valuation standards a. c. stalker, f.f.a. and g. k. … · 137 valuation standards by a. c....

137

VALUATION STANDARDS

by

A. C. STALKER, F.F.A. and G. K. HAZELL, M.A., F.I.A.

[Submitted to the Faculty on 15th March 1976. A synopsis of the paper will be found on page 168].

“ If, a few years ago, a paper had been offerd to the British Association on the subject ov the insolvency of life insurance companies, it woud probably hav been met with the objection that it was ov too theoretical a character. . . .”

T. B. Sprague (1874)¹

1. INTRODUCTION

1.1. This paper seeks to examine the fundamental principles underlying the periodic actuarial investigations of life insurance companies. It attempts to define the attributes of an equitable and efficient set of standards, to classify the causes of failure of life offices and to enumerate the realities of any life office. Having examined the background to the present situation (at 31st December 1975) it then proceeds to attempt to derive a general valuation standard.

2. PRINCIPLES UNDERLYING THE PERIODIC ACTUARIAL INVESTIGATION

2.1. The cardinal purpose of such an investigation is to establish that the office is solvent, that is to say that it can meet the liabilities it has contracted to its policyholders as they fall due. In addition, in this country, an obligation has been laid on the office to meet the “ reasonable expectations ” of its policyholders. Moreover, if it is a proprietary company, the investigation should determine what profit, if any, can be transferred to the profit and loss account of the pro- prietors’ fund. In addition it will obviously be helpful if the investigation can provide the management with guidance regarding the future conduct of the office’s business.

2.2. Underlying any office there is an actuarial model. This can be defined as the aggregate of all assumptions which have been made by actuaries in the past in respect of those contracts which are still in force. The model (or aggregate of models) will be highly idealised (e.g. all lives assured accepted at normal rates for a particular class of contract will be assumed to suffer the same rate of mortality) and in some cases this idealisation will take the form of simplification (e.g. withdrawal rates for contracts carrying guaranteed surrender

Richard Kwan

TFA 35 (1975-1977) 137-194

138 Valuation Standards

values are ignored). Only one thing is certain about the actuarial model; the assumptions on which it was based will prove to be wrong. Thus the periodic investigation can be described as a test as to whether the degree of error has had any effect on the safety of the office.

2.3. This argument leads to the concept of valuing each tranche of business on the assumptions underlying its premium basis. The basic premise here is that, in the future in the aggregate, the assumed actuarial model as defined above will be borne out in practice. Thus essentially it determines how much better (or worse) the office has performed in the past than the actuarial model, taking into account past distributions of surplus. Therefore it is not directly of use in giving guidance as to the future conduct and management of the business, since its view of the future is predetermined and takes no account of changes in the financial scene or in mortality which may have caused serious damage to the financial condition of the office. Thus the premium basis valuation can be rejected because it does not provide a satisfactory objective standard.

2.4. Before leaving consideration of the premium basis valuation it must be observed that it would be perfectly possible for an office to be solvent even though the premium basis valuation liability exceeded the aggregate market value of the office’s assets. For instance it could happen that, although an office was perfectly matched as to assets and liabilities which emerged year by year, the market rate of interest (or rather interest rate pattern) was higher than the rate of interest (or interest rate pattern) which had been employed in calculating the premium rates in the past. Therefore the premium basis valuation of the liabilities would exceed the market value of the assets. This is an example of incompatibility of systems of valuing liabilities and assets. Such an incompatibility is recognised by the supervisory authorities of countries such as Canada where the premium basis type of valuation is common and where the authorities permit carefully controlled hypothetical values of certain types of asset, rather than market values or original cost values, to be included in life office balance sheets.

2.5. The net premium valuation method (more properly called the pure premium method in its completely unmodified form) is a highly idealised view of the future of the office. It produces a smooth range of values from zero at duration zero to unity at maturity in the case of endowment assurances and at ω in the case of whole life contracts. Essentially it is a passive method which establishes a datum line for the calculation of liabilities and variations of other

Valuation Standards 139

elements can be observed in relation to that datum line. The datum line effect is particularly marked if a series of pure premium valuations is made at regular intervals on the same basic actuarial assumptions. The other elements whose variations may be observed are the earning power of the fund in relation to the rate of interest assumed in the valuation, the expenses actually incurred against those assumed and the value position of the investment portfolio. Because of the steadiness of progression it has been highly regarded by actuaries as a tool for equitable distribution of surplus. However one of the difficulties has been to decide what is the correctly corresponding method of valuing the assets.

2.6. When the method was evolved, most of the assets of life offices were unquoted so that virtually the only choice of method of valuation of assets lay between original cost and amortised value. Our professional predecessors tended to use original cost where the asset would be redeemed at a premium on the purchase price and amortised value where it would be redeemed at a discount. The resulting margins were therefore available to take care of the occasional default. Provided that a sufficient margin was left by the actuary between the rate actually earned by the fund and the rate assumed by him in calculating the liability, the pure premium method would throw up surplus with a high degree of equity. This is a very important proviso to which we return at a later stage in the paper. Variations of the method have been made to deal with the problems of initial expenses.

3. ATTRIBUTES OF AN IDEAL VALUATION STANDARD

3.1. Among the various attributes that an ideal valuation standard should have, the following appear of the greatest importance :-

(1) The standard should be clear and unambiguous in its application to any office in any situation.

(2) All offices complying with the standard should have a probability of ruin less than θ and θ should be the same for all offices irrespective of age, type of constitution and type and mix of business transacted.

(3) θ should be small enough so that all offices complying with the standard would be undoubtedly regarded as solvent but not so small that a large number of offices undoubtedly solvent would be unable to comply with the standard.

(4) The standard should not interfere with an equitable emergence and distribution of surplus.

(5) The standard should not require frequent revision.


3.2. (1) is necessary to ensure that all parties concerned will be in agreement that the test is adequate, fair and has been properly applied.

3.3. It is extremely difficult to make certain that a standard complies completely with (2) but it should be a prime aim in devising a standard. Unless it is kept to the forefront when a standard is being evolved, it is likely that the standard will bear too harshly on one class of office while being unduly lenient to another class.

3.4. The purpose of (3) is to produce a fairly sharp cut off. If θ is made too small (i.e. the standard is made unrealistically stringent) then it could prove to be self-defeating because the supervisory authorities would have too many “ doubtful ” cases to investigate further. A considerable proportion of these would eventually be given a clean bill of health and thus failure to comply with the standard would lose a great deal of its meaning. On the other hand, if the standard is fixed realistically then all prudently managed offices will be able to comply with its requirements without difficulty and its discrimination will be reliable. Consequently, every office will take steps to ensure that it complies with the requirements since the stigma of failure to do so would place an unacceptably dark cloud of doubt over its status.

3.5. (5) is in some ways a corollary of (1). Unless a standard can apply throughout many changes of financial and other conditions, one of two things will happen. Either (a) it will have to be altered every few years or (b) it will have to be abandoned in whole or in part. This attribute rules out most absolute standards such as specific rates of interest. However, as will emerge later, there may be some absolutes in a satisfactory standard in the form of certain relationships.

4. CAUSES OF FAILURE OF LIFE OFFICES

4.1. The causes of failure of life offices can be classified into 5 types.

(1) Failure of assets because of defaults. (2) Inadequate earning power of assets to justify the actuary’s

interest assumptions in the aggregate actuarial model. (3) Variation of claim pattern from that implied by the aggregate

actuarial model. (4) Expense outgo in excess of the total expense allowance in

the aggregate actuarial model. (5) Mismatching of assets and liabilities.


4.2. Type (1) is simply the failure of the office’s debtors to honour their contracts.

4.3. Type (2) is where the actuary has been over-optimistic about the rate of interest it would be possible to earn on the assets. The main danger here arises from changes in the long-term rate of interest but could also arise from lack of growth in income from equity and property investments.

4.4. Type (3) obviously includes errors in actuarial estimates of claim probabilities but also includes strains caused by unforeseen out- flows of surrender payments. If large these can undermine the strength of the office whether the surrender values are guaranteed or not.

4.5. Type (4) mainly arises from paying too much for the acquisition of business, not necessarily to independent intermediaries. It also includes the risk from inflation of costs of maintenance of the business on the books. Finally it includes policies lapsing in quan- tities not allowed for by the actuary in his model so that the office fails to receive the allowance it had anticipated necessary to recoup its initial expenses.

4.6. Type (5) failure can arise when premiums have to be invested at a rate of interest that is inadequate in relation to the aggregate actuarial model and any compensating appreciation of assets is insufficient. It can also arise when assets have to be realised in a depressed market and any compensating effect of premiums being able to be invested at rates of interest above those assumed in the aggregate model is insufficient. A particular case of this would be where assets prove to be unmarketable.

4.7. It is, however, unlikely that offices fail merely from one of these causes. In combination they can be much more deadly. For instance the temptation for an office which finds itself in a potential Type (2) situation is to seek to raise its earnings on its investments by moving into higher risk areas or a badly matched position. Such a course may lead it in to a Type (1) or Type (5) failure. Again if the office finds that its asset proceeds are flagging and realisation of assets in an unfavourable market is imminent, it may endeavour to correct this by selling more business and this may lead it into dangers (2) and (4). The same effect could also arise from an attempt to correct a Type (3) situation. Finally the Type (4) situation can be especially dangerous in a period of rising interest rates because the large debt incurred in the financing of new policies accumulates at a higher rate of interest and it becomes more difficult to amortise it out of future annual premium income.


5. REALITIES OF A LIFE OFFICE AT ANY GIVEN TIME

5.1. The ascertainable facts regarding a life office are given below. Some of them are more easily ascertained than others and can be more easily measured.

(1) The assets held by the office, the prices paid for them, and in some cases the prices at which such assets are quoted on a stock exchange.

(2) The sums assured or other benefits and the contingencies upon which these are payable.

(3) The office premiums in force and the contingencies upon which these are payable.

(4) The commissions payable and the conditions under which they are payable.

(5) The rates of mortality applicable.

5.2. The above facts are readily ascertainable and can be accurately measured. The following facts are either not so easily ascertainable or not so easily measured.

(6) Future expenses (other than commission) and especially their incidence.

(7) Future payments of tax. (8) Future bonuses to participating policyholders whose reason-

able expectations must be regarded as a fact. (9) The impact of options included in policies since the burden

which may be placed on an office by a set of options may arise quite abruptly from an unlikely set of circumstances.

(10) The earning power of the assets.

5.3. Any coherent set of valuation standards must deal with all the above facts. There are other facts which are relevant but which need not be dealt with by the standard although they may influence the facts which must be dealt with. The principal one of these is :—

(11) Rates of voluntary termination of policies.

6. BACKGROUND TO THE PRESENT SITUATION

6.1. At the time of writing, the supervision of insurance companies is in a transitional state with certain regulations still to be made in pursuance of the Insurance Companies Act 1974 (ICA 1974). Rules for valuing long-term business liabilities have been proposed in the Department of Trade’s Consultative Note 10 (CN10) and these proposals have been discussed at both the Faculty and Institute of Actuaries following the presentation of the paper “ Proposals for


the Statutory basis of valuation of the liabilities of long-term insurance business ” by R. P. Bews et al.2

6.2. It is a feature of the course of action so far followed that the net premium valuation method has been the one advanced and that attention has been focused on this method and possible modifications to it considered (is it possible that we have been preoccupied with annual premium traditional assurance business and that attention has been diverted from the danger areas of single premium business and unit-linked assurance business ?). Advocates of gross premium or other valuation methods, although speaking with considerable eloquence and logic, have been cast in the role of critics who, in any case, have not suggested any alternative set of rules.

6.3. The shortcomings of the proposed rules were considered at length but the practice of many offices in valuing their assets and liabilities at the end of 1974 would lead one to suppose that either these shortcomings were underestimated or the principles underlying the proposed rules are not widely accepted. Very few offices valuing their assets at 31st December 1974 entered values fully in accordance with the regulations that were to come into force on 1st February following.

6.4. Some shortcomings of the proposed rules need re-emphasis in the light of this country’s current economic position and no doubt other shortcomings have become apparent. In particular, the possibility of investment policy being distorted or investment in equities suppressed merely to satisfy statutory regulations must be abhorrent to those concerned with the vitality of our industries. The distortion of the relationship between policyholders’ bonuses and shareholders’ profits when a “ net premium valuation ” at an increased rate of interest is used is also worthy of mention. The preoccupation with traditional annual premium business could result in the standard of stringency required being very inconsistent in its application to other types of business. It would be grossly unfair if the interests of participating policyholders were adversely affected by over-stringent valuation regulations which led to surplus being held back to the next generation of policyholders and at the same time (under the provisions of the Policyholders Protection Act) these same policyholders were obliged to pick up the bill for the failure of a company operating in a different way and subject to less stringent control. Then there is the implication that those offices which abandoned the “ net premium ” method many years ago have not conducted their affairs in the best actuarial tradition;


also the possibility that numerous offices will request special treatment in order that their business may expand vigorously or that their policyholders may receive more useful information.

6.5. The transition from “ freedom with publicity ” to “ supervision in detail ” is perhaps inevitable bearing in mind the recent failures of insurance companies, the growth of consumerism—caveat vendor, and our membership of the EEC, but the regulations for valuing assets and the proposals for valuing liabilities appear to set a standard of stringency rarely encountered in any country where the life assurance industry is fundamental to the economy. To impose unnecessarily stringent regulations at a time when policyholders are now protected by the Policyholders Protection Act can only adversely affect, the role played by the UK long-term insurance industry in the country’s economy and also the interests of policyholders. While the British actuarial profession, we believe, accepts the goal of a united European economy, and that harmonisa- tion of national insurance regulations must be a step in the path to that goal, we also believe that if the typical dirigiste European system of insurance supervision is too readily accepted, the British insurance industry could contract quite sharply in relation to the size of our economy.

6.6. It has to be admitted that the task undertaken by the supervisory authority is not enviable. To determine at what level a “ plimsoll ” line should be drawn so that there is a sufficient margin of safety yet the vessel ‘can still operate economically demands a very subtle combination of science and judgement. To draw the line after considering the notional dimensions of the vessel rather than the actual dimensions would, however, be a very puzzling approach to the problem !

