hurricanes was the lowest since 1982. Predictions for the 2014 season are for a below average number of hurricanes primarily due to cooler sea temperatures in the Atlantic due to the transition to El Niño (although that is now thought to be slower than previously anticipated). The graph below includes the 2014 predictions.

click to enlargeHistorical Atlantic Storms & Hurricanes I like to look at PMLs as a percentage of net tangible assets (NTA) on a consistent basis across firms to assess exposures from a common equity viewpoint. Many firms include subordinated debt or other forms of hybrid debt in capital when showing their PMLS. For example, Lancashire has approximately $330 million of sub-debt which they include in their capital figures and I have show the difference with and without the sub-debt in the percentages for Lancashire in the graph below on US wind PMLs to illustrate the comparison.

Whether hybrid debt comes in before equity or alongside equity depends upon the exact terms and conditions. The detail of such instruments will determine whether such debt is classified as tier 1, 2 or 3 capital for regulatory purposes under Solvency II (although there are generous transitional timeframes of up to 10 years for existing instruments). The devil is often in the detail and that is another reason why I prefer to exclude them and use a consistent NTA basis.

As per the June 2013 post, firms often classify their US wind exposures by zone but I have taken the highest exposures for each (which may not necessarily be the same zone for each firm).

click to enlargeUS Wind PMLs Q1 2014 These exposures, although expressed as percentages of NTAs, should be considered net of potential profits made for 2014 to assess the real impact upon equity (provided, of course, that the expected profits don’t all come from property catastrophe lines!). If for example we assume a 10% return on NTA across each firm, then the figures above have to be adjusted.

Another issue, also discussed in the previous post, is the return period for similar events that each firms present. For example, the London market firms present Lloyds’ realistic disaster scenarios (RDS) as their PMLs. One such RDS is a repeat of the 1926 Miami hurricane which is predicted to cost $125 billion for the industry if it happened today. For the graph above, I have assumed a 1 in 200 return period for this scenario. The US & Bermudian firms do not present scenarios but points on their occurrence exceedance probability (OEP) curves.

As it is always earthquake season, I also include the PMLs for a California earthquake as per the graph below.

click to enlargeCalifornia EQ PMLs Q1 2014 In terms of current market conditions, the mid-year broker reports are boringly predictable. John Cavanagh, the CEO of Willis Re, commented in their report that “the tentacles of the softening market are spreading far and wide, with no immediate signs of relief. We’ve seen muted demand throughout 2014 and market dynamics are unlikely to change for some time to come. The current market position is increasingly challenging for reinsurers.” Aon Benfield, in their report, stated that “the lowest reinsurance risk margins in a generation stimulate new growth opportunities for insurers and may allow governments to reduce their participation in catastrophe exposed regions as insurance availability and affordability improves”. When people start talking about low pricing leading to new opportunities to take risk, I can but smile. That’s what they said during the last soft market, and the one before that!

Some commentators are making much of the recent withdrawal of the latest Munich Re bond on pricing concerns as an indicator that property catastrophe prices have reached a floor and that the market is reasserting discipline. That may be so but reaching a floor below the technical loss cost level sounds hollow to me when talking about underwriting discipline.

To finish, I have reproducing the graph on Flagstone Re from the June 2013 post as it speaks a thousand words about the dangers of relying too much on the published PMLs. Published PMLs are, after all, only indicators of losses from single events and, by their nature, reflect current (group) thinking from widely used risk management tools.

click to enlargeFlagstone CAT losses Follow-on: It occurred to me after posting that I could compare the PMLs for the selected firms as at Q1 2014 against those from Q1 2013 and the graph below shows the comparison. It does indicate that many firms have taken advantage of cheap reinsurance/retrocession and reduced their net profiles, as highlighted in this post on arbitrage opportunities. Some firms have gone through mergers or business model changes. Endurance, for example, has been changed radically by John Charman (as well as being an aggressive buyer of coverage). Lancashire is one of the only firms whose risk profile has increased using the NTA metric as a result of the Cathedral acquisition and the increase in goodwill.

click to enlargeUS Wind PMLs Q1 2013 vrs 2014

Assessing reinsurers’ catastrophe PMLs

Prior to the recent market wobbles on what a post QE world will look like, a number of reinsurers with relatively high property catastrophe exposures have suffered pullbacks in their stock due to fears about catastrophe pricing pressures (subject of previous post). Credit Suisse downgraded Validus recently stating that “reinsurance has become more of a commodity due to lower barriers to entry and vendor models.”

