Rigorous and quantitative analysis are essential to improving the quality of the reinsurance purchasing decision, according to Oliver Peterken.

An insurer has three key financial decisions to make: how much premium to write; its cost of capital; and reinsurance. The decision-making process for purchasing reinsurance is often neglected.

This situation is surprising as insurers cannot trade without it and reinsurance represents an essential raw material, capital.

Two substantive influences are currently transforming the reinsurance decision-making process from the cost to the capital management domain.

Firstly, the growing influence of the banking sector's treasury risk management techniques is leading insurance company executives to adopt a more vigorous, quantitative approach to their largest risk capital financing decision. Secondly, hardening prices and tightening terms have significantly increased the cost of the reinsurance product and made more urgent the need to understand the value it brings. At the same time regulators, rating agencies and investment analysts are looking for evidence that the reinsurance purchase decision is made in a robust and quantitative manner.

But how can better reinsurance decisions be made? There is no simple, quick solution to this. To improve reinsurance decisions takes time, and four areas need to be addressed:

  • the decision-making process itself;

  • developing a sophisticated understanding of the real cost of reinsurance;

  • accessing the advanced modelling skills to measure the real cost; and

  • calculating an optimum strategic reinsurance solution.

    Better decisions
    There is now considerable evidence from management science research that organisations with effective processes to take decisions (rather than delay them or muddle through) make better quality decisions. Of course, there is a need to be able to respond to short-notice opportunistic situations, but reinsurance purchase is an annual process with over 12 months available to make decisions.

    A better reinsurance decision-making process requires a number of steps. Firstly, capital management objectives need to be set to provide the criteria against which potential reinsurance structures (including alternative deductibles, limits and prices) can be evaluated. Then the past and prospective loss and exposure information for the insurance business need to be analysed, and statistical parameters derived that capture future losses.

    Alternative reinsurance structures need vigorous evaluation, and this can only be done by analysing them in a quantitative, probabilistic model that tests each structure against a large range of potential outcomes. We cannot predict next year's losses, but the likely range of structures can be forecast and probabilities attached. A key stage is, therefore, the development of a computerised business model to provide this reinsurance benchtest.

    Real cost of reinsurance
    Perhaps one of the most important developments in recent management thinking has been awareness of the need to charge for capital. As Peter Drucker said: "Until a business returns a profit that is greater than its cost of capital, it operates at a loss ..." Conventional accounting and traditional ways of evaluating reinsurance have ignored this economic definition of profit.

    However, this economic model of surplus creation is particularly applicable to insurance and reinsurance. Both products require the existence (but not the transfer) of contingent capital to support the implicit put options in an insurance or reinsurance contract. This contingent capital is more commonly known as risk capital.

    The effect of reinsurance is to reduce the amount of risk capital the reinsured needs to hold. For a typical European insurer, catastrophe reinsurance can reduce the risk capital it needs by more than half. For regions with more frequent or more severe catastrophe losses, the effects can be even larger.

    In order to make better reinsurance decisions, the capital effects of reinsurance need to be explicitly taken into account. Traditionally, the analysis has stopped at the underwriting level, i.e. reinsurance premiums less expected claims and adding commission. A more effective analysis also needs to deduct the cost of capital released by the reinsurance programme:

    Reinsurance premiums

    - Expected claims

    - Adding commission

    - Cost of capital released

    = Real cost of reinsurance

    The cost of capital is the capital at risk valued at the insurer's rate of interest. The capital at risk is a probabilistic concept and can be defined as the amount of capital required to meet a monetary loss at a given probability. Typically this is set at the 100- year return period level and is comparable to the banking risk management concept of value at risk (VAR). For insurers without ready access to external equity finance, this level might be increased to the 250-year level. Which level to choose forms an important part of a better decision-making process.

    Reinsurance optimisation
    So far, reinsurance has been considered in terms of the process to decide how much to buy, in what structure to buy and at what price. This has been done in the context of management seeking to maximise their return to shareholders (or stakeholders in the case of mutuals, subject to certain constraints.

    In terms of optimisation theory, the objective function (i.e. what we are trying to maximise) is the economic profit, which is the underwriting profit less a charge for the risk capital implicitly required. However, almost all insurers have restrictions on their reinsurance decisions. Typically, they are constrained by a maximum amount of risk capital available to their business, a target loss ratio and a leverage ratio (a maximum percentage of premiums they can cede to reinsurers). Increasingly, more stringent credit quality thresholds are having a large influence.

    The task for reinsurance optimisation is to identify the combination of reinsurance structures, retentions and limits which produce the largest economic profit while meeting the various risk capital, loss ratio and leverage constraints. Only if this is done in a vigorous, quantified way can better reinsurance decisions really be made.

    By Oliver Peterken
    Oliver Peterken is Head of Willis Re's analytical and consulting services, London Email: