247 ALLOCATION OF SURPLUS IN A MUTUAL LIFE OFFICE by€¦ · general problem of allocation of surplus in a mutual life office. 2. In approaching this subject it has been impossible

247

ALLOCATION OF SURPLUS IN A MUTUAL LIFE OFFICE

by A. N. CALDER, M.A., F.F.A.

and

A. D. SHEDDEN, B.Sc., F.F.A., F.S.A.

[Submitted to the Faculty on 16th November 1970. A synopsis of the paper will be found on page 302.]

INTRODUCTION

1. In a previous paper (T.P.A. vol. 30, p. 393) we examined how

one might make direct allowance for changes in capital value, in

allocating profits to W.P.* policyholders. It was observed in the

discussion of the paper that there was no mention of an estate in

the development we had outlined, although most British life offices

probably have substantial estates and also have profits arising from

N.P. business. However, as was then mentioned, it had been our

intention to write a paper on the general subject of allocation of

surplus, including profits from N.P. business. Having dealt in detail

in the previous paper with some of the technical problems of allowing

for changes in capital value, we consider in this paper the more

general problem of allocation of surplus in a mutual life office.

2. In approaching this subject it has been impossible to ignore the

changes in methods of surplus distribution that have taken place in

recent years. Since the previous paper was written, a large number

of offices have announced systems of special non-vested bonuses

payable on termination of a policy. In many cases these terminal

bonuses are available on surrender as well as on death or maturity

and must be regarded as an integral part of the bonus policies of

these offices. Such offices can no longer be said to be distributing

surplus allocated under a level reversionary bonus system. Under

what bonus system are they operating and what sort of valuation

system must be adopted to ensure that the security of these offices

will be maintained as soundly in the future as it has been in the past ?

Systems of terminal bonuses have arisen under the pressure of

dealing with profits from investment in equities which are far in

excess of what were envisaged when the W.P. premiums were origi-

* Throughout the paper the initials W.P. and N.P. are used to denote “ with profits ” and “ without profits ” respectively.

Richard Kwan

TFA 32 (1969-1971) 247-323

248 Allocation of Surplus in a

nally determined, and we have been particularly concerned, therefore,

with the role of the W.P. policyholders as equity investors. Since,

in our view, the N.P. business of a mutual life office can be regarded

as an equity investment of the W.P. policyholders, there seems to

be some common ground in the allocation of profits from equity

investments and the allocation of profits from N.P. business, and

this is the justification for considering both topics in the one paper.

We have not confined ourselves to these two topics, however, but

have attempted to deal with allocation of surplus in all its aspects.

In order to develop the paper in as general a fashion as possible we

have not presupposed any particular bonus system, and although our

illustrations are largely in respect of individual assurance policies

having reversionary bonuses, it has not been the intention to exclude

other types of W.P. contract from consideration.

3. The development of the paper is based on a definition of surplus

arising from the premise that the W.P. policyholders may be regarded

as the proprietors of a mutual life office. The conclusions reached

in the paper, therefore, are intended to be the logical outcome of

this premise.

We hope that no confusion will arise from the use of the word

“ surplus ” to mean something other than its usual connotation. It

might have been advisable to coin a different word for the occasion,

but no suitable alternative presented itself ; we have therefore

retained the use of the word “ surplus ” in this different sense and our

justification for this is that the usual definition of surplus, as will

be seen, is but a special case of the more general definition which

we have adopted.

We have relegated to the Appendices some material which illus-

trates or supplements the paper, but which is not essential to the

main themes. In addition there is a summary at the end of each

Part of the paper which provides a quick survey of the main points

and conclusions.

PART I

DEFINITION OF SURPLUS

The text book definition of surplus and estate

4. Fisher and Young, in their text book Actuarial Practice of Life

Assurance, define surplus as the difference between the book valuation

of the assets and the published value of the liabilities, including in

Mutual Life Office 249

each case any specific disclosed reserves. They go on to describe the

estate as the sum of

(a) margins in the liabilities and assets ;

(b) additional and contingency reserves disclosed or undisclosed ;

(c) surplus to the extent that it is not distributed ;

and (d) shareholders’ fund.

For a mutual life office item (d) is non-existent but the other items

pertain. The expression “ estate ” connotes a true value of surplus

based on a true valuation of assets and liabilities which can be

conceived of but which cannot be measured exactly. It is not clear

from the definitions how one measures the true reserve for a W.P.

policy, although Anderson (J.I.A. vol. 78, p. 336) has assumed that

this would be obtained from a bonus reserve valuation allowing for

the average bonus supported by new W.P. premiums. If this is

accepted as a valid measure of a W.P. reserve it would appear that

the concept of the estate is that of a free reserve, i.e., a reserve not

allocated to any particular liability but available for the benefit of the

life office as a whole. On this basis the estate is an inheritance which

the new policyholder enters into on joining a life office and which he

passes on to succeeding generations of policyholders on leaving.

5. It is generally accepted that interest on the estate is available

to supplement distributable profits and so to increase bonuses. How-

ever, in an expanding office it is likely that the estate would expand

also, so that instead of the estate providing additional profits for

distribution, the reverse situation might apply. Similarly, if business

declines, the need for an estate declines also, and it ought as a result

to be reduced. This implies that the estate must in fact be regarded

as distributable to W.P. policyholders in the long run and that

although the amount of the estate in terms of liabilities may control

its distribution in total, there ought to be a basis for allocating it

amongst each generation of W.P. policyholders.

We suggest that the solution to the problem of allocation of the

estate becomes simpler if we remove the distinction between surplus

and the estate and adopt a definition of surplus (or the estate) based

upon the concept of ownership. For this purpose it will be necessary

to include in the category of surplus the value of future bonuses.

This latter item appears either implicitly or explicitly amongst the

liabilities in the text book definition of surplus.

A definition of surplus for a proprietary life office

6. In a proprietary life office transacting only N.P. business the

surplus consists initially of shareholders’ capital. This capital is


required to pay for the expense of getting into business and also to provide the necessary contingency reserves without which no form of insurance business can be transacted. Eventually, contingency reserves will be built up from specific loadings and other margins in the premiums, and a shareholders’ surplus will develop out of trading profits not paid to shareholders as cash dividends.

The total surplus of the life office may be said to be the sum of capital, shareholders’ undistributed profits and specific contingency reserves or margins in the valuation bases. The amount of surplus required will depend on various factors including the volume of business, the rate at which business is expanding, the degree of risk involved, the extent to which the value of the invested assets may vary relative to the value of liabilities and the constraints on the valuation base8 for both assets and liabilities.

7. The value of a shareholder’s interest in this surplus is determined not by the apparent amount of surplus available but by the scale and date of emergence of likely future profits. Whatever this value may be, a shareholder’s portion is calculated in proportion to his shareholding. Although he may be said to own a portion of surplus he cannot reduce surplus unilaterally by withdrawing his portion and, therefore, he is able to obtain value for it only if someone else is prepared to buy into the business.

For any shareholder, the profit or loss made on buying shares and subsequently selling them depends on the terms for purchase and sale and the profitability of the business in the period during which the shares were held. Moreover, the value of his shareholding will be increased or decreased by an influx of fresh capital, depending on whether this is used to more or less advantage than the existing capital.

Since the shareholder has no right to have his share in surplus returned to him but must be content to receive what he can get for it in the open market, or on voluntary winding-up of the office, it follows that the shareholding represents his stake in the office.

8. The N.P. policyholders also have a stake in the business and may be thought of as being equivalent to holders of debenture stock in that they do not own the life office but are entitled to the protection of the shareholders’ surplus and capital. If the life office were to fail, then, as with all debenture holders, the N.P. policyholders would have a prior claim on the assets, but of course this safeguard does not provide complete security for their investment. The maximum amount an N.P. policyholder can claim in the event of insolvency


should not necessarily be the guaranteed surrender value of his policy but ought to be the value required to enable him to buy elsewhere another policy giving equivalent benefits, if this value is greater than the surrender value.

9. It follows that where there are no valuation constraints surplus in a proprietary life office transacting only N.P. business can be defined simply as

Surplus = Value of total net assets, less Value of N.P. guaranteed benefits

where net assets is the difference between assets and current liabilities.

A more general definition, which allows for the possibility of valuation constraints and for shareholders’ assets in excess of what is required to operate the life business, is

Surplus = Value of shareholders’ net assets, plus Value of N.P. business.

We shall not attempt at this point to discuss the bases for the valuations implied in these definitions.

A definition of surplus for a mutual life office

10. A mutual life office, like a proprietary life office, requires enough surplus at commencement to support the initial policies. It is unlikely that the first premiums can provide this surplus and so if the mutual office is to commence business as such, and not to start out as a proprietary office and subsequently mutualise, surplus in the form of a cash float must be supplied by guarantors of some description.

The funds supplied must represent money at risk, since once the first W.P. policies are in force they acquire a debenture right similar to that of the N.P. policies in the proprietary life office previously considered. This debenture right is in respect of the benefits guaranteed under the policies, including any reversionary bonuses allotted. N.P. policies, of course, acquire the same rights as in a proprietary life office.

11. Alternative definitions of guaranteed benefits under W.P. policies are available but, whatever definition is adopted, growth in business can take place only if surplus is increased beyond the initial level. Once the business in force is mature the initial “ float ” of surplus can be refunded, since the accumulated surplus from the W.P. policies will be sufficient to support mortality and investment


fluctuations and to finance new business. Although a new W.P.

policy may start to contribute to surplus from commencement it is

the presence of surplus previously supplied but not yet distributed

which makes the assurance possible. Provided there is a suitable

volume of new W.P. business, existing W.P. policyholders can draw

on existing surplus for bonuses which, if reversionary, increase the

total of W.P. guaranteed benefits.

12. Although it can be argued that the motives of a W.P. policy-

holder in a mutual life office are not identical with those of a share-

holder in a proprietary life office, it would seem that in both cases

the functions of surplus are the same, i.e., to support guaranteed

benefits and to provide additional funds for investment. We therefore

can define surplus in a mutual life office in terms of the losses which

can be made without impairing the ability to pay guaranteed benefits,

and so arrive at the alternative definitions :

Surplus = Value of assets less

Value of W.P. guaranteed benefits less

Value of N.P. guaranteed benefits, or

Surplus = Value of W.P. assets less

Value of W.P. guaranteed benefits plus

Value of N.P. business.

In the second of these definitions we have assumed that specific

assets have been assigned to the N.P. business and that the margin

in the value of these assets over the value of N.P. benefits provides

for valuation constraints and contingency reserves in respect of N.P.

business. A similar assumption might have to be made in respect

of W.P. guaranteed benefits.

It should be noted that in defining surplus we use the word

“ guaranteed ” in a contractual sense, rather than to imply fixed

values.

13. Continuing the analogy with the proprietary life office, we can

think of the surplus in a mutual life office as being the total pro-

prietary stake of the existing W.P. policyholders. The portion of

this stake which can be returned to a W.P. policyholder during the

term of his policy and on termination depends on the total amount

of surplus required to be maintained. This in turn depends not only

on the factors previously noted for the proprietary office but also on

bonus policy. Before enlarging on this latter factor we shall first

of all discuss the definition of value of W.P. guaranteed benefits, i.e.,

the guaranteed liabilities under W.P. policies.

Mutual Life Office 253 Guaranteed liabilities under W.P. policies

14. We could define the guaranteed liability under a W.P. policy

in the same way as for an N.P. policy, i.e., as the greater of the

guaranteed surrender value and the single premium sufficient to buy

a policy providing the same guaranteed benefits as are presently

attaching to the policy at the rate of premium specified in the policy.

Since it is not customary to guarantee the surrender value basis for

attaching reversionary bonuses, this debenture right is, therefore, the

greater of

(a) the guaranteed surrender value of sum assured

and (b) the value of sum assured and attaching bonuses less value of

future premiums.

If there are no guaranteed surrender values of sum assured, (b) will

always apply. However, in the early durations of a policy this quantity

may be negative, in which case there is no debenture right under the

policy except, possibly, to the extent of guaranteeing insurability,

and the whole of the W.P. premium, less expenses and cost of life

risk, falls into surplus.

15. Since the definition of guaranteed liability is for the allocation

of surplus in a going concern, a solvency definition, such as is given

above, may be thought to be unnecessarily severe.

A more reasonable basis might be to assume that the W.P. policy

consists of N.P. benefits bought with an N.P. premium, plus a bonus

loading to provide for cash or reversionary bonuses. On this basis,

surplus is increased by the amount of bonus loading in the premiums

and diminished by any allotment of surplus either in cash or in the

form of vested reversionary bonus. This is equivalent to regarding

the value of guaranteed benefits as the value, on an N.P. basis, of paid-up sum assured and vested reversionary bonuses.

In terms of a bonus reserve valuation the surplus build-up could

be taken to be

(i) the accumulation of past bonus loadings less cash bonuses,

less value of vested bonuses

or (ii) the value of future bonuses less the value of future bonus

loadings

or (iii) a net premium reserve at a rate of interest reduced to provide

reserves equivalent to a bonus reserve, less a net premium

reserve at the bonus reserve rate of interest,

where (iii) may be regarded as a rough approximation to (i) and (ii).


16. Some examples are given in Appendix I of the build-up of

surplus under both of the above definitions of guaranteed liability,

assuming that experience is as estimated in the premium basis and

that the reversionary bonuses loaded for in the premiums are allotted

as predicted.

In both cases the ratio of surplus to total fund (taken to be the

full reserve on a bonus reserve basis) is larger in the early durations

and declines to zero as maturity approaches, while the absolute

amount of surplus also rises to a peak and declines to zero eventually.

The amount of surplus changes discretely when a bonus vests and is

shown in the examples as the amount immediately prior to the vesting

of the year’s bonus. As might be expected, the longer term policies

have the largest average ratio of surplus to total fund, but the

variation in this ratio by term of policy is less marked where the

solvency definition of guaranteed liability is used. For a given

premium rate the ratio of surplus to total fund is larger for a higher

underlying interest rate and the corresponding higher rate of assumed

bonus.

17. The two definitions of guaranteed liability may be considered

to represent extreme positions. The solvency definition probably

overstates the protection provided by future bonus loadings since,

in practice, there will be a tendency to surrender if bonus prospects

diminish or, in the extreme case, disappear. On the other hand, the

alternative definition probably understates surplus but might be

acceptable provided the valuation basis for guaranteed liabilities was

less stringent ; it has a possible practical advantage that if we use

net premiums on the valuation basis the value of guaranteed liability

will never be negative.

Factors affecting the size and build-up of surplus

18. Obviously the ratio of surplus to guaranteed liabilities can be

increased by having larger bonus loadings and/or by having a steeply

rising cost of bonus so that surplus is withheld in the early policy

durations. The level reversionary bonus system, as operated in this

country, has both of these features and this is perhaps what contri-

butes largely to the financial soundness of British life offices and also

to the profitability of their W.P. policies. The larger the proportion

of surplus in the fund the greater is the degree of risk which can be

run and hence the greater is the opportunity for profitable investment

in potentially more remunerative types of investment, including the

writing of N.P. business.


19. We have seen previously that the writing of N.P. business requires an allocation of surplus sufficient to maintain the various guarantees under these contracts. A similar allocation of surplus is in effect required to cover fluctuations in the value of W.P. assets relative to W.P. guaranteed liabilities and it would seem that, in general, a notional investment contingency reserve is required equal to an estimate of the maximum amount by which the difference between value of assets and value of liabilities might conceivably change. Such a reserve may be required even if it is considered that no real change in value has taken place. For example, surplus might be required to cover changes in capital value of assets in cases where it was not permissible to change the published basis of valuation of liabilities to conform to the published valuation basis of assets.

The investment contingency reserve is, by definition, a variable quantity and represents an allocation from total surplus as previously defined.

20. The need for an investment contingency reserve is reduced or even eliminated where assets and liabilities can be matched in some way. For example, if some of the guaranteed liabilities were immunised against changes in interest rates by suitable investment in reliable fixed interest securities, and it was the intention to continue this arrangement in the future, or if the liabilities under equity-linked contracts were matched by corresponding equity investments, the values of assets and liabilities would tend to rise and fall in parallel so that little or no investment contingency reserve would be required. In assessing the level of surplus relative to the level of guaranteed liabilities we could deduct ‘the value of such assets and liabilities from their respective sides of the valuation balance sheet, provided we were not otherwise restricted by having to conform to prescribed valuation bases for assets or liabilities.

The asset mix of a W.P. fund

21. The preceding discussion shows clearly that it is not the size of bonus loadings alone which determines the total surplus and hence the degree to which a life office can depart from a position in which assets and liabilities are matched ; the rate at which bonus loadings are converted into guaranteed benefits is of the utmost significance, as is the extent to which surplus is required to support the writing of guaranteed business. We infer that where there is more than one W.P. class the assumption that premiums under all classes of policy are invested in the same mix of the office’s assets may be valid only


if it can be shown that each W.P. class, in isolation, could support that mix of assets.

For example, it is unlikely that the contingency margins, implicit or explicit, in the rates of premium would permit premiums under conventional N.P. policies to be invested in equities to any great extent or would permit a large degree of mismatching of fixed interest investments, yet such investment policies could be pursued provided there was sufficient surplus from other sources. In a mutual life office it is possible for the whole of the W.P. fund and part of the N.P. liabilities to be covered by other than fixed interest securities. This is analogous to the situation in a proprietary life office transacting only N.P. business in which the whole of the shareholders’ fund and a portion of the N.P. liabilities are covered by equity investments. In such circumstances we may think of the N.P. liabilities as equivalent to the debenture stock of an investment trust.

22. It is doubtful whether truly W.P. business can be considered to be invested in the office mix of assets if its bonus loadings, etc., would not allow this mix of investments in isolation. If a particular class of W.P. business cannot be supported by these assets then it is being subsidised by some other portion of the business and therefore is not truly W.P. Where different classes of W.P. business, having markedly different levels of bonus loading, exist in the same office it would seem that the investment policy for each class of business ought to be considered separately and, if necessary, surplus funds accumulated for each class on the basis of differing investment portfolios. A possible solution in this latter situation might be to invest notionally for such a W.P. class in investments suited to the likely surplus level, returning to the class the profits which would have accrued from this investment policy. If this were done, the supporting W.P. class would reap any profit or bear any loss from an investment policy which differed from the notional one.

The investment of funds arising from a particular class of W.P. business in an asset mix which is different from that of the office as a whole does not necessarily preclude that class from contributing to the support of N.P. business and hence from sharing in any N.P. profits.

