ENID is a term widely used, just generally not in South Africa. For some reason we didn’t import the term along with most of Solvency II.

This has nothing to do with the Famous Five. While it is most common in the general insurance space, it is relevant across the spectrum of risk management and assumption setting.

Events Not In Data or “ENID” is the forgotten cousin of “what to do with outliers in your data”.

### Outliers and where to find them

Outliers are observed values substantially different from others in a sample. Some more formal definitions include:

“An

outlieris an observation that lies an abnormal distance from other values in a random sample from a population”“an outlier is an observation point that is distant from other observations”

How to deal with outliers?

Simple question, complex answer. It depends a great deal on the context.

**Ultimately you need to make the judgement call “are these outliers under- or over-represented in the data”. **

If you believe you have a 1 in 100 year event in your 3 year data set, then leaving it in unadjusted will skew your average (as well as the rest of the distribution) away from the true underlying population distribution.

However, it is also key to ask yourself if there are Events Not In Data (ENID) that would be part of the underlying population distribution. Most 3 year samples won’t include a 1 in 100 year event and therefore might understate the average and bias the distribution.

I believe it can be good practice to consider the data with and without the data point. And without could mean capping or omitting entirely. The cut-off point for outliers can be expressed as a multiple of assumed standard deviations based on how much data you have in your sample. It’s obviously also circular in that your estimate of standard deviation depends on whether or not you include the outlier in the estimate of standard deviation!

I said at the start, it depends on the context and the underlying variable.

### Putting Events Not In Data into the data

Outliers may be hard to pin down an define exactly, but they usually appear because they make the results look worse than hoped for and there is plenty of pressure to “fix it”. When experience has been good, because those outlying events did not occur, there is naturally less pressure to go looking for trouble.

Except that’s exactly what one should do.

Just because events are slightly away from the mean or occur somewhat less often doesn’t mean they shouldn’t have been considered prior to the pricing / reserving / business forecasting / assumption setting / risk management process. So in theory, the analyst should already have a view (however accurate) about what to expect away from the expectation. That can be a useful starting point to assess whether an allowance for ENID should be made.

Over time, the views on the shape of the distribution and the reasonability of ENID at various levels will be refined. That is after all, the basics of the Actuarial Control Cycle.

### ENID and skewness

The world we live in seems to be naturally asymmetrical. So many of these ENID are on the down side. Including them contributes to greater variance, greater kurtosis and *also negative skewness*.

### Examples of variables exposed to ENID (aka where to find them)

The list is endless and it might be more practical to think of examples where it could not apply. However, just to make sure you are thinking broadly enough, here are a tiny number of examples.

- general insurance claims (the standard example)
- stock market returns
- corporate defaults
- lapse assumptions (upwards spikes in lapses due to economic conditions or regulatory changes are not every year occurrences)
- expense assumptions (where “one off” costs relating to restructuring or retrenchment are very likely to occur over a 15 year projection period, but hopefully didn’t occur in the last 3 year expense investigation period.)
- rainfall and drought (Cape Town planners, I’m looking at you)

*Remember this list is incomplete, so there will be ENID in this list of ENID affected variables.*

### Events not in data – guidance from the Bank of England

Many firms use reserving methods that project forwards

from historical data. On its own, this is unlikely to satisfy the

Directive requirement for a probability-weighted average of

future cash-flows, since not all possible future cash-flows — or

the events that cause them — may be represented in the data.Although these events are sometimes referred to as

‘binary events’ or ‘extreme events’, such terms suggest that

events not found in the data are necessarily extreme or rare.

This is not the case, so the PRA prefers to use the term ‘events

not in data’, or ENID.Firms should take ENID into account when calculating

technical provisions. Applying a simple percentage uplift

without justification is not an adequate method.Where outliers are removed from the data as part of the

reserving process, this removes events from the data. Firms

should make an allowance for this in the technical provisions

calculation unless they have shown that it would not be

possible for these, or similar, events to occur again in future.

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