1. When a company writes risks across a number of classes, it seems reasonable to anticipate that the values assessed to give a 75% likelihood of sufficiency for each class
2. The reduction from this sum to arrive at the amount assessed to have a 75% chance of covering the company’s total Insurance Liabilities is called the diversification benefit.
3. Correlation, between how the amount ultimately paid compares to the central estimate for different classes can arise in two categories (Direct and Indirect correlation)
DIRECT CORRELATION
1. This category are items affecting the events giving rise to a claim in the first place. Items in this category are most important for correlation of Premium Liability outcomes. They should affect outstanding claims liabilities less, as whether or not such an event has occurred should be known and factored into the Outstanding Claims Liability estimate before the actuarial advice is finalised.
2. An example of this might be the chance of a weather event such as a hailstorm occurring. To a degree, claims cost in say, home buildings and commercial fire classes will be associated because costs in both are likely be higher if such an event occurs.
3. Second category are environmental items affecting the way claims liabilities run-off. An example of this is the tort law reforms that have been implemented across different jurisdictions that, with some retrospective effect, have affected claims run-off patterns. A second example relates to the effect of the business cycle.
4. Direct correlation can be described without the need to refer to the central estimate, but direct correlation nonetheless has implications for the chance that estimates in different classes could be over-adequate together, or inadequate together.
DIRRECT CORRELATIONS WITH INDUSTRY ANALYSIS
1. Direct correlation effects are likely to be assessable with industry analysis.
2. Industry analysis consistent with the correlations of interest would involve appraisal, for a given Company, of the extent to which the estimated outstanding claims liabilities for different classes turns out to be too high or too low compared to the amount that is eventually paid. However public data allowing an appraisal of this correlation for different companies does not exist.
3. For instance, for two companies, A and B, with similar portfolios, one would not expect to be able to draw reasonable conclusions about whether the actuary for Company A has overestimated Insurance Liabilities across a number of classes; based on a knowledge of that the Actuary for Company B did, if the Company B experience was say, in part a result of the actuary overestimating the impact of a change in case reserving methodology.
INDIRECT CORRELATION
1. Indirect correlation refers to sources of association between the adequacy of outstanding claimscost across different classes that arises from sources other than innate connections between cost drivers. They include:
(i) Reliance on case estimates
(ii) Parameter selections that don’t recognise that for skewed distributions the average of past experience is likely to lie below the true mean (estimates not recognising that the mean is greater than the median)
(iii) Assumptions regarding the frequency of large claims (one of the more common and more crucial examples of the previous category)
(iv) Weight given to qualitative company advice regarding portfolio or claims management changes without sufficient scrutiny
(v) Judgement overlays in parameter selection
2. Another source of indirect correlation relates to changes in claims management procedures implemented across a range of classes that might affect their cost. This could be planned ;in which case there may be an ‘Actuary Effect’ (as the actuary determines if and how projection assumptions should be altered) and also a chance that ‘true’ cost changes, could occur (the insurer would be hoping predominantly in the direction of savings). On the other hand it could be unplanned. This might happen if a key claims manager resigned who had control over management of claims across a number of classes.
INDIRECT CORELATION EXAMPLE
1. hypothetical Insurer XYZ might assert that its case estimation practice has been reviewed, and management of litigated claims is moved to a specialist area that aims to set more realistic estimates on these claims, and to settle the claims more quickly. In this hypothetical example, the Approved Actuary will need to form a judgement regarding:
(i) How to investigate and confirm the extent of these changes
(ii) How to incorporate allowance for this change by altering claim development assumptions and assumptions about rates of claim finalisation rate.
2. It is unlikely that the judgement calls will be prove to be completely correct in hindsight when claims have run-off. Consistent application of judgement increases the likelihood that if one class has been underestimated, other classes could be underestimated also.
FACTORS AFFECTING THE STRENGTH OF INDRECT CORRELATION
1. There are both overt and more subtle instance such as:
(i) The influence of the actuary’s own past experience.
(ii) The influence of being cognisant of a situation where the Insurance Liability assessment might give rise to a reported capital adequacy position that is weak (either because the actuary knows without being told, or has this pointed out to them by company management). Some actuaries will have experienced across the board pressure on their estimates where critical thresholds, such as loan covenant triggers loom.
(iii) The influence of not wanting to move too much from the previous basis in successive valuations.
(iv) Attitudes to the extent of the necessity to allow explicitly for superimposed inflation.
(v) How motivated company management is to assist the actuary to arrive at their claim projection assumptions, and the actuary’s reaction to such assistance.
THOUGHTS
1.There will be many instances where indirect sources of correlation will be stronger than the direct sources. Perhaps this will even generally be the case. While they can’t be quantified, indirect correlation sources still need to be recognised when assumptions are set to quantify diversification benefits.
2. Ultimately, like most aspects of Insurance Liability assessment, judgement inevitably plays a significant role. Empirical study on diversification benefit allowance can’t be done due to Changes occurring
3. Changes can occur to the business under consideration that renders the past less relevant. So even if we were in possession of a long history of how outcomes compared with prior estimates, we would not be in a possession of all of the information that we would like to have available. Examples of changes are:
(i) Change to business volume
(ii) Change in the characteristics of the risks covered within a class (underwriting or benefit changes; changes to claims handling; changes to propensity to claim)
4. Changes can occur to the valuation approach.
(i) The actuary may ‘learn’ from past experience.
(ii) There may be a change in which actuary is doing the work.
(iii) There may be improvements to the valuation approach.
(Source: Institute of Actuaries of Australia)
