With-Profits: Reserving and Financial Economics (1987-2004)

Whilst an actuarial consensus on the uneconomical nature of capital guarantees as it pertained to unit-linked business had been established by 1981, this view would typically not extend to the capital guarantees provided under with-profit policies. With-profits business and its guarantees had some undoubtedly significant differences with unit-linked business and its maturity guarantees. In the context of the risks and costs to the life office of providing guarantees, linked and with-profit business had two differences of the utmost importance. First, the office had significant control over the investment strategy of the with-profit fund. If assets performed poorly, they could, in theory, be switched into bonds that matched the guarantees before the surplus funds were exhausted; second, in with-profits, the cost of the guarantees could be borne by other generations of policyholders (rather than the office or estate) through reductions in their future bonuses. If one generation of policyholders did not have accumulated asset values sufficient to meet the minimum guarantee attaching to their policy, this could be funded by reducing the bonuses that would be distributed to other policyholders. These broad powers of actuarial discretion provided risk management levers that could, in principle, substantially mitigate the financial market risks to the office that were created by with-profit guarantees.

Actuaries, and indeed the UK life office regulator, were therefore significantly more sanguine in the 1980s about with-profit guarantees than those found in their unit-linked cousins. There was no body of opinion advocating the extension of the stochastic modelling and probability of ruin approach developed for unit-linked maturity guarantee reserving—the ‘considerable expertise’ that Duncan Ferguson referred to—into the domain of with-profit reserving. This was partly because it would be viewed as unnecessary as the office did not have the same degree of risk exposure, and partly because it would be much harder to model the complexities of with-profit business and actually demonstrate that these risk management levers could be adequately operated by life office actuaries to manage the guarantee risks. This scepticism around the benefits of using stochastic modelling in the actuarial management of with-profit business is well-reflected by Frank Redington’s comments in 1976:

He [Redington] expressed uneasiness at leaning upon computers to answer these unanswerable questions. If there was a beam in the eye of the question, why worry about a mote in the eye of the answer? It was easy to fail on the back of an envelope as with a computer, but a great deal more instructive. This was a countryside to explore on foot and not by fast car.45

Some British life offices did develop and internally use stochastic ‘model offices’ in the 1980s and 1990s, but the application of stochastic models and probability of ruin approaches to British with-profit statutory reserving was deferred for over 20 years until the beginning of the twenty-first century. What about the use of option pricing theory in charging and reserving for with-profit guarantees? We saw above that the (unit-linked) Maturity Guarantees Working Party did not actively make use of option pricing theory in its work on the pricing, reserving and risk management of unit-linked guarantees. However, in the following years the British profession, and in particular David Wilkie, started to explore the potential applicability of option pricing in actuarial work. In 1987, Wilkie published a notable paper on the use of option pricing in the analysis of with-profit guarantees and bonuses with his Institute paper, ‘An Option Pricing Approach to Bonus Policy’.[1]

Wilkie showed that with-profit style pay-outs could be replicated by a mixture of investments in unit-linked funds and put option contracts. The recognition that with-profit guarantees could be considered as a form of put option was not remarkable and, as we saw above, this was first considered by Phelim Boyle some ten years earlier. Wilkie broke new ground, however, by considering how different reversionary bonus strategies could impact on the option costs associated with the guarantees. Wilkie also tentatively suggested that the cost of the options that correspond to the reversionary bonus strategy could be used as a reference point for a deduction from with-profit terminal bonuses as a form of charge for the provision of the guarantee (when the fund performance is good enough for a terminal bonus to be paid).

Wilkie’s approach resulted in relatively high estimates of the guarantee cost as it did not allow for the cost-mitigating with-profit features of office- controlled investment strategy or inter-generational cross-subsidy. A 20-year single-premium contract’s guarantee cost inclusive of reversionary bonuses was estimated to require a deduction from the final proceeds of the policy of, on average, around 15 % to 25 % across a range of stochastic scenarios.[2] It was, however, the natural first step in applying option pricing ideas to with- profit guarantee charging and Wilkie, now established as the British actuarial technical thought-leader of his generation, was the natural actuary to lead the way. The paper also helped to more generally introduce option pricing ideas to the actuarial profession. Collins’s excellent work back in 1982 was never presented at a Staple Inn sessional meeting, and before the presentation of Wilkie’s paper in June 1987, option pricing theory had never been discussed at an Institute sessional meeting. In opening the discussion of Wilkie’s paper, J.M. Maud started with the telling statement:

Until a few months ago I was almost entirely ignorant about option pricing theory. Having been introduced to the subject, I was astonished that a theory with so many obvious uses in actuarial work is so little known to many of us.48

However, British actuarial thinking on the use of option pricing theory in with-profits reserving and risk management lay largely dormant for the next decade. At the start of the 1990s, more pressing matters were at hand. The actuarial profession and its practices in the with-profits sector were under scrutiny like never before. Similar to the experience with unit-linked maturity products 20 years earlier, there was a sense that actuarial methods were failing to keep up with a changing world. With-profit products were under great competitive pressure from the alternative investment vehicles of asset managers and banks. Life offices had evolved their with-profit offerings to compete: ‘conventional’ regular premium with-profit business was on the wane, and was being superseded by ‘unitised’ with-profits, which was a more flexible, recurrent single premium product design. The net premium valuation method was obviously less applicable to the solvency assessment of single premium products, and, in any case, there was concern amongst actuaries at the start of the 1990s that the net premium statutory valuation requirements had become unreasonably stringent.

There was also increasing regulatory pressure to take explicit consideration of Policyholders’ Reasonable Expectations (PRE) in the management of with- profits, and for these considerations to be reflected in with-profit reserving methods. This was not easy in the net premium valuation method, where no explicit allowance was made for the future bonuses that policyholders could reasonable expect to receive. Meanwhile, Canada and Australia had recently enacted new solvency methods that dispensed with net premium valuations. These changes were largely driven by pressure from accounting standard setters to produce valuations that could conform to generally accepted accounting principles. Working parties were established by the Institute and Faculty in 1993 to investigate a modernisation of with-profit reserving methods. This started a process that meandered for a decade as actuarial leaders tried to reconcile their traditional methods and training with the demands of a fastchanging external environment.

One of the first deliverables from this process was the 1996 paper by a working party, led by EG. Scott, which had been established with the remit to investigate alternatives to the net premium valuation for statutory solvency assessment.[3] This paper proposed two fundamental changes to the statutory solvency valuation method for with-profit business: the net premium valuation should be replaced with a gross premium bonus reserve valuation (which should include future reversionary bonuses but not terminal bonuses); and a second value should also be reported, which was intended to be a measure of the ‘realistic’ value of the policy having reference to policyholders’ reasonable expectations (and which was loosely interpreted as the policyholder’s asset share, i.e. the accumulated value of their invested premiums).

The arguments presented in the paper and the profession’s discussion of them rather resembled the actuarial discussions of the late nineteenth century. Net premium liability valuations taken alongside asset market values produced spurious variation in free assets; it did not have regard to the reasonable (bonus) expectations of policyholders; but if a gross premium bonus reserve valuation was used, what level of future bonus should be reserved for? And why did the working party recommend reserving for future reversionary bonuses but not terminal bonuses? (A certain logic for this position existed. European Union legislation required the liabilities to be discounted based on the yield of the assets backing the liabilities. The working party argued that in the scenario that equities did not generate any capital growth, no terminal bonuses would be paid, and hence they could be ignored in a statutory valuation that only took account of equity dividend yields.)

Risk margins were incorporated into the valuation under both the net premium method then in place and in the gross premium approach proposed by Scott’s working party, but there was no rigorous basis for determining what these margins should be. There was no underlying concept of what level of security the solvency valuation should aim to deliver—there was no probability- of-ruin objective. Furthermore, there was no consideration of option pricing ideas or how financial market risk could be managed in with-profits and how reserving methods could be aligned with risk mitigation (i.e. risk-based).

