Homeowners Indications – Getting It Right Mark Homan CAS Ratemaking Seminar March 7-8, 2002 My presentation today will primarily be a review of the example in my paper preceded by a little background. I wish to point out that this technique is not perfected. It is a practical application and certain minor inaccuracies exist. I view it as a large step forward but not the final step.

Key Issue – Cat Loads Ex-cat losses are the largest component Expenses are the next largest Catastrophe Losses may be the smallest component Cat Losses represent the largest source of volatility and uncertainty in HO rates

Determining the Cat Load Traditional Method was Excess Wind Historical period was insufficient for determining expected hurricane loads Hurricane loss models produce the best answer available for future losses Not all regulators will approve filings using models Alternative: utilize cat load in reinsurance

Pragmatic Approach Models give best answer available Loading reinsurance costs is a practical alternative providing reasonable indications Many states specifically allow for the explicit reflection of reinsurance costs

Transactional Cost Approach Add reinsurer’s expenses and profit to expense load Explicit approach; likely to increase regulatory scrutiny Simplest approach Capable of reflecting all costs Difficult (impossible?) to determine expense and profit This is a simple straight forward approach. Only the additional costs need to be dealt with. Biggest problem is that we can’t easily obtain the expense and profit portion of the reinsurance treaty. If we did, the profit and risk load costs may be shocking and some regulators may want to allow only a portion. So what do we do?

Net Loss plus Reinsurance Approach Adjust losses for recoveries; add reinsurance premium as expense Still an explicit approach Avoids need to determine reinsurer expense and profit Requires adjustments to historical losses More accurate loss provision for larger events With this approach, we net out the losses to be net of reinsurance Then we can add in the whole reinsurance premium without regards to what the components are. By loading in the whole reinsurance premium, we capture the reinsurer’s estimate of expected losses in that layer. This may often be greater than what we would estimate. And this may avoid some of the controversy around models while still yielding an adequate premium. Besides, at the end, the reinsurer pays for the losses in the layer, so this is a true reflection of the costs.

Current Situation Expected Recoveries Reinsurance Threshold Graphically, the current situation looks like this…. We have some component of the expected loss provision that is above the reinsurance threshold. This is often the fuzziest portion of the loss provision. That’s why we are having sessions on modeling here. Unless you are doing a method like this, there is no need to identify the portion above the threshold. Historical Loss Provision

Net Loss plus Reinsurance Reinsurance Costs Expected Recoveries Removed Reinsurance Threshold Graphically, here is what you get after this approach… You have identified the specific component of your historical loss provision that is above the treaty threshold and removed it. Or everything but the portion that is your company’s participation. You have replaced it with the reinsurer’s estimate for the losses, shown here larger than what was removed for effect. Historical Loss Provision

Basic Steps Allocate Reinsurance Premium to States Adjust Historical Losses to Net of Recoveries Split Reinsurance Premium by Form Breakdown Reinsurance Expense into Fixed/Variable Portions Develop Indication These are the basic steps to follow in this approach. In the slides that follow, I will outline an example of one way to follow these steps. How you do it will depend on your company’s approach to its reinsurance and current ratemaking procedure. Rather than prescribing an exact method to follow, this is a general approach that can be adapted as needed. At the third step…. The reinsurance cost needs to be broken down by form since the contents forms, 4 and 6 or tenants & condos, do not represent the same level of exposure per premium dollar as the structural forms.

Risk Load Additional Margin to cover volatility in results Viewed in various ways: Extra return to cover higher risk Buffer to absorb uncertainty Additional profit to assure positive return Due to volatility, risk load is present in catastrophe reinsurance

Allocating Premium to States This slide shows an example of allocating reinsurance premiums to state. I am only showing ten states to make it simple. The allocation begins with the expected losses to the treaty by state. This can be based on historical losses, but will most likely come from some sort of cat model. The expected losses are then grossed up by a margin to include the profit, expenses and risk load. Based on our modelling approach, we find that there is still some portion of the premium that remains. This stems from multi-state cats that could breach the treaty. The remaining premium is allocated based on subject premium. You may find that you can allocate all your reinsurance premium based on expected losses in the layer.

Adjusting the Excess Wind Load The next few slides are exploded views of the excess wind procedure that I used in my paper. I am only showing one year and the totals to make this easier to see. The actual historical values are shown. Then the projected non-wind losses at current exposure levels trended out by the cost factor are determined. By multiplying by the wind/non-wind ratio, we can recast the wind losses to current cost and exposure levels. Then we can apply the current reinsurance program to get the losses net of reinsurance. These adjusted wind losses are then used to determine a modified wind/non-wind ratio.

Excess Wind (cont.) The rest of the calculation proceeds as typical for the excess wind procedure. Each year is tested to see if it is greater than 1.5 times the median. If so, it is considered an excess year and the excess ratio is determined which is the amount greater than the median. The average excess ratio (which is excess wind to non-wind) is determined. Then the non-excess portion of the losses is calculated to determine a non-wind/non-excess ratio. This allows us to translate to a base of non-excess losses which is what is used in the calculation.

50 Year (& greater) Event An added wrinkle that we have been using at The Hartford is an augmentation of the ISO excess wind procedure with 50 year events from our model. This represents the average loss expected from events in the top 2 percentile of probability. This allows for the reflection of more extreme events that may not have occurred in the historical period. An excess ratio and a non-wind/non-excess ratio are determined for this event similar to the historical averages. Because we are reflecting this event, we also remove from the historical period any event that would be in the top two percentile to avoid overstating the exposure.

Final Excess Wind Factor This slide shows the calculation of the two excess wind factors. The first is based on the historical period (with any top two percentile events removed). The second is the excess wind factor based on the 50 year events. We take a weighted average of the two factors. The 50 year event, since it is the top two percentile, receives 2% weight with the remaining weight given to the historical period. This results in the final factor shown. You can see that the augmentation has an impact in this example. Although it does increase the load by 25%, since it is a small load, it will have little impact on the indication.

Splitting Premium to Form

Splitting to Form (cont.)

Expense Breakdown

Expense Breakdown This slide is similar to the previous one, showing the expense breakdown for State C. This is included for completeness and to show a contrast to State A.

Territorial Indications Issue - Allocation of Reinsurance Premium to Territory Alternative Approaches Reinsurer Supplied Information Judgemental Damage Rate Indices Modelled Losses

Loss Adjustments As in statewide indication, historical territorial losses are adjusted to net Excess wind factor is applied Can also be adjusted to reflect individual territorial expectations Load in reinsurance costs Develop territorial rate index to allocate statewide rate change

Territorial Example - State A

Remaining Issues Not a perfect method; still have areas to investigate Volatility of reinsurance costs - is smoothing needed? 3 year average? Allocating reinsurance costs by other rating variables beyond territory Adjusting for loss factors not reflected in models, etc.

Conclusion Net Loss plus Reinsurance is recommended approach where models are not accepted Provides reflection of loss costs and risk load as contained in reinsurance premium Still may need use of models to determine gross loss provision

Speaker Contact Information Mark Homan AVP & Actuary, Personal Lines Pricing The Hartford Hartford Plaza, T-1-55 Hartford, CT 06115 Phone: 860/547-2015 Fax: 860/547-2013 E-mail: mhoman@thehartford.com