6.7. We do, however, live in turbulent economic conditions where rates of inflation, interest and stock market prices achieve levels that not so long ago might be regarded as unthinkable. The inductive reasoning by which past experience is used as a guide to the future looks suspect. It is perhaps because of this uncertainty that valuation regulations are necessary, but valuation principles that are widely accepted as adequate during stable conditions may not serve as well in times of economic uncertainty.

7. LEGISLATION

7.1. Section 14 of ICA 74 states that— “ (1) Every insurance company. . . which carries on long

term business—


(a) Shall, once in every three years . . . cause an investigation to be made into its financial condition in respect of that business, including a valuation of its liabilities in respect thereof. . . ; and

(b) when such an investigation has been made, or when at any other time an investigation into the financial condition of the company in respect of its long term business has been made with a view to the distribution of profits, or the results of which are made public, shall cause an abstract of the actuary’s report of the investigation to be made.

(3) For the purpose’ of any investigation to which this section applies the value of any assets and the amount of any liabilities shall be determined in accordance with any applicable valuation regulations . . .”

7.2. There can be little doubt that for a published valuation, the liabilities are to be determined in accordance with the proposed valuation regulations. Section 25 of ICA 74 which refers to allocations to policyholders makes it clear that the “ established surplus ” in respect of which the allocations are made is shown by a valuation in accordance with the valuation regulations that apply to 5.14. The basis on which the cost of bonus calculation is to be performed is presumably identical to that by which the value of the sum assured and existing bonuses has been calculated although this is perhaps implicit rather than stated.

7.3. Section 28 gives the grounds on which the wide powers of intervention conferred on the Secretary of State shall be exercisable, one of which is

“ that the Secretary of State considers the exercise of the power to be desirable for protecting policy holders or potential policy holders of the company against the risk that the company may be unable . . . to fulfil the reasonable expectations of policy holders or potential policy holders ”.

S.28 and S.14 are linked indirectly via S.34 since it would be somewhat illogical if a satisfactory investigation made under S.14 did not indicate that the risk of the company being unable to fulfil “ reasonable expectations ” was small or negligible.

7.4. Before passing on to what policyholders might reasonably expect, or indeed what a reasonable policyholder might expect, it is worth noting that phrases enshrined in the law are subject to

c


interpretation in their full purity and logic by that profession. The interpretation of a phrase may not be what was intended by Parlia- ment and the powers conferred by the enactment may be used in ways not originally envisaged or even in an antipathetic manner.

7.5. In the case of non-participating business the reasonable expectations would at first sight appear to present no difficulties. For traditional business the fulfilment of contractual obligations is not perhaps quite sufficient; the holder of a non-participating policy (or the potential holder of such a policy) can also expect that if he wishes to discontinue his contract prematurely, he may receive a cash amount that is justifiable. If, in calculating this cash sum, the office makes an allowance for depreciation, it should surely be on the basis that the portions of premiums available for investment had been invested with a view to meeting the contractual liabilities.

7.6. The holder of a unit-linked policy might reasonably expect the fulfilment of his contract and, where the mode of operation is not clearly defined, that the company should at least conform to an accepted code of practice.

7.7. For a participating policy, the holder will probably have been provided with an illustration of the possible maturity benefit assuming continuation of the last declared bonus rate at the time the illustration was prepared. He should be aware that at a bonus declaration the same rate of bonus applies to groups of policies. For an open series, is there any reason for the policyholder who effected his policy many years ago to expect more or less in the way of rates of reversionary bonus than the recent entrant to the series ? Surely there is an analogy with the shareholder—but for adverse trading conditions, he may expect an annual dividend of the same order of magnitude as that last declared and that the rate of dividend would be independent of when the shares were purchased.

7.8. In the paper “Bonus distribution with high equity backing” by S. P. L. Kennedy et al.3 it is stated that the working party agreed the principle that:

“basic reversionary bonus rates should be fixed at a level which the office can expect to maintain in the absence of a sustained or substantial change in experience”

It is submitted that there is a strong link between the reasonable expectations of participating policyholders and the rates of bonus most recently declared. (If there has not yet been a bonus declaration for the series, the link must be with the rates of bonus used in any sales material.) In addition to the contractual liabilities and


bonus additions, the participating policyholder may also expect a justifiable surrender value. If allowance is made for depreciation, it could well be on the basis that investment was in equities if this was indeed the case. The possibility of the surrender value of a participating policy being somewhat lower (in terms of premiums paid) than that of a non-participating policy is not necessarily illogical.

7.9. It is suggested that the requirements of the periodic actuarial investigation made under S.14 of ICA 74 are :—

(1) It should be shown that the probability of the company being unable to fulfil its contractual obligations is minimal.

(2) It should be shown that, for a company with participating policyholders, it is likely that a rate of bonus can be maintained which bears a reasonable relation to recently declared rates.

(3) It should be shown that the financial condition of the company will not be adversely affected by the payment of reasonable surrender values where these are not guaranteed nor by the payment of any guaranteed surrender values or other options fixed by contract.

(4) It should demonstrate that surplus will emerge and be divided in an equitable manner.

8. VALUATION—GENERAL CONSIDERATIONS

8.1. Generally speaking, the actuarial profession has been more concerned this century with the equitable emergence and distribution of surplus rather than questions of solvency. The main causes of insolvency were however well known last century and by means of the Life Assurance Companies Act 1870, which, subject to various modifications, has remained with us, insolvency or possible insolvency could generally be detected. It is perhaps worth inserting here the philosophical question—is the occasional insolvency within the industry good or bad for the industry in the long run ?

8.2. In order to determine the likelihood of a life assurance company becoming unable to fulfil the reasonable expectations of its policyholders, it is necessary to construct an actuarial model which can be applied to the available data. This new model will have to differ very considerably from the aggregate actuarial model defined by the premium rates because financial and other circumstances will have changed and the new model must reflect these


changes. Moreover, in building the new model, assumptions as regards the future are inevitable unless total reliance is placed on the market place.

8.3. It could be argued that a perfectly consistent method of valuation would be to allow the “market” to place a value on the office’s assets and liabilities—in the case of the liabilities the value would be the single premiums necessary to reassure the total liabilities with other offices. Apart from the fact that the problem of valuing the liabilities is not solved but merely transferred to another office, it is interesting to surmise the result of such a method in today’s conditions. The insurance companies are able to exert a considerable influence on the prices at which marginal transactions in investments are made. If also the liabilities of offices were valued at the price of marginal reassurance arrangements, then under the conditions where the assets and liabilities are valued at the prices at which marginal transactions between life offices take place, the financial stability of the industry as a whole becomes a self-supporting illusion!

8.4. If a value has to be placed on the assets of a company which depends upon the prices at which actual marginal transactions have taken place or at which hypothetical transactions might take place, it is not possible to progress logically to a valuation of the liabilities that relies on a different philosophy. The best that can be achieved is that consistent actuarial treatment is applied to both assets and liabilities and the value placed on the assets according to this treatment coincides with “market” values.

8.5. In investigating the financial condition of a life office, “market” values, despite their shortcomings, have three particular advantages over valuation by any other method.

(1) The value of assets, as measured by this method, cannot be suddenly increased by one or two investment transactions— i.e. there is little scope for manipulation.

(2) The internal transfer of assets from supporting one set of contracts to another—a process which is continuously taking place—is performed on terms which are determined externally according to the current state of the capital market.

(3) Marginal changes in the liabilities when there is a surrender on guaranteed terms are linked more closely to market values than any other type of value of asset.


In applying a consistent actuarial treatment to assets and liabilities, it is perhaps wise to avoid too much refinement—or embroidery. The pattern of the liabilities can be estimated and changes only slowly, but for a small fund the pattern of assets can be radically altered almost overnight.

8.6. In making an investigation into the financial condition of an office, there are many qualitative assessments that could be made. For instance, the economy of management, standard of underwriting, suitability of investment policy, rate of expansion of business. It is necessary, however, that the assets and liabilities be quantified. In compressing the future asset and liability income and outgo into two amounts, it is inevitable that some insight into the developing pattern of the business is lost—in particular the points at which liquidity strains may arise cannot be immediately identified.

8.7. There are in essence only two types of actuarial model that can be applied to the liabilities. The first is the explicit model where allowance is made for all future revenue items as they are expected to arise. When this model is compressed the result is a gross premium valuation. The alternative for annual premium business is to use mathematical reserves where the allowances for future mortality, expense and profits are subtly combined and cannot be identified. This model when associated with book values of assets can be moulded into one that is useful in allowing for an equitable emergence of surplus and it is perhaps only in these circumstances that it should be called a “net premium method” and regarded in some way as a standard of good conduct. The mathematical reserve model, in respect of non-participating business, is said to break down at low rates of interest since the so called “net premium” may exceed the gross premium. This breakdown is artificial and arises from confusing the two models. The only way the mathematical reserve method can break down is by giving an implausible answer—in extreme conditions (or conditions which seem extreme at the time) this is what it appears to do.

The rate of interest i used in calculating the mathematical reserves is, in essence, a parameter determining the shape of a growth function, and difficulties arise, not necessarily because the model is defective, but when i is of the same order as the rate of interest implicit in the value of the assets and financial conditions are far removed from those assumed in the aggregate actuarial model as described in 2.2.


9. EFFECT OF A MARGIN IN THE RATE OF INTEREST AS APPLIED TO MATHEMATICAL RESERVES FOR NON-

PARTICIPATING BUSINESS

9.1. In “ Financial Guarantees Required from Life Assurance Concerns ”4 the concept of a proportionate margin in the rate of interest was proposed and tables produced showing the effect of a margin in the rate of interest for specimen reserves. The concept of a proportionate margin has been followed in CN10.

9.2. However, there is another angle from which a margin in the rate of interest can be viewed. In the event of a life office coming close to insolvency, little surplus would be distributed and it is illuminating to examine what happens under such conditions. Appendix A shows what happens when a fund is built up earning an extra ½% interest above the valuation interest assumption but all other actuarial assumptions remaining the same. It demonstrates that for a wide variety of contracts, where there is a constant difference between the rate earned by the fund and the rate assumed in the reserve, the fund gains by more proportionately on the reserve when interest rates are high than when they are low.

9.3. The examples given trace reserve and fund from duration 0 onwards but the position starting from any intermediate duration t can be worked out simply by reducing the surplus St at time t to zero and deducting from the fund at subsequent durations St(1+i')n–t where i' is the rate of interest being earned on the fund and n is the subsequent duration at which one wishes to examine the situation. What is interesting is that the difference built up is more marked in immediate annuity reserves than in assurance reserves and thus depends more on the nature of the contract than the level of interest rates.

10. DEPRESSION OF THE RATE OF INTEREST AS APPLIED TO MATHEMATICAL RESERVES FOR

PARTICIPATING BUSINESS

10.1. In dealing with participating business, it has long been realised that if mathematical reserves are used, then in order to allow surplus to emerge during stable conditions to support a level reversionary bonus rate, the parameter i involved should be lower than the rate of interest being earned. The reduction involved


must inevitably depend upon the bonus rates being declared or the premiums being charged or both. Without this artifice, mathematical reserves are not necessarily a standard of good conduct as is illustrated by the “ Bubble Office ” (see Appendix B). This office (which is of course purely hypothetical) declares a bonus rate that can only be maintained by ever-increasing new business. It obtains such business by sales illustrations showing far higher bonus rates than its competitors. Eventually, the bubble bursts, new business ceases and those policyholders left receive inequitably low bonus rates. Thus a further dimension of regulation would be necessary to ensure that the lowering of the valuation rate of interest is sufficient to secure equitable bonus distribution treatment between different generations of policyholders.

11. DETERMINATION OF THE RATE OF INTEREST

11.1. Under the passive, original cost (“ book value ”) method of bringing assets into the company’s balance sheet, the Life Assurance and Annuity Fund could be validly regarded as a continuous function, since its value progressed smoothly from year to year. The only exceptions to this smooth progression were assets written off because of failure of performance by debtors or the occasional writing up of equity or property assets because of intrinsic improvement in the security. The writing down could reasonably be regarded as a charge on income and the writing up either as a single discontinuity in a smooth progression if it were infrequent and large in size (if it were not large there would be no point in making an infrequent adjustment) or frequent and small where it could reasonably be regarded as part of the continuous progression. Because of the continuity of the Fund it was possible to treat the progression of the Fund through the year as = i/ δ where δ = loge (1 + i). The derivation of i demands that the function which is growing is continuous over the range so that the formula

i = implies continuity in the Fund (see Donald5).

11.2. However, the application of market values to assets means that the Fund can no longer be regarded as a growing continuous function since the market valuation is an “ active ” one and therefore the time-honoured formula ceases to be valid under the new conditions. This is not a mere theoretical objection as can be seen by looking at the progress of market values in the calendar year 1974.


11.3. If the Fund is not a continuous function then the only relevant evidence in determining the rate of interest in the valuation basis that can be obtained by reference to the Fund is its earning power at the valuation date. It is not easy to contrive a simple method of calculating this but the average yield being earned at the valuation date weighted by the market values of each investment appears to be a reasonable proxy. However, it is open to criticism that it does not treat equities and freehold property correctly. With the former there is the expectation of an increase in income (otherwise these securities would not be held at “ reverse yield gap ” market values) and in the case of the latter there is often a virtually certain increase in rental income at the date of the next reversion. A further criticism is that this method takes no account of the relative future terms for which these yields may be available. This could be met by including mean terms measured at a rate of interest near to the proxy yield as a further weight but adds greatly to the complexity of the calculation.

11.4. Under the old “ passive ” method it was reasonable to base the determination of the rate of interest on I, the amount credited to the revenue account in the previous year (provided that the revenue account made due allowance for accrued interest on purchases and sales), because the revenue account, apart from the occasional write-ups, led directly from one year’s Fund to the next.

Moreover, there was a built-in self-correcting mechanism because as assets were sold or matured, the book costs tended to move towards market values and the observed rate of interest earned on the fund moved in sympathy. There was thus a damping effect on short-term fluctuations. By imposing market valuation of assets, the revenue account does not lead directly from one year’s Fund to the next nor does the damping effect apply.

11.5. In Rule 2(b) of CN10 it is stipulated that “ amounts of . . . amortisation of redeemable fixed interest investments credited or debited to the appropriate long term business revenue account ” are to be included in the determination of the rate of interest on the Fund. It is difficult to see how amounts of amortisation can be included in a revenue account unless that account is relating one year’s amortised value to the next year’s amortised value on the same basis. And if the asset is on amortised values on the same basis at the beginning and the end of the year it is unlikely that these will both be market values.

11.6. In financial conditions where the rate of interest implicit in market values is far removed from the rates of interest implicit


in the aggregate actuarial model (as defined in 2.2), the evidence of the earning power of the fund at the valuation date is not necessarily the only guide to the rates of interest to be adopted in the valuation. Some attention must be paid to the likely long-term rate of interest at which future investments to the fund are likely to be invested, if the fund is growing, or at which assets will have to be realised, if the fund is contracting.

12. THE EXPLICIT ACTUARIAL MODEL

12.1. Returning to the explicit actuarial model, there are two particular problems before even a start can be made in deriving a valuation standard. Firstly, should any allowance be made for new business ? Secondly, should the portfolio of investments be regarded as being atypical at the date the valuation is made and so hypothetically respread ? The answer to both these questions must surely be no.

12.2. The new business can be subject to quarterly scrutiny and if the premiums charged seem inadequate bearing in mind the acquisition costs there should be ample time for remedial action to be taken. If, in building the actuarial model, allowance for new business were made there would always be a lingering doubt about the financial condition of the office—like the “ bubble office ” there might be a dependence upon new business. In particular the use of gross expenses and net effective interest in a model for ordinary life assurance introduces this doubt.

12.3. In dealing with the portfolio of investments, there is always the possibility of “ window-dressing ” over a period including the valuation date. The quality and quantity of the goods displayed are, however, subject to the valuation of asset regulations. Never- theless, the spread of the portfolio at the valuation date may not be representative of the investment policy normally pursued. For instance, because of the valuation regulations, there may be a tendency to switch from equities to fixed interest stock shortly before the valuation date. However, faute de mieux, the existing portfolio of investments has to be taken as the starting point for an explicit model.

12.4. In respect of the liabilities, the model will allow for the primary benefits that accrue to policyholders who maintain their policies until maturity. Allowance for alternative or incidental benefits (including for convenience the “ benefit ” of lapsing) will


be left until later. Making estimates of mortality, expenses, tax rates and bonus rates, partial cash flow projections can be made for all future years. Although the “ shape ” of these projections is of considerable interest, it is necessary to make fairly sweeping assumptions about the yields that will be available on future new investments and what terms of investment are chosen and also the investments (if any) that will have to be realised and the prices at which they may be realised. It is then possible to see whether all the “ hollows ” in the partial cash flow projection can be filled up or not. Clearly assumptions can be made which make this impossible for any office or possible for every office.

12.5. For a typical office (but not for one transacting only immediate annuity business), it may be many years (if ever) before investments will have to be realised. This gives ample time for investments to be rearranged and is a period during which the market value of investments has no particular relevance to the strength of the office. There will be an infinite variety of investment assumptions that allow a full cash flow projection to be non- negative. The question is—can a set of such assumptions be found that is tenable ?

12.6. The answer to this question depends not only upon the estimates of future mortality, tax, etc., but also (and perhaps more so) on the possible future patterns of investment conditions and investment strategy of the office. An approach along the lines suggested by S. Benjamin6 is not, however, practicable since it is necessary that the assets and liabilities be quantified and it is by reference to the theory of immunisation that rates of interest for a gross premium valuation will be suggested. Among the many difficulties associated with this theory, three particular aspects come to mind in considering a gross premium valuation standard.

12.7. If a block of business is immunised so that

VA = VL and MA = ML

where VA is the market value of the assets VL is value of the liabilities at the rate of interest implicit

in VA MA is the mean term of the value of the assets at the rate

of interest implicit in VA ML is the mean term of the value of the liabilities at the rate

of interest implicit in VA


then, unless the business is absolutely matched, a continuous rearrangement of investments is required as time passes if the block of business is to remain immunised. The situation is a dynamic one and, even under ideal conditions, it is not sufficient to know what the “ rate of interest ” is at any point in time ; the rate of change of this is also required. To cope with this problem and also the practical difficulties it is essential that an office that attempts to immunise its business at all times should have some free reserves. It is suggested that there should be allowance for erosion of investments

i.e., K. VA = VL where K is the erosion factor K 1.

Only if the business is absolutely matched could K = 1. In terms of presentation this would mean that there are always free reserves (called investment, contingency, etc.) amounting to (1 – K)VA.

12.8. If business is immunised or matched in blocks, different types of policy being put together into each block, negative (or unjustifiably low) reserves in respect of individual policies may be hidden amongst VL. This will be illustrated by a very simplified example (mortality, expenses, tax ignored). An office issues two policies simultaneously:—

(a) 20-year endowment assurance Sum Assured = 1100. Annual Premium 17.46.

(b) 19-year annuity certain Purchase Money 982.54. Annuity Per Annum 117.46.

By putting these policies together into the same block, it can be absolutely matched by the purchase of 1000 units of a 10% 20 year stock at par.

If immediately after investing the annuity purchase consideration and the first premium the interest rate changes to 10½% the position becomes:—

Value of endowment assurance 7.98. Value of annuity certain 950.86.

Value of stock 958·44.

If now the endowment assurance were surrendered, it would be difficult to justify to the policyholder a surrender value of 7.98. On the other hand it would be impossible for the actuary to allow a surrender value > 7.98.

If, however, the interest rate had changed to 11½% the position would have become:—


Value of endowment assurance —7·92. Value of annuity certain 892·27.

Value of stock 884·35.

If the endowment assurance lapses, there is a very considerable risk of the office being unable to fulfil its annuity contract (which under- lines the virtues of writing good quality business). This difficulty arises when policies of different types are grouped into a block for immunisation or matching. If an attempt had been made to immunise each policy in its own right, the possibility of insolvency would have been much diminished although the newness of the endowment assurance prevents complete immunisation.

12.9. If a policy is capable of being immunised in its own right at outset, then it is appropriate to use a rate of interest close to that implicit in suitable investments in calculating the premium rate. For most annual premium contracts and some long-term single premium contracts immediate immunisation is not feasible, and a more cautious rate of interest would be used. In valuing such contracts shortly after issue, the use of a rate of interest greater than this cautious rate implies negative or unjustifiably small reserves and instant spurious profit. This latter problem is not one that can be overcome by the inclusion in the model of wastage rates since it can occur for long-term single premium S.226 contracts which cannot in any case be surrendered. Even in the case of ordinary annual premium business it would seem that surrender values and wastage rates could be dependent upon the rate of interest and the difficulty of specifying tables of wastage rates and surrender values at varying rates of interest would probably be insuperable. If reserves are calculated in accordance with the principles that follow it is suggested that these reserves will never be less than a justifiable surrender value. It may be that for practical reasons, or bearing in mind questions of equity, an office chooses to pay a surrender value that is more than would be justifiable (e.g. cash value of bonus additions to a policy at early duration). If this practice is significant, an adjustment to the valuation reserves would be appropriate.

13. PRINCIPLES FOR A GROSS PREMIUM VALUATION STANDARD

13.1. The following are suggested as suitable principles for a gross premium valuation standard for use in association with assets taken at market values.


(1) The liabilities should be valued by a gross premium bonus reserve method. Negative reserves should be eliminated.

(2) Recognised tables of mortality should be used. These tables may be modified according to the experience of the office, if the Actuary judges it to be necessary.

(3) An explicit allowance should be made for future expenses (other than acquisition expenses) reduced to allow for the appropriate rate of tax. An explicit allowance for increases in such expenses should also be made.

The future expenses could be based either on the recent experience of the office or an index of expenses based on an inter-office expense investigation. The former is inevitably subjective since it is necessary to divide expenses between acquisition and non-acquisition (a division which should probably be used in the revenue account in any case). The latter method is more suitable if it is argued that the fund may be closed to new business and administered within the context of an “average” sized life office.

In making allowance for increases in expenses, due regard should be given to the proportion of the investments of an equity type and also to possible technological improvements resulting in greater productivity.

(4) The rates of bonus to be reserved for should be not less than two- thirds of the rates currently being declared.

The figure of two-thirds is somewhat arbitrary but if an office cannot show that it is able to maintain such bonuses, then there is a risk of the reasonable expectations of participating policyholders being impaired. (No reserve should be made for terminal bonuses except where failure to pay such bonuses would be grounds for intervention by the Secretary of State.)

(5) The rate of interest used in valuing each contract should have regard to the rate of interest implicit in the office premium and to the rate of interest implicit in the associated investment(s), allowing for the appropriate rate of tax, and to the degree of immunisation attained.

In calculating the rate of interest implicit in the office premium allowance for mortality, expenses and bonuses should be made in accordance with 2, 3 and 4 above. For annual premium contracts the allowance for initial expenses should be not more than the lesser of two annual premiums and 3% of the Sum Assured. In calculating the rate of interest implicit in variable interest investments, no increase in the annual income should be assumed; any potential increases being set against the requirements of (3) and the


bonus not specifically allowed for in (4). A means of deriving the valuation rate of interest, which is essential to the arguments developed, is explained further in Appendix C.

It is shown that, where the rate of interest implicit in market values ruling at the valuation date differs widely from the long- term rates which it is expected will re-emerge in future, then varying rates of interest are appropriate to each type and each future outstanding term of contract.

(6) Additional reserves should be held to allow for the erosion of invest- meats that could result even if the business were well matched and to ensure that the financial condition of the office would not be adversely affected by the exercise by policyholders of any options in their contracts.

It would be appropriate to hold an explicit investment reserve to allow for the possible erosion of investments. In considering the various options contained in contracts, it is the guaranteed options that require careful scrutiny. To ensure that an office with a high proportion of contracts containing generous guaranteed surrender values is able to fulfil either the primary benefit or the secondary benefit even after a substantial rise in interest rates would require massive additional reserves. Bearing in mind tax considerations, the economic conditions under which it would be advantageous for a policyholder to surrender his contract on guaranteed terms may be very extreme. It is suggested that, generally speaking, it is adequate for the reserve calculated according to 1-5 above to be increased where necessary to the value of any guaranteed options.

14. CONCLUSION

14.1. This paper falls into two parts. The first part outlines the problems and the second part, the authors believe, puts forward a credible and coherent set of solutions. Much of the thinking behind the current concepts of valuation standards took place in the 1960’s. Since then we have had a financial crisis more acute than that of 1929. So in the working lifetime of many senior actuaries the gross rate of interest has swung between 2½%, when savers go on strike, to nearly 20%, when physical commercial investment becomes impossible. Also, since the 1960’s, inflation has accelerated to a rate where it cannot be counteracted by improved administrative efficiency even allowing for the impact of computers. Thus the passive approach adopted by life offices in the past can no longer be universally applied. A more active approach is necessary. This active approach


has already been applied to assets in the new valuation regulations and a logically related approach should, in our view, be similarly applied to liabilities.

ACKNOWLEDGEMENTS

The Authors wish to record their gratitude to Messrs. P. E. Beaven, M. I. Brownstein, R. H. C. Minting and J. E. O’Neill for the assistance given in preparing and checking the numerical examples and tables, and to Miss J. Rodker and Miss J. Cheesman for cheerfully typing various versions of this paper.

REFERENCES

1. SPRAGUE, T. B., M.A. On the Causes of Insolvency in Life Insurance Companies and the best means of detecting, exposing, and preventing it. J.I.A., 20, p. 291.

2. BEWS, R. P., F.F.A., SEYMOUR, P. A. C., M.A., F.I.A., SHAW, A. N. D., F.F.A., and WALES, F. R., F.I.A., F.S.S. Proposals for the Statutory Basis of Valuation of the Liabilities of Long-term Insurance Business. T.F.A., 34, p. 367.

3. FROGGATT, H. W., B.Sc., F.I.A., HODGE, P. E. T., F.I.A., KENNEDY, S. P. L., B.A., F.I.A., and KING, A. S., M.A., F.F.A. Bonus Distribution with High Equity Backing. J.I.A., 103, p. 11.

4. Financial Guarantees Required from Life Assurance Concerns. Published, Paris, 1971, Organisation for Economic Co-operation and Development.

5. DONALD, D. W. A., O.B.E., T.D., F.F.A. Compound Interest and Annuities- Certain, Second Edition, pp. 4/5 and 276/7.

6. BENJAMIN, S., M.A., F.I.A., F.S.S. Theory of Games and its Application to Rate of interest. J.I.A., 85, p. 373.

7. McKELVEY, K. M., F.I.A. Discussion of 2 above.


APPENDIX A

Examples of progress of fund assuming ½% interest margin over valuation rate and all other valuation assumptions exactly fulfilled.

Whole Life Assurances Non Participating SA £1,000

Mortality A67-70 ult

Entry Age Duration Valuation rate 2%

Fund Reserve Ratio % Valuation rate 6·5%

Fund Ratio %

20 5 52·00 51·21 101·54 17·57 17·25 101·86 10 111·37 108·29 102·84 34·50 33·51 102·95

30 5 72·32 71·23 101·53 35·15 34·52 101·83 10 152·09 147·84 102·87 66·20 64·26 103·02

45 5 112·63 110·85 101·61 78·10 76·60 101·96 10 223·94 217·29 103·06 137·62 133·22 103·30

60 5 155·91 153·05 101·87 112·79 110·59 101·99 10 263·69 254·19 103·74 202·39 194·25 104·19

70 5 164·82 161·01 102·37 149·62 145·13 103·09 10 212·73 202·10 105·26 180·19 169·80 106·12

Whole Life Assurances Non Participating SA £1,000

Premium Paying Term 20 years

30 5 132·73 130·75 101·51 37·96 37·39 101·52 10 280·60 272·82 102·85 89·16 86·69 102·97

45 5 169·61 167·00 101·56 79·81 78·54 101·62 10 344·17 334·21 102·98 176·20 169·75 103·21

60 5 188·71 185·36 101·81 126·40 123·99 101·94 10 330·16 318·78 103·57 233·66 224·62 104·02

Endowment Assurances Non Participating SA £1,000

Original term

30 10 5 479·95 472·84 101·50 425·95 419·73 101·48 45 10 5 471·44 464·35 101·53 418·42 412·21 101·51 60 10 5 426·16 419·27 101·64 378·01 371·90 101·64

30 25 5 165·19 162·73 101·51 99·33 97·86 101·50 10 349·65 339·98 102·84 236·35 229·67 102·91

45 25 5 168·85 166·25 101·56 106·91 105·24 101·59 10 342·57 332·65 102·98 239·73 232·47 103·12

60 25 5 172·02 168·92 101·84 123·98 121·61 101·95 10 296·34 285·92 103·64 228·12 219·24 104·05

30 40 5 94·32 92·90 101·53 40·61 40·00 101·53 10 198·88 193·35 102·86 95·52 92·77 102·96

45 40 5 117·31 115·47 101·59 66·41 65.33 101.65 10 233·82 226·90 103·05 143·29 138·73 103·29


Immediate Annuities payable yearly in arrear Purchase Price £1,000

Males a(55) ult Age at

purchase Duration 60 5

10 70 5

10 80 5

10

Valuation rate 5% Valuation rate 13% 806·93 781·30 103·28 862·86 831·97 103·71 609·71 556·80 109·50 715·52 632·33 113·16 647·99 624·16 103·82 693·78 664·90 104·34 366·75 321·59 114·04 435·98 363·43 119·96 412·13 391·42 105·29 437·64 412·35 106·13 138·90 104·53 132·88 172·04 114·97 149·64


The Bubble Office APPENDIX B

This office transacts only 25 year endowments. Premiums are received annually in advance at the beginning of each accounting year. Claims are paid at the beginning of the year. Investments earn exactly 5% p.a. Acquisition costs are 3% of sum assured. Mortality, renewal expenses and tax are ignored. The annual premium is £43·80 per £1,000 sum assured. New business increases at 20% for 24 years. The office values at 4½% with a 3% Zillmer.

