27 July 2009

Published in: ALM

How replicating portfolios can reduce your model run time

There are challenges to making this approach work but the effort can be worth it, explains Vanessa Leung.

With the Solvency II framework directive now in place, insurers are doubling their efforts to prepare for this new regime. For many companies, in particular the larger insurers, this presents an opportunity to align their regulatory models with their internal capital models and risk management systems. While some insurers began their review process early on, for most companies, there is still a significant gap between the current capabilities and what will be required when Solvency II comes into effect in October 2012.

Use Test

Under the new regime, an internal model is expected to satisfy several tests relating to the use, statistical quality, documentation, calibration, validation and profit and loss attribution of the model and results. For most insurers, one of the biggest challenges will be meeting the use test, where they would need to demonstrate that the model is widely used in day-to-day management decisions and plays an important role in risk management and capital assessment and allocation. Any model will therefore not only need to meet regulatory requirements but will also be a platform to aid strategic decision-making.

The most common failure of current systems and models is not being able to produce aggregate risk information sufficiently quickly and accurately to support day-to-day decisionmaking. Systems are often too inflexible to allow investigations into a wide range of possible economic scenarios, which hinders risk monitoring and analysis. It is also common practice for insurers to maintain different models which cover different functions for the same business. This could potentially lead to inconsistencies and introduce further complications in aggregation, delaying the production of the necessary information. All these are areas which insurers are looking to address in order to satisfy the use test under the internal model approval process.

Replicating portfolios

To address some of the above issues, speeding up the models is essential if insurers want to produce faster, more accurate and reliable results.

One of the more immediate techniques to reduce model run time is the use of replicating portfolios. A replicating portfolio is a portfolio of financial instruments chosen to match a portfolio of insurance liabilities as closely as possible. The replicating portfolio, once derived, can act as a proxy for the insurance liabilities - for rapid revaluation in risk monitoring, capital calculations, performance measurement and even just interpreting the liabilities.

As liability values can be updated more or less instantaneously for changes in economic conditions, insurers will be able to

• update and monitor their available capital position and capital requirements frequently, making it practical to monitor the solvency position in real-time
• generate the market risk section of risk dashboards in a short space of time
• produce stochastic distributions of the liabilities, available capital and capital requirements in a practical way and
• investigate a range of economic scenarios within a short period of time.

Challenges in deriving a replicating portfolio

The benefits of replicating portfolios are clear, but successful application is dependent on being able to derive a robust replicating portfolio for the liabilities and this is not always straightforward. Insurers should recognize that judgement and experience will be required and some of these areas are highlighted below.

The set of financial instruments available The approach essentially involves using statistical optimization methods to find the set of financial instruments which fit the liabilities "best" according to defined fitting criteria. However good the optimization method, the quality of fit will depend on the extent to which the liabilities can be reproduced by the pool of candidate instruments available in the optimization approach. A better fit can often be obtained by including instruments that are not available in the market-place. Deriving synthetic instruments to represent the behaviour of the liabilities requires insight into the nature of insurance liabilities.

Successful application is dependent on being able to derive a robust replicating portfolio for the liabilities and this is not always straightforward. 

Choice of economic scenarios A replicating portfolio intended to track the balance sheet may normally only be required to produce liability values under "typical" market movements. In contrast, if the company is interested in an extreme scenario for capital calculation and management, this would require replicating liability values under extreme market movements. There are practical issues in producing a replicating portfolio which fits well under both moderate and extreme market movements. The economic scenarios used in the fitting process should take into account the range of market sensitivities which the replicating portfolio will be expected to be applied to.

Fitting measure and optimization method The optimization algorithm should also be able to avoid the issue of overfitting, i.e. a replicating portfolio that closely matches the behaviour of the economic scenarios used in the fitting but has no forecasting ability. A typical pitfall is to allow the replicating portfolio to include too high a number of financial instruments compared to the number of economic scenarios fitted.

Careful consideration in each of these areas would maximise the insurer's chances of generating a replicating portfolio which is a good fit and gain insight into the behaviour of the liabilities.

Other practical issues

In practice, there can be other implementation issues to overcome before this technique can be put into the day-to-day operation of the company.

Keeping the replicating portfolio up-to-date Adjustments will be required to allow for the non-economic experience differing from that originally assumed together with the general runoff of the liabilities (or new business). Changes to the asset allocation can change the cashflow profile and hence the replicating portfolio. Both of these factors can lead to replicating portfolios having a relatively short "shelf-life" and in practice replicating portfolios tend to be refitted regularly.

Robustness and audit Insurers need to gain confidence in the replicating portfolio by comparing the value of replicating portfolio under a range of market sensitivities with that produced by their actuarial models. This is a necessary and important part of the exercise not only to allow the company to be confident that the management information produced by using the replicating portfolio is as accurate as required, but also to satisfy audit requirements of an internal capital model.

Deriving synthetic instruments to represent the behaviour of the liabilities requires insight into the nature of insurance liabilities. 

Implementation issues As with the implementation of any system, there are more general practical issues which should be considered. To roll this method out across business units, consideration should be given to whether the business units should take ownership in producing the replicating portfolio or whether this is the responsibility of its group central function. Insurers may want to take advantage of the business unit's detailed knowledge of their own products, but might want to set out some criteria for fitting in order to achieve consistency across the business units. Carrying out a pilot study on a couple of business units could be useful in ironing out some initial concerns and practical issues.

Although the time required for full integration of such a technique will vary between companies, most insurers will be able to benefit from some level of implementation in a matter of a few months.

Achieving best practice

Finding a replicating portfolio with a good fit to the liabilities is not guaranteed and success in the implementation for one set of liabilities does not guarantee success for another. Achieving a good fit is something of an art as well as a science, and significantly better results can be attained by applying the knowledge of the liabilities, the purposes to which the replicating portfolio will be put and flexibility in the fitting.

With Solvency II looming, this is a natural time for insurers to review the adequacy of their systems and processes. Insurers are looking for innovative ways to meet the challenging requirements under the new regime. This is an opportunity for insurers to embrace the new replicating portfolio technique, not only to satisfy forthcoming regulatory requirements but also to move towards best practice in risk management.

Vanessa Leung is a consultant, insurance and financial services, at Watson Wyatt Worldwide in the UK.

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