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The Actuary The magazine of the Institute & Faculty of Actuaries
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Sessional meeting: With-profits business

The paper discussed at the meeting was ‘Measuring and managing the economic risks and costs of with-profits business’.
In the paper, the authors, John Hibbert and Craig Turnbull, look at a single conventional with-profits policy, with guarantees borne by the office. Sections 2 and 3 provide a basis for calculating the fair value of guarantees under the specimen policy, covering both the calibration of a market-consistent asset model, and a set of decision rules for bonuses, equity backing ratio, and policyholder behaviour. Within this context the sensitivity to these dynamic rules about the behaviour of the liability is notable (the fair value of the guarantee almost doubles if the office’s bonus and investment policies are fixed).
The paper moves on from this now reasonably familiar territory to consider ways of managing the guarantee costs. Different investment strategies are compared in terms of the distribution of fair value guarantee profit. Guarantee profit is defined as the change in value of assets backing the guarantee, less change in value of guarantees over the following year.
One approach is to construct a delta hedge, based on the sensitivity of guarantees to asset share. This results in a short position in the asset mix of the asset share (falls in asset share increase guarantee costs), and a long position in the risk-free asset. The delta required is substantially reduced by the office’s discretion to reduce bonuses or change investment policy. This hedge portfolio is compared against holding the assets backing the guarantee in cash, or in the asset share mix. If the assets backing the guarantee are invested:
– in cash then the asset proceeds are fixed. The volatility of guarantee profits is simply the volatility of the fair value of guarantees;
– in the asset share this gives increased volatility as the backing assets fall/rise in value in the same circumstances as the guarantee costs rise/fall.
– in the hedge portfolio the volatility of guarantee profits is significantly reduced.
The hedge’s effectiveness in part results from simplifying assumptions. The paper considers relaxing one of these it varies the year-end equity volatility used to value guarantees. To manage the risk of equity volatility increasing, two additional strategies are introduced using (theoretical) OTC derivatives:
– purchasing a put option;
– a collar formed by purchasing a (different) put option and selling a call option with a higher strike price.
The collar appears to be more effective in reducing the volatility of fair value guarantee profit.
The paper concludes with a simple demonstration of possible implications for capital requirements. It takes a hypothetical capital requirement as sufficient to give a 99% probability of meeting the realistic value of guarantees after one year. It demonstrates a significant reduction in capital requirement under this measure if hedged.
At the meeting John Hibbert gave only an overview of the themes in the paper to maximise the time available for discussion. He stated the reasons why these concepts were being explored as being a combination of the experience of recent years, research leading to the ‘technology’ becoming available, and the direction of regulatory thinking. The aim of producing the paper was to explore the links between realistic valuation of guarantees, strategies to reduce exposure, and implications for capital requirements.
He concluded by listing the key challenges, many of which were commented on by subsequent speakers:
– product ‘rules’;
– calibration;
– best-practice risk-management systems;
– communication of results.
Discussion
The discussion was a fairly general one on risk management and capital implications for with-profits, without many specific references to the paper’s approach. A number of speakers admitted to not having made it to the end of the paper. Jeremy Goford spent some time disagreeing with statements in paragraph 1.1.1 but assured the audience he had read beyond this and was impressed with the rest of the content.
In relation to possible (risk-based) capital requirements, a key question is whether calculations will be over one year or the lifetime of the liabilities. The theoretical capital requirement in the paper uses a one-year approach (which is a natural way to present conclusions of a paper looking at hedges over one year). The one-year framework is well established in the banking industry, where it is clearly appropriate because banks can (and do) lay off risks. One speaker expressed concern over whether the one-year approach was appropriate or justifiable for insurers. This led to some discussion as to whether insurers tend to retain risk, even where it is possible to hedge.
Communication of investment policy to policyholders could be a challenge if guarantees are more actively managed.
There was a high degree of support for the practical approach adopted by the authors. It was acknowledged that the paper considered a very simple example, and that some difficult areas would need to be considered: for example, the lack of long-term options on equities, options on property, tax, transaction costs, counterparty risks, mortality variation, and decision rules such as the speed with which management would reduce bonuses.
As a result of changes to accounting standards and prudential regulation, many actuaries are involved in establishing how to measure market-consistent liabilities for with-profits funds. This paper is a welcome introduction to managing a business in this environment.

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