The premium rate supports a 3% compound bonus but the office declares 4% compound as long as it can. After 25 years the office’s ability to maintain 4% bonus is in doubt and new business ceases. For an annual premium of £43·80 the first policyholders obtain maturity proceeds of £2,666 and the last policyholders obtain £1,836. The “ fair ” amount is £2,094.


APPENDIX C

It is assumed that the actuarial basis of the valuation has been decided but for the rates of interest to be used for the various classes of contract. Proceeding at a theoretical level, a method of determining the rate of interest at which each contract should be valued will be suggested. The contracts will be listed in order according to their term and the assets will also be listed in order according to term. A rule for doing this could be defined. The first contract on the list is considered and the types of assets and mixture of such assets that should be associated with the contract decided. The quantity of such assets required to be associated with the contract is not yet known. For the contract under consideration the following can be calculated:—

(u) The value of the contract at any chosen force of interest — call this VL

(b) The mean term of the value of the contract at any chosen force of interest —call this ML

(c) The force of interest implicit in the market value of the associated assets—call this

(d) The mean term of the value of the associated assets at any chosen force of interest —call this MA

(e) The value per unit of the associated assets at any chosen force of interest —call this DA

(f) The force of interest implicit in the premium charged for the contract according to the valuation basis—call this ß.

In addition, two limits in respect of the associated assets will be set.

ß0 = the force of interest below which it is considered unlikely for the force of interest implicit in the market value of the associated assets to fall in the near future.

ß1 = the force of interest above which it is considered unlikely for the force of interest implicit in the market value of the associated assets to rise in the near future.

put = smaller of ß0, ß and = greater of ß1, ß (it is, of course, assumed that

If k is the number of units of associated assets required for a satisfactory situation then k should be determined as follows.

(1) If VL 0 then k = 0 (2) If MA <ML then k.UA = VL

where is the solution of the equation

(A)


lying between and (3) If MA = ML then k.UA = VL (4) If MA >ML then k.UA = VL

where is the solution of the equation

(B)

lying between and

This process is repeated for each contract on the list until either the list of contracts is exhausted and certain assets (or proportions of assets) remain unassociated with any contract or alternatively the assets are exhausted and certain contracts remain with no assets to support them.

Clearly there are an infinite number of possible ways of associating contracts with types and proportions of assets. If no way can be found that leaves sufficient assets unassociated to allow for the erosion mentioned in 12.7 then the overall position is not satisfactory.

The consequence of this process of associating each contract with a quantity of assets is that, to the first order, the quantity of associated assets will be sufficient even if the force of interest implicit in the market value of the assets were to change rapidly to either or and then investment conditions were to remain constant. (In particular the quantity of assets would be sufficient, to the first order, if investment conditions were to change to those implicit in the premium rate and remain stable.) This will be shown for the case where MA < ML :—

+2nd and higher order

terms

+2nd and higher order

terms

+2nd and higher order terms

= 0 to first order.

+2nd and higher order terms

order termsorder terms

2 n d a n d h ig h e r

2 n d a n d


0 to first order.

If condition (4) is satisfied but it is wished to use the market value of the asset, then either the reserve for the liability is increased to

or a force of interest µ must be found so that VL(µ) equals the above expression. Approximate values for µ would be

or

If, for condition (2), is small implying is small then a good approximation to VL is

The transition from forces of interest to rates of interest within the foregoing formulae is sufficiently accurate for our purpose and the rate of interest will be given by :–

i = -1 j = -l i0 = -1 k= -1 i1 = -l z = -1

Now clearly the foregoing process cannot be regarded as anything but a theoretical approach. It allows for a market where the prices of similar types of asset are independent and incorporates all the practical drawbacks associated with the theory of immunisation. Nevertheless, if rules could be defined for associating contracts and assets, and for setting ß0 and ß1 for each contract, a computer program could be written to carry out the process.

In practice, it is suggested that the contracts to be valued should be divided into groups and groups of contracts associated with groups of assets in a similar way to that proposed by McKelvey7. The choice of ß0 and ß1 would depend upon the group of assets concerned and would of course be stated. The rate of interest used in valuing the group of contracts would be not greater than the j (or z) that would result by associating any one contract with the group of assets

Valuation Standards 167 concerned. This method would lead to a system where classes of business were stratified at some inconvenience. It is however suggested that the traditional methods of valuing a class of business at a single rate of interest are not suitable where questions of solvency are concerned. Within this context, to value recently acquired annual premium business at the same rate of interest as that very near to maturity is somewhat illogical.

Example

Consider non-participating 25 year endowment assurances. Age at entry 30. Office annual premium 2.56%. Suppose that immediately before payment of the (t+ 1)th annual premium the gross premium valuation is for a 10,000 SA

= 10,000 A30+t : A67/70 ult

The type of asset to be associated with these assurances is a 25 year fixed interest stock. Coupon 5% (net). Interest annually in arrear. Market value per 1000 nominal 679.76.

t MA (i) i ML (j) j i0 VL (j) kUA (i) VL (i0) kUA (i0) 2 12.614 0.08 401.35 0.0461 0.045 123.88 123.88 177.72 195.75 5 12.614 0.08 73.58 0.0510 0.045 675.34 675.34 977.26 1,067.16

10 12.614 0.08 26.76 0.0615 0.045 1,729.34 1,729.34 2,560.26 2,0732.66 15 12.614 0.08 13.14 0.0786 0.045 3,023.45 3,023.45 4,515.94 4,777.59


SYNOPSIS

The paper seeks to examine the fundamental principles underlying the periodic actuarial investigations of life insurance companies. It attempts to define the attributes of an equitable and efficient set of standards, to classify the causes of failure of life offices and to enumerate the realities of any life office. Having examined the background to the present situation it then proceeds to attempt to derive a general valuation standard.


DISCUSSION

Mr. A. C. Stalker, introducing the paper, said :-First of all I must thank you, Sir, for giving us the opportunity of putting forward our views on this rather controversial topic at a meeting of the Faculty, and we hope that the discussion will be wide-ranging and perhaps cover some points on “ valuation standards ” which may not have been covered in the paper.

Coming to the paper itself, I would point out that the quotation from Dr. Sprague does not contain misprints, it is his own spelling ; we thought that we owed it to one of the great founders of the profession to give him his own spelling. We realise that we have gone over a lot of ground which was covered about five years ago, when entry into Europe was first mooted, but we make no apology for this. Up till a few years ago, it was possible to believe that a life office would have to withstand nothing worse than the inflation of 1914-1920, the financial crisis of 1929-1933,-the low interest rates of 1940-1950 and the high interest rates of the early 1920’s. Since then this country has experienced interest rates about three times as high as in the early 1920’s, a financial crisis more acute than 1929-1933 and an inflation as bad as 1914-1920. Therefore, we make no excuse for re- examining the fundamentals underlying the conduct of our business.

Among investments there are only three types of security in which a life office can invest with any possibility of enjoying independence of performance between each type ; these are fixed interest, equities and property. But performance is not completely independent and about once every generation all three types of investment perform very badly together. Such a combined bad performance has just occurred. In such an environment the use of market values for assets does have considerable attraction. However, this does imply that relevant methods should be used for valuations of liabilities and this paper might be described as a search for inter- secting planes of meaning. Our view is that the market valuation of assets is an active method of valuation and therefore a suitable active method of valuation of liabilities should be used in conjunction. A gross premium bonus reserve method does, we feel, meet this requirement for an active method of valuation of liabilities. However, it is very sensitive to the rate of interest employed. To illustrate this sensitivity per rate of interest, we have done some calculations on two model offices. These model offices were based on the rates of premium currently being charged for long participating business by some of the largest companies. We allowed for discontinuance rates and built up a twenty-year model. The effect of changing the rate of interest from 3¾% to 4% in the case of the whole-life model office reduced the liability from £4,093,000 to ;£3,663,000—a reduction of about 10% in the liability for a change of only ¼% in the valuation rate of interest. For the endowment assurance model office based on endowment assurances maturing at age 60, the reduction was smaller but still very large. In this case the reduction was from £1,718,000 (rate of interest 4¼%) to £1.640.000 (rate of interest 4½%). Thus the reduction rate was 4½% of the liability.‘ These results underline the need for establishing a discipline in the determination of the rate of interest, and we believe that such a discipline is contained in Appendix C.

The example in Appendix C demonstrates that for young business the effective rate of interest used in determining reserves is close to the forecast boundary of possible values of the long-term rate. Where the business is old the effective rate used in determining the reserve is close to the rate

170 Valuation Standards being earned on the invested assets at market values. Business of intermediate age has its reserve determined at intermediate rates of interest. Provided one accepts the limits put on the rates of interest expanding funnel of doubt, the method does seem a reasonable one of approximating to its contours.

Then there is the question of expenses. Our view is that expenses should be based on current expense levels for the office concerned, with allowances for future inflation less future improvements in productivity. Future inflation long-term is probably about 6% per annum, and the long-term rate of productivity improvement is probably about 3%, so that the net worsening of the expense cost is about 3% per annum in the long term. Figures to bear these values out were contained in a recent article by Samuel Britten in the Financial Times which produced annual average compound rates of inflation of about 6% when one excluded periods which were known to be exceptionally inflationary or deflationary, and the compound rates of course were much higher if exceptionally inflationary periods were included, and considerably lower if exceptionally deflationary periods were included. However, when current experience shows that costs are increasing at a rate significantly different from the average long-term rate, then a view should be taken which would blend the current rate into the long-term rate on reasonable assumptions. Regarding long-term improvement of productivity, support for the 3% annual compound assumption can be found from the indices of output at constant factor costs. Taking 1970 as 100 the index of output is estimated to have increased from 60.8 in 1952 to 103.9 in 1972 for all economic activity in the U.K., an annual compound increase of 2.7%. For insurance, banking, finance and business services it is estimated to have increased from 45 in 1952 to 111 in 1972, an annual compound increase of 4.6%. (Source--National Income and Expenditure Blue Book.) Thus an annual compound increase in productivity of 3% seems a reasonable assumption. It is possible that where in the short term there is a major known variation either way from these long-term factors this should be allowed for and blended into the long-term rate. An approach such as this should form a satisfactory discipline in the area of expenses. It is slightly ironic that mortality, the classical actuarial element in a valuation, should receive least attention, but we feel that at the present time the problems associated with mortality are less than those associated with the other two members of the actuarial trinity.

Mr. R. K. Stewart, opening the discussion, said :-We have been re- minded more than once already this session of the words of our Royal Charter which say “ That it is mainly in connection with the proper regulation of the affairs of life offices that the skill and services of an Actuary are called into requisition “. The paper before us tonight is concerned with precisely this area and we are grateful to the authors for bringing the subject before us again. We discussed “ valuation” last session-the paper by the Working Party-but the paper before us tonight is written from quite another angle and it is of great benefit to the profession to have these different views brought before it. The fact that I am not in agreement with the authors on a number of points in no way lessens my appreciation of the value of their paper.

The authors begin in 2.1 by reviewing fundamental principles and setting out the attributes of a valuation standard, and I find myself questioning their very first statement, “ The cardinal purpose is to establish that the office is solvent “. If this were true, the case for an office premium valuation would be strong, but in fact the object of an ideal valuation

Valuation Standards 171 standard is not that of a solvency valuation. The solvency valuation shows whether an office can no longer continue in business, whether it is “ on the rooks “. The object of the regulations is rather to establish a statutory minimum valuation basis which will show whether it is “ standing in to danger “, in the nautical phrase, and so give early warning which will enable remedial action to be taken, if required, to prevent it from ever going “ on the rooks “.

I am in similar disagreement with the authors’ statement in 7.2 that “ There can be little doubt that for a published valuation. the liabilities are to be determined in accordance with the proposed valuation regulations “. This is not the case. An Actuary is not required to use the statutory basis— he has only to demonstrate the adequacy of his chosen valuation basis relative to the minimum standard.

Again, it seems to me that the authors are wrong in suggesting in 7.9 sub-section (4) that the valuation standard ” should demonstrate that surplus will emerge and be divided in an equitable manner “. The statutory valuation basis has no relevance to the equitable division of surplus.

I hope these comments will not be thought hypercritical : the profession has a duty to expound its views on the proposed regulations, but views are unhelpful if they are based on a misrepresentation of the aims of the supervisory authority-aims which were made clear once again by the Under- Secretary of State for Trade at our last Sessional Meeting, and widely circulated thereafter.

