In my previous blog in this series we explored the rationale behind excess of loss rating by looking at a facultative excess of loss placement. Now I want to move to the other side of the family tree and look at the ways an entire portfolio of business can be reinsured on an excess of loss basis.

In the blog post on facultative reinsurance, I explained that statistically losses up to 10% of a property’s value account for 54% of the total of all claims an insurer pays out. These numbers are derived from something called a “first-loss scale,” which is effectively a table of discounts for deductibles that represent percentages of the total value of the property.

There are many different scales in use in the market; some are very general while others focus on different types of property, so an insurer or reinsurer might use one scale for residential business, another for commercial and another for industrial. All of the scales have been built using observed data and therefore differ according to the particular set of data used.

## How it Works

Let’s assume an insurer covers properties valued at up to £100 million and is willing to pay up to the first £10 million of any losses under any policy. There may be many thousands of individual policies or risks in the insurer’s portfolio.

Note that we use the word “risk.” This is very important because large policies often have massive insured values that are spread over a number of locations. The term “risk” is used by insurers to break down the insured property into distinct elements that are likely to be involved in a single fire loss.

Not all of the risks in the portfolio will be valued at exactly £100 million. Indeed, some will be valued at below £10 million and therefore cannot possibly expose our per-risk cover to a loss.

So the first thing we need to do is arrange all the risks into bands of different values, showing the total premium the insurer has charged for all of the risks that fall into each band. This is known as a “risk profile”. Here is an example of how a part of the risk profile might look:

Band | Min S/I | Max S/I | Mid-point | Premium |

A | 0 | 10 | 5 | 3.0 |

B | 10 | 30 | 20 | 4.1 |

C | 30 | 40 | 35 | 3.5 |

G | 70 | 80 | 75 | 0.8 |

The bandings would continue up to the maximum value at risk (in this case £100 million).

It is normal for per-risk covers to be placed in a series of “layers”. The layering depends on several factors, including the levels of past loss activity, as well as any natural “break-points” in the profile (a typical break-point might be a value that represents the maximum sum insured for the residential, as opposed to commercial and industrial risks, but this is not an exact science). For our exercise, let’s look at the following layering:

- 1
^{st}Layer: £40 million excess of £10 million - 2
^{nd}Layer: £50 million excess of £50 million

It is important to remember that the above limits and deductibles apply to each loss, any one risk. That is what makes this a *per-risk*, as opposed to a *catastrophe* cover. We shall deal with catastrophe covers in a later blog.

Let’s look at band B of the profile. The mid-point of the range is £20m, so we shall take that as the average value of all risks falling within this band. These risks would, on average, expose the first layer only. The £10m deductible represents 50% of the average risk value, so we would need to find the deductible discount for 50% from our first loss scale. Let’s call it 83%. We would therefore regard the exposing premium to the first layer as 17% of £4.1m = £0.7m.

Now let’s jump to band G. The mid-point is £75m. Our first layer deductible represents 13% of the mid-point, but the layer ceases to be exposed above £50m which is 67% of the mid-point, so we need to calculate the difference between the first-loss discount for 67% (87% discount) and 13% (57% discount), so the premium exposing the first layer would be 30% of £0.8m. The remaining £25m of value that exposes the second layer would attract approximately 13% of the original premium.

We can use this process throughout each band of the risk profile in order to establish the total amount of premium that would be chargeable to each layer.

## Here’s the Important Part

But these totals ignore one very important fact. Reinsurers will not actually be covering *every loss* on *every risk*. There is a limit as to how much the reinsurers are prepared to pay out in a year. This is governed by how many *reinstatements* are allowed under the contracts.

Whenever there is a claim under an excess of loss contract, the limit is effectively reduced by the amount of the claim. So if our first layer suffered a loss of £40m the cover would be exhausted. Reinsurers will usually allow the insurer to reinstate the cover up to an agreed number of times, but usually will charge an additional premium.

The number of reinstatements and the price charged for them will both be factors for which the reinsurer will give a discount from the total premiums we have calculated by the above method. This is a complex matter that is beyond the scope of this blog.

*Exposure rating* as described above is not the only method of rating excess of loss contracts. There is also *experience rating*, which uses past losses to determine the excess of loss premium, particularly for the lower layers of a programme. I shall try to cover these in later blogs.

*This post was originally published April 11, 2013.*

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good article, educative.