23. Another possibility is to consider that all classes of W.P. business are invested in the same notional asset mix—one that can be supported by each W.P. class in isolation. Any profits and losses arising from an investment policy which departs from one involving the notional asset mix would be allotted to each class in proportion


to its share of surplus. This approach could be followed also in respect of N.P. business.

For example, if the portfolio contains equities, and the notional asset mix is 100% fixed interest, it may be possible to insulate the fund as a whole against fluctuations in the value of equities, and so simulate a fixed interest portfolio, by retaining investment contingency reserves which would form part of the surplus only of those W.P. classes which could support equities. Capital profits on equities would obviously be distributed in proportion to the surplus of each W.P. class, but care would have to be taken to avoid distributing investment income in excess of what might have arisen from a fixed interest portfolio to those classes which could not support an asset mix that included equities.

Summary

24. We define surplus as the difference between the value of assets and the value of guaranteed liabilities. By analogy with the situation in a proprietary life office the ratio of surplus to value of guaranteed liabilities in a mutual life office is of the utmost significance. The size of this ratio (as well as the absolute size of surplus itself) will determine, and in turn may be determined by, the level of new business and the investment and bonus strategies of the office. Since the exigencies of these strategies may affect the return which W.P. policyholders will receive for their contributions to surplus it is important to measure, allocate and control the distribution of this surplus in such a way as to avoid penalising particular groups of W.P. policyholders.

We conclude that the most important determinant in bonus policy is the asset mix and suggest that one cannot judge the significance of an asset mix solely on the various percentages of different types of asset but must have regard to the overall level of surplus in relation to guaranteed liabilities. Bonus policy and asset mix are interrelated and both in turn depend on the investment aims which the life office sets itself in respect of the W.P. policy holders. It may be necessary to distinguish between, on the one hand, surplus which is required to sustain mortality and similar contingencies and to support guarantees and, on the other hand, surplus which is required solely because the investment policy is not consistent with the type of guaranteed liabilities covered.


PART II

MEASUREMENT OF SURPLUS

Valuation for surplus—general points

25. A valuation for surplus in a mutual life office may be said to have these three objectives:

(a) To measure surplus in the light of realistic values of assets and liabilities, having regard to expected future experience.

(b) To examine the level of guaranteed liabilities in relation to surplus.

(c) To investigate the likely future patterns of surplus growth and distribution.

Objectives (a) and (b) are normally subsidiary to objective (c). In order to pursue this latter objective the rate at which the various profits (including profit from N.P. business) are emerging must be measured and compared with the corresponding rates for previous years and an assessment made of such rates for the future. Later we shall argue that a valuation for surplus is in consequence a reassessment of the existing premium bases, but at this stage we shall confine the discussion to some comments on the measurement of the values of assets and liabilities and of rates of investment return.

26. Surplus is a mixture of retrospective and prospective elements. The former represent the accumulated profit which has arisen because experience to date has been better than was anticipated in the premiums charged, and which has not yet been distributed as bonuses, while the latter represent a capitalisation of future experience profits or losses. In most cases it is virtually impossible to separate these two elements; it is easiest to do so where the values of assets and liabilities can be determined without reference to each other. Thus, if assets are dead short and fully guaranteed as to principal, we might feel justified in stating:

Retrospective surplus = Fund less reserves on original premium basis.

Prospective surplus = Reserves on original premium basis less reserves on new premium basis.

In the measurement of prospective surplus we have capitalised future profits or losses in order to put existing business on the same footing as new business. This is not necessarily justified even when assets are dead short, and will always be dead short, because future


profits and losses will emerge at various dates in the future. In valuing these as a lump sum we are assuming implicitly that the expected rate of return on the value of prospective surplus is identical to the rate of interest used in the valuation of liabilities. This is not generally so.

Valuation for surplus in a proprietary life office

27. For a proprietary life office, the transacting of N.P. business is a business venture for which capital is advanced in the hope of gain. The gain is measured in terms of the returns from the business to the shareholder and at any time the value of the business may be measured as the value of the expected returns at the rate or rates of interest which represent the expected rates of return for which a prospective investor will buy either the whole business, or a share in it.

The transacting of N.P. business of necessity requires the ownership of invested assets, bought either with the shareholders’ money or with the policyholders’ premiums. It is important to distinguish between the rate of investment return on these assets and the rate of return on the N.P. business itself.

28. It is convenient to assume that the assets are divided into two portions—assets which are required to cover the N.P. liabilities and contingency reserves, and assets which are at present thought to be surplus to these requirements and which therefore can be regarded as shareholders’ assets. If surplus is taken to be the value of shareholders’ assets then the total rate of return at time t to the shareholders , is the rate of return on shareholders’ assets, , increased by the ratio of N.P. trading profit, NPt, to the value of shareholders’ assets, PVt, i.e.,

These symbols are defined in Appendix II, where this topic is developed symbolically.

29. From Appendix II it is clear that the rate of return on N.P. business is a function of the basis on which the business is valued, just as the investment rate of return on shareholders’ assets is a function of the value put upon them. If the valuation bases for N.P. assets and N.P. liabilities are stringent, it is possible for the rate of return on N.P. business to be very small, or negative, when new business is increasing, even if this business is being done on terms which will

R


eventually yield a profit. In an extreme case the total rate of return to shareholders might be negative, in which event more capital would be required in order to prevent surplus from falling.

It is obvious that the value of the shareholders’ interests cannot in general be determined by rates of return which are based on published valuations and accounts. A realistic value has to be placed on the N.P. business and the published surplus increased by this amount. There are at least two approaches to this problem. The first is to value N.P. assets and N.P. liabilities on more realistic bases; the second is to value the prospective N.P. trading profits which are likely to emerge, on the assumption that the present published valuation constraints will continue to operate.

30. Pursuing this second approach first of all we have

St = vr. NPr + value of shareholders’ assets, r = t+1

where St is the true surplus at time t and the discounting of future N.P. profits, NPr, is at the valuer’s required rate of return. Because of the risk nature of the investment this rate of return ought to be higher than the rate of return on new fixed interest investments, although the same rate may be assumed if conservative estimates of future experience have been made in arriving at the amounts of

NPr. This method of valuing future profits has been discussed in

American actuarial literature. It has been approached as a cash flow problem in which it is assumed implicitly that assets are either dead short or that asset-income and liability-outgo will be perfectly matched at all times in the future so that the net cash flow can be taken to be the N.P. profits emerging on the experience assumed and the published valuation basis. If assets are taken into account in this process it can only be in the determination of the rates of interest which are assumed to prevail in each future year. Strictly speaking, the estimate of future profits should be made not only in respect of existing business but also in respect of future business expected to be written by the present sales force.

31. Where assets are not dead short, or cannot be assumed to match liabilities, the problem of valuing future N.P. profits becomes more difficult, since surpluses or shortages of cash will enter into the cash flow calculations either in the form of transfers to and from shareholders’ surplus or as capital gains or losses on N.P. assets: this is so even when a reasonable prediction of interest rates can be


made. In the circumstances it can only be assumed that the expected future rates of interest make some allowance for this. If N.P. assets consist entirely of dated fixed interest securities it may be relatively easy to make such an allowance.

Immunisation of assets and liabilities will not ease this problem unless there are no constraints on the valuation bases. Provided there are none, however, it would be possible to value assets and liabilities at the current rates of interest using best estimates of future mortality and expense. The remaining assets are not then required and were it not for the need to retain surplus for mortality contingencies, could be valued at current market value. Strictly speaking, since they cannot all be released immediately, some estimate must be made of the way in which they would be run down and the future estimated cash flow valued at the valuer’s expected rate of return.

Alternatively, the anticipated premiums could be reduced so as to make the value of N.P. liabilities equal the value of N.P. assets. The excess premiums would then be valued at the valuer’s expected rate of return. This reduction in premiums can be made in any number of ways, of course, and hence the value of business will depend on how the future excess premiums would be released.

32. The above holds even if assets and liabilities are not immunised, provided they are capable of being immunised, since at no cost to the office the existing assets could, in theory, be switched so as to obtain an immunising portfolio. However, the maximum likely loss arising from a change in interest rates would have to be estimated and a portion of surplus earmarked as an investment contingency reserve to cover it. Excess assets held in this contingency reserve would not necessarily be valued at market value, however, as has been noted above. The extent to which such a contingency reserve must be regarded as an addition to N.P. reserves, rather than as surplus, will depend on the valuer’s assessment of the likely investment policy of the office.

33. As far as the N.P. liabilities are concerned we can eliminate the effect of valuation constraints on the emergence of future profit if we make the assumption that the rates of interest expected to be experienced in the future, i.e., the valuation rates of interest for assets and liabilities, are also the valuer’s expected rate or rates of return. On this basis we have the familiar relationships:

Value of future profits = Value of N.P. liabilities on published basis less value of N.P. liabilities on expected experience basis, or


Value of N.P. business = Value of N.P. assets on published basis less value of N.P. liabilities on expected experience basis.

The valuation of assets is still constrained by the valuation basis. It follows that the first of the alternative approaches to valuing N.P. business, namely

Value of N.P. business = Value of N.P. assets on a realistic basis less value of N.P. liabilities on a realistic basis

is justified only if the valuation basis for N.P. assets is not constrained and the valuer’s expected rate of return is in accordance with the expected experience rates of interest. Since valuation constraints are not likely to be onerous in this country, provided fixed interest liabilities are covered mainly by fixed interest assets, it is thought that these conditions would be satisfied if the valuations of N.P. assets and N.P. liabilities were made at a market rate of interest and if the estimates of future mortality and miscellaneous profits were not over-optimistic.

34. The arguments advanced in the preceding paragraphs suggest that where fixed interest assets and liabilities are involved a valuation of liabilities and covering assets at market rates of interest leads to more precision in the estimate of surplus (i.e., the value of N.P. business).

An objection to valuing at market rates of interest is that in so doing we are really measuring the value of future profits and losses which would emerge if the life office were to stop writing new business and in future were to pursue a consistent policy of immunisation. However, it may be that as far as existing business is concerned the only way to make a profit is not to pursue a policy of immunisation; furthermore, it will normally be the case that the office will continue to write new business on terms which neither the valuer nor the office can predict with accuracy. In these circumstances the immunisation approach to valuation will serve only to indicate the immediate capital effect on surplus if the current rate of interest were suddenly to change.

We are not necessarily further ahead if we adopt the procedure described by Springbett (T.F.A. vol. 28, p. 237) and value at some notional rate of interest. If all assets are fixed interest then, after making the mismatching adjustment which he describes, we are in effect valuing the excess assets at the notional rate of interest, since the assets which equate to the liabilities at the notional rate of


interest will also equate to them at the market rate of interest, even without a mismatching adjustment. However, the valuation of excess assets is a function of the extent to which they must be retained rather than immediately realised for cash and this might well be less than any market or notional value if the required rate of return for the valuer were to exceed the market or the notional rates of return.

If the valuer were convinced that the departure from an immunised position would result in more profit he ought to value the liabilities on a more favourable basis than the assets or make some other equivalent adjustment to his valuation so as to increase the value of surplus. For example, he might take some credit for the potential gain from a change in interest rates. He has to make a prognosis of future investment experience for the market as a whole and also has to make an assessment of the future investment policy of the office and of its ability to do better than the market. Where N.P. assets include equity investments it is impossible to avoid making this kind of assessment.

35. The value of N.P. business, however determined, is a shareholders’ asset which must be added to the published shareholders’ assets in order to measure the “true” worth of the proprietary office. The rate of change in the value of N.P. business must therefore be added to the rate of return based on published figures in order to measure the rate of return on shareholders’ assets, PVt. The true rate of return could be measured in terms of the total surplus,

(St+PVt), rather than in terms of PVt above, but as far as the allocation of profit among the shareholders is concerned it is immaterial which measure is adopted, since the total surplus and trading profits, however measured, are divided among shareholders in proportion to the number of shares held.

The value of N.P. business represents, for the shareholder, an unrealised capital profit for which he would expect to get credit if he were to sell his shares. It is hardly surprising that this should be so, since the N.P. business represents for him an equity investment.

Valuation for surplus in a mutual life office

36. In theory there can be only one major reason for a mutual life office to transact N.P. business and that is to increase profits. (We exclude from consideration additional benefits of a term nature attached to W.P. policies which for simplicity, if for no other reason, are written on an N.P. basis.) Even if N.P. business is not actively


sought, the terms on which it is written must ensure that W.P. policyholders are not likely to suffer in consequence. The aim of a mutual office in transacting N.P. business is virtually identical with that of a proprietary office and the principles underlying the valuation of the N.P. business in a mutual office ought basically to be similar.

37. In Appendix II we develop formulae for rates of return in a mutual life office. The approach is similar to that shown for a proprietary office but in general we have to provide for the possibility of having several classes of W.P. business, each with its own asset mix. By analogy with a proprietary office the N.P. profits are measured in relation to W.P. surplus, since each W.P. class may give quite different support to N.P. business, depending on the size of its bonus loadings and the pace at which surplus is distributed in the form of cash or reversionary bonuses.

It is immaterial whether the N.P. profits are measured in terms of W.P. surplus only or in terms of W.P. surplus increased by including the value of N.P. business, since the value of N.P. business would be allotted in proportion to N.P. surplus.

38. For the purpose of allocating N.P. profits to different W.P. classes on the basis of their respective shares of surplus, allowance should be made for the differing proportion of W.P. surplus required as an investment contingency reserve to cover possible fluctuations in the value of W.P. assets relative to the value of W.P. guaranteed liabilities. One possibility is to reduce the W.P. surplus of each W.P. class by the amount of any such contingency reserve, on the grounds that this surplus is required solely to support the investment policy adopted for each particular W.P. class. On the other hand one could argue that some sort of average or intrinsic value of investment contingency reserve should be regarded as available for the support of N.P. business since, if necessary, existing assets could be sold and replaced by assets whose value would be more stable relative to the value of the guaranteed liabilities.

The above comments are equally valid where notional assets are assigned to a particular W.P. class which cannot support the actual company asset mix. In this case the investment contingency reserves which are allocated among the other W.P. classes will, as a result be supporting indirectly the guaranteed benefits of the W.P. classes having the notional assets. Similarly, where all the W.P. assets are deemed to be invested in notional assets, which all classes can support, the investment contingency reserve would form part of general surplus, analogous to the value of N.P. business, and would be allocated


amongst those W.P. classes which could support the actual asset mix, in proportion to their notional surplus. For purposes of allocating N.P. profits the increase in W.P. surplus arising from the addition of contingency reserves could either be ignored or be based on average or intrinsic values of the investment contingency reserves.

39. Where each class of W.P. business is deemed to have its own asset mix it seems natural to assume that N.P. business also has its own asset mix. Where there is only one class of W.P. business, or where all W.P. classes are deemed to have the same asset mix, there is a choice between assuming that the same asset mix applies to N.P. business or assuming that it continues to have its own asset mix.

This choice would not affect the profits of the office, of course, but if the valuation basis for N.P. business were affected thereby, both the rate of investment return on W.P. assets and the rate of N.P. return on W.P. surplus would be affected, as also would be the value of N.P. surplus. This in turn would affect the distribution of investment and N.P. profits amongst the various W.P. classes. For example, if N.P. business were assigned a substantial proportion of equity assets it may be that, in consequence, N.P. liabilities would be valued more stringently than if only fixed interest assets had been assigned; alternatively, the N.P. reserves may remain unaltered but an investment contingency reserve may be added to the N.P. fund to allow for the greater possible fluctuation in value of assets. The effect in either case might be to increase the N.P. return on surplus but to decrease the investment return on W.P. assets.

40. Whether or not separate assets are assigned to N.P. business the rates of return and the total value of surplus are affected by the valuation basis adopted for N.P. liabilities in the valuation for surplus. As with a proprietary office, it is desirable to avoid an over- stringent valuation basis, but it is likely that in a mutual office there would be considerable caution in capitalising future profits and there would probably be a tendency also to smooth out year-to-year fluctuations in the N.P. rate of return.

Provided future experience is expected to be at least as favourable as that implied in the premium bases for existing contracts, a valuation on the premium bases, together with a valuation of assets at book value, ought always to be justifiable as long as the market value of assets is near book value or is slightly higher. In these circumstances it may be possible to consider valuing liabilities on the premium bases for current new business.

But where fixed interest assets have been bought to cover N.P.


liabilities it would seem more correct to assume that a fixed interest asset mix applies to N.P. liabilities and to value both assets and liabilities on the market value basis, as was described previously for a proprietary office.

41. It would be possible to include the W.P. guaranteed liabilities with the N.P. liabilities in calculating rates of return. In general this would be inappropriate and would only be considered if there were no significant difference in the features of the various W.P. classes. Profits and losses on W.P. guaranteed liabilities ought, in general, to be assigned to the corresponding W.P. class, so that in the valuation of such liabilities allowance should be made for any special contingencies peculiar to a particular W.P. class.

42. The valuation of W.P. assets and W.P. guaranteed liabilities is governed to some extent by the bonus policy of the office and by whether or not it is intended that a W.P. policyholder should under- write his own investment risk to any degree.

We have already noted in paragraph 26 that if assets are dead short it might be appropriate to value the liabilities on the basis for new premiums. If the assets are fixed interest securities of fairly short term then it also may be acceptable to simulate a dead short situation as far as possible by valuing assets on an amortized basis and by valuing liabilities at a rate of interest which takes account of any difference between the future yield from these assets and the premium basis assumptions as to future yields. (This course would not be appropriate if the bonus policy were based on a paid-up immunisation investment policy.)

Similarly, if a longer-dated fixed interest portfolio were involved, a market value approach to valuation, as described for N.P. business, would seem possible, provided that the value of guaranteed liabilities were increased by an appropriate contingency reserve to allow for possible losses due to mis-matching. As with N.P. business the size of such a contingency reserve would be dependent on some assessment of the ability of the office to benefit from mis-matching.

43. If the W.P. assets contain a large proportion of equities, as is likely to be the case in this country, the problem becomes more difficult. The methods of valuation suggested by Springbett (T.F.A. vol. 28, p. 260) would seem appropriate where the policyholder is not bearing his own capital profits and losses, but where it is intended that he do so to any degree it would seem that assets should be valued on a market value basis or, possibly, on a valuation basis


which allows for a considerable degree of unrealised capital profit. The corresponding basis for guaranteed liabilities in these circumstances could be the basis for new premiums. The valuation basis ought not to be more optimistic than this since otherwise we may tend to increase the guaranteed benefits too quickly and not be able to provide a large enough contingency reserve to cover fluctuations in the value of assets relative to the value of guaranteed liabilities.

Summary

Where there are sufficient fixed interest assets to cover the guaranteed liabilities a market valuation basis for assets and liabilities could, of course, be applied.

44. A valuation for surplus is made in order to assess surplus and its rate of emergence as realistically as is safely possible. The proportion of surplus which will be distributed in the form of bonuses as a result of the valuation will, of course, depend on bonus policy as well as on the various constraints put upon a published valuation and the various contingencies which may have to be provided for by allocations from surplus.

As a result of successive valuations, we can arrive at a rate of investment return on W.P. assets and a rate of N.P. return on W.P. surplus. These rates of return are sensitive to the valuation bases for assets and liabilities. In a later section of the paper we illustrate the use of these rates of return in the allocation of surplus to individual policies.

In general we feel that fixed interest assets should be deemed to apply to N.P. liabilities (assuming these are of a fixed interest nature) as far as possible and then to W.P. guaranteed liabilities. This allows a market valuation of assets and liabilities to be made. The N.P. liabilities should then be increased by contingency reserves to cover possible investment and mortality losses. These reserves form part of surplus belonging to W.P. policyholders, but must be maintained for the protection of the N.P. business.

If the W.P. guaranteed liabilities were covered by equities the valuation basis for liabilities could be the basis for new premiums; depending on bonus policy the assets could be valued on a market value basis or on a notional value basis, possibly consistent with the premium basis.


PART III

ALLOCATION OF SURPLUS—PRINCIPLES

Equity in allocation of surplus

45. Surplus has been defined in this paper as a capital item and, therefore, its value may include a capitalisation of future profits and losses. The change in surplus from one year to another will, in general, consist of the net total of the following items:

(a) bonus loadings received, (b) trading profits measured on the valuation basis, (c) changes in the valuation basis of assets and/or guaranteed

liabilities, and (d) value of cash or reversionary bonuses allotted.

Allocation of surplus implies the allotment of all of these items and not merely the allotment of surplus distributed in the year in the form of cash or additional guaranteed benefits following a bonus declaration.

46. It follows from our definition of surplus that in any year’s distribution of surplus we must have regard to the possible distributions of surplus in future years, so that the distribution of surplus or, more properly, the pace of distribution of surplus, will be governed by the long-term business aims of the mutual life office, as reflected particularly in its investment and bonus policies. It would seem that these aims ought to be compatible with the interests and expectations of the W.P. policyholders, so that in their achievement, through the medium of the yearly distributions of surplus, inequity does not arise in the allocation of surplus to the various W.P. classes and to the policies within these classes.

Any discussion of equity in allocation of surplus would seem to require knowledge of the aims and expectations of policyholders.

47. No scheme of insurance would function unless there was inequality of pay-out, nor would lotteries or sweepstakes do so either. Generally speaking, therefore, the concept of equity implies equality of benefit rather than equality of pay-out.

We distinguish between pay-out and benefit in such schemes since the benefit which is paid for under the scheme is the chance of pay-out rather than the pay-out itself. If there is inequity it will arise not because of inequality of pay-out but either because of


inequality in the cost of the same benefit or because of a bias in operating the scheme which results in some person obtaining more benefit than another whose cost of benefit has been the same.

It follows that there may be any number of equitable ways in which the surplus of a mutual life office may be allocated, depending on the definition of benefit under a W.P. policy and the method of assessing its cost.

48. It has been postulated that equity has been achieved under the reversionary bonus system if bonuses have been paid in the form of bonus anticipated by the policyholders and for which their premiums were loaded and if the declared bonuses have been at least up to expection; provided bonus expectations have been met the life office is then free to distribute any excess of surplus in whatever manner it sees fit. Many would regard the maintenance of a stable rate of bonus as in accordance with the policyholders’ expectations, and the investment policy, as well as the policy for surplus distribution, may be directed to this end.

This view has been justified even where the investment portfolio includes equities, on the grounds that the policyholders are entitled to expect a stable rate of bonus and do not want to bear the risk of fluctuations in capital value; provided the investment in equities in the long term proves advantageous to the policyholders as a whole there is no need to allocate with any degree of precision profits in excess of those anticipated. This may be thought of by some as an extension of the insurance principle into the field of investment.

49. One could question the proposition that a system of surplus allotment is fair merely because it satisfies policyholders’ expectations; the real justification for the level reversionary bonus system must lie in the claim that, by charging appropriate premiums in the first instance, the cost of the benefits is equitably assessed even if subsequent experience is different from that assumed in the premium basis. Policyholders have to assume that the cost of a particular system of surplus allotment is fairly assessed because they have few means of proving otherwise and they are usually quite ready to accept variations in the expected system as equally fair provided they appear reasonable.

A more general approach to the definition of equity in surplus allotment would seem to lie in examining the possible aims of policyholders in taking out life assurance and testing the degree to which the operation of the bonus system of the life office is consistent with these aims.


50. We can reasonably expect that any member of a mutual life office has an interest in obtaining life cover and/or in accumulating capital. In some cases the accumulation of capital is a necessary consequence of the method of paying for the life cover, as with a whole of life policy, while in other cases the life cover may be incidental to the accumulation of capital, as with a short-term endowment assurance.

For many purposes both aims are equally important to policyholders and it is convenient to link them together in a single policy rather than to have one contract for life cover and another contract, not necessarily with a life office, for accumulation of capital.

Prospective policyholders can choose various means of accumulating capital, either investing through a life office or some other type of institution, or investing privately, but they must come to a life office for life cover, since this can be given only if there is a pooling of risk with other policyholders. (We exclude from this analysis group policies that are large enough to bear their own mortality risk.) If policyholders have come to a life office to accumulate capital, it may be assumed therefore that, unless their contracts state otherwise, they wish to participate in some pooling of investment risk, or wish the life office to manage the investment of their premiums.

Pooling of risks in general

51. The terms on which pooling of mortality risk takes place are well understood and agreed. It is accepted that pooling should not take place among different generations of policyholders in that, by and large, current policyholders expect to pay for the current level of mortality; but because changes in the levels of mortality occur irregularly from year to year, although there may be a particular trend over a period of years, there is of necessity some pooling among different years of experience.

Since the life office distinguishes between various classes of policyholder in charging for mortality, depending on the characteristics of each class, and charges extra premiums in the case of policyholders entering a particular class whose likely mortality is thought to be significantly more than normal for the class, W.P. policyholders may reasonably conclude that pooling of mortality risk is not to be considered to include subsidising of risk within their own mortality class, or among other mortality classes. In other words, they may expect to pay for the mortality experience of their mortality class in so far as this can be adequately measured, by age, for each year their policies are in force.

Mutual Life Office 271 52. There may be instances when a particular W.P. class is not

large enough to pool the whole of its own mortality risk. In such cases it would be necessary to reinsure the excess mortality risk with another life office or with some other class of business within the same life office. If this were done the mortality profits and losses of the business reinsured would not affect the profits of the particular W.P. class and, in the case where the reinsurance was within the same office, might become part of the N.P. profits of the office. There is no theoretical reason why the whole of the mortality risk of a particular class of W.P. policies should not be dealt with in this way.

Similar considerations apply to the pooling of expenses experience. Normally there is no reason why each W.P. class should not bear its allocated expense cost but, because of the way in which expense costs are assessed, it is much less likely that any “reinsurance” will be necessary. Again, there is no theoretical barrier to the issue of a class of W.P. policies which is not required to bear the risk of fluctuations in future levels of expense, and whose profits and losses on expenses, relative to the expense loadings in the premiums, could be incorporated in the N.P. profits of the office.

53. The principles governing the pooling of investment risk are not so clear. Perhaps this lack of definition stems from the earliest days of the level premium policy, when uncertainty over the current and future level of mortality was the main consideration and the terms on which the excess of the level premium over the current year’s cost of mortality and expense could be invested were of secondary interest. Whatever the reason, it is a curious fact that although the major portion of policyholders’ premiums may be required to provide for the accumulation of capital, rather than to provide for life assurance cover, the terms on which investments and investment profits are to be pooled have not usually been specified by life offices, except for the relatively recently issued equity-linked contracts. These terms have not been enquired into by policyholders to any extent, although the method adopted for the pooling of investment risk is obviously fundamental to any definition of equity in bonus distribution.

We are not helped in this connection by the investment assumptions implicit in actuarial theory as applied to the calculation of premiums. This theory may envisage variations in the rate of interest but does not usually provide for any concomitant capital profits or losses. The most we can suppose is that policyholders may expect premiums and bonuses to reflect changes in investment conditions in some undefined


way. This expectation might be obtained from the office’s approach to the calculation of premiums.

54. It is unlikely that any W.P. policyholders have taken out policies in order to become part-owners of a mutual life office, but no discussion of pooling of risk would be complete without reference to the pooling of proprietary risk. We have already observed that this risk arises because of the guarantees which a life office gives under both N.P. and W.P. policies. In the last resort all surplus is subordinated to maintaining these guarantees; in a mutual office this surplus belongs entirely to the W.P. policyholders.

Previously in this paper we have suggested that different classes of W.P. business may be thought of as supporting N.P. business in proportion to their surplus and therefore ought to share in N.P. profits in similar proportion. We have also argued that each W.P. class ought to bear the cost of its own guarantees. There would seem to be no theoretical objection to extending this concept of proprietary interest to each W.P. policy in so far as this is practicable, provided we can obtain suitable measures of the surplus pertaining to a policy and of the liability under its own guaranteed benefits.

W.P. policyholders as equity investors

55. In Appendix III we consider briefly the different approaches to the pooling of risks adopted

(a) with equity-linked policies, (b) with policies sharing under a contribution system,

and (c) with policies receiving level reversionary bonuses.

These three approaches offer an interesting contrast in their treatment of investments.

In the first two, the rationale of the method of allocation of investment experience is appropriate to the type of assets in which the policy monies are invested. Thus, where investment is wholly in equities, the policyholders bear the full brunt of capital profits and losses as if they had invested in equities through the medium of a unit trust; but where investment is in predominately dated fixed interest securities, under which there is assumed to be little likelihood of long-term capital profit or loss, a savings bank approach is adopted in that interest is allocated amongst policyholders roughly in proportion to reserves.

The reversionary bonus system also involves an allocation of interest in the allotment of bonus other than special bonuses, although


interest may include a spread of capital profits and losses and the method of allocation is not clearly evident, This approach has been taken in spite of the substantial extent to which W.P. policyholders in this country are investors in equities.

56. In considering the extent to which W.P. policyholders are invested in equities it can be argued that it is not sufficient to look at the proportion of equities in a life office’s investment portfolio; we must first of all remove equities required to cover any equity- linked policies and set aside suitable assets to cover the reserves, including contingency reserves, for other types of N.P. business.

If we suppose that fixed interest assets ought to be available in the first instance to support fixed interest N.P. liabilities, it must follow that the proportion of equities in the W.P. fund will be substantially higher than for the office as a whole. Indeed if the supply of fixed interest investments were not sufficient to support N.P. business it would be possible on this basis to have the whole of the W.P. assets consisting of equity investments and to have some equities left over for the N.P. fund. It has previously been noted that in such circumstances the writing of N.P. business, in addition to providing a proprietary profit, would be the means of achieving an element of gearing, comparable to that obtained through the issue of loan stock in an investment trust.

57. To illustrate this thesis the following ratios were derived from Board of Trade Returns published recently by five mutual life offices. These offices all write W.P. group business on a reversionary bonus basis and so such business can be classed as fully W.P.

W.P. reserves Ordinary shares and office and surplus as property investments column (3)

percentage of total as percentage of total as percentage of invested assets column (2) fund

(1) (2) (3) (4) A 61% 64%

B 49% C 63%

25% 105% 51%

D 19% 30%

50% 28% 56% E 43% 24% 50%

These percentages are calculated on the published values of assets and liabilities. If more realistic valuation bases were to be used it is likely that the corresponding percentages in columns (2) and (3) would show increases, but that the resulting percentages in column (4) would be higher also.


With the exception of office A, it is possible that the W.P. guaranteed liabilities, in addition to the N.P. liabilities, could be considered to be covered largely by fixed interest assets.

58. Our definition of surplus implies that the assets of the W.P. policyholders include not only the invested assets hypothecated to the W.P. fund, but also an asset which we have called the value of the N.P. business. Even though the value of this may be expressed as the difference between two fixed interest quantities, the N.P. business can be regarded as an equity investment. On this assumption the percentage of W.P. funds considered to be invested in equities could be even higher than is apparently the case. The percentages shown above support the view that in many cases more than half of the W.P. policyholders’ funds are invested in equities.

Since, in most investment activities, it is usually assumed that an investor in equities undertakes a greater risk than a fixed interest investor, in order to make a potentially larger gain, it would seem that this feature of equity investment ought to be reflected, to some extent, in the allocation of surplus to W.P. policyholders.

Allocation of equity and proprietary profits

59. We have already seen that where policies are written having guaranteed benefits which are fixed interest in nature, substantial equity investment is possible only where large bonus loadings allow sufficient surplus to be set aside to cover possible swings in capital value and possible interest deficiencies. These swings in value are absorbed by the W.P. policyholders as a whole and we must ascertain to what extent such swings in value affect particular policies within any W.P. class.

Before discussing how the risk of asset fluctuation may be equitably divided amongst policyholders we consider first the effect of the basis of asset valuation on the W.P. class as a whole. To simplify the problem we discuss it entirely in terms of the fluctuation in value of the equity assets.

60. Where surplus for the W.P. class as a whole is determined in terms of a valuation of assets at level V, then there must be enough surplus to cover both the value of guaranteed liabilities and the share in value of N.P. business if assets were valued at the basic level B, namely, the lowest level to which equity prices are thought likely to fall. This means that the investment contingency reserve must represent the difference between the value of assets at level V and


their value at level B. When assets are bought or sold the contingency reserve is reduced by this difference while the difference between the value of assets at level B and their value at level M, the market value level, represents a debit or credit to unassigned surplus, i.e., that surplus which remains after deducting the investment contingency reserve and the value of N.P. business. The size of this entry is independent of the valuation level V. The unassigned surplus and, in consequence, the size of contingency reserve will also be affected if level B is changed.

Where rates of return are expressed in terms of investment income and changes in capital value at level V then the nearer this level is to level M the closer is the resultant return to the return from equity investments. If level V were to approach level B the rates of return would always exclude a measure of capital appreciation and, although they may be more stable, they would always deprive the existing policyholders as a whole of some of the benefit of equity investment. (In effect we would have reserved part of the surplus from consideration altogether.) However it is possible that some policyholders might in fact do better under valuations at level B, because they might buy in at a low level and possibly benefit from a subsequent write-up of level B.

It would appear that a level of valuation other than level M would be consistent with the usual consequences of equity investment only if the values were chosen so as to represent average or trend values of level M. Such values would be chosen so as to remove the effect of temporary fluctuations in market values due to features which were not thought to affect the long-term market assessment of their worth. If we denote such notional values as level N values then it follows that level N values may be above or below level M values for various periods. We have previously argued that the investment contingency reserve measured in terms of such values might be added to unassigned surplus for purposes of allocating profits for N.P. business.

61. The approach to the allocation of equity capital profits and losses amongst policies within a particular W.P. class depends on whether or not each policy can support the fall in value of assets from level V to level B as far as its own guaranteed liabilities are concerned. It would seem that this is a matter of choice to be determined by the bonus policy.

Suppose that the bonus policy were directed so that every policy could at least support a fall in the value of assets from level V’ to level B at any particular time. Then we would achieve a measure of

S


fairness if the asset fluctuations at level V' were reflected in the rate of return while the difference in asset fluctuation at levels V and V' was regarded in the same category as N.P. profits and was allocated in proportion to the surplus available for its support, i.e., the portion of the investment contingency reserve represented by the difference in levels V and V' would be allocated in proportion to surplus.

If level V' were equivalent to level B the whole of the allocation of profits and losses beyond those measured at level B, including profits and losses on purchases and sales, would be allocated in proportion to the unassigned surplus of each policy. This does not seem to be particularly equitable, even if level V were equivalent to level M, in view of the uneven rate at which capital profits emerge: it is then likely to be the case that a policy whose surplus has borne the risk of equity investment in the past may be deprived of the benefits of rises in equity values just as it is approaching maturity and its surplus is falling. However, there might be some attraction in this method if the changes in capital value, as measured with respect to level V, emerged more or less evenly, because one might be able to justify the process as involving a change in investment mix throughout the term of the policy, the investment mix becoming riskier when surplus was increased and safer when surplus was reduced.

If level V were equivalent to level M and level V' were equivalent to level N it might be possible to ignore fluctuations in the values relative to levels M and N as far as distribution in proportion to surplus was concerned, on the grounds that such fluctuations would, eventually, cancel out. If this were done it would be the equivalent of having level V and level V' the same and equivalent to the level N of the notional asset values representing the trend of equity prices.

62. From the preceding discussion we arrive at three possible approaches to the equitable allocation of equity profits.

The first approach is to use market values to obtain the rate of return on assets and to direct the distribution of surplus so that each policy can, as far as possible, support a drop in the Value of assets to level B, the base level. This is equivalent to a unit trust approach but it is not the exact equivalent since there is no guarantee to pool investment experience on this basis.

The second approach is to use notional trend values to obtain the rate of return on assets and to direct the distribution of surplus so that each policy can support a drop in value of assets from level N to level B. This is really equivalent to the first approach, assuming that changes in equity values occur smoothly rather than erratically, but

Mutual Life Office

Summary

277

in effect ignores the distribution of the difference in surplus arising from the difference between values at level M and level N.

The third approach is to base the rates of return on assets whose values are at a level V' which is above level B but which gives values which are more stable than values at level M. In this approach the W.P. policyholders bear only a portion of their full share of the risk of asset fluctuations at all durations and the balance of this risk is borne by policies in the W.P. class in proportion to the assumed surplus under each policy, as measured on the basis of asset values at level B.

63. Under the first two of the above mentioned approaches it might be possible to consider surplus based on notional values as an addition to unassigned surplus for the purpose of allocation of profits from N.P. business, provided these values were relatively stable.

Apart from this, however, the use of stable equity values based on some measure of intrinsic value is inconsistent with the usual consequences of equity investment unless such values reflect the trend in the market’s view. The more violent fluctuations in value can be removed, if one wishes, by use of notional values but ought these to be chosen so as to ignore the fact that equities have been deliberately chosen in preference to fixed interest investments? Such an approach might be reasonable where equities form a relatively small proportion of assets but does not seem to be appropriate in cases where the major portion of assets consists of equities.

64. In this section of the paper we have defined allocation of surplus to include the subdivision of surplus in the capital sense among the W.P. policyholders. We have also defined equity as being achieved if the benefits to policyholders are provided on equivalent terms and have suggested that the benefits provided ought to be consistent with the aims of policyholders in coming to the life office. It would appear that costing of benefits on equivalent terms implies a contribution approach to the allocation of surplus, since we cannot assume in general that costing on the basis of premiums alone would be completely equitable.

Mortality benefits and the incidence of expenses are reasonably well defined and their cost can be satisfactorily pooled and allocated by a contribution approach employing the same principles as are inherent in the determination of N.P. premiums.


In order to apply a contribution approach, definitions of the type of investment benefits expected and of an appropriate method of pooling of investment experience must be obtained, even though these are not always implied in the normal W.P. contracts. In this connection we feel that the high proportion of equities among W.P. assets, including in the category of equity the N.P. business supported by W.P. policyholders, is the determining factor in arriving at these definitions, and in itself would justify a contribution approach if no other justification were available.

65. A contribution approach is implied in the development of rates of investment return which incorporate changes in capital value. The disadvantage of using market values for this purpose is that the policyholders are treated as if they had equity-linked contracts and in the absence of any specific undertaking by the life office to the policyholder it has to be assumed that policyholders do not want their benefits to vary to the extremes possible under such contracts. On the other hand we do not feel that they can avoid altogether the consequences of being equity investors if a substantial proportion of assets is in equities and therefore have suggested that the use of more stable values, which still reflect market trends, would be appropriate in the circumstances. A portion of the asset fluctuation might, however, be covered by surplus as a whole, rather than by each policy at every duration.

A unit trust approach to the allocation of investment experience, based on such asset values, represents a simple method of assessing the investment contribution and is consistent with both the equity- linked and the savings bank methods of pooling of investment risk. The allocation of proprietary profits from N.P. business could be made on similar principles but with reference to the surplus available under each policy which is not required to support its own guaranteed benefits rather than to the share in assets provisionally assigned to it under the contribution system adopted.

66. If the above contribution approach were adopted we could end up by allocating the entire assets and surplus among the W.P. policyholders. Assuming this were possible nothing would be left over since all contingency reserves would be appropriately allocated also. Such allocation would be, of course, provisional, since in assessing the surplus which a W.P. policyholder would take with him on termination regard would be paid to fluctuations in mortality and other experience and also to the total surplus requirements of the office.


If a provisional allocation were not made, SO that a large amount of surplus was retained as a general contingency reserve, there would be a danger that unexpected experience might impinge inequitably on some policies. For example, in an expanding company, policies leaving the office might not receive back a measure of their unused contribution to this reserve even though there was enough new W.P. business to keep surplus at a safe level. A provisional allocation of surplus would allow one to decide whether this experience should be apportioned over all policies, or only over certain classes of policies, and would also provide a means of assessing each policy’s share.

PART IV

ALLOCATION OF SURPLUS IN PRACTICE

Asset Shares and Surplus Shares

67. We have seen that the contribution approach to the allocation of surplus implies that the total value of assets and surplus can be apportioned, at least on a provisional basis, among the W.P. policyholders, just as in the valuation of guaranteed benefits it is possible to assess an actuarial reserve for each policy. For conveni- ence, we call the provisional apportionment of assets to a policy its asset share and we call the difference between the asset share of a policy and the value of its guaranteed benefits the surplus share of the policy. Both asset share and surplus share are dependent on the method of subdivision of assets and surplus and on the method adopted for valuation of assets and liabilities; these depend not only on the types of assets and liabilities but also on the bonus policy of the office.

Surplus shares imply ownership in the sense that they might form a basis for the distribution of surplus in the winding-up of a life office, but the real purpose in developing asset shares and surplus shares is the guidance of the distribution of surplus along equitable lines.

Appendix I shows specimens of prospective surplus shares, calculated on the premium basis, on the assumption that surplus will be distributed in the form of level reversionary bonuses.

68. In Appendix IV general formulae are developed for the asset share and the surplus share of a W.P. policy, showing how allowance can be made for the allocation of N.P. profits on the assumption that the W.P. class to which the policy belongs is deemed to contribute


surplus towards the support of N.P. business. The method chosen involves the use of investment rates of return on the assets deemed to belong to the W.P. class and rates of return on N.P. business obtained by dividing the total N.P. profit by the surplus deemed to be available for support of N.P. business. The development of these rates of return has been discussed in Part II of the paper.

The investment rate of return involves interest and also, in general, a measure of the change in capital values, and is applied to the accumulation of premiums less expenses and cost of life assurance, etc. One of the elements in this accumulation is the N.P. profit, which is measured as the product of the surplus share, or a portion thereof, and the overall rate of return on N.P. business.

69. The form of the asset share is independent of the assumptions made in valuing assets and liabilities, and of the asset mix in which the policy is assumed to be invested, except to the extent that some of the capital profits and losses may be lumped with N.P. profits if they arise outwith the variations in asset values from which are derived the investment rates of return.

If assets are dead short the rates of investment return reduce to rates of interest and this results in a savings bank approach to allocation of investment experience. If market values of assets are used the rates of return represent a mixture of investment income and changes in capital value and the allocation of investment experience is virtually the same as in a unit trust.

Whatever values of assets are used the N.P. rates of return would be applied to the surplus deemed to be available for the support of N.P. business and not necessarily to surplus defined as the difference between value of assets and value of guaranteed liabilities. Where notional values of assets are used, the distinction between these two definitions might disappear.

70. The conclusions reached in the previous section in regard to equity investments imply that where the W.P. policyholders assume some or all of the risk of asset fluctuations the surplus shares at all durations ought to be large enough to cover at least the difference between the notional values used and the lowest likely market values. Such surplus shares would still be available for the protection of the office as a whole.

Where the intention is to measure investment experience on the basis of market values, the surplus share would have to cover the difference between actual market values and the lowest likely market values, but since there is no guarantee to pay out on this basis the


difference is still available for support of other guarantees. This is the justification for using intrinsic values in such cases for measuring the portion of the surplus share which determines a policy’s share of N.P. profits.

71. Where the investment rates of return are based entirely on fixed interest investments it is likely that the rates for each year will represent a trend of office experience. This will depend on the values at which the fixed interest investments are held but unless market values are used such rates will incorporate a spreading of capital profits and losses, realised and unrealised.

It is possible that policyholders paying large single premiums may feel that if their premiums are paid at a time when interest rates on new money are high their assumed rate of return should give greater weight to the current rates of interest. Similarly, when current rates of interest are low, it may be argued by policyholders with annual premium contracts that policyholders paying large single premiums are being treated too favourably. One could say that by allowing for market values of fixed interest securities in obtaining the investment rates of return, whether or not market values are used in assessing the total surplus which can be distributed, suitable recognition is made of this problem. However, use of market values would result in such policies being credited with capital profits, or assessed with capital losses, incurred because the policy term was not necessarily suited to the average term of the fixed interest portfolio. We have already noted that the dating of this portfolio is chosen with regard to the liabilities as a whole and on some expectation of the trend of future interest rates, and so may not be suited to particular policies. The problem generally is whether one ought to have a differential rate of fixed interest return depending on premium- Paying and/or benefit term.

72. The construction of a series of investment generations or the creation of a set of segregated funds within a given W.P. class are possible solutions to the problem stated above, where large group policies are involved, but it is doubtful if this would be practicable or satisfactory for the mass of individual policies.

Where the portfolio consists entirely of dated fixed interest stocks it may be sufficient to make partial allowance for changes in value with interest rate, e.g., to use values which are some way between market values and amortized values. This would give some credit for the incidence of time of payment without exposing single premium and short-term policies to the full blast of changes in market values


which result from an unsuitably long-dated portfolio. If the portfolio were liable to be long, it would seem that the only solution would be to create a notional fund of relatively short-dated securities, valued at market values, which would be hypothecated to single premium and short-term policies. This would be roughly equivalent to a paid-up immunisation approach and would imply that such policies would not benefit fully from the overall investment policy. This disadvantage could hardly be avoided under the circumstances.

Determination of W.P. premiums using asset shares

73. The determination of suitable W.P. premiums forms an integral part of any system of allocation of surplus. Although, under a contribution approach, an attempt is made to allocate with equity the surplus earned by the W.P. premiums, the surplus objectives of the office are more likely to be achieved if the W.P. premiums are based on estimates of likely future experience and bonuses. It is therefore undesirable to determine W.P. premiums without first deciding on the investment and proprietary roles of the W.P. policyholders. This will determine whether small or large bonus loadings are necessary.

In order to ensure that any system of allotment of cash or reversionary bonuses will leave a satisfactory level of surplus undistributed at each policy duration, it will be necessary to construct hypothetical asset shares to compare with hypothetical values of guaranteed benefits, including vested bonuses, at each duration. The level of surplus deemed to be satisfactory will be chosen having regard to the type of asset mix envisaged and the degree to which policyholders are to bear their share of the investment risk. Even if there were to be no equity investment it would usually be desirable to have a build-up of surplus in the earlier durations in order to provide for the contingency of having to reduce the bonuses later if experience were to become adverse. At the very minimum this has to be sufficient to ensure that the guaranteed liabilities would be properly safeguarded even if future experience were to be considerably worse than expected; with this in mind the asset shares could be compared against values of future guaranteed benefits on bases of varying stringency.

74. It can be seen that in the general case the W.P. premiums, however calculated, are tested for a particular contract in the light of an assumed experience and bonus policy by projecting the trend of future surplus under the contract. In fact this projection might


be done on several assumptions in order to check that the projected cash or reversionary bonuses are well covered, and to arrive at suitable minimum W.P. premiums. If larger W.P. premiums are to be charged the minimum premiums could be increased by a fixed percentage. Such a process ensures that there is reasonable consistency among the premiums of similar policies of different terms.

In testing W.P. premiums by means of asset shares one can either base the surplus estimates on the most likely future experience or simply calculate such contracts as illustrations of what might happen under various specified circumstances. An argument for the former approach would be that it is probably desirable to maintain some continuity in the size of bonuses allotted to different generations of policyholders, even though, under a contribution approach, one generation will not be favoured at the expense of another merely because of different assumptions made when determining the premiums. On the other hand, the higher the proportion of equity investments the more difficult it becomes to predict experience and the more one would tend to think of the estimates as illustrations of what could happen.

75. In the estimate of future experience there should also be an allowance for the likely level of profits on N.P. business. This must be made on a realistic basis because the N.P. rate of return may, as we have seen, be low, or even negative, if calculated on a published basis, due either to a stringent published valuation basis or to a rapid increase in new business, or to a combination of these factors. How- ever, the stringency of the valuation basis and the relative proportion of N.P. business must be kept in mind in determining the pattern of the distribution of surplus over the policy term—the greater the proportion of N.P. business and the greater the rate of growth, the more surplus must be held back in the earlier durations.

The estimate of N.P. profits can only be made on the basis of past trends unless there are specific grounds for thinking otherwise. Since the level of N.P. profits depends on a combination of the profitability of the N.P. business and the volume of N.P. business written relative to the volume of W.P. business written, the former in turn depending on the forces of competition and on future experience, any estimate of the future level of N.P. profits is necessarily imprecise. There would be a natural tendency for the estimate to be conservative.

Valuation for surplus

76. In Part II an outline was given of the objectives of a valuation for surplus. The paper now concludes with a brief description of


how such a valuation might be done for a particular life office. This description illustrates some of the points discussed previously in the paper.

77. It is possible to perform a valuation for surplus only if the bonus policy of the life office, and the corresponding investment policy, are known. It is assumed that the office intends that W.P. policyholders be invested substantially in equities and that each policyholder bears a fair share of the risks of such an investment policy; at the same time it is not intended to expose individual policyholders to the full rigours of equity investment. It is assumed also that the office hopes to distribute surplus by means of level vested reversionary bonuses, supplemented by non-vested bonuses which are available only on termination, but that it is not committed to such a policy. This method of surplus distribution has the dual advantages of being simple and of enabling surplus to be held back in sufficient quantities to provide the necessary overall surplus for expansion of N.P. business and investment in equities.

The further assumption is made that about half of the liabilities are in respect of N.P. business and that these are covered by fixed interest assets. It is also assumed that about one-third of the assets by book value are equities. Thus the investment policy is largely consistent with the office’s view of the role of the W.P. policyholders.

78. The first step is to remove from the valuation any special classes of W.P. policyholders which are considered to be self-supporting and to have a separate set of assets assigned to them. Similarly, it is necessary to eliminate assets and liabilities which are matched because of specific guarantees, e.g., equity-linked contracts and any portion of ordinary contracts which contain similar equity-linked guarantees. Sufficient fixed interest assets are then deemed to be assigned to cover the N.P. liabilities, including contingency reserves, and on this assumption the value of N.P. business is obtained in accordance with the principles suggested in Part II of the paper.

Equities and fixed interest assets assigned to the W.P. business are valued using notional values which represent trend values rather than values based on some measure of intrinsic worth. These values will not fluctuate as sharply as market values but may be revised at least once a year. It is possible for the notional values to be greater than the corresponding market values but they are more likely to be below market values than above them. W.P. guaranteed liabilities are all fixed interest in nature and are valued on a basis consistent with the premium basis for new N.P. business rather than on a


notional value or a market value basis, because they cannot be covered by the fixed interest assets in the W.P. fund.

79. The surplus revealed by this valuation is measured by

Notional value of W.P. assets plus Value of N.P. business, less Value of W.P. guaranteed benefits.

It is assumed that a separate N.P. fund is kept containing the fixed interest assets notionally assigned to this fund. The value of N.P. business is the difference between the value of assets and liabilities on a market value basis, i.e., the N.P. surplus revealed by a market value valuation. This surplus will include an investment contingency reserve in respect of fluctuations in N.P. assets relative to N.P. liabilities. The N.P. surplus is notionally allocated to W.P. policyholders in proportion to their W.P. surplus and value for it can be obtained provided it can be transferred safely to the W.P. policyholders on termination of their contracts or on allotment of reversionary bonuses.

Rates of return on W.P. assets and on N.P. business will be calculated from these values and from the corresponding values obtained from previous valuations of assets and liabilities.

80. The next step in the valuation for surplus is to develop asset shares and surplus shares for a network of policies, having different ages at entry, durations and terms, using rates of return values calculated over a period of years. These values would be smoothed in order further to dampen down fluctuations, but should reflect the trend in the values of the rates of return.

A more complete set of asset shares and surplus shares per unit policy is then developed by interpolation from the network figures, and office totals obtained by multiplying the unit values by valuation totals of policies in force. The total of asset shares should agree reasonably well with the total of W.P. assets plus value of N.P. business, while the total of surplus shares should agree with this latter total less the value of W.P. guaranteed liabilities. Closer agreement could be obtained if required by adjusting the rates of return.

81. In calculating the rates of return it is assumed that all changes in the notional values of assets are incorporated in the rates of investment return rather than allotted in proportion to surplus. This approach would be consistent with the policy of the office and would


imply that the surplus share, at each duration, should be at least

sufficient to cover the difference between the asset share based on

notional asset values and an asset share based on a more pessimistic

view of possible market values.

It will be necessary to test that this relationship is likely to continue

in the future if the present scale of reversionary bonus is maintained

and in addition to test the effect of variations in future experience

on future bonus levels. A series of projections of bonuses (both

reversionary and terminal) can be made assuming varying levels of

future experience to maturity of a policy, with or without allowance

for N.P. profits. The relationship between the reversionary bonus

and the terminal bonus will depend partly on the level of notional

asset values and partly on whether or not there is a commitment to

pay the same level rate of reversionary bonus to all policies.

The future experience assumed need not be that implied in the

valuation basis for guaranteed liabilities, nor are we confined to

assuming one rate of return throughout the future term of a contract.

As part of the testing process the asset shares would be reduced to

amounts which did not allow for unrealised capital profits beyond

what has been allowed for on a book write-up of assets and the size

of level reversionary bonus examined on various assumptions as to

future experiences. Apart from this, similar considerations would

apply as when calculating W.P. premiums.

32. The minimum amount of surplus to be retained as not available

for distribution must include the value of N.P. business and the

values of the investment contingency reserves, and allow for the value

of present W.P. guaranteed benefits on a stringent basis reflecting

possible adverse experience in the future. However, this minimum

is likely to be exceeded because of the inclusion in the surplus pro-

jections of future reversionary bonus on the tentative scales.

The amount of surplus which can be distributed in the year is also controlled by the published valuation bases for assets and liabilities.

These bases may act as a constraint on the possible bonus policy

derived from the valuation for surplus. If possible, this type of constraint should be avoided since it will make it more difficult to

maintain a level reversionary bonus system and at the same time

retain equity in surplus allocation.

Summary

83. Comparison of the processes involved in calculating W.P.

premiums and valuing for surplus shows that a very similar procedure

is followed in both operations, but in the latter account must be


taken of the present assets and liabilities as well as of possible future conditions. The valuation for surplus is therefore to be regarded as a reassessment of the premium scale. The process of reassessment is continuous, particularly if the investment policy is equity orientated, because there is considerable uncertainty as to future conditions and all that one can do is to steer a conservative course in the most likely direction and check the position frequently in the light of events.


APPENDIX I

HYPOTHETICAL BUILDING-UP OF SURPLUS UNDER ENDOWMENT ASSURANCE POLICIES

The meaning of fund, guaranteed benefits and surplus are in accordance with the descriptions given in paragraphs 14, 15 and 16 of the paper, i.e., we have

Surplus = Fund-Value of guaranteed benefits.

Since a discontinuity in surplus arises at a bonus declaration it seems more correct to measure surplus immediately prior to the bonus distribution, i.e., to exclude the t-th year bonus from the value of guaranteed benefits.

If the premium for an 12 year W.P. endowment assurance issued at age x is calculated assuming interest at i% p.a. and future compound bonus at b% p.a. then :

(i) Fund = bonus reserve on premium basis, i.e.,

where S = sum assured

Bt = attaching bonus after t years

and

(ii) Value of guaranteed benefits = X or Y where X is the greater of

(a) the net premium reserve for the sum assured, i.e.,

(this represents the surrender value of the sum assured) and (b) the gross premium reserve for the sum assured and

attaching bonus, i.e.,

(this represents the single premium required to buy an N.P. policy which will provide the guaranteed benefits on the continuation of the office premium)

and Y is the net premium reserve for the sum assured and attaching bonus, i.e.,

(this represents the reserve for the N.P. portion of the policy plus the reserve for surplus allotted in the form of additional guaranteed benefits).

