**David Forfar discusses the build-up and use of a with-profits estate, in line with regulatory principles**

*"Unless a hedging strategy can be followed, at least approximately, and the necessary instruments are available, the mathematical methods for calculating option values may be interesting but are of no practical application." *British Actuarial Journal, 11, p312.

The Financial Services Authority's (FSA) Treating Customers Fairly (TCF) principle is: "A firm must pay due regard to the interests of customers and treat them fairly" and the Conflicts of Interest (CofI) principle is: "A firm must manage conflicts of interest fairly, both between itself and its customers and between a customer and another client" (FSA Handbook, PRIN 2.1.1). The FSA is quoted in Money Management (January 2008) as saying that there will be "serious consequences" for life offices if the TCF principle is not observed.

A with-profits estate (the inherited estate is the expression used to describe surplus assets in the with-profits fund) is typically built up from transfers of small charges on the premiums from existing and matured with-profits policies (or from their maturity pay-outs) and from surpluses on non-profit business. With-profits contracts are not pure investment contracts, like unit trusts, but contain important financial guarantees. If policyholders with different types of financial guarantee are all to be treated fairly and the conflict of interest between shareholders, existing and new policyholders is to be managed fairly, then an estate is necessary. The estate should be commensurate with the size of the financial guarantee which is unhedged or unhedgeable owing to the 'incompleteness' of the market (the so-called 'naked' part).

**An estate needs to be internal to the with-profits fund**

It is becoming clear that the managers of shareholder companies are reluctant to use shareholder equity external to the with-profits fund (for example, the shareholder/ non-profit fund) for meeting financial guarantees/options or for smoothing (holding back some of the profits made by the fund in good years and using them to pay out more in poorer years). This is because of the conflict of interest between shareholders and policyholders, namely:

>> It damages shareholder equity and the share price if shareholder equity external to the with-profits fund has to be transferred into the with-profits fund

>> The shareholder can only take 11.11% of declared bonuses out of the with-profits fund

>> If the shareholder makes a loan to the with-profits fund, he/she may never receive the loan back

>> The shareholder may wish to move money from shareholder equity in the subsidiary, to the parent company.

**An estate is required to meet the TCF principle**

This need for an estate, if the FSA's TCF principle is to be observed, was illustrated by a letter to Money Management in 2004. A correspondent wrote about the practice of a major life office with regard to the financial guarantee on its with-profits endowments. The guarantee was that the maturity value would not be less than the sum assured increased by contractual bonuses.

The correspondent maintained that the practice was not meeting the FSA's TCF principle since, if the guarantee 'bit', the money required would have to be taken from other customers' unsmoothed asset-shares and this would be unfair. Asset-share means the premiums, less expenses and charge paid to the estate, at the investment return achieved. The with-profits office wrote back that this was not so, as the money required if the guarantee bit, would be taken from the estate and this would not be unfair to those policies where the financial guarantee did not bite.

**Regulatory principle of reserving for financial guarantees/options, size of estate and stochastic modelling**

Stochastic projection takes account of the bond/equity distribution of the fund and provides a distribution for the difference between projected liabilities and corresponding asset-shares. It shows the size of the 'upper tail' (a measure of VAR) and the degree to which the guarantees are naked.

A premium charge (or charge at maturity), reflecting the expected cost of the financial guarantee, will normally be based on the average cost of many future scenarios. It is an FSA requirement that financial guarantees/ options are valued but the FSA valuation meets only the average of the distribution of liabilities (para. 176 http://fsahandbook.info/FSA/html/ handbook/INSPRU/1/3). As guarantees/options can, at best, only be partially hedged, that means that the asset-share will be insufficient in the financial circumstances of guarantees 'biting'. Then the estate will have to be relied upon to meet TCF requirements.

**Guaranteed Investment Return (GIR) example**

Take, for example, a with-profits contract for £50 per month, for a 20-year term, which invests 40%/60% in bonds/equities and, for simplicity, contractual bonus is nil. If the GIR is 95% of premiums rolled up at 3.5%, the 'guaranteed fund' is £16 423. The investment in bonds (95% of £20 per month at 7%, say) will only cover some 59% of the guaranteed fund. Thus the bonds, if their mean term equals the term of the policy, will only hedge part of the guaranteed fund leaving the aggregate investment in equities of £6840 (0.95 x 30 x 12 x 20) to cover the remaining £6733 (16 423 x 0.41), the naked guarantee.

A 'market consistent' valuation may use option pricing methodology but this assumes the guarantee/option is, or can be, hedged. This is not the case for a long-term naked guarantee/ option (there are no instruments long enough) so the upper tail of the liability distribution has to be taken into account (and not only the average value). The naked guarantee might require, in this example, a charge of around 2% of the premium, with a standard deviation of 4%, to meet the guarantee. Therefore, a policyholders' estate of around 10% (taking two standard deviations above) may be adequate, giving a total estate of around 11% (10 / 0.8889) of corresponding liabilities.

