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The Actuary The magazine of the Institute & Faculty of Actuaries
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Non-life reinsurance and organisational behaviour

Reinsurance is generally the most important risk
management and capital management tool for a non-life insurer. In recent years, and especially
during 2004 with an FSA-driven spurt, many companies have been looking critically at their reinsurance buying practices. These companies generally perceive that they are ‘big enough’ to retain more risk, but are finding it difficult to unwind convoluted reinsurance programmes so opaque that their value, or otherwise, cannot easily be assessed.
These companies are observing a symptom. Complicated reinsurance programmes arise because many buyers of reinsurance, each with a narrow focus, will not collectively buy optimal reinsurance. But, as any good doctor knows, addressing the underlying problem will provide a longer-lasting solution than dealing with a symptom.

Hierarchy of risk aversion
The first step in understanding what is going wrong is to look at the motivations of those that are buying reinsurance. It is generally true that those in charge of the business units (BUs) of an insurer closest to the coalface are most risk-averse in terms of their own unit’s results. This is because they cannot easily diversify themselves away from this particular job/line of business/profit-centre, as they tend to be locked into their own team and its performance. These I call the ‘BU managers’.
For those higher up in the hierarchy of a non-life insurer, a given profit-centre’s volatility can be absorbed to a greater extent, so the individuals are less risk-averse. For example, the volatility of the results of a small UK branch of a German company will tend to mean more to the UK branch manager than to the company’s CEO who is able to absorb this within a much larger portfolio.
Ultimately, the shareholders of the company (or other owners in the case of a mutual or government body), provided they are informed and have appropriate expectations, will be most able to diversify their exposure from an individual profit-centre’s volatility.
But who makes most reinsurance buying decisions? The answer, for many companies, is the BU manager. The most risk-averse individuals in the insurer make some of the most important risk/reward decisions. This is an example of a ‘principalagent conflict’ of the classic kind discussed extensively in economics: the manager (agent) who acts on behalf of shareholders (principals) makes different decisions from those the shareholders would make themselves.
Digging one level deeper into insurers’ organisational behaviour is instructive and sheds light on how to address this conflict.
Capital and shareholders
From a ‘capital’ viewpoint, reinsurance can be valued by considering its benefit in terms of reduced capital. This is one element of the well-documented capital allocation role that generally falls within an actuarial department’s responsibilities. The idea is that buying reinsurance reduces overall portfolio risk, thereby reducing the capital required to support the portfolio. Because capital has a cost, this risk-reduction has a quantifiable benefit. I use the following terminology to crystallise this concept of capital benefit (for a given reinsurance contract or programme):
demand premium = expected loss cost
PLUS the value of capital relieved
This is a theoretical figure that can be estimated for all reinsurance a company buys (expressed here for simplicity ignoring the effect of overhead and friction costs). It is the maximum the direct company should pay for the reinsurance any actual premium less than the demand premium represents value-creation for the company.
On the other side of the equation, of course, the reinsurer is working out his minimum premium as statistical mean losses plus a capital charge, leading to the following terminology:
supply premium = expected loss cost
PLUS the cost of capital charged
This is also a theoretical figure (again ignoring costs), representing the minimum the reinsurer should charge.
The demand/supply premium framework, although rooted in theory, is applied practically when we consider that it has given us the parameters within which the ‘real world’ commercial environment should operate. Reinsurance negotiations that lead to a price above the supply premium but below the demand premium give rise to ‘winwin transactions’, as illustrated in figure 1 left.
While this framework is not necessarily the way to maximise value from reinsurance buying, it is certainly a useful starting point for reinsurance strategy (eg target areas where you estimate both a low supply premium and a high demand premium). It is also an indispensable tool for reinsurance tactics, providing a maximum price that should be paid for each programme or contract, therefore avoiding value destruction from reinsurance. Furthermore, it can sometimes lead to interesting discussions if, say, the reinsurer’s view of expected loss cost is significantly different (inevitably higher!) than the cedant’s.
I believe that, subject to modelling being sufficiently credible to inform such important decisions, the demand/supply premium framework is the best starting point to provide reinsurance decisions aligned with the capital providers’ views.