Mutual Life Office

TABLE I

i=4% b = 2%

289

10 year endowment maturing at age 50. = 98.542 per mil

Value of guaranteed Surplus

(Surplus÷Fund)

Fund benefits percentage

Duration (F)

X Y F-X F-Y (F-X)÷F (F-Y)÷F

2 206.2 169.1 183.7 37.1 22.5 18 11 5 547.8 449.2 517.0 98.6 30.8 18 6 7 799.5 718.5 767.9 81.0 31.6 10 4

10 1219.0 1195.1 1195.1 23.9 23.9 2 2



(Surplus+ Fund) percentage

Duration Fund benefits

(F)


5 177.2 99.0 131.5 78.2 45.7 44 26 10 392.5 218.9 311.4 173.6 81.1 44 21 15 652.2 392.4 545.0 259.8 107.2 40 16 20 964.6 736.2 847.8 228.4 116.8 24 12 25 1342.9 1181.8 1243.7 161.1 99.2 12 7 30 1811.4 1775.9 1775.9 35.5 35.5 2 2



(Surplus÷Fund)

Duration Fund benefits

percentage

(F)


5 101.6 40.0 57.2 61.6 44.4 61 44 15 375.9 148.3 243.4 227.6 132.5 61 35 25 776.5 402.2 563.4 374.3 213.1 48 27 35 1340.8 974.6 1087.4 366.2 253.4 27 19 45 2139.0 1906.4 1953.5 232.6 185.5 11 9 50 2691.6 2638.8 2638.8 52.8 52.8 2 2


TABLE II

i = 6% b = 3%


Value of

Fund guaranteed Surplus

(Surplus÷Fund)

Duration benefits

percentage

(F)


2 209.0 155.6 164.5 53.4 34.5 26 17 5 572.3 425.8 519.8 146.5 52.5 28 9 7 853.1 730.5 797.7 122.6 55.4 14 6

10 1343.9 1304.8 1304.8 39.1 39.1 3 3



(Surplus÷Fund)

Fund percentage

Duration benefits

(F)


175.4 74.2 105.9 101.2 69.5 58 40 10 409.7 172.7 233.8 237.0 135.9 58 33 15 720.8 360.5 525.6 360.3 195.2 50 27 20 1132.5 776.8 902.0 355.7 230.5 31 20 25 1681.0 1398.6 1471.0 282.4 210.0 17 12 30 2427.3 2356.6 2356.6 70.7 70.7 3 3



(Surplus÷Fund)

Fund benefits percentage

Duration (F)

X Y F-X F-Y (F-X)÷F (F-Y)÷E

5 92.3 23.7 36.5 68.6 55.8 74 60 15 380.9 97.7 185.2 283.2 195.7 74 51 25 889.9 379.2 521.4 510.7 368.5 57 41 35 1753.7 1130.5 1236.3 623.2 517.4 36 30 45 3223.8 2727.4 2775.0 496.4 448.8 15 14

50 4383.9 4256.2 4256.2 127.7 127.7 3 3


APPENDIX II

RATES OF RETURN

Basic principles

1. Consider a class of policies for which a life office holds a segregated group of assets.

At time t, let Vt = value of the assets, or fund, where value is not defined at

this stage and may be market value, book value, etc. It = rate of change of fund due to receipt of net investment income. Ct = rate of change of fund due to change in capital value of

investments. Ft = rate of change of fund due to receipt of net income from

non-investment operations. Then

where

and are the rates of change of the unit fund due to investment and non-investment operations respectively.

Similarly, if there are K such funds, each with a different group of segregated assets,

(1)

where

Proprietary life office

2. Consider now a proprietary life office transacting only N.P. business. On the assumption that there is no reason for requiring different asset mixes for different segments of the assurance liabilities, there are two funds-the assets covering the assurance liabilities and the assets held for the shareholders’ fund. The situation could be described in terms of equation 1 above but this would not show specifically any transfer of profits from the assurance fund to the shareholders’ fund.

Assume that any profits or losses arising from the N.P. business

T


are settled immediately by transfer respectively to or from the shareholders’ fund.

At time t, let

PVt = value of shareholders’ or proprietors’ fund.

NVt = valuation reserve in respect of the N.P. business.

NPt = profit from N.P. business.

= rate of change of unit fund K due to investment operations (i.e., the rate of investment return).

= rate of change of unit fund K due to non-investment operations, excluding transfers of profits or losses.

= rate of return per unit of shareholders’ fund from investment and assurance operations.

K is used to represent P or N, as the case may be.

The equations corresponding to equation (1) above are

(2)

(3)

where results from changes in shareholders’ capital and the payment of dividends to shareholders.

By definition

so that

and

(4)

(5)

i.e., the total return to the shareholders’ fund from investment and insurance operations is

(a) investment return (interest and capital) from the assets in both funds

plus (b) net assurance income to N.P. fund less (c) change in N.P. reserves, including changes in contingency

reserves and changes resulting from changes in the valuation basis.

If the investment mix for both funds is assumed to be the same,


3. Suppose the values of derived above have been obtained from a published valuation under which N.P. assets and liabilities, NAt and NVt respectively, are valued conservatively. (NAt = NVt).

If these values become NAt and NVt respectively in a valuation for surplus

(6)

(7)

and

if measured in terms of PVt (8)

if measured in terms of PVt. (9)

The above expressions assume that the allocation of investment income between the two funds is unchanged as a result of the revaluation.

Mutual life office

4. It would be possible to apply equations 4 and 5 to a mutual life office consisting of one W.P. fund and one N.P. fund, where the W.P. fund and N.P. fund of the mutual office were considered equivalent to the shareholders’ fund and the assurance fund of the proprietary office respectively. However, this would imply that the N.P. profits were allotted in proportion to the W.P. fund, whereas the proprietary interest of the W.P. policyholders is considered to be measured in terms of the portion of W.P. surplus deemed to be available directly for the support of N.P. business.

To allow for this, the W.P. fund must be split as follows :

In respect of one W.P. class, W, at time t, let

= valuation reserves in respect of the W.P. guaranteed benefits in the W.P. class.

= value of surplus pertaining to the W.P. class.

= value of surplus pertaining to the W.P. class that is considered available for the support of N.P. business.

= profit from the W.P. guaranteed benefits.

294 Then

Allocation of Surplus in a

(10)

(11)

(12)

(13)

and

where

= rate of return from N.P. business.

Both portions of the W.P. fund are assumed to be subject to the same rate of investment return,

If is measured in terms of a gross premium valuation, excluding

bonus loadings, represents the net of (bonus loadings less cost of bonus) at time t.

5. Suppose the N.P. business is revalued as described in paragraph 3 above, then as before

(14)

(15)

It follows that

(16)

and

(17)

while

if measured in terms of (19)

again assuming that the allocation of investment income to the N.P.

fund is unaltered.


6. Where the rates of return, are based on values of assets which differ from market values, whether or not the values are chosen to provide for a smoothing out of fluctuations in market value, the “ true ” values of the funds, are expressed in terms of the market value of the assets, and the values of surplus become

where

(20)

Also

(21)

7. If the entire W.P. fund, is deemed to be invested in a set of notional assets, as described in paragraph 23 of the paper, so that the investment risks in respect of the actual portfolio are under- written by some of the W.P. classes only, the values of and

could be adjusted to values and based on market values, for those funds which can support the actual asset mix, while the change in capital values, and investment income, in respect of the W.P. funds which cannot support the actual asset mix are apportioned to these funds which can, in proportion to their surplus as measured on a notional value basis.

i.e. for funds which support the actual asset mix

where (22)

(23)

the summation K being taken over all W.P. funds which do not support the actual asset mix, and the summation W’ being taken over those funds which do.

Similarly

where

(24)

(25)


APPENDIX III

THREE APPROACHES TO THE POOLING OF RISKS

Pooling of risks under equity-linked policies

1. There are many varieties of equity-linked policy. Considering the type where the policyholders do not receive bonuses, i.e., where they are essentially N.P. policyholders, the office guarantees expenses and, in some cases, income, but does not guarantee capital except for a minimum sum assured on death, and, possibly, on maturity. The rules for distributing investment profits and losses are well defined and, indeed, are automatic and although policyholders pay a premium to cover the cost of the capital guarantee any profits or losses on this account are allocated elsewhere. It follows, by definition, that particular assets are deemed to be hypothecated to this class of policy and each policy’s share in the assets is determined on unit trust principles.

2. Where equity-linked contracts are issued on a W.P. basis it is usually in order to allocate interest income, less the experienced cost of mortality and expenses, and profits or losses arising from any capital guarantee. The interest income from the hypothecated assets is probably pooled in the same way as the capital profits and losses and allocated on unit trust principles. In determining profits and losses, mortality and expense costs could be pooled with other classes of business having similar mortality and expense characteristics, but the cost of the capital guarantee ought to be borne only by this class of policy. It would seem impractical for this to be done until a considerable volume of business has developed and until then the risk would have to be “reinsured” with the rest of the office by deducting a “premium” from the overall profits of the class (other than capital profits).

Pooling of risks under the North American contribution system

3. This system was developed in the context of a mutual life office having little or no N.P. business, and any proprietary risk in respect of the guaranteed benefits under W.P. policies is intended to be borne by the policyholders. Broadly speaking, the excess of premiums paid over what is required to maintain the reserves for guaranteed benefits is returned to the policyholders, year-to-year fluctuations in experience being smoothed out in this process. The emergence of surplus can be controlled by choosing a more or less stringent valuation basis or, more directly, by reducing the returns

Mutual Life Office 297 in the earlier durations and thus building up specific contingency reserves or surplus. Normally the contingency reserves act as buffers to absorb violent fluctuation in surplus flow, and there will be also a tendency for surplus to be stored up when profits are high in order to be able to maintain the bonus scales if experience worsens in the future.

This system is best regarded as involving a return of excess premium. The rules for determining the allocation of surplus are essentially those applied in assessing N.P. premiums, i.e., the effort is made to charge policyholders no more or less than they might have been charged had their experience been predictable at the outset. It should be emphasised that this is not done simply by dividing up the year’s profits, The total amount of distributable surplus is determined after allowing for the trend of future earnings and for contingency reserves ; it is this amount which is distributed in proportion to the various contributions to surplus from interest, mortality and expense. The interest, mortality and expense experiences assumed in calculating the proportionate contributions are based on trends rather than on a single year’s experience.

4. The pooling of mortality and expense experience is essentially as described in paragraph 51 of the paper—the fact that the premium or the reserve may be based on an out-of-date mortality table is of little consequence, since this affects mainly the emergence of surplus and not the actual cost of mortality for which the policy is charged.

5. The pooling of investment experience involves some transfer of profits and losses among different generations. Usually capital profits and losses are relatively small and are merged with interest profit and spread over a period of years, the fluctuations being absorbed by the contingency reserves. This is quite satisfactory in the context of the investments made, since these are predominantly dated fixed interest securities, or mortgages, and many of the fixed interest securities can be held in the balance sheet at their amortized values.

This type of asset structure leads to a “savings bank” approach to the allocation of interest, policyholders being allocated their share of the total interest income (on a “trend” basis rather than on a current year basis) in proportion either to their reserve, or to some approximation to their reserve. But because the investments are not dead short it is possible for the earned rate of interest to be affected by the level of new business—for example, a large influx of new policyholders at a time when interest rates are rising would


cause the earned rate of interest to rise faster than it otherwise might have done.

This situation is thought of as being seriously inequitable only where very large single premiums are being paid, as under group annuity policies. In such circumstances attempts have been made to follow some kind of generation approach in order to give more direct credit for investment conditions at the time of purchase.

6. Miscellaneous profits, including any of a proprietary nature, are usually allocated in proportion to the other items of surplus although profits or losses which can be identified with any particular class of policy may be allocated directly to that class. No theory has been developed for the allocation of proprietary profits in cases where the W.P. policyholders support a sizeable volume of N.P. business.

In conclusion it may be noted that the determination of new W.P. premiums is concomitant with the development of a scale of projected cash bonuses, based on an assumed experience, so that the premiums are in effect loaded to pay for the projected bonuses. Because of the relatively stable nature of the assets the bonus loading need not be large and can be of the order of 20% of premiums.

Pooling of risks under the level reversionary bonus system

7. Strictly speaking, a level reversionary bonus system is one in which surplus is allocated in the form of reversionary bonuses calculated at the same rate per sum assured and/or bonus throughout the policy term. In practice, bonus rates will vary by year of experience, although usually the rate will be the same within each W.P. class regardless of age at issue, duration, or type of policy.

Under this system all surplus, including surplus arising from bonus loadings, is pooled and distributed according to the relatively simple bonus formulae ; no attempt is made to allocate surplus in excess of bonus loadings to particular policies according to any theory of pooling of risk. The equitable nature of this bonus system is based on three features :

(a) The premium basis incorporates an estimate of likely mortality and expense and a loading for a rate of reversionary bonus which is a substantial proportion of the current declared rate of bonus.

(b) It can be shown that for most policies a rising bonus rate can compensate for a rising interest rate to the extent that, for long periods, it may not be necessary to change significantly

Mutual Life Office 299 the level of W.P. premiums which support the current rate of bonus.

(c) The valuation basis for liabilities can be altered to reflect current experience.

8. Where the investments are fixed interest in nature they can be of varying datings, from dead short to dead long, and it may be a matter of policy to vary deliberately the average dating in order to gain a higher return. In these circumstances the investment policy may not be the one which is most suitable for particular categories of life assurance policies were each category to be considered in isolation, since claims may have to be paid in full at times when the market value of the assets may be considerably lower than the book value. The notional loss is in effect made up by the continuing policyholders, who similarly benefit from any notional profits when conditions are reversed. Even if an immunising policy were adopted (and we would question whether such a policy is justified for W.P. business) it is unlikely that there would be any attempt to differentiate bonus rates according to date of entry.

9. As with the contribution system, the theory of the reversionary bonus system implies that capital profits and losses either are relatively small or emerge smoothly to affect the overall rate of interest gradually. Where the investment policy is such that the capital profits and losses may be large, the traditional way of dealing with them is to build up an undisclosed reserve in order to buffer the fund against large fluctuations due to sustaining realised or unrealised capital profits and losses. (There has, in fact, been a trend in the last two years towards showing such reserves in the balance sheet). Realised profits and losses are therefore rarely large enough to affect bonus in any one year but from time to time it has been considered advisable to take credit for substantial amounts of capital profit, sometimes unrealised, and this is often done by declaring special bonuses. Such bonuses by their very nature cannot be loaded for in the premiums and therefore it is necessary to pay some regard to the manner in which they were derived so that they may be allocated equitably. This implies a contribution approach and it is likely that most special bonuses which are vested on declaration take some account of the average funds which the various W.P. policyholders have entrusted to the life office during the period in which the special profits accrued.

10. Apart from the special bonuses referred to above, it is likely


that reversionary bonuses will change only gradually to reflect chang- ing conditions. This implies a smoothing of experience from year to year on principles which, overall, may not be very different from those adopted under the contribution system ; the degree of smoothing may be greater because of the longer dating of the investments and because the distribution of surplus is controlled by the assumption of a future level rate of bonus. It is possible that a contribution approach would give roughly similar results at maturity for most endowment assurance policies, given the same investment and valuation conditions and surplus policy.

It is interesting to note that the reasons advanced for the equity of the reversionary bonus system assume essentially the same definition of equity as forms the basis of the contribution system.

APPENDIX IV

ASSET SHARES AND SURPLUS SHARES

1. A valuation group of W.P. policies can be considered as a sub- fund within a W.P. class. Suppose that there are It policies at time t for the same class of policy, age at issue and year of issue, and that the distribution of surplus is such that at all durations each policy can support the asset mix of the W.P. class. Then the same rates of investment return, P δ Tt, can be used for the group of policies as for the W.P. class.

In respect of each of the lt policies, at time t, let

PVt = asset share. SVt = surplus share. GVt = value of guaranteed benefit, defined as the reserve less

value of future bonus loadings. SVNt = value of surplus that is considered available for the

support of N.P. business. GPt = profit from the guaranteed benefits.

= experienced force of mortality. = experienced force of withdrawal.

Pt = policy premium net of expenses. Dt = benefit paid on death, net of expenses of claim. Wt = benefit paid on withdrawal, net of expenses of claim. St = benefit paid on surviving to time t. C = cash bonus.


Bt = value of vested reversionary bonus allotted (on the same valuation basis as

= change in due to change in valuation basis. = net premium on the valuation basis for i.e. Pt

less bonus loading. Then

where

= rate of return from N.P. business, as defined in Appendix II.

2. The above formulae have been developed on the basis of one particular definition of W.P. guaranteed benefits and therefore would have to be modified if other definitions of W.P. guaranteed benefits

were adopted. The formula for shows that the usual asset

share relationship applies but with the addition of an element of N.P. profit.

3. Where the rates of return are based on values of assets which differ from market values and the policy does not thus bear its full share of fluctuation in asset values, as described in paragraph 62 of Part III, a third element is added to the asset share equation. This is

where

= surplus share with assets valued at the basic level B, below which they are unlikely to fall

= asset share with assets valued at market value.

This additional element could be ignored if the values of assets on which and are based were chosen so that, over a period,

was small.


SYNOPSIS

This paper sets out to demonstrate a set of principles for the allocation of surplus in a mutual life office.

Surplus is defined as a capital item and the principles governing its measurement and allocation are developed without regard to the method by which surplus may be distributed in the form of cash or additional guaranteed benefits. Particular attention is paid to the special problems arising where there is substantial investment in equities or where a substantial portion of surplus comes from the profits of without profits business.


DISCUSSION

Mr. A. N. Calder, introducing the paper, said :—The paper which we have the honour to present this afternoon is, as the title indicates, concerned with the allocation of surplus in a mutual life office. Reference is made in the Introduction to our first paper almost three years ago and to the desire we had then to examine the effects of applying the principles and techniques described in that paper. I think it would be true to say that what we have now produced is something rather different from what we had in mind three years ago. While some of the material is the same, we have introduced further ideas and have developed others along different lines. The starting-point is really a generalised definition of surplus from which we advance by regarding W.P. policy holders as the proprietors of a mutual life office and by considering N.P. “business as a particular equity investment of these proprietors. Our next step is to base an allocation of surplus on a contribution approach on the grounds of achieving equity and to do this we have used some of the techniques from our first paper to develop asset shares which incorporate rates of return from Stock Exchange investments and from investment in N.P. business. As we progress we notice, and in fact are guided by, the interaction of the ratio of surplus to the value of guaranteed liabilities, the level of new business, the asset mix and bonus and investment policies. The need to arrange an investment policy so that the asset mix appropriate to a class of business in isolation is adopted is of paramount importance and serious inequity would result if this were not allowed for in an allocation of surplus.

