The historical capped loss costs for each insurance unit are then given by . For cotton in district GJ8, only the 2000 loss cost of 56% exceeds the LCC of 40% and so only that loss cost is reduced to 40% in this step. Table 12 lists the LCC based on an LCCP of 90, and capped loss cost histories for all insurance units in the Gujarat.

Table 12. Cotton in Gujarat: capped weighted average historical loss costs

|**District**|**Loss cost**<br>**cap (LCC)**||**Cappe**|**d Weig**|**hted av**|**erage h**|**istorica**|**l loss co**|**st for d**|**istrict**||
|---|---|---|---|---|---|---|---|---|---|---|---|
||<br>**at 90%**|**1998**|**1999**|**2000**|**2001**|**2002**|**2003**|**2004**|**2005**|**2006**|**2007**|
|[1]|[2]|[3]|[4]|[5]|[6]|[7]|[8]|[9]|[10]|[11]|[12]|
|GJ1|5%|0%|1%|5%|3%|5%|1%|1%|1%|5%|2%|
|GJ2|30%|0%|9%|30%|30%|11%|0%|2%|0%|0%|0%|
|GJ3|11%|2%|9%|9%|11%|11%|0%|0%|0%|3%|0%|
|GJ4|10%|0%|2%|9%|10%|1%|0%|0%|0%|4%|1%|
|GJ5|3%|0%|0%|2%|2%|0%|3%|0%|0%|1%|3%|
|GJ6|36%|1%|14%|36%|36%|9%|5%|2%|0%|0%|1%|
|GJ7|6%|0%|0%|6%|6%|0%|0%|0%|0%|0%|0%|
|GJ8|40%|2%|24%|40%|35%|39%|0%|0%|0%|4%|3%|
|GJ9|18%|0%|17%|8%|16%|18%|5%|1%|1%|2%|2%|
|GJ10|12%|4%|12%|12%|4%|12%|0%|4%|0%|0%|0%|
|GJ11|4%|0%|2%|3%|2%|4%|3%|2%|0%|2%|4%|
|GJ12|62%|2%|27%|62%|49%|62%|2%|3%|2%|4%|2%|
|GJ13|21%|0%|4%|5%|3%|21%|0%|0%|0%|19%|2%|
|GJ14|11%|0%|0%|10%|4%|11%|4%|1%|0%|0%|0%|

# <u>Actuarial justification</u>

The intention of the cap and Capped Excess Load is to spread statistically insignificant large losses over a large base so that pricing is robust to outliers. For example, one very bad crop year in a particularly district may be just as likely to have happened in other districts within the state. It may therefore be appropriate to spread the effect on rates of such a year over a broader base than the district.

Bühlmann’s Empirical Bayes Credibility Theory, which will be applied in the next step, is a linear process, and thus extreme outliers can present difficulties requiring special attention. A technique commonly used in conjunction with credibility weighting is to cap large losses before the application of Credibility Theory. Capping large losses then adding back the probability mass may be actuarially sound as infrequent events lack statistically credibility. A properly chosen cap may not only add stability, but may even make the methodology more accurate by eliminating extremes.

Actuarial judgment is required in the choice of cap percentile, as this may substantially affect the degree of smoothing of rates within the state. If the LCCP is set to be too high, the presence of outliers may lead to a low credibility factor Z. If the LCCP is set to be too low, the LCC could be 0% for a large number of districts. Based on the data analysed in this note a LCCP between 85% and 100% is suggested, although this may depend on the specific historical data and historical claim payment frequency. The LCCP could be chosen at the crop/state level.

Since extreme losses are removed from each insurance unit’s experience in this step, it is appropriate to add them back later at a broader level, so that rates are not underestimated. These excess amounts will be added back in the _Capped excess load_ subsection below.

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