As we head deeper into the US hurricane season, it is worth reviewing the disclosures of a number of reinsurers in relation to catastrophe exposures, specifically their probable maximum losses or PMLs . In 2012 S&P’s influential annual publication – Global Reinsurance Highlights – there is an interesting article called “Just How Much Capital Is At Risk”. The article looked at net PMLs as a percentage of total adjusted capital (TAC), an S&P determined calculation, and also examined relative tail heaviness of PMLs disclosed by different companies. The article concluded that “by focusing on tail heaviness, we may have one additional tool to uncover which reinsurers could be most affected by such an event”. In other words, not only is the amount of the PMLs for different perils important but the shape of the curve across different return periods (e.g. 1 in 50 years, 1 in 100 years, 1 in 250 years, etc.) is also an important indicator of relative exposures. The graphs below show the net PMLs as a percentage of TAC and the net PMLs as a percentage of aggregate limits for the S&P sample of insurers and reinsurers.

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PML as % of S&P capital

PML as % of aggregate limit

Given the uncertainties around reported PMLs discussed in this post, I particularly like seeing PMLs as a percentage of aggregate limits. In the days before the now common use of catastrophic models (by such vendor firms as RMS, AIR and Eqecat), underwriters would subjectively calculate their PMLs as a percentage of their maximum possible loss or MPL (in the past when unlimited coverage was more common an estimate of the maximum loss was made whereas today the MPL is simply the sum of aggregate limits). This practise, being subjective, was obviously open to abuse (and often proved woefully inadequate). It is interesting to note however that some of the commonly used MPL percentages applied for peak exposures in certain markets were higher than those used today from the vendor models at high return periods.

The vendor modellers themselves are very open about the limitations in their models and regularly discuss the sources of uncertainty in their models. There are two main areas of uncertainty – primary and secondary – highlighted in the models. Some also refer to tertiary uncertainty in the uses of model outputs.

Primary uncertainty relates to the uncertainty in determining events in time, in space, in intensity, and in spatial distribution. There is often limited historical data (sampling error) to draw upon, particularly for large events. For example, scientific data on the physical characteristics of historical events such as hurricanes or earthquakes are only as reliable for the past 100 odd years as the instruments available at the time of the event. Even then, due to changes in factors like population density, the space over which many events were recorded may lack important physical elements of the event. Also, there are many unknowns relating to catastrophic events and we are continuously learning new facts as this article on the 2011 Japan quake illustrates.

Each of the vendor modellers build a catalogue of possible events by supplementing known historical events with other possible events (i.e. they fit a tail to known sample). Even though the vendor modellers stress that they do not predict events, their event catalogues determine implied probabilities that are now dominant in the catastrophe reinsurance pricing discovery process. These catalogues are subject to external validation from institutions such as Florida Commission which certifies models for use in setting property rates (and have an interest in ensuring rates stay as low as possible).

Secondary uncertainty relates to data on possible damages from an event like soil type, property structures, construction materials, location and aspect, building standards and such like factors (other factors include liquefaction, landslides, fires following an event, business interruption, etc.). Considerable strides, especially in the US, have taken place in reducing secondary uncertainties in developed insurance markets as databases have grown although Asia and parts of Europe still lag.

A Guy Carpenter report from December 2011 on uncertainty in models estimates crude confidence levels of -40%/+90% for PMLs at national level and -60%/+170% for PMLs at State level. These are significant levels and illustrate how all loss estimates produced by models must be treated with care and a healthy degree of scepticism.

Disclosures by reinsurers have also improved in recent years in relation to specific events. In the recent past, many reinsurers simply disclosed point estimates for their largest losses. Some still do. Indeed some, such as the well-respected Renaissance Re, still do not disclose any such figures on the basis that such disclosures are often misinterpreted by analysts and investors. Those that do disclose figures do so with comprehensive disclaimers. One of my favourites is “investors should not rely on information provided when considering an investment in the company”!

Comparing disclosed PMLs between reinsurers is rife with difficulty. Issues to consider include how firms define zonal areas, whether they use a vendor model or a proprietary model, whether model options such as storm surge are included, how model results are blended, and annual aggregation methodologies. These are all critical considerations and the detail provided in reinsurers’ disclosures is often insufficient to make a detailed determination. An example of the difficulty is comparing the disclosures of two of the largest reinsurers – Munich Re and Swiss Re. Both disclose PMLs for Atlantic wind and European storm on a 1 in 200 year return basis. Munich Re’s net loss estimate for each event is 18% and 11% respectively of its net tangible assets and Swiss Re’s net loss estimate for each event is 11% and 10% respectively of its net tangible assets.  However, the comparison is of limited use as Munich’s is on an aggregate VaR basis and Swiss Re’s is on the basis of pre-tax impact on economic capital of each single event.