P&L viewpoint and BU managers
If the ‘capital’ viewpoint, which aligns interests most closely with the owners of the business, leads to the demand/supply premium framework, what is informing the decisions made by the BU managers?
These individuals are usually given profit and loss (P&L) accountability for a subsection of the business. An example might be the marine underwriter at a Lloyd’s operation writing 10% of the insurer’s premium. P&L accountability is generally a good thing in that it means a BU manager ‘owns’ his or her own performance. This autonomy and accountability usually takes the form of having a single profit target (eg loss ratio or combined ratio) for each year, and being assessed in relation to this target.
The trouble with this approach is that it focuses on one number, and typically does not reflect the risk/reward trade-offs that the capital providers would value. In essence, the P&L approach cannot truly allow for the infinite risk/reward trade-offs that the capital approach can.
This is shown in figure 2 in the form of schematic utility curves. The ‘correct’ curve is represented as the utility of capital owners, while the curve that probably represents the one that reinsurance decisions are usually based on is that of the BU managers. This shows a dramatic change at the ‘target profit’ level. Managers are strongly motivated to hit their profit target (this is culturally important in most insurers), and so highly value not falling short in terms of job security, bonus protection, and influence in the organisation. However, they typically are not motivated to strive to exceed the profit target as this would risk falling short.
It is clearly desirable, and standard practice, to give BU managers P&L accountability and autonomy. But when an insurer does so, by focusing on single annual profit targets (generally necessary for clarity and simplicity), it thereby creates the environment for inefficient and even value-destroying reinsurance decisions. Thus BU managers are often willing to sell all their upside to protect their downside!

Internal and external reinsurance
We have seen that the inefficiencies in reinsurance buying often arise through principalagent conflicts in an insurer. These conflicts, in turn, are necessary by-products of clear and simple management of profit-centres owing to how individuals are motivated and how they consequently make decisions.
One solution clearly would be to take away all reinsurance decision-making responsibility from BU managers. Some insurers have done this, but it may be culturally quite drastic and there is definitely a negative effect of removing individuals’ autonomy: resentment. A preferred solution may be to place some or all of each profit-centre’s reinsurance into an internal reinsurance provider. The risk that this reinsurer takes should be analysed and appropriately priced, and the internal process by which risk is transferred should be transparent and equitable.
Internal reinsurance can overcome the principalagent conflicts in reinsurance buying:
– It retains the benefit of autonomy for the BU managers in that they can still purchase reinsurance (albeit solely or mainly internally) to protect their result.
– It ensures the retention of risk commensurate with the insurer’s balance sheet, ie it can avoid external reinsurance that doesn’t provide a capital benefit.
With the internal reinsurer taking on much of the big risk in the organisation, it becomes a profit-centre in its own right and can be appropriately valued and managed often as a separately capitalised subsidiary.
Therefore, the internal reinsurer will be able to access the external reinsurance market but will have the ability to restructure and repackage its risks to be able to use reinsurance intelligently. When contracts are well structured, when moral hazard is minimised, and when the underlying risk is capable of being modelled, most reinsurance can be placed. Naturally when reinsurance does not go through the sausage-machine of standard classes with line-underwriters at reinsurers, it takes more attention and sometimes commands bigger profit margins for the reinsurers as a proportion of the premium they receive. But it can also represent much better value to the buyer of reinsurance, even with these higher margins.
An example reinsurance structure, retaining some outwards reinsurance placement directly by the BU managers but with most being bought from the internal reinsurer, is shown in figure 3. This includes stop loss reinsurance covering the internal reinsurer generally a difficult treaty to place, but often available when the risk is analysed and the rationale for purchase is clear.
As always with innovative business practices, internal reinsurance must be managed with discipline and with clear rules of engagement. Indeed, some cases have not worked well when the internal reinsurance either under- or overprices its internal business, or provides ‘reinsurance of last resort’ for risk that the profit-centres should never have taken in the first case! But if implemented properly, internal reinsurance can provide capital value without compromising the autonomy of the BU manager.

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