The two key recommendations of the Scott working party—that the net premium valuation be replaced by a gross premium bonus reserve valuation for conventional with-profits, and that a second valuation be submitted that reflected the terminal bonus expectations of policyholders—were broadly rejected by the actuarial profession. So another working party was established in 1996 with terms of reference to determine whether the ideas put forward by Scott could be developed into something better. This new working party, led by P.W. Wright, published a paper reporting their findings in 1998.[4]

It rejected the key recommendations of the Scott working party and recommended that the net premium method be retained for conventional with- profits. However, part of their reasoning for this recommendation was not that the Scott working party’s findings were necessarily flawed, but rather that conventional with-profits business was now being written in such low volumes that a major change in its valuation method was hard to justify. As Frankland put it at the Institute discussion:

At the start of this century prophetic actuaries spoke of the 20th century being that in which a replacement would finally be found for the net premium valuation method. Today’s prophets appear to accept that, within a decade, the replacement of the net premium valuation method for conventional with-profits business will cease to be a matter of materiality in the valuation of a with-profits life office.51

Like the Scott working party, the Wright working party recognised that solvency and PRE must be taken into account in reserving for unitised with- profits business. But unlike Scott, the Wright working party advocated achieving this through a single reserving figure which would be somewhat akin to the greater of the two calculations suggested by Scott. The first would be a ‘bonus reserve test’ which would be the present value of guaranteed maturity values. Like in the with-profit regulations of the time, this present value would be calculated in a ‘resilience’ scenario that featured a prescribed series of stresses to assumptions. This scenario was not explicitly assessed using stochastic models and probabilities of ruin as per the unit-linked maturity guarantee reserving practices, but its intention was fundamentally similar (the effect was not so severe because the tests were weaker than the tails produced by the stochastic equity modelling of the Maturity Guarantees Working Party and because asset allocations were less risky for with-profit business). The important point that the Wright working party advanced was that it was not sufficient for this reserve to be based only on the current level of the guarantee—some explicit allowance must be made for future reversionary bonuses that would be consistent with PRE. The allowance should be consistent with the reversionary bonuses that would be paid in the circumstances assumed in the statutory valuation basis (including those used in the resilience test). Like the Scott working party, the Wright working party argued that no allowance should be made for terminal bonus in this leg of the calculation (this was a principle that was much cherished by British life offices and its actuaries and that was only permitted in EU legislation after a great deal of political horse-trading).

The second leg of the reserving calculation was the surrender value of the policy that was consistent with PRE. This would generally be closely related to the asset share of the policy (i.e. the accumulated value of the premiums at experienced investment return, net of charges and expenses). A requirement for the reserve for a with-profit policy to have a floor that was equal to or close to asset share implied that the policy could not provide substantial capital support to the business, even when the level of guarantee was very low. PRE implied that terminal bonuses had to be reserved for after all—even if it was only the terminal bonus that had ‘accrued’ within current surrender values. The Institute discussion of these proposals was very mixed. To some, the principle of reserving for terminal bonus was anathema, and they argued that PRE did not mean a ‘guarantee’ of a surrender value that was closely related to the policy’s asset share. To others, the proposals were merely a codification of then-prevailing best practices. But whether they liked it or not, some 40 years after the first terminal bonuses were paid on British with-profit policies, it appeared inevitable that regulatory pressure on the explicit treatment of PRE would result in their inclusion in statutory solvency assessment.

During this episode of statutory reserving navel-gazing and prevarication, there was very little research published by the profession on the application of option pricing concepts to reserving or charging for with-profit guarantees. That changed, however, in the late 1990s. Over the period between 1997 and 2004 several important papers were published on this topic. By the mid- 1990s, the profession’s internal debates on if and how to use financial economic ideas had become increasingly strained and adversarial. This perhaps reflected a more general malaise that was impacting on the profession and its traditional areas of focus. Actuaries were facing an unprecedented degree of scrutiny from others in the financial, regulatory and even legal sectors. Financial economics was increasingly being viewed by some actuaries as a threat to their core doctrines rather than as a tool they could utilise. Criticism emerged, especially in the pensions field (discussed below in Chap. 6), that suggested some actuarial struggles were arising from their economic illiteracy. Some actuarial ‘traditionalists’ now rejected financial economic thinking, not on the grounds that it was a nice theory with no practical utility (Corby and Nowell’s position), or because it needed to be considered more thoroughly in order to make use of it (Collins and Wilkie’s position), but because it was simply wrong and ought to be wholly rejected.

This latter view was the position of Robert Clarkson, who made his arguments in a Journal paper, An Actuarial Theory of Option Pricing’, published in 1997.[5] This paper must surely rank highly on the list of the most eccentric papers ever published by an actuarial journal. Clarkson took the reader on a journey that pondered the ideas of many great thinkers such as Einstein, Keynes, Bernoulli, Newton, Adam Smith, Mandelbrot, Halley, Hayek and himself before concluding that ‘we have to abandon this [Black-Scholes] methodology completely’[6] and ‘it seems unscientific in the extreme not to conclude that a completely new paradigm of option pricing is urgently required’.[7] This rejection was based on the argument that ‘its formal mathematical derivation is completely detached from reality’.[8]

He rejected the most basic and general insights of well-established option pricing theory. He argued that it was ‘commonsense’ that a call (put) option price must increase (decrease) with the expected return on the underlying asset.[9] This whimsical rejection of the risk-neutral valuation concept would have been plausibly breathtaking to other financial professionals. Clarkson proposed a ‘new approach’ to option pricing. But it was fundamentally the same one that had been advocated for unit-linked maturity guarantee pricing back in the 1970s by Benjamin and Wilkie: calculate the guarantee price as the real-world expected cashflow, discounted at a rate consistent with a static asset mix, and add a loading for the cost of the capital that would be required to support the risk associated with the (unhedged) option. Clarkson also argued that financial markets exhibit ‘systematic over-reaction’ and that the expected cashflows and capital should therefore be calculated on the basis of a mean-reverting stochastic process, which again was consistent with the Maturity Guarantees Working Party. Beyond the hyperbole, his proposed grand new idea was not new at all. If anything, it was an anachronism. It failed to produce prices consistent with put-call parity—the most basic (and model-independent) fundamental property of put and call option pricing. Clarkson did have many sensible practical observations to make, and his general critique of the limitations of economic theory to practical financial practice was not without some basis, but his overall position was so extreme and out-of-touch with the modern financial sector that it was an embarrassing reflection on the British actuarial profession that it provided a platform for such views in the late 1990s.

The Faculty discussion of the paper highlighted that by this point in time an impressive generation of younger British actuaries such as Kemp, Cairns, Exley, Smith, Mehta, Macdonald, Speed and Bowie had emerged who had independently developed expertise in financial economics and who worried that the British actuarial profession was dangerously behind other financial professionals in their positive utilisation of these ideas. Bowie gave a particularly impassioned speech where he argued that ‘it is nothing short of misplaced arrogance to repudiate a perfectly respectable and successful science on the basis of a criticism [use of abstract or unrealistic models] to which our own profession is also subject’.[10] This ultimately bode well for the ‘catching- up’ that the profession would go on to undertake in the 2000s.

In the late 1990s with-profit funds were experiencing a period of difficult publicity that required life offices and the actuarial profession to be clearer about how the product worked and, in particular, which policyholders were paying for what. Improving the transparency around guarantee costs and how they were charged for was increasingly another important factor—along with PRE and financial reporting requirements—driving change in actuarial methods in with-profits. As an appointed actuary commented at an Institute sessional meeting in April 2000:

Recent events, including guaranteed annuity options, potential mortgage endowment shortfalls, and a public suspicion that life offices have “squirreled away” policyholder money over the years in the form of orphan estates, have made the public and consumer press less inclined to trust life companies and the “black box” processes of the traditional with-profits fund.[11]

A flurry of papers was produced between 1999 and 2004 that significantly enhanced the actuarial profession’s thinking on the application of option pricing ideas to the assessment of the costs and risks associated with with- profit guarantees. These papers provided new insights into potential transparent guarantee charging and risk management approaches for with-profits. The first of these papers, A Market-Based Approach to Pricing With-Profit Guarantees’,[12] was published in 1999 by the Faculty of Actuaries’ Bonus and Valuation Research Group. The group was led by David Hare, who would go on to become President of the Institute and Faculty in 2013. The paper can be viewed as a natural, if somewhat belated, development of Wilkie’s 1987

with-profits and options paper and the 1980 Maturity Guarantees Working Party paper. The British actuarial profession’s 1990s issues with quantitative techniques and financial economics were referred to by Hare in his introduction of the paper at the Faculty sessional meeting: ‘Mention of the word “stochastic” can cause some actuarial eyes to glaze over, and the inclusion of equations like the Black-Scholes pricing formula can prove major deterrents to a wide readership of a paper’.60

