Stormy forecast

Dimitris Papachristou examines whether North Atlantic hurricane clustering is a new reality

Memories in insurance are often short. After Hurricane Andrew in 1992 caused problems for London Market insurers, there were not many hurricane losses until 2004, when four major hurricanes seriously impaired the profitability of several insurers. The following year, three major hurricanes – including Katrina – hit the US, leading to talk of increased hurricane activity and clustering. The debate then faded until, in 2017, a number of strong hurricanes caused much damage to the US and Caribbean. Climate change has put the Atlantic Basin in the spotlight, with a renewed interest in clustering.

Figure 1 shows loss volatility between years. I produced this figure using the Weinkle et al. (Nature Sustainability, 2018) dataset: recalculated (normalised) historical hurricane losses adjusted for inflation and changes in exposure, such as the increase in the property stock and wealth. 

We observe both high year-to-year volatility and an increasing trend in annual damage costs. If one agrees with the normalisation of losses in Weinkle, then the observed increase reveals a recent increase in risk. 

Popular insurance wisdom often claims that annual hurricane losses come from one large hurricane rather than a high frequency of hurricanes in the same season. Figure 1 dispels this myth. There are years with high losses from a single catastrophic hurricane, such as 1992 and 2012 (Hurricanes Andrew and Sandy respectively), but there are also years in which high losses came from a number of major hurricanes, as in 2004, 2005 and 2017.

Atmospheric science, in particular hurricane modelling, has progressed meaningfully during the past 40 years. Compelling accounts of this evolution can be found in the books Divine Wind by Professor Kerry Emanuel and Storm Surge by Professor Adam Sobel. Atmospheric models are good at predicting hurricane paths and their potential maximum intensity, but significantly less so at predicting hurricane genesis and frequency. My focus is the statistical analysis of the number of major hurricanes in the North Atlantic since 1950, although bear in mind the number of hurricanes is only one of many factors of hurricane activity affecting insurance losses. 

Expected hurricane number and variance

I used publicly available data from the HURDAT database of North Atlantic hurricanes, maintained by the National Oceanic and Atmospheric Administration to analyse the annual number of North Atlantic hurricanes that reached category 3 or higher (>180 km/hour) at some point before they dissipated. 

Kossin et al. (Journal of Climate, June 2010) categorise hurricanes in four groups according to climatological characteristics. 

Figure 2 displays analysis for two groups containing some of the most dangerous major hurricanes. Group A hurricanes start near Africa and gather energy as they travel across the Atlantic; about one in five make landfall on the US east coast, around Georgia and the Carolinas. Group B hurricanes have straighter paths and are thus stronger, with approximately one in two hitting Florida or Gulf of Mexico states. 

Figure 2 shows the trend against the actual historical number and average number of major hurricanes since 1950. For both groups we see an increasing trend and higher frequency in recent years compared to the average of the 68-year period under examination. 

In Figure 1 and Figure 2, the recent trend in hurricane activity is significantly higher than the longer-term average. These trends ought to be considered in risk and capital management.

Is there an increasing trend? 

The trend for Group A exhibits cyclical characteristics. However, there is increasing evidence in academic literature that the decrease in major hurricanes in the 1960s and 1970s was not part of a cycle, but due to the temporary increase in sulphate aerosols that humans put in the atmosphere before environmental laws limited their use. These gases reflect sunlight and reduce sea temperature, which provides energy for hurricanes. This research suggests that the increasing trend is likely to be real and not just the peak of a cycle.

For Group B, in addition to the increasing trend, we observe a high volatility – higher than the volatility allowed for by Poisson distribution. In each of 2004, 2005 and 2017 there were four major hurricanes in the Atlantic Basin; the average annual number is closer to one.     

The probability of multiple hurricanes occurring in the same year doubles if we use the most recent trends (including volatility) rather than the long-term simple average. Do the catastrophe models used in insurance allow sufficiently for the additional volatility (over-dispersion) and increasing trend observed in recent years?

