With such an array of criteria used to establish capital requirements, whose role is it to come up with the "right" model? asks Eamonn McMurrough

How much capital does an insurer need to be considered financially sound? This is a crucial question for the insurance industry, to which at present there seems to be no straightforward answer. Industry regulators and rating agencies have their versions, based on their risk assessment processes, models and methodologies. An insurance company may also have a version of its own, often driven by a desire to use return on capital as a measure of performance and input into strategic planning. Historically, what mattered most was the capital required to maintain credit ratings because this affected share price, market share and the cost of new capital.

Today, industry regulators across the world are raising the bar on risk management. Simple tests based on premium income or claims incurred are being replaced by risk-based calculations, such as Solvency II, which is due to be fully implemented by 2010. These new standards will be more complex and demanding than the old ones, raising the prospect of regulatory capital becoming an operational constraint for a significant number of insurance companies. It is likely that in the future insurance companies will find it more difficult to regard regulatory returns on solvency as a discreet exercise, divorced from their mainstream business decisions.

Under pressure from both regulators and rating agencies, risk management is set to become one of the main business drivers for an insurance company, where capital requirements are calculated as a by-product of business decisions and capital implications are recognised prospectively. From the corporate governance point of view, this is a sound practice and therefore should be encouraged. At the same time, it must be recognised that risk management and financial theories have advanced significantly over the past 20 years in parallel with the rapid evolution of IT. As a consequence, the measurement of risks and their interaction is based on a combination of constantly evolving theory and complex processing, and the interpretation of findings and outcomes requires specialist knowledge.

THE CAPITAL CONUNDRUM

This leaves many directors of insurance companies in a difficult position.

They are required to take responsibility for risk management and understand the risk dynamics of their business yet they have to rely on other people for the interpretation of essential data. This poses a question about the role directors of insurance companies should be expected to play in the overall risk management process.

In a world characterised by growing uncertainty it is essential to ask the right questions. Directors of insurance companies must be able to challenge the results of capital models applied to their business, seeking to justify the modelling assumptions and conclusions. For example, the question "How much capital do we need?" will produce different answers, based on the different criteria applied by regulators, rating agencies, investors, accountants and actuaries. It is the responsibility of the directors to understand and explain any variations in capital requirements and establish clarity of expectations.

Clarity of expectations is particularly important because in the end there is no right answer to the question "How much capital do we need?" In this respect, establishing capital requirements is very different from valuing a liability, for example. There may be a range of plausible liability values from the outset, but eventually, with hindsight, it should be possible to quantify what the correct provision should have been. Similarly, evidence of consistent under-pricing will emerge with experience. When it comes to capital, we do not have the benefit of hindsight and must be prepared to operate in the environment of constant uncertainty.

Asking the right questions from the start will enable directors of insurance companies to place a greater responsibility on professional advisors such as rating agencies to provide an explanation of the assumptions, logic, conclusions, scope and limitations of their models. Those experts will be required to communicate their methodologies clearly because as Albert Einstein once said, "If you can't explain it simply, you don't understand it well enough."

Another question posed by the increasing sophistication of industry regulators in terms of capital modelling is the future role of rating agencies in the insurance industry. We already have evidence of converging regulatory requirements in different parts of the world. Are regulators likely, at some point in the future, to replicate the analysis performed by rating agencies in identifying relative credit risks of different insurers and reinsurers? Conversely, is it possible that regulators will eventually outsource capital modelling to rating agencies? In any case, there is a trend towards a greater consistency of modelling methodologies, which will only benefit directors of insurance companies in the future.

So what are the important factors for directors to consider when applying capital modelling techniques?

Scope and limitations of the model: Make sure the business scope of the capital model is clear and well defined. This may sound obvious but it is not always the case. Some liabilities may be excluded or be given special treatment (for example, latent disease or finite reinsurance), or the scope of the exercise may be restricted to certain territories or classes of business. The more we understand about the scope of the model the easier it would be to question its findings and output later on.

Risk measure and solvency standard: Examples of risk measures are value at risk (VAR) and tail value at risk (TVAR). To say that the capital required is at 99% VAR is to say that there is a 1% chance of running out of capital, or 1% "probability of ruin". VAR has recently lost favour on technical grounds and TVAR is now widely used (TVAR is a coherent risk measure, VAR is not). Whereas VAR defines a threshold above which the capital is exhausted, TVAR takes an average over all such scenarios. In practice, the choice of solvency standard, eg 99% or 99.5%, is more critical than the risk measure used.

Time horizon: The longer the time horizon the more chance there is for things to go wrong. Many models use a one-year time horizon with 99.5% TVAR. If the time horizon is extended to three or five years, the standard is relaxed. The UK Financial Services Authority has indicated that appropriate standards are 99.5% for one year, 98.5% for three years and 97.5% for five years.

Extreme events: Following a period of devastating natural disasters, potential for catastrophic losses will loom large in any assessment of capital requirements. The most widely used proprietary catastrophe modelling packages will produce different probable maximum loss (PML) estimates for a given scenario, and it is helpful to have a rational basis for selection, other than selecting the most favourable result.

Modelling dependencies: This is a technically challenging area for capital modellers. The simplest assumption is that all risks are independent, but this is usually unrealistic. If risks are positively correlated they are likely to go wrong together, which would demand more capital. Conversely, if risks are negatively correlated there is a diversification benefit and less capital is needed. How dependencies have been modelled should be clearly explained.

Valuation basis: Assets and liabilities may be included in the model at balance sheet values, or as "best estimates". Any margins in balance sheet values represent implicit capital and should be clearly explained wherever possible.

Model uncertainty: It is essential to remember that the results of any model are just estimates, and therefore always have a margin of error.

How reliable are those results? How sensitive are the answers to small variations in assumptions or model parameters? If the results are unstable, it may be an indication of weakness in the business plan, perhaps due to unprotected exposures, large losses or a lack of diversification of risks.

When applying capital modelling techniques, it must always be remembered that we are not dealing with the real world. As George Box, an eminent statistician, once said, "All models are wrong, but some models are useful".

Any capital model is a simplified description of a complex business, and can therefore only capture and describe the main factors and interactions in a fairly crude way. Capital models should be used to inform a debate on capital requirements, but should always be regarded with a degree of suspicion.

If a capital model is being used to achieve an external standard, for example, to arrive at a credit rating by a rating agency, then whether the answer is "correct" is academic; the model will either achieve its purpose or it will not. If the analysis is for internal performance measurement, this question may have more practical relevance, especially if applying different risk measures, standards and time horizons would influence business decisions. The acid test is whether the capital model and its results are useful in managing the business, and the "right" model is the one that is most useful.

- Eamonn McMurrough is a partner and actuary at JLT Re.