Stephen Britt and Ted Dew explain how dynamic financial analysis can be used to answer reinsurers' capital management questions.

In today's reinsurance market, the optimal use of capital is increasingly a focal point for management. If the role of every enterprise is to increase value to its owners, then under-utilised capital is a drain that must be put to work. Volatile worldwide financial markets have created an environment in which capital providers can demand competitive returns that meet or exceed management expectations.

In assessing the efficient use of capital, the reinsurer must be able to answer the following questions:
• How much capital is needed?
• How should capital be allocated across business segments?
• What happens if there are impediments (rating agency or regulatory) to the optimum use of capital?
Dynamic financial analysis (DFA) is a tool that can be used to answer reinsurers' capital management questions.

Dynamic financial analysis
DFA refers to computer programmes that model multiple alternative results from a specified operational strategy. For reinsurers, this means producing numerous scenarios of potential asset values and underwriting returns resulting from the investments made and policies written. While traditional reinsurance management analyses investment performance separately from underwriting, the modern DFA approach deals with the assets and liabilities together under a consistent set of scenarios. Using this modern DFA approach allows management to determine how the risks inherent in their assets interact with the risks inherent in their liabilities. Traditional management ignores this important interaction.

Carefully implemented, DFA will provide the mechanical tools to answer a company's capital questions. Figure 1 presents a breakdown of a typical DFA engine.At the top of the diagram are the economic scenarios. The economic scenario generator needs to be comprehensive, modelling not only interest rate risk but also inflation risk in its various guises, equity return, currency and, possibly, credit and economic risks. These economic factors - which can be managed but not necessarily diversified - are frequently shared between both the assets and liabilities of a reinsurer.

Below the scenarios lie the items that flow into a reinsurer's financial statements. The DFA programme must be able to model the products the reinsurer seeks to offer and the investments it might undertake. The model needs to reflect how each product and asset responds to changes in economic variables, in other products or assets, to the product and asset over time (serial correlation), and in the timing of payment, and to random fluctuation (noise). When properly set up, each iteration of the DFA programme will produce a realistic potential outcome.

Below the products and assets are the corporate strategies available to the reinsurer. The DFA model must be able to model the enterprise as it stands, but more importantly it must be able to model potential strategies. It must incorporate a set of decision rules that reflect how company management will respond to dynamic events that occur within a specific scenario. For instance, if a catastrophe requires immediate large claims payments, the model must include decision rules that describe in what order the investments are sold to meet those responsibilities.

Finally, the model calculates the distribution of financial results from these strategies. By running the model under multiple operational strategies, reinsurers can use their own risk and reward measures to rank alternative strategies.

How much capital is needed to support the enterprise?
Why does a reinsurer need capital? Policyholders (or their surrogates, rating agencies and regulators) must have confidence that the reinsurer will be able to pay claims in an orderly manner as they fall due. Capital provides this confidence. The higher the amount of capital allocated to a particular policy, the more confident the policyholder that the claim will be paid.

However, owners of the reinsurers' capital require a return on that capital. If we assume that: (1) the policy price is determined by the market; (2) the profit margin on the contract is fixed; and (3) the return on capital is a function of the amount of capital committed to back the policy, then we arrive at two conflicting conclusions.

• Policyholders will face a trade-off between the degree of confidence they desire (measured by the amount of capital backing the policy) and the price they are willing to pay;

• Owners will face a trade-off between amount of capital they are willing to commit and the return on that capital.

This conflict is akin to the traditional supply-and-demand curves of economics, but in this case the goal is to adjust either (1) the amount of capital backing the contract or (2) the strategies driving the return on capital in order to satisfy both constraints.

DFA is useful in this context because it can quantify the likelihood that a reinsurer meets its claim obligations and, where claims cannot be met in full, the degree of shortfall. In other words, DFA can measure the degree of policyholder confidence associated with a specific level of capital. A reinsurer can review the distribution of results produced by a DFA model and focus on those which are unfavourable - where either the reinsurer's capital falls below acceptable levels or the return on invested capital is inadequate (see Figure 2).

A suitable capital-based risk measure would reflect both the probability that a shortfall will occur and the severity of the shortfall. Similarly, a suitable return-based risk measure would reflect both the probability of an inadequate return and the amount of that inadequacy.

How should capital be allocated across business segments?
A DFA model can also be used in three separate runs to determine the capital required by business segment. When allocating capital to business segment, it is important to consider the benefit of diversifying into multiple business segments (lines of business, types of contract, territory, etc).

Generally, the capital required for a combination of several business segments is less than the sum of the capital required for each business segment individually. The difference between the combined capital requirement and the sum of the individual capital requirements is the diversification benefit.This diversification benefit should be allocated back to each individual business segment. This distribution of capital should reflect the marginal contribution that the business segment makes to the total diversification benefit.

For example, assume that a reinsurer writes three lines of business. A DFA model can be used to determine the capital required to write each line of business. For line of business A in isolation is $10 million. For line of business B it is $20 million and for line of business C it is $5 million. Running a DFA model a fourth time for all three lines combined, the reinsurer determines that the combined capital requirement is $29 million. Therefore, the total diversification benefit is $6 million ($10 million + $20 million + $5 million - $29 million = $6 million).

One simple method to allocate the $6 million reduced capital requirement requires the reinsurer to calculate the marginal diversification benefit for each line of business. To do this, the reinsurer runs a DFA model for lines B and C combined alone. Assuming that the capital requirement for lines B and C combined is $24 million, the marginal diversification benefit for writing line of business A is equal to $5 million ($10 million + $24 million - $29 million = $5 million). Similar DFA runs and calculations can be performed to estimate the marginal diversification benefit for lines B and C.

Finally, the $6 million total diversification benefit is allocated in proportion to each of the marginal diversification benefits. In our example, $2 million, which is 5/15ths of the $6 million total diversification benefit, is allocated to line of business A. This reduces the capital requirement for line of business A from $10 million to $8 million.

How are impediments to the optimum use of capital addressed?
Rating agencies and regulators, acting on behalf of policyholders, develop their own viewpoint of the capital required by reinsurers. The US risk-based capital requirements are an example of regulators' external estimates. Rating agencies use their own approaches to establish capital adequacy.

In making these assessments, rating agents and regulators do not have access to as much information as the reinsurer and may err on the side of conservatism in assessing capital adequacy. The reinsurer has these options:

• Approach the agencies with details of its own capital modelling in an effort to convince them to change their minds; or
• Understand the rules of capital adequacy requirements and utilise them to reduce the level of over-capitalisation. As an example, the US capital adequacy requirements tend to over-state the required capital in each risk segment but also overstate the diversification benefits of various risk sources. This outcome suggests a strategy of diversification - seeking multiple sources of risk that do not add significantly to total portfolio risk capital but which do generate additional return.
The amount of capital and its efficient use are principal driving forces behind the reinsurance industry. Reinsurers with the ability to measure their required capital, and the impact of various strategies for deployment of capital, are clearly ahead of the game. DFA is a powerful tool in assisting in capital management.

Stephen Britt is an asset consultant in the Hartford office of Tillinghast-Towers Perrin. He is a fellow of the Institute of Actuaries Australia and a chartered financial analyst and specialises in improving the performance of financial institutions with advice supported by stochastic modelling and optimisation techniques. Tel: +1 (860) 843 7000.

Ted Dew is a principal of Tillinghast-Towers Perrin and the manager of the Bermuda office. He is a fellow of the Casualty Actuarial Society and a member of the American Academy of Actuaries and has created models to estimate underwriting returns on capital, toxic tort liabilities, and insured Y2K damage. Tel: +1 (441) 295 8863.