One of the issues when modelling infrequent events, such as major hurricanes, is the limited amount of data. One of the questions frequently asked is whether statistical models can detect small trends in scarce volatile hurricane data. Statistics provides the tools to check the reliability of our answers. The trends in Figure 2 are present at a less than 10% level of significance. It is easy to check that the probability of having three years with four major hurricanes in a period of 68 years, from a Poisson distribution with mean around 0.8 hurricanes, is only 2%. Other tests show it is more likely than not that there has been an increase in frequency and volatility of major hurricanes in recent years. 

"The probability of multiple hurricanes occurring in the same year doubles if we use the most recent trends rather than the long-term simple average"

Can we see a clear increase in landfalls?

The above analysis refers to the number of hurricanes in the Atlantic Basin, not the number of landfalls in the US. Some argue that we have not seen similar trends in the number of hurricanes that make landfall in the US, and this is what matters for insurance losses. Some practitioners, in their interpretations of various scientific papers, argue that while the strength and paths of hurricanes have changed near the US because of climate change, there have also been changes in wind shear, so we do not see increased landfalls. However, my reading of the papers does not support such claims.

The increased volatility (over-dispersion) is measurable for both hurricanes in the Atlantic Basin and landfalls. However, it is true that the increase in the expected number of landfalls is not as obvious as the increased number of hurricanes in the Atlantic Basin. This can be better explained with statistics than with dubious interpretations of scientific research. Only a few major hurricanes form in the Atlantic Basin every year, and even fewer make landfalls, so it is harder to detect any slowly increasing landfall trend. 

I simulated many 68-year periods (1950-2017) of hurricanes, assuming the increasing trends in Figure 2 and the constant probability of landfalls. Then I counted annual landfalls to try to detect trends. In 50% of the simulations I was unable to detect the known assumed simulated trend in landfalls. This suggests that if the increasing trend in the Atlantic Basin presented in Figure 2 is true, these increasing trends will not be detected in landfalls with a 50% probability. Given the lack of scientific evidence for hurricane path changes, statistical analysis indicates that we have been lucky not to see a larger number of hurricane landfalls. However, there is no guarantee that we will continue to be lucky. 

Does it matter? 

Does this matter for insurance losses? It depends. The impact can be significant for insurers with exposures in Florida, where the over-dispersion of the number of hurricanes is high – particularly so for lower excess of loss reinsurance layers, and especially second and third-loss (back-up) reinsurance covers. 

Assuming that the shape of market loss severity is similar to that fitted to normalised losses, a compound Poisson/negative binomial distribution could give us some estimates of the impact of increased number of hurricanes. Figure 3 shows approximate estimates of the impact of higher-than-average and assumed volatility in the number of major hurricanes. The impact could be more than a 30% increase in the one in 200 annual aggregate loss. 

Figure 4 shows that the lower (higher-frequency) excess of loss layers are impacted more heavily than the higher (lower-frequency) ones. For example, the lower reinsured layer in the figure, which has 10% probability of being hit, has a one in 200 loss equal to one limit of 20. If both the mean and variance of the number of losses increases by 50%, then the one in 200 loss equals two limits of 40 (ignoring reinstatement premiums). The impact is even bigger for the lower second and third loss layers. Additionally, the extreme percentiles of the aggregate loss distribution are also sensitive to assumptions about the severity of loss.

I would like to thank my colleagues Alex Ntelekos for starting this work and co-authoring a Bank Underground blog (bit.ly/2Wc2CQ0), and Cristina Sanchez-Estrada, Nylesh Shah, Ryan Li and Giorgis Hadzilacos for useful comments and suggestions.
 

Dimitris Papachristou is the research chief actuary at the PRA’s General Insurance Risk Specialists department, Bank of England. This article expresses the views of the author and not necessarily those of his employer