**GIR and Guaranteed Annuity Rates (GAR) example**

Take, for example, a 20-year single premium (of £4126) pension contract (retirement age 65), with a GIR specified as above, and a GAR of 11.11% and, for simplicity, the contractual bonus is again assumed nil. The guaranteed fund is £7800 and the 'guaranteed annuity' is £867 per annum (7800 x 0.1111) and, therefore, there are two guarantees. Assuming a bond/equity split of 50%, the bond component, if invested in long-term bonds yielding a little over 7%, would hedge the guaranteed annuity, excluding the increase in longevity. But the increase in longevity of 40% (from 15 to 21 years today) might mean that only an annuity of £715 per annum could be hedged.

**Type 1 GAR**

The initial equity component of £2063 might provide a maturity value of £7585 and an annuity of £568 per annum (assuming a GAR at 65 of 7.5%) giving an 'annuity payable' of £1283 per annum (715 + 568). Where the terminal bonus (TB) is calculated from the annuity payable, the TB takes account not only of the investment returns achieved but also of the current bond yields and longevity. Thus the (annuity-based) TB is 48% (1283 / 867 = 1.48).

This is equivalent to a Type 1 GAR, where the GAR only applies to the guaranteed fund to establish a guaranteed annuity of 'guaranteed fund x GAR' per annum. At policy maturity, these longer-term bonds might be worth £9521, plus equities worth £7585 giving a fund of £17 106 corresponding to an alternative open-market option (OMO) (See Income and Corporation Taxes Act 1988, 622(1) (a)) of £17 106 and an (OMO-based) TB of 119% (17 106 = 1283 / 0.075 and 17 106 / 7800 = 2.19).

As the example concerns a single premium contract, the two financial guarantees (they cannot bite at the same time) may cost the estate about the same as in the above monthly premium example. One or other of the guarantees may bite if 1) equity values fall 2) if interest rates fall or 3) if longevity increases, but an estate of some 10% should be able to cope, particularly if the life office moves into longer-term bonds as bond yields fall.

**Type 2 GAR**

If the terminal bonus is based purely on the investment returns achieved, and not also on the current bond yields and longevity, this guarantee is equivalent to a Type 2 GAR. In this case the GAR of 11.11% (or a fixed ratio, like 9:1) applies to the whole of the maturity value to establish an annuity payable of (guaranteed fund + terminal bonus) x GAR per annum. In the example, the annuity payable would be £1900 per annum (17 106 x 0.1111) and the (annuity-based) terminal bonus would be 119% (17 106 / 7800 = 2.19).

The OMO would be the value of the annuity payable, namely £25 333 (1900 / 0.075) corresponding to an (OMO-based) TB of 225% (25 333 / 7800 = 3.25). Long-term bonds (or swaptions) protect the guaranteed annuity if there is a fall in bond yields. There is currently no traded instrument that enables long-term equity risk, longevity risk (or retirement at any time between 60 and 70) to be hedged.

It is noted that the Type 2 GAR annuity payable is some 48% more than the Type 1 GAR annuity payable of £1283 per annum. A financial guarantee of a Type 2 GAR is, economically speaking, asking a life office for the nearly impossible, although required when approving the rules of pension schemes [the HMRC benefit rules are written in terms of an amount of pension thus, for a defined benefit scheme which also provides a cash benefit, a fixed ratio typically 9:1 at age 65 and equivalent to a GAR of 11.11% is required to convert the cash into an amount of pension, in order to obtain HMRC approval".

It requires the life office to invest simultaneously to provide whichever is the better value of: the cash maturity value of the contract; and the present value of annuity payable equal to the maturity value multiplied by the GAR rate. The maximum that could reasonably be charged for this guarantee is 10% of premiums but the actual cost, in this example, is 48% more than the policy's cash maturity value.

Thus a Type 2 GAR is a financial guarantee of quite a different order from a Type 1 GAR and demands an estate, depending on how much GAR business has been written, several times that in the above examples, if the TCF principle is to be observed.

**Ownership of the estate **The with-profits funds of major life offices are now closed to new business (Money Management, Nov 2007, p63). Their estate is thus being distributed as declared bonus to policyholders with the shareholders receiving, as of right, one-ninth (11.11%) of declared bonuses whether contractual or non-contractual. It is normally assumed that, because of this, the shareholder 'owns' 11.11%, and the policyholders 88.89%, of the estate. In the case of the few remaining offices where there is new with-profits business, the estate needs to be large enough to also cope fairly with any naked guarantees in the new business.

**New business and mis-selling **Writing new business at an uneconomic premium, particularly if it has naked guarantees, would require the capitalised value of the shortfall in premium to be met immediately by a transfer from the estate. This would seem to conflict with a charge, commensurate with the financial guarantees, being transferred to the estate by existing policyholders and would seem to conflict, in respect of new/existing policyholders with the CofI principle. Existing policyholders may feel they are not being treated fairly.

As any mis-selling of policies is arguably the fault of management, but not of policyholders, it would seem unfair, and a possible infringement of TCF and CofI, to take all of the cost of mis-selling claims from policyholders.

*David Forfar is a former appointed actuary of Scottish Widows and currently supervises MSc Projects at Heriot- Watt University.*