In the guide issued by the profession it is stated to be the Appointed Actuary’s duty to ensure that he is at all times satisfied that the financial position of the office is satisfactory. The valuation itself is only a part of the means by which the Actuary ensures this. He must watch surrender terms, and he must, in relation to premium rates, watch both bonus illustrations and bonus declarations. Unless the Actuary is in control of these he has lost control of the financial affairs even before he ever starts the valuation. The supervisory authority recognises the central role which the Actuary must have in the operation of long-term business, and relies on his professional integrity in a much broader sense than just carrying out the statutory valuation once a year. For that reason the Actuary’s position is to be strengthened through the requirements of regulations in relation to supporting actuarial certificates. In this connection I might refer to guaranteed surrender values, which I feel have been a major contributory cause of all these requirements. It has been my view for some time that the profession should strongly recommend that the definition of long-term business be amended to exclude any contract which provides, in its first ten years, a guaranteed surrender value of fixed amount freely upliftable by the policyholder. If this exclusion were to be made. there would be an immediate return of confidence in the maintenance of high financial standards in the life assurance industry, without interfering with the commercial freedom through the introduction of regulations which could restrict expansion and investment, stifle innovation and perhaps distort management policy. The position is quite different with surrender values which are not of any guaranteed amount, and I cannot accept the authors’ contention in 4.4 that the strength of an office can be undermined by the unforeseen outflow of such surrender values. It is incumbent on the Actuary to see that surrender value terms do not weaken his sound financial base and to limit the outflow which can take place before he is given the opportunity to review these terms. For all offices in a strongly competitive situation, the position of Appointed Actuary is ideally a full-time one.

The same degree of control is required in the context of premium rates,

172 Valuation Standards and this brings me to the problem put forward by the authors in Appendix B, the “ Bubble Office ” problem. The solution to that problem is not to be found in valuation regulations, but in the Actuary’s test of the adequacy of the current premium rates in relation to the sales illustrations being issued. In order to fulfil the reasonable expectation of a potential policyholder the Actuary must be satisfied that the premium rate currently being charged could earn the bonus being illustrated provided there was no substantial change in experience. In the event of a war or a severe economic crisis, however, a reasonable policyholder must expect bonus to be significantly cut back. There is no reason why he should expect the last declaration rate to be maintained in these circumstances.

I cannot, therefore, support the fourth principle in 13.1 that “ The rates of bonus to be reserved for should be not less than two-thirds of the rates currently being declared “. The authors admit this is arbitrary. It is certainly not logical. Logic points to the rate which is being used in the current sales literature. If terminal bonus is being shown in the illustrations then the terminal bonus should be reserved for in the calculations. In a valuation such as is envisaged by the authors, where every possible item of future profit is being capitalised and taken into credit, there must be an obligation to reserve for the full bonus rates illustrated. However, such a method does not lend itself to explicit definition in regulations ; for one thing, it can be manipulated, and for another it does not conform to the authors’ first attribute in 3.1 that it “ should be clear and unambiguous “. In short, therefore, it is not suitable for control purposes.

This question of bonus is critical. It is one thing for bonus to be out back because of crisis conditions ; it is quite another for it to be out back because bonus loadings have been distributed unnecessarily to others than those who contributed them. At our last meeting the Under-Secretary of State said that the supervisory authority expected companies “ not to take credit for the value of future bonus loadings “. This principle points to the use of the net premium method, subject to the net premiums being less than the gross premiums by the necessary margins. For control purposes the measure of good conduct in providing for the reasonable expectations of policyholders is achieved by preventing a company from taking credit for future bonus loadings. This method of reserving for future bonus is automatic. It requires a test of the adequacy of future premiums but, subject to that, it shuts off the future and in effect values paid-up benefits calculated on the net premium basis, thus treating liabilities on a basis consistent with the break-up value treatment of the assets. It ignores future profits by taking no credit for the future margin between office and net premiums, but values future losses because of the limit placed on the net premium by reference to the office premium. It is an ideal standard for a control system. Why then do the authors reject it? They claim it is over-stringent but adduce no proof to substantiate this, other than their comment in 6.3 that very few offices valued their assets at the end of 1974 in accordance with the rules which are now in force. It seems, therefore, that the authors feel the over-stringency arises when the market rate of interest reaches a level which is associated with a very high rate of inflation. This would, in fact, be a period during which the financial position of the long-term business fund would be under real pressure, and a time when security is the first requirement and must override the pretended equity of maintaining bonus rates. If, therefore, the valuation standard would have shown up the difficulties of that time, that is a factor in its favour : in fact, in its absence, many offices did not reduce surrender values or even terminal bonus, and continued to issue illustrations showing

Valuation Standards 173 terminal bonus. Perhaps it is the authors who are overestimating the shortcomings of the net premium method rather than the offices who are underestimating them.

If the net premium valuation is not as unsatisfactory as the authors suggest, is the gross premium valuation as satisfactory as they do suggest? Let us look again at the question of guaranteed surrender values, and the possibility of loss arising from them if assets are mismatched and the market rate of interest rises. It seems to me that the authors do not sufficiently stress the danger in a gross premium valuation of covering up this loss by taking credit for the margins in future premiums which might never be received. If the financial position is actually satisfactory this can be explained to the supervisory authority. basis has achieved its purpose !

If it is not, then the statutory In the converse situation, when the market

rate of interest falls below the rate implicit in the office premium, guaranteed surrender values cease to be the problem and the worry will be the valuation of future premiums. In this situation it would be of the utmost importance to test the adequacy of the premium rates for new business. In the net premium valuation, it would be the office premium less expenses alone, which would be valued, but by the authors’ method they would reserve also for future bonus and so be even more stringent. In neither case, therefore, can I see any objection to the net premium method which must force one to seek an alternative standard. A further point which could be mentioned is that in a gross premium valuation, such as the authors recommend, with all margins of profit discounted, it is essential to provide for the liability to Case VI tax on the pension business fund.

The authors warn us that a gross premium valuation is particularly sensitive to the interest assumption and so they discuss the determination of the rate of interest at some length. In 12.9 they show that in valuing annual premium contracts shortly after issue, the use of a rate of interest greater than a cautious rate produces instant spurious profit. This feature would be avoided in the net premium method, but with admirable courage in the face of these practical difficulties, which they freely acknowledge, the authors proceed to develop their method of derivation in Appendix C culminating with the words “ clearly the foregoing process cannot be regarded as anything but a theoretical approach . . . and incorporates all the practical drawbacks associated with the theory of immunisation. Nevertheless, . . . a computer program could be written . . .” In practice, with their method, groups of assets are associated with groups of liabilities according to outstanding duration. This leads to valuation in sections at a variety of rates of interest, determined according to the relationship between the mean term of the liabilities and the mean term of the assets. It is not suitable as a standard method. I say nothing about its suitability in any individual case-the Actuary can explain his choice of method to the supervisory authority. It is its use as a standard we are being asked to consider.

The authors’ objection to adding all the durations together and valuing total business and total assets in bulk is in 12.8—the possibility of “ negative (or unjustifiably low reserves) being hidden” in the bulk valuation. Once again, it must be said that the difficulty arises from valuing gross premiums-a net premium method eliminates the problem and makes the calculation work a practicable proposition. In any case, however, this gross premium method could not readily be defined in statutory rules, and does not meet the authors’ own stipulation of being “ clear and unambiguous “. For control purposes it would be preferable to have the rate of interest to be adopted specified by the supervisory authority, on a basis linked to an index of long-term British Government securities. It would, thus, auto-


matically adjust in line with the market level of assets. It would, also, negate the manipulation and “ window-dressing ” to which the authors refer and by fixing the valuation rate independently of the yield on the equities and property held, it would treat these assets in the manner the authors seek in 11.3. Indeed, one is left at this stage with the impression that the authors in their exploration have reached a “ Cape of Storms “. The only justification for choosing that route would be if the alternative route– the net premium method-had more serious disadvantages than any that have been disclosed to us. In the absence of that evidence, while we must, once again, express our gratitude to the authors for carrying out this exploration, and causing us to reconsider this subject, my own conclusion, Mr. President, given in terms which one of the authors, being a member of our Faculty, will understand, is that their case for a gross premium method as a valuation standard must be found “ Not proven “.

Mr. A. D. Shedden: —I found this paper both interesting end thought provoking, and indeed there are many facets of it that one could discuss, but I want to confine my discussion entirely to the material in Appendix C, where the authors demonstrate a technique for finding what they term a safe valuation rate of interest for a contract, when the market rate of interest is higher than the long-term rate assumed in the premium basis. I have been exploring this problem recently also, and so I am particularly interested in what the authors have to say. The approach of the authors is essentially one of associating assets with liabilities in such a way that their values are equal when both are valued at the same safe rate of interest. Depending on the relative dating of assets and liabilities, this safe rate of interest may be above or below the current market rate and is chosen so that, if the same assets and liabilities are valued at the market rate, the value of assets would exceed the value of liabilities. Accordingly, a rate of interest is then found for valuing the liabilities on a more stringent basis so as to remove what may be termed the “ mismatching surplus “. In the examples given in Appendix C, the mismatching surplus is not entirely eliminated. This is because there is a first-degree approximation introduced into the determination of the valuation force of interest and the subsequent transition to a rate of interest j. Incidentally, I think that slightly simpler expressions might be obtained for the equations (A) and (B) if MA and ML were taken to be functions of in all cases.

Since the object of the exercise is, as I have said, to value the liabilities on a basis that ensures that the mismatching surplus is eliminated, it would seem that this basis could have been reached more directly, perhaps, by trial and error valuations at different rates of interest. Indeed, such a process could have been applied to the liabilities as a whole and a common valuation rate j obtained rather than separately for each asset. Thus, while I accept the theoretical arguments for valuing the liabilities at different rates of interest, I do not think it would make any real practical difference to do so for the cases given in the example, given that there is the same overall constraint in the value of liabilities when assets are valued at the market rate. There would, of course, be a real difference in practice if the rate of interest i0, i.e. the safe rate of interest, were chosen so as to be different for each contract; in an actual valuation one might well wish to choose different values of is depending on the relative dating of assets and liabilities and on the tax situation.

The method described in Appendix C for obtaining the rate of interest j which is used for valuing the liabilities could, in some circumstances, result in the reserves being inadequate. In the first place, the value of j depends

Valuation Standards 175 on the value chosen for i0 and the gross premium reserves in the example at the end of Appendix C are very sensitive to changes in interest, especially at short durations. For example, at duration 2, nearly 2½ times as much of the specified asset is needed if i0 is taken as 4% instead of 4½% and about 5 times as much if i0 is taken as 3%. Thus a considerable deficiency could potentially arise if the value of i0 were too optimistic. In the second place there is a possibility that a deficiency might arise at the rate of interest between the market rate i and the lower (or upper) limiting rate i0. Thus, considering again the example in Appendix C, I suspect that if the calculation were to be done for the twenty-year duration case, it would be found that the valuation rate of interest j would be greater than 8%, i.e. the market rate, and that more assets might be needed had the calculation been done for a market rate of, say, 7%.

The second type of error that I have described arises partly because of the first degree approximations inherent in the method illustrated. Ideally, the rate of interest i0 in the example should be chosen so that assets and liabilities are more or less immunised against loss on any change in interest rate above or below i0. That might even be said to be the minimum situation. If we adopt this criterion for the cases in the example, we find that the particular asset is too short-dated for it to be possible at any rate of interest to immunise the liability at durations two, five and ten years. For these cases, then, i0 must be taken as 0% in the limit, and the corresponding values of j to eliminate the mismatching adjustment when the market rate is 8%, turn out to be approximately 1.9%, 3.1% and 5.7% respectively, somewhat lower values of j than appear in the example. The fifteen-year duration case, on the other hand, is immunised at around 7% interest, so that i0 can be taken to be this rate; the corresponding value of j is around 7.9% which is virtually the same as in the example.

The values of j that I have quoted for the immunised position have not been estimated using the authors’ method, but by the following rather simple process, which I will describe using the authors’ notation.- Values of the liability and a quantity of the assets are plotted for different rates of interest, andthe rate of interest found for which the ratio of the value of the liability VL to the value of the asset UA is a maximum. If at that rate of interest, let us call it im, we calculate k, where kUA(i)m = VL(i)m then the required assets at any other rate of interest i must be kUA(i) and to eliminate the mismatching surplus that will arise if liabilities were to be valued at this rate, it is necessary to value liabilities at a rate j, such that VL(j) kUA(i). This is essentially what the authors are doing, but for an immunising rate of interest rather than a safe rate of interest.

Excessive accuracy is out of place in such a calculation, and it will probably be sufficient to value assets and liabilities at a few rates of interest and obtain intermediate values by interpolation. Indeed, the operation could be done en bloc for a whole portfolio of assets and liabilities or for major sections thereof, and is not invalid by virtue of guaranteed options such as surrender values and so on. Apart from providing an approximate assessment of the degree to which assets and liabilities are immunised, such an approach could be useful for comparing the relative strengths of valuations performed against different levels of asset prices.

In my opinion, much work remains to be done before actuaries become equipped to employ immunisation or semi-immunisation techniques confidently in the sort of actuarial valuation which we will be required to do in the future. While I would argue that the authors have not gone quite far enough in this direction, I am in considerable agreement as to the sort of approach we should be aiming at. It is obvious that a method such


as is demonstrated in the Appendix goes some way towards providing or hinting at a technique for safely valuing on a gross premium basis. The authors are, therefore, to be congratulated on what may indirectly, perhaps, be a most useful contribution to the debate on the respective merits of net premium and gross premium valuations.

Mr. K. M. McKelvey:—I would explain my presence here tonight as a semi-self-invited guest by item 7 of the Bibliography attached to the excellent paper which we are met to discuss. It came as little surprise to me to find myself much in sympathy with the authors’ general approach. In its work related to life office valuations the whole profession faces a common dilemma, namely that with so many unknown or indeterminable variables it is hard to know where to begin. There appear broadly to be two schools of thought. One. embodied in CN10. starts with the value of the assets, and can quite properly claim the virtue that the value chosen (market value) is, at least in the main (property can be a problem, of course), an objective one determined by forces independent of the Actuary. The other school of thought, typified by tonight’s authors and others including myself, starts with the unknown average future rate of interest and in effect says that whatever assumption as to this factor (actually this is not quite what the authors say, this is what I say, but it is the same school of thought) is currently decreed appropriate in setting premium rates for renewable non-profit business is equally appropriate in carrying out an actuarial valuation of assets and liabilities. Both schools of thought then share with minor variations the view that, however determined, the same valuation rate of interest should be used to value both assets and liabilities. Given the initial assumption and the shared view as to the link between the asset valuation and liability valuation, each school then, in effect, seems to me to use a kind of “ bed of Procrustes ” approach to make everything else that should fit in, fit in. It is, I think, the Procrustean overtones of both approaches which lead to the weaknesses of each.

