There is no such thing as ”good statistics”!

This article, written by Norwegian Hull Club's Business Intelligence Director Christian Irgens, was published in Lloyd's List 19th September 2006 under the title "Why good statistics are just a myth".

Daily optimism and annual realism is said to be an enjoyable route to a prosperous life. The former without the latter is just as much the recipe to bankruptcy in general and marine insurance losses in particular. When marine insurers convene at the annual IUMI-conference for talks of risk assessment these days, their aim is seemingly to put this year's 3-days of realism behind them.

The problem of mispriced insurance is much older than the marine insurance industry. In year 230 the praetorian prefect Domitius Ulpianus produced a table of annuity values that was the best table available until almost 1700. It was used until 1814. Although a remarkable achievement; today the "Ulpianus-method" is known somewhat derogatory by actuaries as a simplistic method that systematically overestimates the premium of annuities. Both in terms of model persistency and systematic mispriced risk, the story of Ulpianus has its analogies in marine insurance. Regrettably the analogy is less important than the contrast: compared to marine insurance Ulpianus' approach was rocket science, and contrary to the Romans; marine insurers systematically underestimate the risk.

The task
Compared to non-marine commercial insurance, premium calculation in Hull & Machinery insurance should be fairly simple. The claims are (usually) limited to the insured value, the notification and settlement of claims is fairly quick, the conditions are standardised, aggregation risk is low, the risks facing the vessel are fairly stable (for a given trade), vessel design and operation are becoming more homogeneous, it is easy to access an abundance of technical and operational details of the vessel, there are hundreds or thousands of fairly comparable vessels available and the claim frequency is fairly high. Compared to workers compensation, general liability or even commercial fire insurance this is a luxurious position. The pitch is perfect for statistical models, and a growing number of such models have been developed during the last few years. But even though the going should be good, market practice makes it remarkably "soft in places"...

A revolution in the offing?
Before we turn to the well known criticism of market practice lets pause for some consideration of what has taken place in the companies in recent years. Regrettably the topic of risk modelling has a somewhat alchemic aura, both in terms of aim, secrecy and practitioners' dubious understanding of the underlying details. This makes it hard to assess the current level of risk modelling expertise in marine insurance. Even so, it is probably fair to say that many marine insurers have added more science to their underwriting process over the past 5-10 years than they did the previous 50-100 years. Over the next few years this development will accelerate as a consequence of new regulation (Solvency II) and increased attention from rating agencies. No refining, no future dining. More on that later on.

The problem
Statistics from the Central Union of Marine Underwriters in Norway (CEFOR) show a 20 year Hull & Machinery loss ratio of 117% and a 10 year loss ratio of 113%. The years with technical gross profit are few and far between. Reports from other markets and longer periods show the same results. How these "non-profit organisations" survive is one of the few unresolved marine mysteries. Even though the question of survival is a mystery, the root cause of the problem is not.

The problem can be described by the following misapprehensions. Firstly, underwriting losses are understood to be the consequence of a small number of "bad guys" - the majority of clients are "good guys". Extremists of this school of thought will claim that no-claim bonuses and profit commissions doesn't cost the underwriter anything, because the payout is only triggered on accounts with profits. Secondly, there is widespread belief among clients, brokers and a surprisingly large number of underwriters that every fleet is an island (or perhaps rather an archipelago) with limited resemblance to any other fleet in the world. Thirdly, a high and often fairly stable frequency of small claims makes it tempting to assume that fleet statistics give a good basis for predicting future claims. Fourthly, some of the prevailing exposure based models are based on rather simplistic rules of thumb regarding dollar pr. gross ton or deadweight ton. This reduces the credibility of exposure based models. Fifthly, late reporting and development of claim reserves is considered "Interesting, But Not Relevant" at a fleet level. Last but by no means least, underwriters and clients regard the 3-5 year fleet statistic as if it is was a credit facility: after claims free years the client is in credit and can claim a discount, while after total losses the underwriter will set the impossible target of re-establishing balance within the next few years. This lethal cocktail of delusion is the direct cause of the malfunctioning market:
- Clients experience extreme price hikes following large losses. The impact on underwriters' profit is limited however, due to the limited number of clients with large losses.
- Clients experience discount based on "good statistics". The effect on clients' insurance cost is usually moderate. Due to the large number of fleets with "good statistics" the impact on underwriters' profit is huge however. Studies have shown that random variation (and the skewness of the distribution) implies that approximately 70% of the fleets are better than the long term average in a 3 year period.
- The effect of the discounts based on "good statistics" by far out-weighs the effect of the price hikes based on "bad statistics", and the inevitable result is underwriting losses.
- Compared to the cost of a total loss, late reporting and adverse development of reserves might not look material at a fleet level. Less than 90% of the claim cost is normally reported at the end of a 3 year period however. If the fleet statistics are compiled 2 months before renewal, another 2/36 = 6% of the claims are missing. If not adjusted for, these 2/36 + 34/36*10% = 15% will represent a bigger aggregated loss for the underwriter than most total losses.
- Current practice puts the focus on the wrong clients. The problem is not the unfortunate clients with the big losses, but insufficient premium from the vast majority of clients with "good statistics".
- Focus on fleet statistics exacerbates the premium cycles. In a soft market, discounts will be given as long as 3-5 years statistics looks good - even though the current premium is far lower than the premium in the statistics. The opposite occurs in a hard market.

Together the above results in a market where premium varies more than claims, long term underwriting losses are inevitable and the most basic function of the insurance product (risk relief) is not delivered.

The future
Even though it takes more than an actuary to kill the sanguine spirit of a marine underwriter, I'd like to end this commentary on a positive note. In 2010 the European Union will most likely introduce the "Solvency II" solvency regulations. The effects could be far reaching. In addition to stricter and more sophisticated capital requirements, these regulations require good internal control and risk management and increased disclosure and transparency. For most companies the change will imply increased insight in the risk they undertake. For some companies (especially the ones that do not develop internal risk models) the regulations imply stricter capital requirements and thus increased reliance on reinsurance. With increased insight and stricter requirements from regulators and reinsurers there might actually be hope that the ugly duckling of insurance is growing up!

Christian Irgens MSc (Actuary), MBA
Former Chairman of CEFOR Statistics Forum