Risk coefficients
The starting point of agriculture insurance hail tariff determination is to calculate the ‘loss cost’, i.e. the aggregate loss occurring in the period under observation divided by the sum insured, derived from historical hail loss data. In terms of unit, individual tariffs apply to a geographical zone and crop type (each crop having a particular sensitivity to damage), defined by market; Australia, for example, defines 332 ‘shires’, whilst Turkey has 920 ‘districts’.

It is reasonable to expect, as many do, that the extent of damage caused by a hail storm of particular intensity to a particular crop type will be similar for risks in locations with comparable climates, cropping and loss adjustment methods. Based on this assumption, it is possible to aggregate portfolio, location-specific loss cost data across geographical divisions and with this to calculate a series of ratios that describe the relative sensitivity of each crop type to a defined ‘reference’ crop, such as wheat. Individual loss cost data points are normalized to the reference crop by dividing by the risk coefficient. To be representative, supporting loss cost data must exclude the effects of sustained, widespread damage cost, retentions, deductibles, loss adjustment expenses and total loss compensation.



Advantages
The methodology has the advantage of increasing the amount of supporting data for rating via normalization, without losing any portfolio, location-specific loss cost information. Individual tariff confidence is increased and tariff comparisons can be made between markets and insurers. In addition, if historical or planned coefficient adjustments are shared between insurers and reinsurers, the coefficients enable a systematic ‘as if’ analysis to be carried out for reinsurance pricing. As long as the risk coefficients are regularly updated and verified with new data, rating accuracy is significantly enhanced by this methodology.

Mathematical reliability

Using individual loss costs
During our recent study into risk coefficients, individual loss cost damage points revealed the following sources of inaccuracy in respect of a 100% loss cost correlation between different crop types:

1. Total loss: there is no multiplicative connection if the more sensitive crop type (crop 2 in figure 1) has already suffered a total loss, as might happen in a catastrophe event for example, because the damage rate is limited upwards to 100 percent.
2. There is inter-dependency between the risk coefficient and the particular degree of damage to the ‘hardier’ crop (crop 1 in figure 2). 
3. The relative sensitivity of crops during their growth can change. Sugar beet and potatoes, for example, become less sensitive to hail towards the end of their vegetation period, as opposed to rape for which the opposite is true.
4. Changes in climate over time can alter the relative differences between how crops develop in different climate zones, so that growth stages, which thus far ran parallel, may now begin to diverge from one another.
5. Hail is a very local hazard, and therefore the geographical units for risk assessment must be very small in order that one can assume that a hail front will hit all crops in that unit with the same severity.

Using average loss cost

We then analysed average loss costs to determine whether this technique would deliver a more mathe­matically reliable methodology.

Indeed, as average value coefficients already contain the reduced coefficients for high losses, they solve the problem of total loss (we are no longer searching for a coefficient that is correct for every degree of damage). Similar comments apply to the uncertainty in respect of the exact curve progression: The problem is solved as long as a sub-division into small, medium and high loss costs is comparable in various areas.

If the main hail season occurs in more or less the same period over an area, the impact of relative differences in growth stages is also eliminated by using average value. In addition, phase shifts during growth are not generally to be expected within a country: If they are, average value is not reliable. Possible shifts caused by global warming should be taken into consideration and any ‘no longer representative’ data possibly left out.

Finally, with average value, we no longer require small geographical units to be able to assume an ‘as homogenous as possible’ hail intensity, on condition that there are no systematic problems in the data. For example: If the sub-divided regions of a country’s tariff system are reasonably large and there are areas within one region which are more exposed to hail than others. This is (at least for the purposes of coefficient calculation) not problematic. However, if one crop type is always cultivated in the exposed areas and the other not, then the coefficient also contains geographic factors which could lead to false results.

Risk coefficients can therefore be a mathematically reliable methodology, but only in markets that are not significantly impacted by any of the aforementioned issues.



Non-uniformity of risk coefficients
When we compared the risk coefficients received in a recent survey1 from markets with similar climates and cropping methods, we observed reasonable uniformity in the coefficients for grain crops, with some exceptions. For example, figure 3 shows relative coefficient consistency for most field crops and markets, apart from in the cases of maize and rape. Given the similar cropping methods and climate, the differences could only relate to the respective quality downgrade criteria. We also observed notable variations in some fruit and vegetable crops, which again could relate to quality downgrade criteria: Exported fruit, for example, is subject to stricter quality deductions than fruit intended for local markets, and thus may receive a lower coefficient.

Conclusion
With our thanks to the AIAG, this study drew interesting conclusions, though mostly of an exemplary nature due to the level of data. Using average values, risk coefficients are mathematically reliable in markets without significant problems with any of the aforementioned inaccuracy drivers, and as long as the coefficients are regularly updated and verified to maintain and improve the reliability of the pricing tool.

As a global reinsurer, differing risk assumptions between clients and markets are a central aspect of our own risk analyses process. They reveal otherwise hidden aspects of a risk, and/or that pricing may not be optimal, in which case the reasons behind this need to be understood. For agriculture insurers, a pooled risk coefficient database could provide important additional data to improve and compare risk analysis, and could serve as a mechanism for further and more extensive discussions into hail sensitivity and pricing methodologies.