The implications of a contribution approach are examined with the resulting need for a suitable method of pooling investment experience. In particular, an investment policy which incorporates a high proportion of equities provides of its own accord a justification for a contribution approach. The extent to which a W.P. policyholder should be exposed or, indeed, expects to be exposed to the full effects of equity investment is examined and an approach using trend values rather than market values of assets would appear to have some merit.

I feel that it would be useful at this point to interpolate a few remarks regarding our adoption of the contribution principle which may not have been stressed in the paper. To a large extent we have been influenced by the trend in recent years to declaring special bonuses in addition to normal reversionary bonuses. We feel that if we depart from a situation in which W.P. policies are written on approximately equivalent terms, so that broad equity is achieved by means of a level reversionary bonus system, then some measure is required of the relative entitlement to surplus of different classes of W.P. policy. In other words, if we attempt to distinguish between different classes of W.P. policy, then we feel we are forced into considering a contribution approach to give an indication of what constitutes equitable shares of surplus for policies which can be said to belong to different W.P. classes. We feel, therefore, that what we have described in the paper could be used (in circumstances where it is felt that this is desirable) to get a measure of the entitlement to equitable shares of surplus for policies from different W.P. classes rather than for different policies within a given W.P. class. Such a measure would be an invaluable guide in determining the level of surplus which can in equity be considered as belonging to a particular class of W.P. policies. Whether, in fact. this approach should

304 Allocation of Surplus in a be taken further and applied to individual policies within a given W.P. class, as illustrated in the paper, is clearly a matter of judgment having regard to the type of W.P. contract and the degree to which such refinement would be of any significance. At least it could be used as a means of testing for gross inequity in surplus allocation.

Reverting to the paper itself, we have ended our journey by examining the results of applying the afore-mentioned principles to a valuation for surplus, deciding in the process that such a valuation can be regarded as a reassessment of the premium scale. During our travels we have indicated four shortcuts, each of which appears as a summary of a Part of the paper. We have also, however, made several detours and for the benefit of those of us who wish to keep to the straight and narrow we have called such detours “Appendices". The principles of the paper are not seriously obscured by omitting to read the Appendices and they may be examined at the reader’s leisure, except perhaps Appendices II and IV which may be examined only at the reader’s peril.

I should like to conclude these introductory remarks by emphasising that the opinions expressed in the paper belong solely to the authors and for that reason, if for no other, we expect them to be challenged. This, of course, is the purpose of the discussion and if Mr. Shedden is looking forward to it with slightly less enthusiasm than I am, then I am sure this is only because he has to reply to it.

Mr. R. Hogarth, opening the discussion, said :—Tonight’s paper describes a possible system of allocation of capital profit and dividend income and profit from N.P. business in a mutual life office, based on the premise that the W.P. policyholders are the proprietors of the office and using the asset share technique made familiar to us by the previous paper by the same authors. Justification for this premise is said to arise because the estate rises and falls with the volume of business in force and so can be regarded as distributable to the W.P. policyholders in the long run. Surplus, therefore, does not have its usual meaning but, defined as the difference between the values of the assets and the guaranteed liabilities, it includes the office’s estate.

In Part I of the paper, the authors are concerned with definitions and draw an analogy between the shareholders of a proprietary life office transacting only N.P. business and the W.P. policyholders of a mutual life office transacting all types of life and pensions business. The solvency basis they apply to valuing N.P. guaranteed liabilities in the proprietary office represents the debenture right of the N.P. policyholder to the value required to buy elsewhere another policy giving him equivalent benefits and, although a similar approach to mutual office W.P. policies is described, this undervalues the guaranteed benefit and so exaggerates surplus. The second method of valuing the paid-up sum assured and vested reversionary bonus on a N.P. premium basis seems more appropriate in the context of a continuing fund. From Appendix I it can be seen that the use of this method reduces the surplus under a new endowment policy by up to a half compared with the solvency approach, this surplus being equivalent to the reserve to pay future bonus arising from the usual effect of the increasing cost of level bonus paid by level annual premiums. The absolute size of the percentages does not seem high when one considers the recent and current fall in the level of the U.K. equity market, especially if one deducts the value of the bonus about to be declared, but it must be remembered that the figures apply to new policies and are calculated on the premium basis. No free reserve or portion of the estate has therefore been included.


This surplus together with the office’s estate is available for the various factors listed by the authors in paragraph 6 and for bonus policy. The authors then go on to measure surplus by means of a valuation for surplus, their intention being to derive rates of return on (i) the W.P. assets including both capital appreciation and interest and (ii) the W.P. surplus applied to support N.P. business. With such a valuation one should use fairly consistent bases in placing a value on both assets and liabilities and, while one can argue as the authors do that if one is segregating W.P. and N.P. business this consistency need not extend over both divisions, such an approach can lead to a different value being placed on £100 nominal of 2½% Treasury depending on the liability it is deemed to cover.

Continuing the analogy between the shareholders and the W.P. policyholders, the authors discuss means of placing a value on the N.P. business of the proprietary office so that the rate of return on shareholders’ surplus supporting this business may be found. The first method they discuss ob- tains this value by discounting future profits from this business released by the published valuation basis. Withdrawals from the N.P. class by surrender or lapse may mean a profit on this basis if the value paid is within the reserve, but the net result at early durations may be a loss—a drain on surplus advanced by the shareholders to finance new business strain. Would the authors include allowance for these withdrawals in, for example, the N.P. whole of life class projection as well as the estimate of future new business that strict theory requires ?

The second method of valuation proposed for this business uses market rates of interest to obtain the value of the guaranteed liabilities and the covering fixed interest assets. With the present high level of market interest rates, negative values will occur at quite high durations in certain classes so that the question of including an allowance for withdrawals again arises. The use of market rates of interest which vary from year to year means that the value of this business will also vary. A proprietary office transacting only N.P. business is an artificial concept except possibly for a very young office and in considering the segregation of this business in the case of the mutual office it is important to remember that if the office taken as a whole is in a matched position then the N.P. business standing on its own is unlikely to be. Any loss from mis-matching in the N.P. division may be offset by profit on the W.P. side. The authors should therefore consider this mis-matching question as a whole and the two mis-matching contingency reserves they mention in paragraphs 32 and 42 should be combined to produce a smaller net figure depending on the extent to which the whole office is not matched.

The bases of valuation proposed for use in this valuation for surplus depend on the type of assets that are deemed to cover the liabilities so that, if the assets for the W.P. business are largely equities, then something close to market values can be used for assets while for guaranteed liabilities a basis akin to that from new premiums is suggested. If fixed interest assets are available to cover such liabilities, a market value basis may be adopted in a similar way as for N.P. business. As already mentioned, this means that the fixed interest stocks making up the balance of the covering equities will be valued on a different basis from the fixed interest stocks covering N.P. liabilities. This is probably better avoided and, in view of the advantage of the use of a rate of interest which varies little from year to year, the long-term rate of interest expected from future investments over the average term of the business should be used. With this, the values of guaranteed liabilities would progress more evenly.

With regard to paragraph 34 it would be a brave valuer who would make


allowance for profit from a departure from an immunised position before that profit has been earned. How far ahead does one look in taking such a view of the market? Surely not long enough to worry about waiting until the profit does eventuate. In any event it may never do so if the view held is proved wrong and then one will drain surplus of two amounts—the profit one did not make and the loss that one did. Even now, with the gilt market down in the bargain basement, yields at their historic high point and interest rates falling in other countries, a case might be made for going short in the short term.

Appendix II develops symbolically the rates of return for the two types of office allowing for W.P. classes which cannot support the actual asset mix of the office as described in paragraphs 21 to 23. This illustrates the development of the rates of return used by the authors to allocate surplus to individual policies in later parts of the paper.

In Parts III and IV of the paper the authors attempt to allocate the surplus they have determined in the earlier parts of the paper. Because their definition of surplus includes the estate and the reserves for future bonuses, they must determine how much can safely be distributed as cash or reversionary bonus and how much should be retained. The amount retained will depend on the bonus policy of the office and how it in turn determines the relationship between the reversionary bonus and any terminal bonus. Surplus will also be needed to maintain investment contingency reserves to cover possible depreciation in assets and to provide reserves for mortality and investment losses in non-profit business.

The authors talk of considering the expectations of policyholders to help them in their decision but surely, if policyholders have come to an office, they either know or should know of its traditions and these will almost certainly involve pooling of investment risk and a maintainable reversionary bonus, possibly augmented by a special or terminal bonus of more recent origin, by which means may be distributed capital profits possibly in excess of those needed to recompense for the shortfall in interest from the original equity investments.

The paper does mention pooling of investment risk in paragraph 50 but when it turns to considering pooling of risks in general, while it is quite happy about pooling mortality and expense risk, it baulks at pooling of investment risk mainly because the policy document does not usually say specifically that this will happen. The authors, therefore, see no theoretical objection to a contribution method applied to individual policies which will in addition smooth any inequity in the premium basis, provided that measures of the surplus pertaining to a policy and of the liability under its own guaranteed liabilities can be obtained. This is fine for a new office but with a mature mutual office it is likely that a sizeable estate exists and this estate is in the nature of a free reserve passed on by succeeding generations of policyholders and augmented to grow with the office. This estate will likely be providing a good part of current reversionary bonuses as can be seen by comparing current W.P. premiums and the bonuses they can them- selves support with current levels of reversionary bonus.

Can a reasonable basis be found for the allocation of this estate to individual policies? The authors do not seem to answer this question. In paragraph 66 they raise the possibility of provisionally allocating all the assets and surplus among the W.P. policyholders but no basis is defined for doing this. Indeed one gains the impression from Parts III and IV that a new office is being considered, i.e., one without any estate. There does seem to be a danger that, if the estate is provisionally allocated, then by not seeing the wood for the trees one will distribute as bonus part of this estate.


By not allocating it, one can keep a watch on its size relative to the total volume of business and in addition one can maintain a new business policy that will keep each class of new business at approximately the correct level.

This is not to say, however, that the authors’ method is not extremely flexible and exclusion of the estate from the provisional allocations does not mean that capital profits and losses and interest income from the assets of the estate cannot be included in some measure in the investment rates of return. This would be a means of allowing a policy close to maturity to share in any late rises in equity values when, as in paragraph 61, it could be argued that most of the benefits are fixed interest in nature and should be covered by corresponding assets. Allocation of capital losses, on the other hand, might not be so welcome. What the method does demand is a clear idea of the bonus policy of the office in question and in using it one would clearly adopt a conservative approach with regard to much of the surplus build-up. For example, one could visualize much of the capital appreciation being retained until the last possible moment when it would be paid as terminal bonus. It is possible that an office would adopt a more normal approach to its reversionary bonus and use the authors’ contribution technique to determine entitlement to its terminal bonus. There are obviously endless combinations and permutations possible and, provided sufficient controls on what is allocated, what is distributed and what is retained are maintained, the system could well provide results very similar to present methods involving terminal bonus distributed on a contribution approach.

I would like now to mention the formulae for asset shares and surplus shares representing the difference between the asset share of a policy and the value of its guaranteed benefits. These are developed symbolically in Appendix IV. The calculations are retrospective and the rate of investment return is applied to the asset share. As the asset shares exclude any portion of the office’s estate, it is important that the rates of investment return derived in Appendix II are based on W.P. policyholders’ assets excluding the estate and that any capital appreciation or loss, or dividend income arising from the assets of the estate allocated to the W.P. policyholders, is allocated in terms of those W.P. assets. In the same way, the practical valuation for surplus from paragraph 76 onwards and the comparison of asset values for the valuation totals in force with the W.P. policyholders’ assets in paragraph 80 both exclude the estate.

While I have followed the authors in thinking of their system mainly in terms of the ordinary business of the mutual life office, there are obvious extensions of their theory to W.P. group pension schemes where lower bonus loadings may be the rule and there is a younger fund and a smaller estate with, perhaps, support from the W.P. surplus of ordinary policyholders.

I experienced some difficulty in reading this paper, partly due to the authors’ definition of surplus which at times jumped from a more normal usage to their special usage, partly from disappearance of the estate, partly from the fecundity of their imaginations in producing their system and in putting up ideas and almost as quickly knocking them down or adding to them, and partly to my own inexperience in this field. The authors are to be congratulated, not only for their industry, but also for writing, if my multiplication is correct, one Faculty paper each.

Mr. W. L. Gemmell:—I would like to thank the authors Messrs. Calder and Shedden for a very comprehensive paper. Like the opener, I had some difficulty with it and, to be a bit more blunt than he was, there were some

U


parts that I did not understand. However, it seems to me that the authors put the paper in the context of modern day practice by their reference in paragraph 2 to terminal bonuses. In fact, terminal bonuses have at first sight given scope for applying the theories developed in the paper which hardly seemed to exist before they came to the fore. I think, therefore, it is instructive to focus on terminal bonuses and ask ourselves whether in practice the paper offers a tool for distributing such bonuses.

Historically, terminal bonuses, as I understand it, were introduced mainly in 1969 following a doubling of equity prices over the two years 1967-1968, and, as mentioned by the authors again in paragraph 2, they were intended to deal with the equity profits arising from this period. When they were first introduced, offices issued all sorts of dire warnings about rates of terminal bonuses not being expected to hold up in all circumstances and the fair likelihood of their being reduced with changes in the equity market. Even to-day a large proportion of the offices who declare terminal bonuses do not include them in their illustrations for new business. Now, at this point in 1969, as I think the authors imply, the stage was set for a new era in surplus distribution—one might say a new dimension in bonus equity; but what has happened since then? Equity prices have slipped back to, in the main, pre-1968 levels but terminal bonuses have been maintained or increased, and even more offices have jumped on the band- waggon over the last twelve months; so, where are we now? It seems to me that offices have apparently decided to ignore the very conditions which would justify reductions in terminal bonuses. Now, therefore, W.P. policyholders would be justified in assuming that they will never be reduced or at least are no more likely to be reduced than the level reversionary bonus rate. In the main, terminal bonuses are expressed either as a flat percentage of vested bonuses or as an approximation thereto. So, if we now accept that they are unlikely to be reduced, they appear to be simply flat non-vested additions to our old friend the level reversionary bonus. As such, it becomes clear that the practical working out of terminal bonuses gives no real scope for greater equity in the technical sense than we had previous to their introduction.

My conclusion is, therefore, that, except possibly in the basic decision as to how much surplus to divide, there is little scope for applying the authors’ theories in practice. In any case, I personally do not find myself attracted to the idea of an actuary in an ivory tower having the power to decide on a discriminatory type of bonus distribution. Those of us who have been in North America are aware that in general the so-called contribution system as operated there produces in practice no greater degree of equity than the British system. Let us therefore continue our traditional system which puts the W.P. policyholder in the same position in a mutual life office as a shareholder is in a joint stock company, i.e., if it is deemed appropriate to distribute more surplus then all “dividends” are increased proportionately. As in a joint stock company, where special distributions like rights issues, script issues and so on occur, I think that there is a case in a life office for similar distributions which might take the form of special or terminal bonuses, but again I believe that, continuing the parallel, we should do this in the only way which is demonstrably equitable from the policyholders’ point of view and that is in proportion to each policyholder’s basic expectation, which is the level reversionary bonus.

Mr. R. G. Mallett:—I feel a somewhat reluctant contributor to the discussion as I too found the paper rather difficult to read and understand. Perhaps that is due to age and years since qualification. Nevertheless, I


would like to express appreciation to the authors for within the space of three years coming along a second time—it is rather like a Gilbert and Sullivan partnership. They have now produced a second magnum opus and, as with a lot of music, I sometimes have to hear it more than once before I can appreciate it, so it is with this paper. I must obviously read it again.

Now, my great interest of course is on the practical side, the practical application of the theory expressed here. It certainly intrigues me but I wonder whether the system envisaged here would not be difficult to apply in practice since that part of the surplus, for example, the non-participating surplus, spread over in proportion to asset shares, would require knowledge of all the surplus shares for each year in the past. I am inclined to think that this would be an impossible situation unless an office can plan such an operation over many years and possess the suitable processing machinery.

The other point I would make is with regard to the calculation of the notional values for equity investments. A formula of value of expected income, less tax, would seem to be suitable in a market which moved without violent fluctuations. I wonder how it is possible to equate this with the violent fluctuations that have in fact occurred during the past few years. A policyholder would understandably not wish to be subject to all the fluctuations but a policyholder withdrawing when notional values are higher than market values obviously benefits as compared with the case when notional values are lower than market values. The question is, how far from market values should the notional values be allowed to go?

Mr. J. Young:—In paragraph 68 of the paper the statement is made that the investment rate of return involves interest and also in general a measure of the change in capital values and is applied to the accumulation of premiums less expenses, the cost of life assurance, etc. Now the algebra of this is specified in Appendix IV where I think the important items covered by the etc. are shown. At the beginning of Appendix IV it is reasoned that the same rate of investment return can be used for the group of policies in question as applies to the W.P. class as a whole and, therefore, I get the impression that the rate of investment return applicable to the W.P. class as a whole is being justified for use with all sub-groups within the class.

Unless I have misunderstood the algebra, I find this justification a little difficult to accept. The authors clearly differentiate between N.P. business as a whole and W.P. business and they seem to be saying that all W.P. business of whatever nature within the general W.P. class can be made subject to the same rate of investment return, but I am left wondering whether this is justifiable. It is, for example, possible at the extreme to envisage a one year W.P. endowment assurance. This is virtually a N.P. policy; in theory, no part of its premium should be invested in other than fixed interest securities. To this extent it is in the same category as N.P. business. If the assumption is made that part of the premium is invested in equities, a risk is being taken which in theory cannot possibly be justified, so I see no justification in equity for applying a rate of investment return which includes capital appreciation from equities to this contract.

From that point, one can move to a 5 year W.P. endowment assurance, a 10 year assurance and so on; as the original term of the W.P. endowment assurance increases, a progressively greater part of the premium is available for investment in equities without putting at risk the gradually mounting guaranteed liabilities resulting from the vesting of the reversionary bonus, although from a duration of about two-thirds of the original term and thereafter dis-investment rather than investment takes place.


I am not suggesting that in practice total regard should be paid to this situation but that in equity some weight should be given to it.

It may be that, since the accumulation of the surplus share, as indicated in the formula in Appendix IV, is basically an accumulation of bonus loadings received less the value of reversionary bonus allotted, some account is taken of the point I am trying to make, but it is the factor applied in making the accumulation, namely, the investment rate of return applicable to the whole W.P. class, that troubles me in so far as W.P. policies of a different term are concerned.