The Hare paper applied the Maturity Guarantees Working Party’s approach to reserving for guarantees—a probability-of-ruin approach using a 1 % probability and a stochastic equity model with mean-reverting properties—to determine the reserves required for with-profit guarantees at various durations and with various levels of equity backing ratio (which were assumed to be static). Unsurprisingly given the similarity in methodology, these results were consistent with the Maturity Guarantees Working Party results. The paper also considered a guarantee charging approach that had two components: the expected (real-world) guarantee shortfall plus a loading for the cost associated with the capital that would need to be held to maintain a 1 % probability of ruin. As discussed above, this was consistent with the 1970s thinking of Benjamin and Wilkie, and also with the more recent writings of Clarkson. The paper then went on to also consider a ‘market-based’ approach to pricing the guarantee. That is, put options (and their market prices) were used to match the guarantees (for a given equity asset allocation). They introduced an interesting wrinkle to the use of options—they argued that in order to compare with the capital-based approach, the strategy should not pay out on guarantee shortfalls beyond the 1 % probability of ruin level, and so the strategy involved a put spread where the office sold a put option with a strike at the equity index value at the 1 % probability of ruin level. They concluded that the two approaches to pricing the guarantees produced broadly comparable results (though this would naturally be a function of subjective parameter choices for the expected-shortfall-plus-cost-of-capital-loading approach). Like in the Wilkie 1987 paper, these with-profit guarantee costs were generally higher than was intuitive to with-profit actuaries because it made no allowance for the cost-mitigation levers that were available to the with-profit actuary (such as reducing the fund’s equity asset allocation level when surplus assets were eroded).

At the start of the 2000s, significant changes in global insurance financial reporting and UK insurance regulation were afoot. In 1997, the International Accounting Standards Board started work on developing a new accounting standard for insurance. In the following years its intention became clear: the principle driving the Standard would be that a balance sheet-driven approach should be used for insurance firms’ financial reporting; profit should be measured as the change in the value of assets and liabilities; and those valuations should be done at fair value (which, for deep and liquid markets, meant market value). The Faculty and Institute Life Board established a working party in 1999 to consider what a ‘fair value’ approach to asset and liability valuation ‘might offer for the development of an improved approach to reporting for prudential supervisory purposes’.[13] The terms of reference of the working party provided the motivation:

It is recognised that the existing methods of actuarial valuation for long-term

insurance, particularly for supervisory purposes, are inadequate for their purpose under certain circumstances and economic conditions.

This would be the third actuarial working party in ten years to make an attempt at improving actuarial methods for life office statutory reserving. It would be easy to suspect it was a task that was beyond the profession. But this time was rather different: now the profession merely had to follow the lead given to it from outside. Historically, financial reporting was based on adjustments to the actuary’s statutory solvency valuations (the ‘modified statutory basis’). Now the roles would be reversed. Financial reporting standards would lead the specification of the profit reporting requirements, and the job at hand for the actuarial profession was to consider how these developments could help the profession make their necessary improvements in statutory valuations.

This Fair Value Working Party, chaired by C.J. Hairs, presented its findings at Institute and Faculty meetings in November 2001 and their paper was published in the British Actuarial Journal in 2002.[14] Its findings were fairly revolutionary in comparison to the progress of the Scott and Wright working parties. This working party supported the fair value approach to financial reporting. More fundamentally, it concluded that prudential solvency assessment should also be based on the fair value approach. They advocated a risk- based capital system for with-profits that made explicit use of probabilistic models and a defined probability of ruin; the ruin event could be defined not simply as failing to fund all liability cashflows as they fell due, but as fair value insolvency over some specified time horizon that should be related to the time taken to close out risk positions. They recognised that with-profit liabilities would require market-consistent stochastic models to estimate fair values, and these models would likely need to be complex in order to adequately capture management actions. There was no mention of net premium valuations.

All this was quite revolutionary and it is fascinating to see that relatively little dissension arose in the Faculty and Institute discussions of the paper. Thirty years after Benjamin’s aborted unit-linked maturity guarantee paper on stochastic reserving approaches, the actuarial profession had now come to accept that such principles should be implemented in with-profit funds, the traditionally undisputed home of actuarial judgement and discretion. But the profession was now dancing to someone else’s tune. The UK financial regulator, the Financial Services Authority (FSA), the International Association of Insurance Supervisors and the International Association of Actuaries had all recently suggested a move to a more risk-based capital system that could reduce the scale of regulatory arbitrage that prevailed between countries and between insurers and banks. The emerging New Basel Capital Accord for banks would use probabilistic models and even encouraged institutions to develop their own internal models for capital assessment.

