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The Actuary The magazine of the Institute & Faculty of Actuaries
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The changing nature of risk

When I first began my time in general
insurance, over 40 years ago, one of
the first publications to catch my eye was the ASTIN bulletin. This was a journal by actuaries seemingly for the exclusive use of actuaries, since no one else in the insurance business could make either head or tail of it. I noticed that many of the papers began with the sentence: ‘Let X1, X2, X3 Xn, be a set of n independent random variables’.

Rare occurrence
As my experience in general insurance grew, it soon became apparent to me how rarely I came across variables, random or otherwise, which were independent. As the years have passed, this concept has assumed increasing importance in all branches of insurance, including life, in which the simple and obvious example is where a number of company managers take a charter flight to a conference, thus putting their company group life scheme at risk. Associated with the idea of independence is that of accumulation of risks across the various classes of insurance. The events of 11 September 2001 illustrated both these notions all too clearly, as evidenced by the fact that a great number of office workers, policemen, and firemen were killed, and losses sustained in property, casualty, motor, and aviation.
This is, of course, something with which insurers and reinsurers have been familiar for many years, especially in the area of natural disasters, but after 11 September we must, I believe, conduct a more thorough practical investigation into a problem where theory may offer some help but, I fear, may prove somewhat inadequate in many respects. The study would involve rating of risks, the setting of retentions, the detailed construction of a reinsurance protection programme, and the prudent calculation of reserves.

Political risks
Insurance and reinsurance companies have always been aware of the problems of transacting business in different parts of the world, but it has become more important to make use of the statistical information which exists in respect of economic, fiscal, investment, and financial conditions in a country, as well as to understand how insurance and reinsurance business is supervised and controlled. Various indices of stability are available which can give valuable clues to how safe it might be to transact business. Actuaries will have to become more widely involved in the process of analysing the components of risk.
Rating
Rating is far too wide a subject to cover in anything other than broad terms. Suffice it to say that we shall have to develop techniques which make allowance for the non-independence of risks, the accumulation factor, and political risks. Property insurance is unusual among the various classes, in that the object insured does not move. It is here that we can see that the chance of fire or damage to a building or other structure may not be independent of that relating to the building next door. The events of 11 September clearly illustrate this point. Many years ago it was common practice for the fire department of an insurance company to keep detailed street maps of cities on which would be marked the important properties insured by the company. In this way the company would be fully aware of the accumulation of risk and therefore be in a position to take action, for example in its reinsurance programme.
In property business, unlike in life business, a claim may be for 100% down to practically 0% of the insured sum. In these circumstances the underwriter of a company determines what is called the maximum probable loss (MPL) in order to arrive at the premium rate. While one cannot test an individual MPL, a rough check can be made on this process by comparing the sum of the claims with the sum of the MPLs. Actuaries must develop many other practical ‘actual to expected’ tests of this nature. In all these activities any attempt at precision is usually out of place.

Retentions
This is a subject that has received little practical attention in general insurance. For example, in property insurance it seems that the retention has evolved empirically over many years, increasing as a company’s size increases. Some years ago I found that for UK companies the retention was roughly equal to ?(1,000 times premium income). There seemed no theoretical reason for this; it just seemed to work.
From a risk point of view it is clear that the retention must not be set too high; on the other hand, if a company tries to play safe and fixes a low retention, it will find itself paying too much for its reinsurance.
The components of a risk are frequency and severity, so not only will a company be anxious to restrict the size of any individual claim, it will also wish to limit the total claims amount. It can seek to do this by effecting stop loss cover, but once again it must keep an eye on the amount it is paying for its reinsurance protection. The danger is that, after the payment of the reinsurance premiums, it will be left with too little premium to pay for the claims within its retention. This is a complex problem that I believe actuaries are well qualified to tackle.