The concept of the investment rate of return is a combination of two items; the first is an interest increment which is precisely ascertainable and therefore can be taken at the full realised amount; the second is a capital increment which, though ascertainable at any time, i.e., the market value, is not permanently certain and so it has to be taken in at some notional value and even that value, the authors seem to be conceding, is uncertain. Hence the qualifying phrase in paragraph 68, “in general, a measure of the change in capital values”.

I wonder, therefore, whether the surplus share of a policy which may be about to mature is being kept low to an extent depending on perhaps a subjective view of the valuer of the day, and at a time perhaps when market values of equities are at a much higher level. The policy in question then leaves the fund taking its liability with it, but nevertheless leaving a part of its surplus share in the fund. The authors’ methods do seem to involve some smoothing over a period of capital surplus arising from equity investment. This may be inevitable but its extent may depend on the subjective opinions of valuers from time to time. I could not, therefore, make up my mind as to the measure of equity in this process and my feeling was reinforced at what I felt was rather a lack of development in the paper of the relationship between the reversionary bonus and the terminal bonus. Again the authors comment that this relationship will depend partly on the level of the notional asset values and partly on whether or not there is a commitment to pay the same level rate of reversionary bonus to all policies. I felt that the paper had stopped short at this rather critical point.

Mr. A. U. Lyburn:—I would like to take up Mr. Calder’s challenge to pass a few comments mainly because I am not altogether happy about the contents of paragraphs 21 to 23. One implication of these paragraphs is that if we have two classes of W.P. business. Class A with a high bonus- loading and Class B with a low bonus-loading, then Class A is entitled to more of any surplus then Class B. On the basis that Class A policyholders run greater risks than Class B policyholders I think most of us would go along with this philosophy in general—but just how far? Let us accept that the bonus loading for Class B would not allow the office mix of assets in isolation but suppose also that Class B has turned out to be very profitable from investment or mortality or both, so that the surplus available for Class A is substantially higher than it would have been had Class B not been written. Should it all go to Class A? I think not.

In other words on the assumptions that the public have taken out Class A policies for sound protection and investment, that investments have been, as they should be. sound and that one of the investments is Class B policies, then it, overall, substantial surplus has been generated, I suggest that Class B policies may be entitled to more of the surplus than would arise from a notional fund, the only justification for which under these circumstances appears to me to be that its new money yield matches the basic guaranteed interest rate for Class B.


This theme can be developed further by supposing that we have two types of business, type X and type Y. Type X consists of W.P. and N.P. policies and type Y consists only of N.P. policies. Under these circumstances there can be little doubt that such surplus as can be, or perhaps need be, or perhaps should be released goes to the W.P. policyholders of type X. Is this still the case if the office starts to write W.P. business of type Y, or should part of the estate which it is presumed has been built up by N.P. business of type Y hereafter be allocated for the use of W.P. policies of type Y? I think there is some justification for this latter approach.

Mr. J. M. G. Smart:—I am entering the lists mounted on a small hobby- horse which seems to have the same sort of performance as that recently ridden by Mr. Gemmell and Mr. Young. I always like to start from square one, which is before this paper even begins, and to make sure we are solving the right problem. It seems to me that there is too much reverence accorded to capital gains and too little to what policyholders expect. We must in fact go further back. I think, to the aim of the office in its existence. This is ‘quite different from the aims of the policyholders, to which the authors pay admirable attention. If the aim is to maximise the return to existing policyholders, that is one thing but if not, and I think for most of us it is not, and we want to keep open for new business (perhaps because more business means a spread of overheads) then we must think again, and the treatment of capital gains is radically different in the two cases. In the first case, obviously, you want to close the fund, the fund eventually decreases and capital gains which have hitherto been notional are then realised into fact. In the other case they remain notional because capital values in a growing fund are, until realised, of no relevance except as an indication of the income earning capacity of the asset in question, income naturally including for this purpose both interest or dividend and capital distribution. In my opinion, therefore, capital values should largely be ignored as ephemeral. This contrasts rather strongly with the view in the excerpt from paragraph 68 quoted by Mr. Young. This brings me in a slightly roundabout way to the point that it seems to me of doubtful morality, to say the least, for an established office to start awarding bonuses on a system different from that expected by current policyholders when they effected their policies. By introducing a new series of policies the system can be changed but retrospective alterations must result in inequity and consequently injustice, not the equity sought by the authors. After all, how can any prospective policyholder choose an office if that office is liable to change its rules? Why pick a W.P. policy at all if N.P. contracts are going to collect some bonus, as some people advocate? And, as some- body mentioned earlier, what would equity shareholders say if a company gratuitously increased interest on debentures? Yet this sort of thing is advocated by many who nevertheless, for example, criticise the Govern- ment for trying to escalate graduated pensions.

To my mind, the problem is one of our own making and is being solved in the wrong way. If at present, using quite arbitrary figures, we can earn 9% on a gilt-edged stock but 5% on an equity share and we buy the equity we should for the purposes of a traditional valuation for bonus write up the equity price each year by the net of 4% at our effective tax rate. Moreover, even if it is considered relevant, only the difference between the market value and this written-up value is real capital gain, in the same way as for practical purposes only the excess of bonus on a policy over that loaded for is real bonus. So, looked at intelligently (which means my way!) not


only is the apparent capital gains problem very much reduced but what, remains becomes irrelevant. This remainder is looked at in its true role of income producer and can be incorporated into a more scientific valuation, probably on a bonus reserve basis designed to provide the uniform reversionary bonus that the policyholder expects. In this connection I approve the definition of “estate” at the end of paragraph 4—my wording in another similar context recently was that the estate of a continuing office, and I think the “continuing” is important, represents the truly surplus assets which enabled the existing generation of policyholders to effect their policies with this office on competitive terms at the time and which, assuming that the aim of the office is to continue in business, will enable future policyholders to do so also. The existence of an estate makes it very easy, however, for an established office to give the current generation of policy holders too much. In a way, they do own the office but on my view of the aim of the office they have agreed to forswear part of their inheritance, as it were, to ensure the continuance of business. In other words, the continuance of the office, which requires competitive terms, is a kind of liability for which part at least of the estate forms the corresponding asset. The contribution approach is all right for a new office but is not correct, surely, for an established office operating so far on level reversionary bonuses. If proposers want unit-linked policies let them have unit-linked policies which involve short-term investment by the proposer, whatever it is by the office, and involve also the possibility of negative bonuses (so to speak) but even so sophisticated a compromise, for I think that is what it is, as the authors suggest seems a doubtful starter.

To sum up, the continuing offices which we actually have to-day should use a discounted cash flow technique to provide a uniform reversionary bonus and to provide the encouragement of new business in accordance with their aim; capital values are delusions, retrospective calculations are misleading and odd bonuses are anathema.

Mr. T. M. Springbett:—While I do not agree with all that Mr. Smart has said, I agree with a certain amount of it. I would not agree that capital profits are things that one should ignore, nor would I agree that the uniform reversionary bonus system in present circumstances deals adequately with the question of a fairly equitable distribution of profits. I welcome very much any opportunities there are for actuaries to discuss this question of terminal bonuses and the difficult problems that successful equity investment has introduced into the division of surplus. There has been a very marked reluctance by actuaries to discuss the methods by which capital profits should be distributed and I welcome the authors’ paper this evening because it is a step in the right direction. Whether this reluctance to discuss terminal bonuses is due to the desire of actuaries to keep their particular office’s philosophy about bonus distribution very much a secret or whether it is due to the lack of a satisfactory theoretical basis has probably been made reasonably clear this evening.

Now, reverting to the paper, I must admit that I am not on the same wavelength as the authors. I cannot say that I received their message loud and clear and I do not think I am the only one in this respect. That is perhaps because like Mr. Mallett I have rather an old receiver, but I have my doubts about that. As I understand it, the authors’ proposition is to value the assets and liabilities on an experience basis except perhaps they do not take the ordinary shares at full market value, then a certain capital sum is arrived at and this is the value of the present and future surplus. Part of this is allocated to a contingency fund and not divided,


although I am by no means clear as to how the amount of this contingency fund is arrived at, and the balance is considered as available for distribution. This may well be distributed as a reversionary bonus now and in the future and when a policy becomes a claim any amount under-distributed in the past is taken care of by a terminal bonus. That very briefly is what I get from the process which is set out in the authors’ paper.

Coming to Mr. Smart’s remarks, I have a good deal of sympathy with his view of an established office as a going concern where there is a margin between the rate of bonus which is supported by the premium rates and the actual rate of bonus which is declared. This, as he says, implies that there is an estate and the policyholders expect the rate of bonus to be maintained except in very adverse financial circumstances. Assuming that the bonus to be declared is at a rate that the office expects to be able to maintain on reasonable assumptions as to the future, the estate is automatically increased as new business is added and the business in force expands. It is unfortunate, but necessary, that if there is a very unexpec- tedly large influx of W.P. new business this in itself may make it difficult to maintain the declared rate of bonus. The estate needs to be kept at an adequate level, and the only way to do this may be to cut down the bonus rate and thus, in effect, the difference between the rate of bonus for which the premiums are loaded and the rate of bonus declared.

The policyholders expect that the rate of bonus will be the maximum rate which can be declared but this is hardly consistent in the short run at any rate with the investment of part of the fund in ordinary shares, especially when there is a reverse yield gap of the order of 5% as there is at present. Unless the surplus is arrived at on a capitalised basis like the authors use, and unless ordinary shares are taken in at full market values, the existing policyholders are not going to get the full bonus which is due to them. But we can hardly make a distribution on the basis of current market values which may vary quite considerably in the next few years and may fall. It is this particular aspect that seems to me most important in the realm of terminal bonuses. With terminal bonuses one can vary the bonus fairly readily, the bonus is not guaranteed and one can decide what the rate of terminal bonus is to be for a particular moment of time on the basis of what the market values of equities are. This gives a great flexi- bility whereas if bonuses are declared as reversionary bonuses they become guaranteed benefits and there if no possibility of altering them in the future. It seems to me, therefore, essential that, if policyholders are going to get the benefit of equity investment and if a W.P. policyholder is not going to be penalised when his policy matures because part of the fund has been invested in ordinary shares which are yielding maybe 5% less than Govern- ment securities, one must have some system of terminal bonuses whereby the benefits are not guaranteed, for the reversionary bonus system will not cope by itself. It is probably the case in many offices that, if they sold all their ordinary shares and bought fixed interest securities, the yield on their funds would rise very considerably and they would feel quite happy to increase their reversionary bonus, but it is rather unfortunate that existing W.P. policyholders cannot get the benefit of that increased reversionary bonus except by the introduction of some form of terminal bonus, and that seems to be one of the main justifications for introducing terminal bonus.

I mention this particularly in connection with Mr. Smart’s remarks, because I have some sympathy with his view that W.P. policyholders entering now have the benefit of the estate which has been built up from capital profits in the past and from free reserves and when in their turn their policies become claims this estate should be passed on to the new generation


of policyholders. The capital of the estate is not free for distribution; but on the other hand I do feel that in a time when there is a large reverse yield gap offices are in duty bound to try and be as fair As they can to their W.P. policyholders and to ensure as far as they are able that when a policy becomes a claim it gets a fair share of the profits it has earned, even though these profits may not actually have come out of income but may instead have come from capital appreciation on ordinary shares. I am afraid I have probably not expressed myself particularly lucidly, but my main point is to support Mr. Smart to some extent but also to make clear that I feel that there is very much a place in these days for terminal bonuses.

Mr. A. P. Limb, closing the discussion, said:—I would like in my turn to add my tribute to the authors. They have written a, wide ranging paper and, although their theme was the allocation of surplus in a mutual life office, they have in developing that theme referred to many of the main problems involved in the actuarial management of a life office. The lively, somewhat provocative and well-sustained discussion will I am sure have gratified the authors but we shall remain in their debt for the continued stimulus which their paper will provide. There have been questioned in the discussion many of the assumptions made explicitly and implicitly by the authors. Mr. Gemmell appeared to feel that bonuses were suspect if not in accordance with policyholders’ expectations; Mr. Smart felt that the authors made too much of capital profits; Mr. Young questioned the applicability of a system assuming a uniform rate of investment return; I shall compound the authors’ opportunity for revenge by questioning more of their assumptions and premises.

I would like firstly to mention in passing that I agree completely with Mr. Springbett that it is the pressure of investment in equities which has given rise to terminal bonuses, not specifically that equity investment has been more successful than anticipated as the authors suggest in paragraph 2, although undoubtedly equity investment has I think in the main been more successful than expected. Furthermore, I disagree with the statement that the authors make in paragraph 2 that the beauty of a reversionary bonus system used to be that it produced equity when conditions differed from those expected when the investments were made. Even if the investments made are purely fixed interest, if the rate of return differs substantially from that assumed in the premium calculations considerable inequity can in fact arise if the office operates a simple reversionary bonus system as opposed to a compound reversionary bonus system.

In paragraph 3 the authors set out their premise that W.P. policyholders may be regarded as the proprietors of a mutual life office. Earlier, in paragraph 2, they state their view that the N.P. business of a mutual life office can be regarded as an equity investment of the W.P. policyholders. Both of those statements are true in a sense, but they seem to me to carry quite inadmissible implications. The first statement that W.P. policyholders may be regarded as the proprietors of a mutual life office is true in the sense that if the office were to cease writing new business, the whole of the funds would, one supposes, after satisfying N.P. policyholders rights, be distributed eventually amongst surviving W.P. policyholders. However, as numerous speakers have mentioned this evening, no set of W.P. policyholders existing at any particular time can, in an office which is continuing to write new business, reasonably claim that by the time they have ceased to be on the books there should be returned to them the whole of the office’s assets, other of course than those required to satisfy N.P. policyholders’ rights and those built up by future policyholders. To make such a


claim would not only be tantamount to preventing the office from writing future business, since it would not have the necessary contingency reserves available, but would be patently unfair since this set of policyholders, like all other policyholders, enjoyed from the moment they joined the fund the protection of an inheritance which they had not built up, and they must expect to leave an inheritance behind. In this sense, then, it surely cannot be said that the W.P. policyholders are entirely the proprietors of the office. They are rather, in part at least, life tenants of the inheritance which of course is not a fixed quantity. This inheritance of course is part of the surplus as defined by the authors. As I understand them, they assert that the surplus shares developed in Appendix IV and described in Part 4 of the paper in words provide a means of allocating the total surplus but, like the opener, I do not think that the inheritance which I have just mentioned (and I apologise for coining yet another word, or at any rate using yet another word) is incorporated in the asset shares or the surplus shares developed by the authors, so that the total surplus is not in fact allocated. This seems to me to be quite proper since the inheritance cannot be said to belong to the W.P. policyholders in a continuing office. The fact that they would get it if the office were to stop writing new business is a separate point. Similarly the suggestion made in the introduction that the N.P. business of a mutual office can be regarded as an equity investment of the W.P. policyholders needs in my view careful interpretation. It is true that profits from the writing of N.P. business do not go to the N.P. policyholders and part or the whole of them may be distributed to W.P. policyholders. It is also true that there are no guaranteed profits to be had for the W.P. policyholders from the writing of N.P. business, and, in the sense that the W.P. policyholders will get some or all of the profits accruing from the writing of N.P. business, and that such profits are neither fixed nor guaranteed, one may say that N.P. business constitutes an equity investment of the W.P. policyholders. However, one attempts to make investments on the best possible terms. Are we then to conclude that a mutual office should sell N.P. business on the highest level of premium rates possible so that, taking due account of the diminished volume of sales likely to be made as higher premium rates are set, the profit to the office is maximised? This concept. seems to me to be untenable. It implies that the aspirations towards equity, which bulk so large when bonus distribution is considered, are to be abandoned when fixing N.P. premium rates. None the less the statement that N.P. business is an equity investment of W.P. policyholders might be held to imply such an approach.

I found when reading this paper that the question “What are the aims of the mutual life office?”, already raised by Mr. Smart, recurred often to mind. In my view the first of these aims is to ensure the just fulfilment of existing contracts, and the second is to sell new business on terms which may be expected to give future and current policyholders a fair deal. There are, I think, other aims too but one can say that the second aim cannot be fulfilled if the office sets out to maximise profit from each N.P. policy.

The first part of the paper is concerned with the definition of surplus. One of the difficulties to be overcome in discussing the workings of a life assurance fund is that terms such as surplus, estate, inheritance, are used by different authors to means different things, and worse still are not always defined at all. As I understand them, the authors are using the words “estate” and “surplus” indifferently in paragraph 4 to mean the difference between the value of assets calculated on the basis actually to be experienced and the value of liabilities similarly computed. They point


out that this figure can be conceived of but not measured exactly since of course no one can say on what terms future investments can be bought or sold, what dividends will be paid, what investment policy will be followed, when existing liabilities will go off the books and on what terms. The figure is also affected, as the authors note, by the view taken as to how to measure the proper reserve for a W.P. policy. I am quite ready to use the words “estate” and “surplus” in this way and I think the simplest way to think of the idea is to say that the surplus or estate is an estimate of the cash which the office could lose and still be able to fulfil its liabilities on existing business if all the assumptions inherent in the valuation of assets and liabilities were fulfilled, including the assumptions underlying the calculations of W.P. reserves with their implications regarding future bonuses to be declared. This emphasises the interdependence of the estimate of surplus and the valuation assumptions made for assets and liabilities. Surplus in the sense in which the word is defined in paragraph 4 seems to me to consist of the following parts—first, retrospective surplus from business currently in force, second, prospective surplus from business currently in force, and third, the balance of surplus which I call the inheritance. Retrospective surplus from business currently in force can be defined as the difference between the fund built up from premiums received from business in force on the basis actually experienced as to investment return, mortality and expenses and bonuses declared or paid, and the fund which would have been built up on the premium basis assumptions. Prospective surplus from business currently in force is the difference between the fund required to satisfy future liabilities for business in force, assuming future experience will follow the premium basis assumptions, and the fund required if the expected future experience materialises. Retrospective and prospective funds on the premium basis for business in force are equal. The sum of retrospective and prospective surpluses from business currently in force, that is, the present value of the total surplus from business currently in force, appears to be the sum allocated by means of the authors’ surplus shares as described in Appendix IV. As far as I can see the inheritance which may be thought of as retrospective surplus from business no longer in force is not allocated, and this seems to be in conflict with statements made in the paper in paragraphs 5 and 80—a number of speakers have covered this point, and I am looking forward to the authors’ explanation. We may enquire why the office needs surplus and, in particular, why it needs an inheritance. Part of the answer of course is that the reserve basis which is thought appropriate for estimating surplus is inadequate for a published valuation basis. The authors’ wording in paragraph 29 appears to suggest that there is a distinction between a published basis and a realistic basis, but I think that any implication that published bases are necessarily unrealistic is unfortunate. The office no doubt hopes that published reserves are unnecessarily strong but this hope may prove un- justified. When published reserve bases are used the prospective surplus on existing business may well be negative and the inheritance may be needed to prevent the total surplus from being negative. This would certainly be the case in an office expanding rapidly enough, whether the expansion were in N.P. business or W.P. business and of course excessive expansion would cause this to occur even with the support of an inheritance. Prom the formula for the rate of return to W.P. policyholders developed in Appendix II, it is evident, as the authors state, for the case of the proprietary office in paragraph 29, that if the valuation bases for N.P. business are stringent, rapidly expanding N.P. business can bring a negative return to W.P. policyholders. The control of the rate of expansion of N.P.


business must therefore be a matter of concern to life office management. One might add that the need to keep surplus at an adequate level relative to liabilities can also, as Mr. Springbett mentioned, put strain on the bonus if W.P. business expands too rapidly. As the authors point out in several places, not all of the surplus is distributable; the factors influencing the amount which must be retained include the degree of mis-matching, investment contingency reserves, the volume of business, the expansion rate. the degree of risk involved and the value of future bonus. It is very tempting to try to devise a formula to quantify the more elusive of these considerations, but with or without the aid of a computer, I believe that such a formula is impossible to find and one is forced in the end to rely on judgment. One might try, for example, to find the size of investment contingency reserve required so that there was a 99% chance of such a reserve being adequate. On somewhat dubious assumptions, and with an unimaginable amount of labour, one might even find an answer, but one is still left with the question whether a 99% chance of having a sufficient reserve is too conservative, correct or grossly irresponsible. I mention this matter because I suspect that the inequity which may arise because part of the surplus is wrongly allocated amongst W.P. policyholders when a bonus distribution is being considered, may well be far less important than the inequity which is provoked by failure to assess and control properly the factors which govern the amount of surplus which cannot be distributed but must be retained by the office.