The main weaknesses of the CN10 approach, as I see them, were rehearsed in this Hall fourteen months ago and I will not weary you with them tonight. The flaw in the alternative approach, which in common with the authors I nevertheless prefer, is the difficulty of establishing an objective value of the assets. Hence, the argument of the CN10 adherents runs, there is a further advantage of the CN10 method, namely that being mechanistic it can be relatively simply policed by regulatory authorities. However, I beg leave to doubt, given the enormous complexity of the life assurance valuation process, whether there can be a satisfactory method which is easily policed. Moreover, it is my view that, at a time when interest rates underlying the current market value of assets are historically high, the ability to satisfy a CN10 test requires not mere solvency or even adequacy, but something far more. I would remind you that if net premiums valued are computed at a valuation rate of interest derived from current market values of assets they are likely to be half or less of the office premiums for non-profit business ; while if net premiums valued are computed at a rate of interest near to that of the actuarial model to which the authors allude in paragraph 2.2, while the interest rate used for the valuation process is derived from the current market value of assets, negative values can be thrown up of such magnitude that their elimination increases the value of liabilities by something of the order of one-third.

So much for general comment. You will be sorry in more detailed comment to hear that I have marked no less than fifteen passages in tonight’s paper upon which I would like to speak . However, the good news is that I


shall not take up your time with the majority of them because what I would have said could in each case have been paraphrased by “ I agree ”.

Dealing quickly with a minority of my points though, namely those which involve perplexity or dissent, I start by mentioning paragraph 2.2, merely wanting to say that I do not understand it. On paragraph 6.4, doing my “ Daniel in the lions’ den ” act, I would suggest that the unfairness described in that paragraph 6.4 was by no means absent in the 150 years prior to the enactment of the Insurance Companies Act 1974.

The words “ justifiable ” in paragraph 7.5 and “ reasonable ” in paragraph 7.9(3) beg a big question which would form the basis of a discussion on its own ; it is all about surrender values. My question is “ justifiable in the light of what considerations ?”. For those of us who follow the financial press the subject is topical. Should the life office which has attracted comment under this heading in that press jeopardise its ability to fulfil contractual obligations or should it, as it is doing, make every effort to meet those obligations even if, because the gross redemption yield on appropriate government stocks has risen from 5½% per annum when the office was founded to 13% per annum now, a conventional surrender value would greatly exceed the reserve?

Paragraph 9.2, I find extremely interesting. It seems to be heading towards the conclusion that a proportionate interest margin is precisely the wrong shape. If that is the authors’ view why did they not say so?

As to paragraph 11.5, it has so far been my understanding that the practical application of Rule 2(b) of CN10 runs something as follows. One values all the investments by compound interest discount methods at various rates of interest in order to ascertain what rate of interest must be used in that process in order to reproduce the aggregate market value. In so doing one automatically brings in future income and redemption proceeds of redeemable fixed interest stocks. Also one ignores any possibility of future increases in income on equity and property investments, hence leading to the shortcomings which are rightly pointed out in paragraphs 6.4 and 11.3 of the paper.

I have two comments on paragraph 13.1. On the first point in that paragraph, I would have thought that there would have been no significant negative values under the authors’ approach. If there are some, and they are not eliminated, and the policies shortly lapse, the bonus will have to come down. But let us not overlook the analogy drawn at the end of paragraph 7.7 with the shareholder, with which I find myself (and I think an earlier speaker found himself to some extent) much in sympathy. Like another earlier speaker I do not agree with the two-thirds in point (4) of paragraph 13.1. Having done as realistic a bonus reserve office premium valuation as I can do. I would then regard the rate of bonus to be declared as that which that valuation tells me can be declared now, end, if on balance, my complete set of assumptions is fulfilled, can be maintained throughout the future lifetime of the existing business.

My thanks to the authors for an excellent and stimulating contribution to the continuing debate which I hope, with acknowledgements to my former colleagues in Glasgow, will always remain “ amicable ”.

Mr. J. R. Gibb:—I was very disappointed at the authors’ acceptance of the apparent inevitability of more detailed regulation of the insurance industry. The paper is entitled “ Valuation Standards ” and like all standards they are not maintained by regulations but by people. Failure to meet proper standards is a failure by actuaries both collectively and

E


individually. Collaboration with a government machine which seems to me to have been proved to be ineffective is no solution at all.

Now in paragraph 8.1 the authors ask what I think is a very important question, “ Is the occasional insolvency good for the industry ? ” And I think the answer is “Yes ”. Bankruptcies are rather like seagulls, not very beautiful but they are very effective at cleaning up and leaving a healthier environment for the survivors. The recent insolvencies are in a way helpful to actuaries. It had become very difficult to allow properly for something which had not happened for a very long time, and I think it is probably fair to say that some carelessness or lack of caution has crept into some valuation bases and the cold wind of insolvency helps to restore the balance.

Now at present we seem to be in the middle of a blast of hot air from the Department of Trade. This seems to me to be a classic case of “ bolting the stable door after the horse has gone ”, but even worse the proposals seem to be a reinforcement of a system that had not worked. I can see no justification for the belief that more complex regulations by the Department of Trade will improve the position.

There are three lessons, I think, to be drawn from recent insolvencies. The first is that the consumer is not such an idiot as people tend to make out. His reasonable expectations of the regulations surprisingly quickly turn to suspicion and keep them from succumbing to the pressure and false figuring of companies that are in a rocky way, and I think this is why a very high rate of expense is a very common danger sign, and it is also very probably fair to say that those who were parted from their money probably deserved to be. Two. as far as I can see. the Department of Trade failed to protect the public ; ‘and three, the Faculty and the Institute together do not seem to me to have done anything very effective about what appears to have been reckless behaviour. And I do think that we cannot disparage the Depart- ment of Trade for failing to protect the public when we take no action ourselves, Discipline I would have thought is the price of freedom.

Mr. J. M. G. Smart:—I regret having to sound somewhat destructive in criticism of what is, in many ways, a valiant effort to advance valuation technology into the twentieth century, but like previous papers in recent years on the subject of valuation and solvency this one conveys to me the same desperate effort to avoid the obvious. I agree that a realistic method involves finding out how much assets we have left at the end of the day (since if we have any at all we are solvent on the set of assumptions used), and I accept that there is a certain ingenuity in the authors’ method, but it is not clear what conclusions they are trying to reach, and imagination boggles at the thought of applying it in practice. Even if such expressions as “ mean term ” have a meaning (one wonders for example whether the authors propose to incorporate a surrender rate in their calculations for the policy) the actuary would require much application of icebags to get his sums done.

This is a pity because the authors have made some good points and have indeed occasionally found the right road albeit without apparently recog- nising it as such. Attribute (2) in 3.1 correctly introduces the fundamental concept of probability of insolvency, but this aspect later gets played molto diminuendo—in 7.9(1) the probability is merely required to be “ minimal ” (does this mean less than 50%, which is in effect what current regulations require?) and by the end, as far as I can see, it has got lost altogether. Again, the last sentence of 8.6 recognises the important loss of information resulting from valuation to the present day, but later this


practice is still being indulged in. Then, as other speakers have mentioned, paragraphs 11.3, 4 and 5 and elsewhere, such as sub-paragraphs (4) (6) and (6) of 13.1, introduce a number of arbitrary assertions and even “red herrings ” and the result is that the principles suggested in paragraph 13.1 come as something of a non-sequitur. We are almost back where we started. Indeed, it is not clear for what purpose such a valuation is being done, item 4 appearing to rule out solvency or bonus declaration. Also it would seem to work well only for an office which is matched, while what most of us want is quantification of the risk being taken by not being matched. I hope I am not misunderstanding the authors.

Now, having said that the authors have avoided the obvious, I must clearly justify my position by stating what I consider the obvious to be, in case it isn’t. Firstly I want to scrap valuation in favour of evaluation, so let me repeat the definition I have already suggested in this hall— solvency is the ability to meet your obligations:

Next. harking back to my schooldays when each proposition in Euclid or whatever was laid out in the form “Given, Required, Construction and Proof ”, what are we given? We are given details of certain liabilities in the form of policies with all their options and so on, and of certain assets which will help us to meet those liabilities.

What is required? It is required to answer a question which (in general form in the first instance) is—Given certain assumptions, what is the probability of insolvency? This implies that assumptions are of two types. There are some aspects, such as inflation and tax rates, which, while no doubt having in retrospect a frequency distribution, are not really matters of probability. These we must make firm assumptions about. Others, such as mortality (and perhaps, if not interest rates themselves, at least the relationship between the going rate of interest and the rate of inflation). are more suitably subjects of probability treatment, and our initial assumption is of the mean expected value. It may be that all aspects should be dealt with in the latter way but this would be prohibitively cumbersome and in any case we can probably find out what we want to know with a satisfactory degree of confidence without it. So, for example, the question might be “ Given an absence of new business, the continuation of bonuses at current rates, and certain assumptions about future rates of mortality, expense, surrender, inflation, tax and so on, what is the probability that we can meet our liabilities ? ”. The Department of Trade might ask the same question for statutory purposes but with alternatively zero or the current future bonus rate and laying down the other assumptions to make. The probability element here requires that we must expect to have to do at least two full evaluations for a given set of non-probability-treated basis items. We might, for example, do the first such using the mean expected values of the probabilistic items and the second using values one standard deviation away from the mean, the side of the mean being chosen such that all variations from the mean are against, or all for, the office. Finding out from these two how much assets we have left at the end of the day will give us an idea of how many ’s to incorporate in our next try. If we eventually square our assets and liabilities using variations 2 against the office, we can conclude that for that set of given assumptions we have only about a 2½% chance of insolvency, which is pretty good. Remember that for real life offices solvency is never a certainty—all the assured lives could die this year. The authors’ 0 could well be of the order of 20%.

Construction. This is straightforward once one adjusts one’s mind to it. We take the business and the assumptions and follow their working out over time, just as will actually happen in real life. We will discover the


degree of mismatching, in other words when we have to sell or buy assets and on what terms consistent with the other assumptions we are making, and at the end of the day, which may of course be 100 years, we find if we have a surplus or deficit of assets. Note in particular that our concern with the rate of interest is reduced to that on the amount of mismatchment.

As far as proof is concerned, I am afraid that, like that of the pudding, it is in the eating, and since I have not been able to devote time to producing any actual results I cannot help here. Nevertheless, I am absolutely convinced that this is the right way to go about evaluation of a live office, and even if the point at which an office becomes insolvent (which I take to mean that the probability of insolvency exceeds 50%) remains a bit in- determinate, the method should provide good and sound warning of its approach.

But one of the great beauties of this method is that the set of assumptions one is forced to make constitutes a basis, perhaps the basis, and further perhaps the first real basis the Actuary has ever devised ! All up till now has tended to be working formula, which usually means an unknown basis wearing an impenetrable mask. Anyway, this basis can be used equally for premium rate calculation, deriving surrender value and policy alteration bases and so on. Also by studying the results of the working-out process, with or without the assumed introduction of new business, one could guide one’s investment colleagues and/or sales staff into courses of action designed to improve the situation—it’s beautiful ! I can see difficulties in the way of getting such a method accepted for statutory return purposes, but apart from that it shines for me like a beacon marking our ultimate haven. All partial approaches appear pale substitutes by comparison.

Mr. L. W. G. Tutt:—Like others, may I first be permitted to add my congratulations to Messrs. Stalker and Hazell for their most interesting paper which calls upon us again to consider regulations, one possible consequence of which, according to them, is a sharp relative contraction in the British insurance industry. For my part, I feel it may be questioned whether the combination of the asset regulations already published, and the liability regulations as proposed, are the ideal solution, not so much on grounds of over-stringency, which the authors impute, but more on questions regarding the compatibility of the two. In some economic conditions market values of some assets can oscillate quite sharply, such as not completely to attune with prospective yield, and not fully sympathetically with prospective non-acquisition expenses allowing for incidence, and I am led to think, although my personal preference is for affairs to be conducted explicitly anyway, that an approach which can give direct regard to the variable relationships between the valuation components, has some merit. The interaction of the valuation elements, such as interest, expenses, and bonus allowances, can be complex in an unstable economy, and their suppression into a single valuation parameter can involve valuation consequences difficult to construe properly from such an exercise on its own. I do not feel that it would necessarily be illogical to regard each of the valuation elements as singly of high possible consequence, or possibly worthy of separate enumeration. For example, as regards the expenses element, Bews et al. in T. F. A. 34, page 391, stated that “ The most severe financial strain to which a company is subject in inflationary conditions is the runaway escalation of expenses ”. Moreover, the principle, that adequate margins over the current rate of expenses should be kept in the valuation of liabilities in order to provide for future renewal expenses, has received some general support. Thus the principle put forward this evening


by Messrs. Stalker and Hazell that an allowance should be made for future expenses on an explicit basis does not occur to me as being inconsistent. If I have understood some previous remarks correctly, there seems to have been a suggestion that a proper allowance for expenses pointed to a net premium valuation. I do not quite see this since the interest basis of the net premiums in a net premium valuation is essentially artificial. In other words I do not see how an explicit allowance for expenses necessarily points away from a proper allowance. There are a number of points made by the authors which I would wish to consider further before commenting, such as their suggested bases, but the broad principles they deduce, deriving from the compression of an explicit model where allowance is made for all future revenue items, suggest to me a plea for realism, well worthy of further professional consideration.

