Estimating Sydney PMLs - which is the most important natural hazard?

Earthquakes, severe hailstorms and floods all have the potential to cause considerable property damage – and Australia’s largest exposure to these risks is in Sydney. Until recently the Australian insurance industry has focused on earthquake probable maximum losses (PMLs) when managing the risk through reinsurance. The 14 April 1999 hailstorm, which resulted in Australia’s largest insured loss, raised the profile of severe storms as contender for the most important natural hazard. Moreover, as the Australian insurance industry moves slowly towards offering full flood insurance for residential properties, anecdotal evidence suggests that flood could also become a very important insured peril in Sydney. This paper aims to provide insight into the relative importance of the three natural hazards via PML analyses of a single synthetic portfolio for each (and assuming flood is insured).

Risk Frontiers has developed loss estimation tools for each of the three perils. HailAUS and QuakeAUS are probabilistic models that generate thousands of synthetic events over long simulation periods (50,000 - 100,000 years), calculate the associated losses and produce loss vs. probability of exceedance statistics. HailAUS currently includes motor and residential building and contents lines in Sydney and Brisbane. QuakeAUS covers residential building and contents in Sydney, Melbourne, Adelaide and Perth. FloodAUS is a flood risk model with a damage estimation module that estimates losses for specific flood return periods for individual catchments. All models have been discussed in earlier editions of the Risk Frontiers Quarterly Newsletter.

Figure 1: Earthquake, flood and hailstorm loss curves for a hypothetical portfolio in Sydney

The synthetic residential portfolio is derived from four real portfolios in Sydney. The portfolio has approximately 90,000 houses spread across ICA Zones 41, 42 and 43. Each house is assumed to have both building and contents cover, and the average building sum insured is approximately $184,000 and the average contents sum insured around $61,000.

The portfolio data are at postcode level resolution, and running the data through HailAUS and QuakeAUS is straightforward. Estimating flood losses is more complicated for two reasons. Firstly, the exact location of houses within each postcode is required because of the defined spatial boundaries of flooding. So the portfolio was disaggregated into hypothetical address locations in accordance with the distribution of all addresses within the floodplains of the three main rivers in Sydney – Georges River, Hawkesbury-Nepean River and the Upper Parramatta River. That is, the synthetic portfolio has the same proportion of addresses below the level of the ARI 20-year flood, between the ARI 20 and 50 year level etc as the whole population of addresses. Secondly, the nature of rainfall in Sydney means that flooding in the catchments is neither fully correlated (wherein losses for the same ARI could be simply added) nor independent (exceedance probabilities of the same losses could be added). We do know, however, that the potential cost of flooding in the Hawkesbury-Nepean catchment dominates the calculation. In Figure 1 the maximum flood loss curve represents the sum of the loss curves for the three catchments, while the loss curve for the Hawkesbury-Nepean is shown separately. The combined loss curve for the catchments will lie somewhere between these bounds.

Since motor losses will inevitably be associated with residential losses for these perils it is instructive to combine motor and household loss curves. For HailAUS we assumed 1.24 vehicles per house based on Australian Bureau of Statistics data for the Sydney Statistical Division (ABS 2001, 2002), and used a representative average sum insured value. To include flood motor losses we adjusted loss figures contained in an Environmental Impact Statement for the Warragamba Dam auxiliary spillway (ERM, 1996). Insufficient reliable data means that earthquake motor losses are not included.

As shown in Figure 1, incorporating motor losses makes hailstorm the most expensive hazard up to return periods of about 900 years. If household losses only are considered, then hailstorm is more expensive than earthquake and flood for all events with average recurrence intervals less than 500 years. Plotting the losses for the full range of return periods as shown in Figure 2 at a log-log scale illustrates the dominance of earthquake losses for very rare events (almost 4 times the combined motor-residential hail loss at ARI 10,000 years).

Figure 2: Earthquake, flood and hailstorm loss curves for a hypothetical portfolio in Sydney (on log-log scale)

We note that the combined PML for the three hazards shown in Figure 2 is not simply the sum of the individual peril losses for each recurrence interval. Rather the probability of a given loss being exceeded in a year is the sum of the probabilities of that loss being exceeded by the individual perils. This concept was explained in detail in Risk Frontiers Quarterly Newsletter December 2002.

