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The Actuary The magazine of the Institute & Faculty of Actuaries

Learning to sail in all winds

W ith the recent market downturn, there
has been a renewed focus on cycle man-
agement by investors, regulators, auditors, and rating agencies. In September alone, Standard & Poor’s branded it the ‘key to reinsurer financial strength’ and it is was rated the number one risk for the london market in PricewaterhouseCoopers’ 2005 London Market Survey.
Despite the (re)insurers’ press statements on their focus on cycle management, there have been few details on the specific strategies that are being adopted and their practical implications.
The traditional approach to cycle management has been through capacity management, adjusting total capacity (ie volumes of business written) across the cycle. There are, however, some emerging techniques, based on dynamic pricing strategies, which may yield better results than capacity management on its own.

Capacity management
This is the most common approach to cycle management. It consists of adjusting the amount of total capacity in order to deliver the return on equity that has been promised to shareholders. In a soft market, this means returning capital to the shareholders and focusing on the opportunities that are available for meeting the target return. Conversely, one would have to raise additional capital as prospects brighten.
Although theoretically appealing, capacity management is fraught with practical difficulties. Raising and returning capital are not straightforward, especially on the scales required to achieve efficient cycle management. There are few companies that can, and are willing to, halve their capital base within a year of markets softening in order to maintain their return on equity. Also, as hurricane Katrina has reminded us, the right time to increase capacity is not necessarily the most practical one. After a catastrophe, a (re)insurer has typically just lost a large part of its capital and also has to compete with other players for additional capital. In the words of Benjamin Franklin: ‘Necessity never made a good bargain.’
Capacity management can be an efficient tool for cycle management, but its practical difficulties limit its use to large and sporadic adjustments, which prevents it from being an active management strategy.
Another approach, rather than adjusting capacity to manage the cycle, is to adjust the price charged. This is called ‘revenue management’.

Revenue management
Insurers are now beginning to use pricing strategies based on the revenue management techniques developed by the airlines in the 1980s. These strategies have also been introduced to other industries, such as hospitality and car rental, in which firms face the challenge of maximising the return on a fixed supply of perishable goods.
In the case of an airline, revenue management systems based on historical booking patterns are used to estimate the likelihood of spare capacity at departure. Airlines need to balance the risk of not selling that capacity with the opportunity cost of passing up a ‘premium customer’ who is willing to pay a higher price. As the departure date approaches, airlines would prefer to fill up the spare capacity with people buying discounted tickets, rather than risk an empty flight. Conversely, if there are a large number of early bookings, the risk of an empty flight goes down and the system would hold out for the ‘premium customer’, thereby commanding higher fares for the remaining seats.
The concept of revenue management is to adjust prices dynamically to reflect:
– spare capacity at that point in time; and
– expectations for future demand.
Based on this, companies can use sophisticated algorithms to derive the optimum pricing strategy.
These techniques can prove relevant to the (re)insurance industry where:
– capacity is fixed for the year determined by capital constraints from the regulator, ratings agency, or internal to the firm;
– capacity is perishable unused capacity in one period cannot be rolled over to the next;
– the price for the capacity is the profit load or target return on equity (RoE); and
– the fluctuations in supply and demand are reflected in the insurance cycle.
The following example illustrates how revenue management can support strategic pricing decisions over the insurance cycle.

A practical example
We consider for simplicity a two line insurer over a five-year horizon. Business line 1 (L(1)) has a short cycle while L(2) has a longer one. In addition to the standard insurance cycle, there is an unexpected capacity shock, for example a natural catastrophe or a major player leaving the market, at the end of year 4, which has the effect of increasing the market RoE for L(2).
The revenue management framework allows us to look at the optimum strategy from two different perspectives:
– The price-setting strategy determining the target RoE over the five-year period; and
– The strategy for allocating capacity between lines of business.
Figure 1 shows the market RoE, in plain lines, along with the target RoE derived from the model, in dotted lines.
Figure 2 shows the allocation of capacity between the two lines.
There are three phases in our illustration:

Phase 1 L(1) and L(2) are softening
The market returns for both business lines are falling, with L(1) falling off more rapidly. As can be seen from figure 1, the model indicates that the (re)insurer should initially undercut the market to write high volumes when there are still high market returns, but towards the end of the period when returns are poor the (re)insurer should be selective, cherry picking the business written, by setting its target RoE higher than the market returns.
Translating this into allocation of capacity, initially the volumes written in the two lines should be similar, to maximise the benefits from diversification. In the latter part of the period the diversification benefit is outweighed by negative market returns from L(1), so a minimal amount of L(1) is written.

Phase 2 L(1) market is hardening
With L(1) rates rapidly hardening from its negative market returns, figure 1 shows the optimum pricing strategy is to cherry pick the business written early in the period, and keep a low but positive target RoE. This leads to low volumes but allows the spare capacity to be used in the latter months where returns are greater.
Figure 2 shows that, as expected, the capacity written shifts from L(2) to L(1) to take advantage of the hardening market.

Phase 3 Capacity shock
The capacity shock increases the market RoE for L(2) rapidly; after this, it falls off throughout the remainder of the year.
The optimum (re)insurer’s strategy is to chase this profitable business, slightly undercutting the market to win new business, but still achieving good returns. The (re)insurer can also afford to increase its prices on L(1), albeit to a lower extent, as the good conditions on L(2) allows him to be more selective.
Figure 2 shows that to optimise profit there needs to be a shift in the volume of business written from L(1) into L(2); this then progressively reverses as returns from L(2) start to fall.

Formalising intuition
In many ways, revenue management is only a formalisation of the underwriters’ intuition. With their knowledge of market conditions, underwriters seek to strike the balance between volume and profit, but we should not underestimate the benefits of formalisation and modelling to support and optimise decisions regarding pricing, volumes, and allocation of capacity. A good illustration of this is in the realm of catastrophe aggregate monitoring, where sophisticated models have long surpassed intuition and mental calculations.
A simple sailing analogy can be useful to contrast capacity and revenue management. While the former deals with selecting the size of your boat, the latter helps you adapt your sails to the wind conditions. These approaches are complementary and, when implemented effectively, can give companies the ability to sail in all winds.