Miss M. C. Allanach:—I have read this paper with very great interest, but not I must confess without some initial confusion as to its basic purpose. This confusion stemmed from my assuming from the opening paragraphs, i.e. the reference to “ examining the fundamental principles underlying the periodic actuarial investigations of life insurance companies ”, combined with the variety of “ purposes ” listed in 2.1, that the authors were seeking one single valuation approach which would meet all the requirements of 2.1. Since, in my own view, it is impossible to produce one single valuation method appropriate for both solvency (or “ adequacy ”) testing, and equitable bonus distributions, I immediately skipped to the end of the paper to see what miraculous basis the authors had in fact evolved which could do all of these things ! Well, of course, the adaptation of the gross premium method which they have produced does do a number of things, as various people have indicated tonight, but certainly not, I think, all that was set out in 2.1. At this point the authors will no doubt be relieved to know that I did return to read the paper logically from beginning to end, and then of course it became clearer to me (although no doubt they will correct me in their reply if I am wrong), that their main purpose was in fact set out in section 6. This is that their emphasis is on solvency as the cardinal purpose of a valuation, and in particular in 6.2 they add that one of their purposes is to attempt to remedy the omission of the advocates of the gross premium method in that they had not provided a possible alternative set of rules for solvency (or “ adequacy ”) purposes. It has been, therefore, from this angle primarily that I have looked at the paper, although as I will mention later, I think there are certainly areas, which other speakers have mentioned, where the authors’ method would be useful for other purposes as well. But from a purely solvency (or “ adequacy ”) standard, the first question I then asked myself was whether the solutions they propounded could be written into statutory valuation rules, in such a way that the bases could be readily judged by the statutory authorities, as to their adequacy or appropriateness for a particular office. It seemed to me that the rules set out did not in fact meet this particular requirement ; they had a number of defects because, although apparently expressed in explicit terms, in practice a number of assumptions were of necessity implicit, and perhaps I could just take two or three examples. Take 13.1, rule 3, for example on expenses (expenses have been referred to by several speakers) ; reference is made in rule 3 to an explicit allowance for expenses and for increases in them, but in the immediately following paragraph there is reference to the subjectivity of the method of actually obtaining the relevant expenses. Furthermore, later on, when the authors are dealing with the assessment of interest income, they in fact decide to


ignore the possibility of increasing income from equity and property and to leave this to be set off implicitly against the possibility of increased expenses in the future.

What precision is there in this from a regulatory point of view? I am not in any way underestimating the difficulties of the problem, but I am simply commenting from a regulatory point of view.

Next take rule 4 on bonuses ; I share the view of a number of speakers that an arbitrary rule of two-thirds, while it is certainly explicit, could have very different effects as between, for example a simple and compound bonus office, or between one distributing the bulk of its surplus in reversionary form or one where a large proportion of its bonuses were distributed by way of a terminal bonus, so that, I think, a method which had some regard to the offices’ method of bonus distribution is essential.

Thirdly, take rule 5, where the authors are referring to the assessment of interest income. It did not seem to me that this was really an explicit method and, as a number of people have indicated, it would be an extremely difficult one to put into practical terms, but also, as I said earlier, the authors do in fact ignore completely future increases in equity and property income. It does seem to me that to ignore this completely (although I have great sympathy in so doing from a point of view of a solvency basis) is not in fact compatible with the authors’ market value approach.

I am in fact an advocate of the net premium approach for statutory purposes, and of course the claim can be made that I am criticising the authors’ solution without any reference to possible criticisms of the net premium method. Can I just say briefly, therefore, how I think the net premium method does meet the criticisms that I have levelled at the author’s solution. As regards expenses, I did comment on this angle when I was in Edinburgh a year ago, so I will not add to that except to say that to a very broad extent, the net premium method does make some automatic allowance for inflation in the margin between office and net premium, because the margins widen as interest rates rise. While this is not the complete answer it does at least move in the right direction.

As regards bonuses, I wondered whether I could endeavour to build some sort of bridge between what is obviously otherwise an increasing gulf between those of us who support the net premium method and those who support the gross premium or, as I prefer to call it in the with-profit context, a bonus reserve method. Perhaps I could just say here that I think the crux of the argument arises from what is referred to in 10.1 of the paper and which I term the “ level emergence margin ” implicit in the net premium method. In fact the “ level emergence margin ” itself is to some extent as subjective as the two-thirds bonus rate to which the authors have referred but it is more flexible. I wonder whether in fact those who advocate a bonus reserve method have made a comparison of it (on a “ net ” basis, i.e. ignoring expenses) with the net premium method (with a “ level emergence ” margin). What I have in mind is a net premium bonus reserve approach allowing for future bonuses, setting off against the benefits future net premiums which included a bonus loading. It is relatively easy then to equate reserves on this basis to reserves on what I call the “ traditional ” net premium approach (with a “ level emergence ” margin).

I hope you will forgive me for stating what is the obvious, but there is a bridge here I think between the two methods because there is a level emergence margin of a sort in the proposed regulations, which varies with the interest rate. It is open to offices to use a larger margin if they so wish and if their bonus situation is such that it makes it appropriate, and I therefore think that we are perhaps not as far apart as it might appear.


I think, however, at the end of the day the net premium approach has the advantage of being readily definable for statutory purposes, and in view of the points I have just made about its flexibility, I would have thought that it was not too far removed from a standard which proponents of the bonus reserve method, might, at least on a net basis, be able to give some support to. Certainly, if the “ Bubble Office ” in 10.1 had used the net premium approach with a “ level emergence margin ”‚ I do not think it would have been in quite the straits it appeared to be in.

There was one further point I would like to mention which emerged in Appendix C which I think is also something which is likely to require to be taken account of. and it is connected with what I will describe briefly as the “ matching ” situation. In Appendix C the authors do bring out very clearly the adjustments which are required, both if one is matched short or matched lone. It is formulae (A) and (B) of Appendix C to which I am referring, and we have of course to be concerned with this unmatched situation, whatever method is involved. The point I would like to make here is that I think we have up to now been concerning ourselves primarily with the reinvestment rate if invested short, but it is also important to remember that we have also to concern ourselves with the possibility of realisation of investments at a time when interest rates have risen, and I think this point should be borne in mind in any set of rules that emerges.

Mr. C. M. Stewart:—The authors have made some very interesting proposals on the supervision of life assurance but as you know, Mr. President, the die is now cast on the system to be introduced, probably this year, in the United Kingdom and it will be based generally on the principles set out in Consultative Note No. 10, to which the authors refer in their paper. There will, however, be a few relatively minor changes. For example, following the criticisms made a year ago, here and in other places, the method of deriving the rate of interest to be used has been changed. It will now have regard to the yield on the assets actually held at the valuation date rather than the yield derived from items in the previous year’s revenue account. It will also give some prominence to the rate of interest to be assumed for future investments, and indeed it is the intention of the authorities to make known their own view in that regard which, I know, will please a number of actuaries, but the authors will be pleased to know that there is no new move in the direction of the dirigiste system in operation in most continental countries. The aim here is still to find a system which does not control life insurance operations but frees those operations from control to the optimum extent which is consistent with the Department of Trade meeting its obligations to Parliament and the public for the protection of policyholders, and as you know, Mr. President, it is much more difficult to design a scheme of that sort, which seeks a balance, than it is to design a simple control system.

There are many similarities between the principles proposed by the authors and those in the Government’s scheme. The authors take assets at market value and give cogent reasons for doing this, and they make no bones about excluding negative policy values and covering any guaranteed surrender values or other options. Their major concern, it seems to me, is to remove the possibility of what they describe as a “ Bubble Office ” being allowed to operate under a net premium regime. In the past, in the absence of any rules at all, it was always open to a company to operate a “ Bubble Office ” and presumably it was the integrity of the company’s own Actuary which prevented this. In the future, presumably actuaries will still feel it incumbent upon them to ensure that there is an equitable


emergence and distribution of surplus, in order to meet the reasonable expectations of policyholders, and if they met any opposition in doing this, they would certainly have the support of the authorities, given the new powers in the Insurance Companies Act which refer explicitly to the reasonable expectations of policyholders. The authors may like to know that in the course of the consultations last year, the Department of Trade did make a suggestion that the rules should include some words placing upon the Actuary responsibility for the equitable distribution of surplus. The reception to that suggestion was uniformly hostile, broadly speaking I think for the reasons given by the opener which are perfectly well understood, so the proposal was withdrawn, but I believe it has now been re- mitted to the joint Institute and Faculty Working Party on Financial Standards for possible inclusion in the guidance notes for Appointed Actuaries. If it were to appear there then it would very effectively eliminate the possibility of a “ Bubble Office ” operation being attempted in future.

I found Appendix C very interesting, Mr. President, but I do wonder how closely one could expect a supervisory authority, even advised by the Government Actuary, to concern itself with this amount of detail. If I were the Actuary of a company and I wanted to know exactly what was the financial condition and profit-earning capacity of the business, then I would certainly adopt a method of valuation of both assets and liabilities which allowed explicitly for all the relevant factors—future bonuses, future expenses, future dividends and so on—but I am doubtful how far a supervisory authority could be invited to involve itself to that extent without crossing the threshold which brings us to just the system of control which the authors fear. The authors do not go so far as to suggest this, but they do move in that direction and, as is apparent from what was said here a month ago by the Parliamentary Under-Secretary of State, it is his Department’s wish to play a passive rather than an active role in the matter of companies’ bonus rates.

May I quickly make some detailed observations on the proposals in the paper?

(1) The very important limiting rates of interest i0 and i1 are relegated to the small print. It seems to me they merit much more prominence than this. It is in these rates at least as much as in the method that the control lies.

(2) The authors—and I would not disagree with them—state that no increase should be assumed in the dividend yield on variable interest investments, but I wonder if explicit provision for two-thirds of the current bonus rate would therefore be appropriate both for a company which invested 75% of its assets in equities and for one which invested only 25% in equities. Would not actuarial judgement still be called for in these two cases?

(3) While I do not suggest that allowance should be made for terminal bonuses, I am not sure how important a discrimination it is to make no allowance at all.

(4) Following on from (3), there is no obligation on companies to distribute surplus by means of a reversionary bonus, although in fact in this country most do, but the authors do not say what standard should be imposed on a company which did not, for example one which imported the American system of cash bonuses.

(5) I could not see where in the authors’ proposals a margin for contingencies was provided, something which is central to all supervisory systems.


May I end, Mr. President, with a question for the authors which has some topicality? In a number of places in their paper they refer to the need to give a policyholder who wishes to surrender his policy for cash what they term a “reasonable” or a “justifiable” amount. I think we all know roughly what they mean, but my question is this. Old established companies are paying tax on the excess of their investment income over management expenses and therefore liabilities are valued on a net rate of interest. There are companies, however, whose accumulated investment income from the time they started in business is still less than their accumulated management expenses and they have not yet, and will not for some years to come, suffer any tax on investment income and they would therefore be entitled to value on a gross rate of interest for the appropriate period. Do the authors consider that the reasonable amount payable on surrender should be different in the two cases, and if not, would they go so far as to say that the gross company, notwithstanding its unrelieved management expenses from past years, should nevertheless set up reserves on a net interest basis?

Mr. A. D. Wilkie:—I did not come prepared to speak but I feel I must join Mr. Smart in the wilderness to show that he is not entirely alone ; I am glad that he has already said half of what I had half thought of saying as the discussion developed. It strikes me that we are in danger as a profession. We have been in the position for the last 100 years, from 1870 to 1960 or so, of having had to deal with the stochastic problems only of mortality rates ; because we have large numbers of lives assured, the variance of the expected number of death claims, the main influence on the variance of the possible results in Mr. Smart’s valuation process, is really quite small and so can be ignored. We could work on expected values alone. But since the war, in particular since the 1960’s, the problem of variation in interest earnings has become far more important. All the discussion this evening has been about what interest rate to use ; it has not been about what mortality table to use. There has been reference to what expenses to allow for in the future as well, but nine-tenths of the discussion is about interest rates.

The problem is that interest rates have become stochastically variable sorts of things, with probability distributions attached to them. So the whole business of trying to fix a statutory valuation basis, whether on a net premium or a gross premium or a bonus reserve method, based on the idea of discounted present values at one single rate of interest, is quite inappropriate to present-day conditions. The profession as a whole is, or certainly should be, in a bit of a turmoil as to what is now the right method of valuing life offices.

A lot of the difficulties have obviously arisen because of treating the future as if you could replace a probability distribution by its expected value. You set out with an expected value idea about what the course of interest rates might be ; you plot how Government securities prices would move if they tracked from their present value to their redemption value ; and you offer guaranteed surrender values so close to those prices that if interest rates rise by a small amount the company goes bust. Other companies do the same sort of thing with equities. They sell policies guaranteeing to invest all or a large part of the premiums in equity investment with all the potential rise in price being guaranteed to be returned to the policyholder, but with any loss being borne by the company. Such companies have virtually no reserves with which they can actually meet such losses, because all the losses will occur at the same time—all the

F

lot larger than we would like to think it is.

186 Valuation Standards policies maturing in a given year expiring with units at the same sort of market price. This will happen for all companies simultaneously, so I will follow Mr. Gibb and stick my neck out, but with reference to the future. I would guess that sometime between 1984 and the end of the century those companies that issue index-linked contracts with guarantees on death or maturity or surrender have a very high probability of all going bust simultaneously, unless they increase their reserves to something like 50% of their sums assured, which is about the right statutory level which would be required.

I produce this figure of 50% because I have approached the problem in the same way as Mr. Smart. I have taken equities as a single roll-up type of unit, taking both market values of capital and reinvested interest into account, and treated them as if the force of interest in successive years was random, and Normally distributed with a mean arguably between about 4% and 8% and a standard deviation which is fairly certainly about 17% to 20% per year. The actual spread is a little wider than that ; it is a

“fatter-tailed ” distribution. The experience in 1974 was at a one in a thousand level on the way down and 1975 was a one in something rather larger on the way up. My Normal assumption is thus a rather optimistic basis and gives too low probabilities of insolvency.