The PMLs summarised in Table 1 highlight the primacy of hailstorm losses at the important ARI 250-year probability and the rapid increase in earthquake losses at high return periods.

Table 1: Modelled PMLs ($M) for a hypothetical Sydney portfolio

The effect of including motor in the earthquake analysis is not known, but is unlikely to be significant at the low return periods. Even if motor increased the overall earthquake losses by 20%, we can still safely draw the following conclusions:

  • Hail is the most expensive hazard for all average recurrence intervals up to at least 600 years.
  • If flood were fully insured it would be more important than earthquake up to about the 300-year recurrence interval.
  • For very low probability losses, earthquake is easily the most expensive hazard.

The reader is cautioned that the numerical results will not duplicate PMLs for any individual insurer unless the company were to hold a book that exactly mimics the hypothetical portfolio in terms of geography, building occupancy and construction type. As a consulting service, Risk Frontiers can calculate the PMLs for individual companies’ portfolios for the three perils addressed in this paper. HailAUS is also available on a 3-year licence basis to allow insurers and reinsurers to model their portfolios in-house with respect to the critical hailstorm hazard.


Australian Bureau of Statistics 2001, Motor Vehicle Census in NSW, 31st March 2001, Catalogue Number 9309.0.

Australian Bureau of Statistics 2002, Census of Population and Housing: Sydney…A Social Atlas, Catalogue Number 2030.1.

ERM Mitchell McCotter 1996, Proposed Warragamba Dam Auxiliary Spillway Environmental Impact Statement, for Sydney Water Corporation, 4 vols.

For further information please contact:
Roy Leigh
Telephone: +61-2-9850 9683
Facsimile: +61-2-9850 9394
Email: riskfrontiers



The "Retirement' of Professor Russell Blong

As many of you will not have failed to notice, Russell has stepped down after nine years as Director of Risk Frontiers. The actual process of retiring was so enjoyable, and the generosity of our industry sponsors so overwhelming, that Russell’s doctor committed him to two weeks detoxification therapy. Russell, in his inimical fashion, chose to take this at the Betty Ford Clinic in Hawaii. Doctors express some hope that his liver will recover provided that he takes all necessary steps to reduce his breakfast consumption of Maitai’s and respect the authenticity of this national Hawaiian dish by including fruit juice in the cocktail.

This is not the place to eulogise Russell’s many and varied contributions to the study of Natural Hazards – he is, after all, not yet dead, despite rumours to the contrary and his being awarded the title of Emeritus Professor, an honour which we are led to believe is normally conferred posthumously. Russell will continue to play an important role in the Centre concerning himself with new business development, organising our industry teaching obligations and harassing graduate students. What’s changed you might well ask?

Still any careful biographer would be remiss in ignoring how much Risk Frontiers has evolved under Russell’s direction. Russell himself is fond of recounting how his first loss model was written in a primitive spreadsheet language to predict the consequences for Rabaul from an eruption of Tavurvur and Vulcan. This model took one year to debug - mainly due to incompatibilities between Microsoft and Russell’s Pidgin English - and considered three possible scenarios. When the volcano did actually erupt in 1994, it respected none of Russell’s erudite analyses and scholarship, erupting in the wrong place, with the wrong wind direction and with consequences that had been only partially anticipated. Russell was right on one score, however, it did make one hell of a mess!

With the benefits of advances in computing power, we can now perform fully probabilistic analyses on a wide range of natural hazards besides just volcanoes, be wrong many more times, and much more efficiently. This surely is progress for which Russell can take much of the responsibility.

We wish Russell all the best in his retirement. Risk Frontiers will continue under the new leadership of Professor John McAneney. John expects to continue Russell’s legacy of wild unrepentant mutterings and hysterical ideas about PMLs and other arcane concepts of interest to the insurance industry.


Benfield Greig
Swiss Re
Guy Carpenter
IAG Insurance (NRMA)
Aon Re
Employers Re
CGU Insurance
Gerling Global
Royal & Sun Alliance