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The Actuary The magazine of the Institute & Faculty of Actuaries
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The time horizon conundrum

The move from market-wide formula-based to firm-specific capital calculations was something that some market participants had been requesting for a long time and which was eventually implemented as the ICAS (individual capital adequacy standards) regime.
However, the phrase ‘the devil is in the detail’ has never been so apt! Moving from a simple capital calculation formula to having to identify all the material risks taken on by a firm and quantify them to the extent that they represent a 1-in-200-year event in today’s risk environment was never going to be easy. Initially there was a lot of confusion as the market got to grips with the practical realities of the new regime. Some of the early issues were dealt with fairly quickly while others were addressed through the FSA’s bulletins, conferences, and, more recently, their consultation paper CP06/16.
But much still remains and is anticipated to continue to be debated until well after the implementation of Solvency II (the anticipated Europe-wide capital requirements, which are currently expected to be implemented in 2010-2011). One particular area of ambiguity relates to what time horizon should be used for the purposes of the individual capital assessment (ICA) which is the firm’s own assessment of their regulatory capital requirements. This is the area that we address in this article, illustrated using the results of a survey carried out for the recent GIRO conference.

Components
To consider the ambiguity surrounding time horizon, we first need to understand the main components of any capital calculation. These are the risk profile, the risk measure, and the risk tolerance (or appetite or confidence level).

Risk profile
A risk profile requires a risk definition such as the potential loss to retained earnings or statutory insolvency, together with the type of risks to be included and the quantification of them.
The FSA has not explicitly stipulated the risk definition to use for regulatory capital purposes, although implicitly they have stated that it is in relation to ensuring ‘policyholder liabilities are met as and when they fall due’. Solvency II is likely to be clearer on risk definition due to its clear linkage with the accounting basis (IFRS). On the other hand, the FSA has stipulated what types of risk should be considered, often referred to as the Prudential Sourcebook risk categories (ie insurance risk, credit risk, market risk, group risk, operational risk, and liquidity risk). However, a common mistake is to assume that these risks are well defined and therefore to focus on quantifying the risks instead. In fact, some of the more fundamental issues yet to be resolved are in relation to risk identification rather than quantification.
For example, from a time horizon viewpoint the main questions relate to the extent to which the following risks should be included within the ICA:
– risks emanating from writing new business (eg the underwriting cycle); and
– risks associated with the potential run-off of the business (eg reserve volatility).
These risks should be an important determinate of the methodology and assumptions used to quantify them (eg what is an appropriate projection period that reflects the full underlying risks in relation to reserve volatility?). However, the methodology and assumptions used in quantifying these risks are often influenced by perceived regulatory requirements rather than through proper risk identification.

Risk measure/risk tolerance
Risk measure and tolerance answer the question ‘What capital do we need, given a certain risk profile?’ In the case of ICA, the risk measure is value-at-risk and the risk tolerance is 99.5%, or something comparable.

What do we mean by time horizon?
From the above analysis of the components of a capital calculation, time horizon is clearly a feature of the risk profile alone. More specifically, it relates to risk identification, rather than quantification, and the extent to which risks emanating from new business or run-off are taken into account within the capital calculation.
The extent to which such time horizon-related risks should be included is a matter of perspective. From a regulatory standpoint any risks that may affect the ability to pay policyholder liabilities as they fall due need to be considered. Although this may not be aligned with the corporate perspective, the capital framework should be flexible enough to allow for such differences and in doing so embed the ICA within the business, as originally envisaged by the regulators in Canary Wharf and in future also from those in Brussels.

The time horizon survey
The survey carried out for the recent GIRO conference was aimed at establishing whether there was any market consensus regarding those aspects of risk identification relating to time horizon. The survey collected information relating to the methodology and assumptions used in quantifying time horizon risks rather than the extent to which they were taken into account. This was partly due to the practicalities of collecting the information, but also to facilitate capital comparisons. Risk tolerance information was also collected to further assess the degree of consistency across the market.

Participation
153 responses were received, although only 65 had sufficient information to be used for our analysis (perhaps supporting our previous comments relating to the focus being on quantification rather than identification). There was no overall bias in respondents to any one sector. In fact, the responses were evenly split between the London (including Lloyd’s) market, the UK company market, international firms, and other firms, which consisted mainly of consultants.

Results
The main results from the survey were as follows:
1 New business period No consensus: 33% one year, 23% three years, 27% five years, 17% other
2 Projection period No consensus: Approx. 40% apply a projection period of more than 5 years
3 Recognition of ultimate losses No consensus: 45% recognise deteriorations over time, while 55% recognise the deterioration to ultimate immediately
4 Risk tolerance No consensus: 55% state confidence level is a function of the projection period whereas 45% state it is a function of the new business period.
5 Run-off basis Broad consensus: Approx 70% assume going-concern
Although some of the above differences will be due to firm-specific features (eg types of business written), we believe there is still overwhelming evidence that there is no consensus within the general insurance market on a number of crucial time horizon issues. The one area where there was broad market consensus was in relation to a going-concern rather than a run-off basis. Interestingly the proposals set out in CP06/16 relate to a run-off basis.

Financial Impact
A fictitious firm was considered with its ICA dependent upon some of the questions from the survey (see table 1 across). To calculate the ICA we assumed some other generic assumptions (eg underwriting risk only, expected profitability, correlations between years).
The range of answers from the survey produced a range of ICAs for our fictitious company, based upon the underlying generic assumptions. Figure 1 shows the range of ICAs produced and the frequency with which participants used the associated time horizon methodology, assumptions, and risk tolerance.
The lowest ICA in figure 1 related to one year of new business, ultimate losses developed over time, one-year projection period, ongoing basis, and a 99.5% risk tolerance. The most common ICA approach applied five years of new business, ultimate losses recognised over time, five-year projection period, ongoing basis, and a 97.5% risk tolerance.
The wide variation in ICAs as a result of differences in time horizon methodology, assumptions and risk tolerances is highly dependent on our underlying generic assumptions. However, we believe this analysis is still indicative of substantive differences in risk profiles across the market, as a consequence of the treatment of time horizon risks and the potential lack of focus on risk identification.

Closing comments
It is expected that firms will have different risk profiles, but large differences in regulatory capital due to subtle differences in the treatment of time horizon risks is a cause for concern. Arguably the risk tolerance should be amended to take into account such differences in order to maintain a degree of consistency across the market.
So how do we adjust the risk tolerance to take into account differences in the risk profile due to time horizon risks? The additional flexibility of a firm-specific capital calculation brings potential benefits (eg potential for lower capital requirements for firms and better risk management). However, it also places greater demands on both firms who have to produce an ICA and the regulator who tries to ensure consistency. At a time when the framework for Solvency II is being devised, the authors believe further debate on issues such as the time horizon conundrum is needed now to ensure that the benefits of the new capital regime can be maximised.

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