Meanwhile, the UK’s FSA published consultations in 2002 and 2003 that would ultimately enshrine these concepts in the statutory solvency system.[15] It required market-based measures of with-profit liabilities and guarantee costs. Whilst the actuarial profession may have been fairly sanguine about its reserving methods for conventional with-profits business, the UK regulator was not. In particular, the regulator was concerned with ‘the risk that a firm using the net premium method might fail to keep enough reserves to meet a policyholder’s reasonable expectations that bonuses would increase (if markets improve, and asset values increase)’.[16] The FSA proposed a ‘twin peaks’ approach where the firm would need to hold the greater of two values: the net premium valuation currently undertaken in accordance with EU legislation; and a ‘realistic present value of expected future contractual liabilities plus projected fair discretionary bonus payments’.[16]

What did this ‘realistic present value’ imply? The first task was to codify the ‘projected discretionary bonus payments’ in a way consistent with PRE. For this, the with-profit fund would be required by the FSA to set out its with- profit bonus, smoothing and investment policies to policyholders in a document called ‘Principles and Practices of Financial Management’. The realistic present value had to be assessed using assumptions consistent with those documented policies. Once the pattern of these discretionary payments had been specified, they then needed to be valued. The consultations were unambiguous in their intentions in this regard: ‘For the purposes of valuing the contracts and the embedded options and guarantees ... the methods require market consistency i.e. the use of model assumptions, or option prices that replicate the costs of hedging such risks in the market’.[18]

The FSA was the first insurance regulator in the world to attempt to implement such a reserving method for complex long-term life business such as with-profits. But the initiative did not come completely out of the blue. It can be seen as the natural conclusion of a process, led from outside the actuarial profession, to put in place objective, transparent, measures of risk and capital in life business that reduced the reliance on actuarial judgement and discretion. An alignment of regulatory reserving methods with financial reporting standards was also an increasingly important driver (and was a prime motivation of the abandonment of the net premium valuation method in Canada and Australia). The FSA proposals aligned with emerging International Accounting Standards Board’s proposals around fair value accounting.

The FSA was also not intent on allowing any undue delay to the implementation of their radical proposals. For more than a decade, the British actuarial profession had prevaricated over reserving methods for with-profit business. The FSA’s proposals of 2002 and 2003, which were far more radical and created quite significant new intellectual and technological demands, were to be implemented in 2004. The actuarial profession had some work to do and three papers were published in the British Actuarial Journal in 2003 and 2004 that proposed how these market-consistent or realistic valuations of with-profit liabilities could be undertaken.[19] Up until this point in time, no stochastic methods had been used in with-profit statutory reserving. The FSA proposals didn’t merely try to bring with-profits reserving in line with unit-linked maturity guarantee reserving as was discussed by Hare et al. It went much further, defining a fundamental shift in how to quantify a reserving requirement—the reserving requirement was to be based on the 99.5th percentile of the one-year change in the fair value balance sheet rather than on a percentile of the ultimate cashflow shortfall that could emerge over the full run-off of the liability outgo (i.e. over 30 or 40 years or more). As Hibbert and Turnbull wrote in the introduction to their paper:

Actuarial philosophy towards the valuation of liabilities has traditionally been based on the notion of funding ... the funding approach will tell us what reserves are required to meet the liabilities [cashflows] with a given level of confidence. By contrast, the thinking behind the economic valuation of a liability is very different. The economic value is defined as the sum of money required to establish a portfolio of assets that — provided that they are invested in a particular way — will replicate the liability as closely as possible. This special portfolio is called the hedge portfolio.[20]

Smith and Sheldon’s introduction provides further background on the industry and regulatory context:

The introduction of the realistic balance sheet is, in part, a response to the difficulties that un-hedged guarantees have caused the life industry in recent years. Reliance on long-term solvency tests runs the risk that we overlook more imminent problems, compounded by the use of over-optimistic assumptions and models used to determine capital needs. While there has been some criticism of the transfer of banking techniques to life assurance, the rate of deterioration in life offices’ finances over the last three years demands a greater focus on the short term.[21]