The sections of the paper dealing with the relationship of surplus and asset mix I found particularly interesting. The authors state that in a mutual life office it is possible for the whole of the W.P. fund and part of the N.P. liabilities to be covered by other than fixed interest securities. I am unable to see how this situation could arise if the office takes the view that guaranteed liabilities should be covered by reliable fixed interest securities, since it is surely hardly likely that the value of guaranteed liabilities under W.P. policies will be nil in total. Again, the authors suggest that if a particular class of W.P. business cannot be supported by the office mix of assets it is being subsidised by some other portion of the business. I cannot see that this necessarily follows. I think it depends on the distribution of profits arising. In general, different classes of W.P. policy and different durations within the same class, as Mr. Young observed, will not support the same asset mix. It is not practicable, nor is it in my view desirable, to hypothecate assets in any but the broadest terms and yet without doing this the development of asset shares is undoubtedly an approximate business. The authors, I think, recognise this when they call for some smoothing of investment rates of return.

The question of what the policyholder expects arises on a number of occasions in the paper and has been mentioned in the discussion earlier. It arises mainly in the context of the degree to which he expects to pool investment risks and the bonus policy which he expects the office to follow. As actuaries we are prone to speculate on policyholders’ expectations, though I think the only way to find out would be to conduct market research. For my part, I doubt if one policyholder in a thousand has any clear idea of what he expects in the matter of pooling investment risks, though I have no doubt that he would be more articulate where bonuses were concerned. I do, however, feel confident that he expects simplicity in bonus distributions and simplicity I think we must produce. This does not necessarily, however, limit us to a level reversionary bonus system in my view.

Mr. President, I have already no doubt said too much. I agree whole-


heartedly with one of the main conclusions of the paper, that a primary aim of a valuation for surplus is to re-assess premium scales and generally to re-examine the workings of the fund to see that equity together with prudence is being preserved. If I have cavilled at some of the authors’ ideas I hope they will none the less accept my reiterated tribute. This is a most interesting and most fertile paper which I am sure we have all greatly enjoyed.

Mr. A. D. Shedden, replying to the discussion, said :—On these occasions I wish that there were a chance to reply to each speaker as soon as he has sat down; we might then be better able to remember what he has just said and so reply more effectively.

I think it was Mr. Springbett who said that he was not sure whether or not he had received the message “loud and clear“. Well, my recollection of Mr. Springbett’s remarks is that he received the message as loud and clear as anybody else. My general impression of the discussion is that our message has not been clearly received; the length of the paper may have been partly to blame for this as there is evidence that some of those taking part in this discussion had not read the paper thoroughly. I am sure that if they were to read it again they might find that some of their criticisms were not justified and that we are not as far removed from their views as might be supposed. Rather than reply to the discussion in detail at this time I shall confine my reply to two matters of principle which were raised by various speakers and which we thought had been covered in the paper.

Both Mr. Smart and Mr. Limb referred in their discussion to the aims of a mutual life office and I agree that a discussion of allocation of surplus in a mutual life office must also be a discussion of the aims of the office. We have said in the paper that the investment and bonus policies of a mutual life office are not only very closely linked but also form the basis for under- standing how profits may be equitably distributed. I would think it obvious that the investment and bonus policies must be a reflection of the aims of the office’s management. Unfortunately the theoretical owners of the office, the W.P. policyholders, cannot determine its aims; they do not have the chance in practice to do so and if they did have the chance they would not be able to do it anyway. A difficulty is that the aims of management are rarely clear or expressed; but this situation may change and it may be that pressure will be put on life office managements to define more of their policies, i.e., strategies, as far as W.P. policyholders are concerned, just as other financial institutions, competing with them for the public’s money, have to do.

The need for more clearly expressed aims can be understood when considering the question of equity investment. We did not feature equity investment in the paper to show that it was more profitable than fixed interest investment but to show that the risk was much greater, as is evident from a glance at to-day’s papers. I do not think the W.P. policyholders realise the nature of the risk they are taking, bearing in mind the demonstrations in the paper that in looking at the degree to which the W.P. policyholder is an equity investor one should not look at the total proportion of equities in the fund but must set off the N.P. liabilities against the fixed interest assets thus regarding these liabilities as negative fixed interest assets.

The other matter raised in the discussion to which I wish to reply now has to do with the definition of surplus and the related question of the estate, or the inheritance as it has also been called. The definition of surplus is fundamental to the paper—in fact the paper cannot be developed until


one disposes of it. The very word “estate” has the connotation of an inheritance, i.e., something that is handed down to be used for a time and then passed on to someone else. Now, if there were such an inheritance, say, at the end of the last war, from previous generations of policyholders, it would not go far nowadays when one considers the growth in companies’ assets since then. It is obvious that the growth of surplus, and the growth of the estate as it is normally defined, has come from policyholders’ money; moreover, the distribution of policies by duration suggests that the major portion of surplus has arisen relatively recently.

We argue that this surplus must belong provisionally to the current W.P. policyholders and in the paper we attempt to deal with the problem of its allocation. It follows that in our formulae we must allow for a subdivision of this surplus, including the estate, inheritance or whatever it is called. A policyholder joining the office starts sharing in it via the rate of return on surplus and at the same time contributes a share of his premiums towards its maintenance. The formulae therefore hold for an established office as well as for a new office, the only difference being that a new office must start off with some surplus which does not belong to the W.P. policyholders (unless they are prepared to waive the guarantees under their policies) and which is needed to maintain the office until the surplus of the W.P. policyholders is large enough to take over this function.

Mr. President, that is all I wish to say at this time. We hope to do more justice to the points raised in the discussion in our written reply. In closing, I am sure that Mr. Calder joins with me in warmly thanking those who took part in the discussion.

The President (Mr. D. W. A. Donald):—Thank you, Mr. Shedden. As Mr. Springbett said this is one of the most important subjects that face an actuary at the present time and we are very grateful indeed to you and Mr. Calder for having given the Faculty a much needed chance to discuss it. On such a well-worn subject it would have been if not perhaps easy, at least not difficult, to have produced a paper which would have said nothing new and with which no one would have disagreed. You, as the discussion showed to-night, did not fall into that trap. You may, initially in fact, have felt that there was more criticism than approval for what you have said; even if that were so it is a measure of how stimulating your paper has been. We are extremely grateful to you for having given us this chance and I would ask the Members of the Faculty to show their appreciation very warmly.

The authors subsequently wrote :—In reviewing the discussion, it has become apparent that there has been a sort of language barrier which has not been crossed by some of the speakers. Perhaps a more exact analogy would be to think of the reaction of a student of classical music listening for the first time to music written in the 12-tone scale. His criteria for judging good and bad, or right and wrong, will have no relevance to the system of music he is listening to and so he will probably feel confused and baffled. Perhaps it was so with this paper. We set ‘out to discuss the subject of allocation of surplus in as general a manner as we could. To do this we had to remove any preconceived notion of how surplus might be distributed, since we felt that the principles ought to be valid whatever the bonus system. Because of this we exclude from our definition of the valuation of guaranteed benefits any provision, explicit or implicit, for future bonus, since to do otherwise at that stage would beg the question how to allocate surplus equitably. This exclusion is also necessary in order to


assess the extent to which the surplus of the office, as a whole, is sufficient for the risks the office is undertaking—hence our insistence that the ratio of surplus (our definition) to the value of guaranteed benefits is a most significant one from the management point of view. Of course, if one has given policyholders to understand that a particular method of surplus distribution will be followed the office will try to keen to that method as far as possible—this surely does not imply “that to be equitable one is obliged to follow the method at all times.

Our general approach to the allocation of surplus, involving asset shares and surplus shares, was developed to be used as a guide to controlling the equitable allocation of surplus within whatever bonus system was adopted, and especially where widely varying types of bonus system and W.P. contracts were in operation within the same office. Although the general approach is based on contribution principles, it does not follow, as some speakers seem to have supposed, that an office must cease to distribute surplus by means of level reversionary bonuses, since it ought to be possible to deal with any inequity by introducing a suitable system of terminal bonuses. On the other hand, Mr. Hogarth’s suggestion that the allocation of terminal bonuses might be made by a contribution technique, while allocation of reversionary bonuses might follow a normal approach, seems to draw an artificial distinction between two sources of surplus, even though he was envisaging that the terminal bonus would be on account of capital profits arising from equity investment.

Most of the misunderstanding of the paper has arisen from the definition of surplus adopted in paragraphs 6-12; the main difference from the text- book definition given in paragraph 4 is that our definition includes in surplus the value of future bonuses instead of including them explicitly or implicitly in the value of future guaranteed liabilities. It was assumed by Messrs. Hogarth and Limb that the estate is excluded from our definition of surplus and hence that it is not allocated provisionally; this, of course, is not so since we did not at any stage (including the algebraic development) exclude the estate from our definition of surplus.

The reason for this is fundamental to the paper, for we have great difficulty in conceiving of an entity called the estate which is separate from surplus in general and which cannot be considered the property of the current W.P. policyholders; the nearest we could get to such a concept would be to regard the estate as the proprietary interest of the W.P. policyholders, as distinct from their investment interest. In this respect we might begin to agree with Mr. Smart and Mr. Limb, and possibly with Mr. Springbett, in regarding the estate as necessary for the continued trans- action of new business, but we part company with them by regarding this portion of surplus as being allocatable (but not necessarily distributable) to current W.P. policyholders just as, in a proprietary office, the shareholders’ capital and surplus which exists for the sole purpose of enabling the office to transact business cannot be returned to shareholders if the office is to continue in force, but most definitely is their property. In fact, the analogy with the proprietary office was introduced into this paper solely to clarify this point and much of the expressed disagreement with the views in this paper springs from failure to appreciate the dual role which W.P. policy holders play in a mutual office, i.e., as proprietors and as customers. Just as a shareholder can get value for his proprietary interest by selling his shares. so can a W.P. policyholder be allocated a share in the estate and obtain value for it if new W.P. policyholders join and take over the proprietary function. Mr. Springbett commented that the estate was not distributable and if he meant by this that the estate would be included


with contingency reserves in assessing the amount of total surplus that could not be distributed at a bonus declaration, we would certainly agree with him if the office was a continuing entity and not a closed fund. However this need not imply that current policyholders will not benefit from the estate since there will be a transfer of the estate from one generation of W.P. policyholders to another for which the outgoing W.P. policyholders can receive value provided there is a sufficient volume of new W.P. policyholders to take over the estate. The real difficulty with the estate is in defining it, measuring it and separating it from other parts of surplus. We concluded that this could not be done and that, possibly, such a separation was meaningless. Hence we abandoned any attempt to make such a separation and moved over to a definition of surplus based solely on assets and guaranteed liabilities.

We deal now with some miscellaneous points raised by speakers. Mr. Hogarth refers to some valuation problems. We admit that some

of our comments in regard to valuing W.P. business have more relevance to a valuation for purchase of shares of a proprietary office than to a valuation for assessing surplus in a mutual office. The discounting of future published valuation surpluses and the taking credit for departure from an immunised position might fall into this category but it is obvious that any proper valuation for surplus must permit of negative values coupled with an allowance for withdrawals. The allowance for withdrawals should be as realistic as possible, bearing in mind that a withdrawal could mean either a profit or a loss, depending on circumstances, and that in some cases we might be balancing a current profit against either future losses or, more likely, the lack of future profits.

Mr. Hogarth also comments that the use of market values in valuing N.P. business implies that its value varies with the rate of interest. This is hardly surprising, since to a prospective purchaser of N.P. business invested solely in fixed interest securities the net value must be regarded, to some extent, in the same way as a fixed interest security, after allowing for margins in the valuation basis to cover contingencies. For allocation of surplus in a mutual office we admit that we would either use leas variable rates of interest or smooth the rates of return on N.P. business.

Mr. Gemmell regards the contributions system as having dubious value, although, paradoxically, he advocates putting the W.P. policyholders in the position of a shareholder. This is in fact what we have attempted to do in the paper, but since shareholders’ profits and share values are determined on the numerical basis of shares, we felt that a similar approach, i.e., a contribution approach, was essential to achieve this object in a mutual life office. Moreover, the paper envisages an office with different classes of W.P. business, not all having surplus distributed by means of level reversionary bonus, and in such circumstances it is necessary to adopt some kind of a contribution approach—at least to the extent of allocating the profits in total to each W.P. class. In these circumstances, also, it is less obvious that equity is achieved by distributing bonus in the way expected, although as we have previously remarked, one would attempt to do so as far as possible.

Mr. Mallett wonders about the degree to which our approach is practical. With computers it is no doubt possible, but for individual policies in this country it is likely that the system would be used mainly to produce test values to be used as guides for avoiding gross inequities. For group policies a case could be made for going into more detail but here again the nature of the business and the size of profits being distributed would affect the answer. Mr. Mallett goes on to refer to our suggestion of the use of notional values


for equities and asks how one decides on the degree of divergence from market values. Again we have no direct answer to this question but it seems clear that with a large proportion of equities in the portfolio the main fluctuations in market values must be followed.

Mr Young’s difficulties with Appendix IV are, we think, based on a misreading, for in paragraph 1 of this Appendix we suppose that the distribution of surplus is such that at all durations each policy can support the full asset mix of the W.P. class (i.e., the W.P. class of which the policy is a member). This is the justification for us to use the same rate of return at all durations for each member of the class. In the body of the paper we discuss the situation where each policy in the W.P. class does not support at all durations the asset mix which can be supported by the W.P. class as a whole and suggest that this can be dealt with through the technique of using special, more stable, values of assets and distributing the fluctuations in excess of these values in proportion to surplus. We do not favour the use of this technique where the proportion of equities is high and logic seems to demand in such circumstances a considerable margin between the value of the asset share and the value of the guaranteed liabilities and so a fairly large, if fluctuating, terminal bonus could be payable. The lack of development of the relationship between the terminal bonus and reversionary bonus, to which Mr. Young alludes, is mainly due to the paper having been written without any specific bonus system in mind.

Mr. Lyburn suggests that a W.P. class need not be required to support its own asset mix in order to benefit from the investment profits if these are unduly large and he appears to have support from Mr. Limb on this point. There may be circumstances when this has to be done because the terms of the contracts have not been clearly enough defined but in general it sounds like a “heads I win, tails you lose” proposition. Would Mr. Lyburn extend his thesis to allow investment profits to be given to N.P. policies? However, we do agree with the second part of his remarks in that if a new class of W.P. policies were to be introduced then in theory there would be no objection to it sharing in the estate on the same principles as new members of existing W.P. classes. The extent to which a new W.P. class would share in surplus is, we think, governed by the principles which were enunciated in the paper and developed largely with this problem in mind.

Mr Smart’s remarks about the unimportance of capital gains have been adequately answered by Mr Springbett and the other points raised by him have been covered by our earlier remarks.

Mr. Springbett’s comments on the possible inequities of distributing surplus solely by means of a level reversionary bonus are entirely in harmony with the concepts developed in the paper. The relationship between value of assets and value of guaranteed liabilities controls the degree to which guaranteed liabilities can be increased by declarations of reversionary bonus, as Mr. Springbett says, and we would feel that his remarks apply in to a wider sense than merely where equity investments are involved.

We have replied earlier to Mr Limb’s remarks about the ownership of an “inheritance” and its exclusion from the asset share development. Mr. Limb wonders whether our philosophy in regard to N.P. business implies that a mutual office should sell it on terms fixed so as to maximise the return to the office. He is correct in this surmise. We cannot think that this implies a lack of equity as long as the policyholder has a free choice between a W.P. contract and a N.P. contract. Mr. Limb also thinks it unfortunate that we suggest there is a distinction between a realistic valuation basis and a published valuation basis. In so far as a W.P. basis


is concerned there must be a difference since the published basis has to allow for future bonus, but apart from this the difference must surely arise partly because of the different basis on which assets may be valued and partly because the margins which exist in the published basis have no place in a valuation for surplus of the sort we are describing since we are valuing not for distributable surplus but for total surplus.

We would agree with Mr. Limb’s comments on the difficulty of determining the total amount of surplus that has to be set aside for the safety of the office as not being immediately distributable. Because of this difficulty it is likely that offices will tend to play safe and underdistribute. It is therefore important to emphasise allocation of surplus as distinct from distribution of surplus and in this respect we are touching on the same problem of equity raised by Mr. Springbett in regard to equity profits. We do not feel that such difficulties should be made the excuse for not attempting to allocate surplus as fairly as possible.

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247 ALLOCATION OF SURPLUS IN A MUTUAL LIFE OFFICE by€¦ · general problem of allocation of surplus in a mutual life office. 2. In approaching this subject it has been impossible