Most reinsurers disclose their PMLs on an occurrence exceedance probability (OEP) basis. The OEP curve is essentially the probability distribution of the loss amount given an event, combined with an assumed frequency of an event. Other bases used for determining PMLs include an aggregate exceedance probability (AEP) basis or an average annual loss (AAL) basis. The AEP curves show aggregate annual losses and how single event losses are aggregated or ranked when calculating (each vendor has their own methodology) the AEP is critical to understand for comparisons. The AAL is the mean value of a loss exceedance probability distribution and is the expected loss per year averaged over a defined period.

An example of the potential misleading nature of disclosed PMLs is the case of Flagstone Re. Formed after Hurricane Katrina, Flagstone’s business model was based upon building a portfolio of catastrophe risks with an emphasis upon non-US risks. Although US risks carry the highest premium (by value and rate on line), they are also the most competitive. The idea was that superior risk premia could be delivered by a diverse portfolio sourced from less competitive markets. Flagstone reported their annual aggregate PML on a 1 in 100 and 1 in 250 year basis. As the graph below shows, Flagstone were hit by a frequency of smaller losses in 2010 and particularly in 2011 that resulted in aggregate losses far in excess of their reported PMLs. The losses invalidated their business model and the firm was sold to Validus in 2012 at approximately 80% of book value. Flagstone’s CEO, David Brown, stated at the closing of the sale that “the idea was that we did not want to put all of our eggs in the US basket and that would have been a successful approach had the pattern of the previous 30 to 40 years continued”.

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Flagstone CAT losses

The graphs below show a sample of reinsurer’s PML disclosures as at end Q1 2013 as a percentage of net tangible assets. Some reinsurers show their PMLs as a percentage of capital including hybrid or contingent capital. For the sake of comparisons, I have not included such hybrid or contingent capital in the net tangible assets calculations in the graphs below.

US Windstorm (click to enlarge)

US windstorm PMLs 2013

US & Japan Earthquake (click to enlarge)

US & Japan PMLs 2013

As per the S&P article, its important to look at the shape of PML curves as well as the levels for different events. For example, the shape of Lancashire PML curve stands out in the earthquake graphs and for the US gulf of Mexico storm. Montpelier for US quake and AXIS for Japan quakes also stand out in terms of the increased exposure levels at higher return periods. In terms of the level of exposure, Validus stands out on US wind, Endurance on US quake, and Catlin & Amlin on Japan quake.

Any investor in this space must form their own view on the likelihood of major catastrophes when determining their own risk appetite. When assessing the probabilities of historical events reoccurring, care must be taken to ensure past events are viewed on the basis of existing exposures. Irrespective of whether you are a believer in the impact of climate changes (which I am), graphs such as the one below (based off Swiss Re data inflated to 2012) are often used in industry. They imply an increasing trend in insured losses in the future.

Historical Insured Losses (click to enlarge)1990 to 2012 historical insured catastrophe losses Swiss ReThe reality is that as the world population increases resulting in higher housing density in catastrophe exposed areas such as coast lines the past needs to be viewed in terms of todays exposures. Pictures of Ocean Drive in Florida in 1926 and in 2000 best illustrates the point (click to enlarge).

Ocean Drive Florida 1926 & 2000

There has been interesting analysis performed in the past on exposure adjusting or normalising US hurricane losses by academics most notably by Roger Pielke (as the updated graph on his blog shows). Historical windstorms in the US run through commercial catastrophe models with todays exposure data on housing density and construction types shows a similar trend to those of Pielke’s graph. The historical trend from these analyses shows a more variable trend which is a lot less certain than increasing trend in the graph based off Swiss Re data. These losses suggest that the 1970s and 1980s may have been decades of reduced US hurricane activity relative to history and that more recent decades are returning to a more “normal” activity levels for US windstorms.

In conclusion, reviewing PMLs disclosed by reinsurers provides an interesting insight into potential exposures to specific events. However, the disclosures are only as good as the underlying methodology used in their calculation. Hopefully, in the future, further detail will be provided to investors on these PML calculations so that real and meaningful comparisons can be made. Notwithstanding what PMLs may show, investors need to understand the potential for catastrophic events and adapt their risk appetite accordingly.