Hibbert and Turnbull’s (2003) paper presented an approach to economic valuation of with-profit liabilities that could be viewed as an evolutionary next step beyond the approaches of Wilkie in 1987 and Hare et al. in 2000. As was noted above, the Wilkie and Hare papers did not attempt to identify how the unique features of with-profits—the forms of discretion that the life office has in managing the product—could impact on the assessed cost of with-profit guarantees. As a result, they produced counterintuitively high measures for the guarantee cost. This failing had become well-understood. The Fair Value Working Party’s 2002 paper had noted ‘stochastic models of with-profits funds often show alarmingly high ruin probabilities because of inadequate modelling of management actions in adverse scenarios’.[22]

Hibbert and Turnbull suggested that a stochastic simulation approach— with an asset model calibrated to observable market prices—could be used to fully capture the impact on guarantee costs of the with-profit fund’s ability to dynamically revise investment policy and bonus policy. Naturally, any results would be highly sensitive to the form that this dynamism was assumed to take, but this point had already been addressed by the FSA’s requirement for the ‘Principles and Practices of Financial Management’ documentation.

One of Hibbert and Turnbull’s points of emphasis was that the market- consistent valuation methodology could also be used to identify the hedging required in the estate to mitigate the risks left behind after the available (PRE-compliant) management actions had been implemented. Simulation modelling together with a codification of the with-profit funds’ actuarial management levers could allow the costs and risks of with-profit guarantees to be analysed like any other derivative contract, albeit a complex one.

The Hibbert and Turnbull case study results suggested that the economic cost of guarantees could be as much as halved by allowing for the life office’s ability to dynamically manage investment policy and bonus policy under assumptions that were typical of the time. Dullaway and Needlemans 2004 paper provided additional illustrative results of the impact on liability valuation of dynamic rules for the discretionary management features of with- profits business, again highlighting that these effects were material and could be captured by a simulation model.

The paper by Sheldon and Smith further discussed the technical challenges of market-consistent valuation of life business—particularly for the calibration of market-consistent asset models (choice of risk-free asset, extrapolation of implied volatilities, and so on). It highlighted the important point that market-consistent valuation of very long-term, complex liabilities could never be completely objective, even if that was the desire of the regulator. The paper also showed how some formulations of dynamic management actions could be captured in closed-form guarantee pricing formulae, thereby avoiding the need for the ‘brute-force’ method of Monte Carlo simulation.

Collectively, these three papers provided a technical grounding for the actuarial implementation of market-consistent valuation of long-term life assurance liabilities. Such techniques could be used in solvency reserving, guarantee pricing and hedging of the market risk created by the guarantees. The FSA’s 2004 timetable was successfully met. The use of market-consistent valuation as a basis for life assurance reserving went on to be adopted more widely—for example, in the European Union’s Solvency II system. The experience demonstrated that whilst the British actuarial profession had arguably lost its ability to be a master of its own destiny, it was capable of technical excellence in implementation when it was told what needed to be done.

  • [1] Wilkie (1987).
  • [2] Wilkie (1987), p. 55.
  • [3] Scott et al. (1996).
  • [4] Wright et al. (1998).
  • [5] Clarkson (1997).
  • [6] Clarkson (1997), p. 333.
  • [7] Clarkson (1997), p. 335.
  • [8] Clarkson (1997), p. 367.
  • [9] Clarkson (1997), p.335.
  • [10] Bowie, in Discussion, Clarkson (1997), p. 385.
  • [11] Saunders in Discussion, Hare et al. (2000), p. 722.
  • [12] Hare et al. (2000).
  • [13] Hare et al. (2000), p. 204.
  • [14] Hairs et al. (2002).
  • [15] Financial Services Authority (2002), Financial Services Authority (2003).
  • [16] Financial Services Authority (2003), p. 11.
  • [17] Financial Services Authority (2003), p. 11.
  • [18] Financial Services Authority (2003), p. 23.
  • [19] Hibbert and Turnbull (2003), Dullaway and Needleman (2004), Sheldon and Smith (2004).
  • [20] Hibbert and Turnbull (2003), p. 726.
  • [21] Sheldon and Smith (2004), p. 547.
  • [22] Hairs et al. (2002), p. 233.
 
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