Reinsurance
Unlike life assurance, where a person can only die once, it is clearly possible in other classes of insurance to sustain more than one claim in a year. So a company has to decide how many reinstatements of its cover are necessary.
The establishment of a company’s reinsurance protection programme is a complex and difficult problem. The process involves the determination of what are termed vertical and horizontal protections. Vertical protections cover the large claims and are expensive. This means that it is a matter of some importance how many large claims the company wants to cover. This is the horizontal protection. Suppose it has cover for claims of up to £100m with two reinstatements. If it is unfortunate enough to get three claims of this size, then all may be well, always assuming it can recover on its reinsurance; if it suffers four or more claims, then it is on its own for these additional claims.
For smaller claims it can usually afford to purchase reinsurance cover with 10, 20, or 30 reinstatements. Some actuaries have been getting to grips with this fascinating problem and have expressed it in graphic terms, making it simpler to spot gaps and deficiencies in the protection programme.

Safety of reinsurers
It is all very well to talk about the adequacy or otherwise of reinsurance protection, but it must never be forgotten that reinsurance is placed with reinsurers who themselves are looking for their own safety. Therefore in placing its reinsurance a company must have a concern for who its reinsurers are. This has an echo in the comments on political risks mentioned above. In passing it must be said that this is a matter of no small importance to supervisory authorities. I am convinced that safety of insurers and reinsurers is something to which actuaries can apply their minds.

Early warning tests
Some 25 years ago the National Association of Insurance Commissioners in the US developed a series of about a dozen tests designed to identify those companies that might be getting into difficulties. No one test would be sufficient in itself, nor would the tests be a substitute for deeper financial analysis.
A couple of examples are sufficient to show how the tests work:
– Test 1 Ratio of net written premiums to surplus. The usual standard for this ratio is 300%. In the UK we would use the reciprocal 33% which is equivalent to the solvency margin. I prefer the US measure, which has an intuitive appeal for every £1 of surplus a company can write up to £3 of premium income.
– Test 2 Change in written premium income. This test looks at the premium growth rate and is obviously concerned with too rapid a growth or decrease. The usual range is from an increase of 33% to a decrease of 33%.
The tests can be used over time to compare progress within companies and between companies. Comparisons between companies clearly lend themselves to ranking methods. It is my belief that non-parametric tests can and should be used more in our work than they are. These clearly have to be used with care and, once again, actuaries are the ideal profession to investigate and improve the type and quality of tests.

Reserves
This is a subject of great interest to actuaries, and those who are interested will find much to delight them in the actuarial journals. Triangles of claims development are a familiar sight and methods of projecting them are in a state of continuous evolution.
Here we can bring our abilities to bear in a practical way to assist the claims management of a company. In attempting to calculate the ultimate losses for each underwriting year we should observe that an estimate made as at 31 December 2000 must pass through 31 December 2001 on its way to the ultimate. So it is a salutary exercise to compare the total claims actually incurred as at 31 December 2001 with the estimate produced by the ultimate claims formula employed as at 31 December 2000. The presence of actuaries has made a fundamental difference in this field, in that they have persuaded the industry and the supervisory authorities that a method of calculating reserves must be capable of being described in a way that enables a third party to reproduce the actuary’s figures. It must also be capable of being verified and tested in the light of subsequent experience.

11 September 2001
The atrocities of 11 September 2001 which, using Franklin D Roosevelt’s words after Pearl Harbor, will ‘live in infamy’, have served to bring ever more closely to our attention the complex risks which now face the world insurance and reinsurance industries. We have to think even more deeply about the nature of risk, the non-independence of risks, the accumulation risks, how we rate the business, how we fix retentions, and how we plan a reinsurance protection programme. And we will have to calculate what additional factors have to be built into our premium rates and reserve calculations, together with the determination of tests to warn of problems which may lie ahead. We will also need to ascertain whether there is sufficient reinsurance capacity and to check on the willingness or otherwise of insurers and reinsurers to accept certain risks. We as actuaries must be closely involved in all of this.
Speaking as one who in 1944, as a small boy, watched helplessly as the flying bomb flew across the sky and destroyed Staple Inn, I can only say with others that nothing will ever be the same again.

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