Now, with that sort of basis for equity-type investment, with a similar sort of basis for property-type investment but with a lower variance, and with some other basis which I have not yet worked out for fixed interest investment, I think it is possible not just to do two calculations to evaluate how much one finally has in the kitty in the year 2076 or whenever the last surviving centenarian has died. It is not too difficult to do 10,000 evaluations and get a probability distribution of the results. One can do this by picking suitable random numbers with a suitable computer, and get a probability distribution using a certain deterministic basis in respect of mortality and possibly withdrawals, and a random basis in respect of different types of investment, possibly with different inflation rates and therefore different rates of inflation of expenses. If you put them all into the pot together and pick random numbers for all the variables you want, you still get the effect of the total spread for the final results. Now I do not know what that spread of answers would look like, and I do not know what probability level any statutory authority or any actuary might suggest is suitable for demonstrating solvency. I would rather be able to look at the distribution first before deciding on the value of the probability of ruin. I have not seen any such distribution for any real live office, but I rather suspect, with Mr. Smart, that for existing offices might be an awful

Mr. P. Giles :—I would like to follow on a point moved towards by the last speaker and mentioned by the opener. At the end of Section 13 the need for careful scrutiny of guaranteed options is stated. In spite of the effect of tax considerations it must be true that these guarantees still form one of the most serious risks to solvency. I would maintain that it is not enough to increase the reserve according to Principles 1 to 5 up to the (current) value of any guaranteed options. The statement in Section 13 that massive additional reserves could in unlikely circumstances be necessary to ensure solvency only confirms that another Principle is needed to cover this contingency. I propose that a seventh Principle should provide for any secondary benefit that is in the first place guaranteed by the contract and in the second place would require a larger reserve than that required by the primary contract if the rate of interest were to increase by

Valuation Standards 187 a half (or reduce by a third). This Principle should require a special reserve to be allocated to cover this contingency explicitly. However, the total of any such option reserves should be divided into two portions, one applicable to the risk of interest rates rising and the other to the risk of their falling. Only the larger of these portions need be explicitly reserved since only one such contingency can actually arise at one time.

In considering this difficulty of providing for guaranteed options it must be remembered that the contractual benefit can be treated as the secondary benefit if the life assurance company so desires. This would make matching to the primary guaranteed surrender benefit very simple and would eliminate the rate of interest from its valuation-the liability becomes an immediate cash liability. The option reserve needed then applies to the risk of a fall in interest rates.

To come to another point in the paper, I was fascinated by the picture given in paragraph 8.3 of the life assurance industry becoming a self- supporting illusion. There must be a fallacy in this argument because it can equally be applied to non-life insurance to show that that industry has been for many years a successful self-supporting illusion. Inflation is causing that industry worries at present, but it has survived many catas- trophes with very much less in the way of a statistical foundation than the life-assurance industry has. Would we claim that a statistical foundation is a hindrance to successful insurance? Or is it the re-insurance network that has enabled non-life insurance to flourish as an apparent illusion? If so, then small or new life insurance companies should be persuaded to make more use of re-insurance facilities. Perhaps the new regulations may help this trend.

Mr. D.C. Hoskins :–I have been listening to all the previous speakers, admiring their eloquence, but I have been wondering at times whether I have really been thinking of the same subject. There have been fascinating discussions of great complex points, but I must say, when I read the paper and thought of the subject. I was thinking of a working practical basis that would allow people to control life offices. I tried to set out the purpose as I saw it and putting it simply I came out with, (i) control over all without onerous restrictions, (ii) the ability to spot quickly any companies heading for trouble.

Now, we have heard tonight many opinions-we can do it this way, we can do it that way-who is to say who is right, who is to say who is wrong? The companies that have headed for trouble-was it with criminal intent? Was it with over-optimism of what the future would bring? who is to say? If it is criminal intent, how can one possibly safeguard against this without such an intensive audit as to be almost impossible for a single Government department to undertake for all companies. That is a problem I am afraid I have to dismiss. But let us be charitable and suppose that it is over-optimism on the parts of the various people concerned; this is easy to consider from the complexities of the discussions this evening. So my reaction, and possibly this is an over-simplification, is to say, let us for statutory purposes fix as many items as we can, because there is a gulf between- saying, “ well possibly we could be generous and allow such and such per cent ” and deliberately saving. “ Oh dear, we will have to mislead and alter our figures to enable us to pass statutory investigation “. Now, I think with one you can say, “ Well let’s squeeze out the extra ½% “, but to deliberately defraud is a totally different concept.

So, for statutory purposes I would accept basically what is in Section 13. I would go further in fact and say that when it comes to Item 3 (an explicit

I88 Valuation Standards

allowance for increases in such expenses) the Government should set out what that should be. Like a number of others, when it comes to Item 4, I should say the full rate of bonus. Item 5 I would say a fixed rate of interest, as somebody has previously suggested, based on,” for example, Consols. The idea is to fix as many items as possible and come out with an answer at the end. Not to try and come out with an answer that balances liabilities and assets at 100% but to see what percentage emerges. Now, from an examination of this each year the Department would be able to assess the performance of various companies. Fuller examination could follow if there were problems. I am not sure, personally, if my suggestion were carried out, what the answer would come to ; it may well be 120%. Now, to my mind the Department’s role would be to look at this figure and in the following year when a figure comes in about 125%, quickly dismiss that company and say, “ well his solvency position is better than last year, we can ignore him for the moment, but let us concentrate on this company which is down to 110% “, and preliminary investigations could be made based on this.

I would go even further on the subject of bonus, following up the comments of misleading the public. The rate of bonus to be reserved should be not less than two-thirds of the rate currently being declared (I have already said I would make it 100% but could we even go further and say in fact that we put it the other way round, and that no company may use for illustration purposes any rate higher than that employed in its previous valuation return?

Mr. J. M. MacLaren, closing the discussion, said :-It is interesting to reflect that it is exactly two hundred years ago this month that the Actuary of “ Equitable Life ” completed his first ever valuation of a life office. Some would say that we have not moved very greatly from his methods.

Messrs. Stalker and Hazell start with a discussion in Section 3 of an ideal solvency standard, and this has certainly been much discussed this evening. To me it carries little conviction and lacks practical application. Solvency they see as having a probability of ruin less than some small quantity, but they give little indication of their idea of the appropriate magnitude, or how to quantify it. They do indeed say that a large number of undoubtedly solvent offices should not fail, but they leave us with the impression that a small number are going to fail! Such a view of solvency is misguided in my opinion-to me it is a condition of the present not a prediction of the future. Different offices will be liable to different future hazards. Professional re-assurers may fear heavy mortality, annuity offices light mortality. A traditional non-profit office will fear deflation and falling interest rates, whilst a unit-linked operation will fear inflation of costs beyond fixed expense allowances in premiums. As the authors admit later, historical induction is an uncertain guide to the future, so how can we estimate the likelihood of different types of adversity? To me solvency is an altogether simpler concept and I should have no great difficulty in accepting market values of assets as an appropriate standard for the Department of Trade, if only they would follow the logic of this concept on the liabilities side. A blinding flash of the obvious might then reveal that the only valid comparison can be with the market value of the liabilities, and this itself can only depend on the nature of those liabilities and on the market. Identical engagements must have identical values for all offices valuing on the same day, and that in practice means a prescribed standard basis at prescribed rates of interest-the same for all. A convenient interest basis is ready to hand in the form of the F.T.-Actuaries 20-year Gilt index.

Valuation Standards 189 I wonder why in Section 12 the authors deliberately reject such an

approach, which they classify as a notional reinvestment of assets. Frankly I cannot see why, since they show themselves to be conscious of the absurdity of an office being forced to reinvest in second-rate, high-yielding, fixed-interest securities, in order to be allowed to value at an increased rate of interest. That way madness lies. To me a liability valuation is an assessment of the sum which the prudent (I almost said “ Prudential “) insurer would consider requisite to assume ‘the engagements in question: The actual yield on the assets held is irrelevant and indeed the liability valuation can be made in the absence of any assets at all. Surely we are not saying that the existence of assets invested in a particular way can increase the value of the liabilities by depressing the appropriate rate of interest? Some actuaries prefer to regard a valuation as the inter-relationship between assets and liabilities-a logical position but it has nothing to do with solvency valuations for Department of Trade purposes where the comparison must be with market values. What is needed then from the Department is a minimum liability standard at a prescribed rate of interest depending on the market, with which we can all, or almost all, happily comply, and then do the real calculations according to our tastes and talents. But I fear, if I heard Mr. Stewart of the Department right, they are un- repentant on this one.

I turn to the more difficult question of bases. The authors have made a valiant attempt to convince us that the realities of the business can only be reflected in the gross premium bonus reserve valuation. I am a moderate man in these matters and certainly a pure premium valuation is somewhat divorced from reality, but it does have great stability. Take a twenty-year endowment assurance duration ten years. The pure premium reserve per £100 is £38 at 5%, £36 at 6% and £34 at 7% ; hardly a great variation. What is more, everyone, I think, will agree that even the lowest figure is adequate because the business we wrote ten years ago has very ample premiums in today’s conditions. It is interesting to reflect that whole-life non-profit premiums have fallen on average by 2½% per annum over the last fifteen years, whereas the natural increase by age is only 4% to 5% per annum. This means that gross premium reserves would tend to be very low as a result of this. The pure premium reserve, even at quite a high rate of interest, is strong for non-profit business, but also even at somewhat lower rates of interest, as the authors’ “ Bubble Office ” illustrates, it is weak for with-profit business, especially in a compound bonus office. These I think are desirable attributes for a regulatory system. Advocates of bonus reserve are usually compelled to compromise, as Stalker and Hazell have done, by suggesting that only two-thirds of future bonus needs to be valued. I must say that I agree with the critics, Mr. Stewart for one and Miss Allanach, who have said that they cannot possibly agree with this, nor indeed can many of us agree with their omission of terminal bonus from the reckoning. With some offices, at least, terminal bonus is almost “ copper bottomed “. It seems pointless to make a valuation on the bonus reserve basis if it does not in fact value every penny of projected benefits. What standard ought we to apply to participating business? It seems to me the authors might have made the deficiencies of the “ Bubble Office ” basis rather more clear if they had allowed it to declare on each occasion the full bonus apparently available. In Year 1, for example, it is clear that the valuation allowed a declaration of 6% not 4%. because the loading surplus of 2% in reversion produces 6%, but at the end of the term the loading surplus remains only 2%, and the interest surplus of ½% on twice the sum assured only enables the declaration at 3% simple or 1½% com-


pound. So even to operate a simple bonus system requires a basis which re- leases surplus more appropriately. Actually a 4% interest basis would have allowed rather too much bonus in the early years. What basis should the office have chosen to allow the emergence of 3% compound annually? As 2% (the difference between 5% earned and 3%, the justified bonus rate) is clearly the correct interest basis for finding the value of S + B, it might seem that a 2% pure premium basis would do. However, this basis is too strong as the high pure premium leaves too little loading surplus, so strictly speaking a hybrid basis would be best, using 2% interest factors for the S + B but valuing higher net premiums at a higher rate of interest. The alternative procedure would seem to be to use a higher hybrid rate of interest. The danger of thinking in terms of a hybrid rate is that it obscures the reality, which is that the cash value of bonuses ought still to be found at 2%, even although this value is greater than the apparent valuation reserve. We have lately seen a trend towards the super-compound bonus, meaning that bonuses on bonus are assumed to be at a higher rate than on the sum assured. Such offices require valuation factors at even lower rates of interest.

I do not myself share the view put forward in some quarters that assump tions about reinvestment rates or future expenses should enter at all into a regulatory system based on pure premium reserves. This is to confuse two wholly diverse concepts. Pure premium reserves may be zillmerised, they should certainly not be bowdlerised. We should, in my view, be entering the realms of fantasy if we allowed it to be supposed that pure premium reserves at, for example, 6% interest for non-profit business, were otherwise than extremely adequate in current conditions. As for the zillmer, I am sorry that a wholly misguided form of zillmer based on percentage of sum assured should be taking root in regulations just at the moment we are moving to revised bases of commission related to premiums. My suggestion for regulatory purposes would be a maximum zillmer of 5% of the pure premium. To attribute to a £10,000 whole life policy at a premium of a £100 a year ten times the expenses we attribute to a £l,000 policy at the same premium, would have seemed absurd even when commission was so related, and will seem even more absurd in future.

We have had some interesting prophecies from the floor tonight, and, indeed, March 15th is the traditional opening of the sooth-saying season. Mr. Wilkie has prophesied disaster in the 1980’s and has suggested that some of us are not nearly as solvent as we would like to think.

Mr. President, like the discussion, I seem occasionally to have digressed from the strict confines of the paper. It has been a wide ranging and interesting debate and our authors must feel very pleased at the way their efforts have been received. If they have not necessarily succeeded in converting us to seeing things their way they have certainly produced a most interesting discussion and they have provoked us into looking afresh at our judgements and prejudices.

The President (Mr. M. D. Thornton) :—Some reference has been made in the discussion to “ Bubble Offices ” and even to offices set up with “ criminal intent “. I wonder if that is perhaps a little strong. I had occasion some time ago to do what might be called some historical research and I came across the Chairman’s speech of an old Scottish mutual office for the annual meeting in 1871. Now, you will recall the 1870 Act regulating life assurance which remained in force virtually unchanged for almost 100 years—100 years of successful running of life assurance offices. In 1871, this particular Chairman said, “ The Life Assurance Companies Bill which recently became law has made great changes in the accounts of offices. These are no hard-


ship at all to a well-run company like our own but put grave obstacles in the way of those offices which have been got up for the purpose of taking in the public “. For almost 100 years there were no circumstances which could make anyone even think that any office had been “ got up for the purpose of taking in the public “. Such a question arises only when offices get into difficulties, and this occurred when successive governments deliberately chose inflation as a way to protect employment. Since they put the economy of the country at risk by allowing very high inflation, almost hyper-inflation, I think it is not so much the offices which got into difficulties that should be blamed as these Governments. No life offices can be sure of remaining solvent if a Government is prepared by its own actions to jeopardise the business of the country in pursuit of its own ends. That is the position which we practically reached in this country.

Regarding those offices which did get into difficulties, few people are in a position to judge whether these resulted from errors of judgement by the actuary, or, as I have suggested, from errors of judgement by the Govern- ment leading to circumstances beyond the control of the management of the office. If there is a complaint about any actuary to the Faculty under Rule 36, that complaint will certainly be dealt with and considered carefully by the Council of the Faculty. I am glad to say that we have had no complaint as far as I know in 120 years. Until we receive one it is the duty of the profession to support its members, just as it is the duty of the members, in the words of the motto of the Institute, to support the profession. These duties and obligations are equal and balancing and without any complaint, and in circumstances, which in many cases and for many people, were beyond control, it is not the duty of the profession to go “ witch-hunting “.

This is the only contribution I wish myself to make this evening. It is one of the privileges of being President that you can decide to what part of the discussion you are replying yourself and to what part you are inviting the authors to reply ! To the remainder of the discussion it gives me much pleasure now to invite Mr. Hazell to reply.

Mr. G. K. Hazell, replying to the discussion, said :-One of the prime aims in producing this paper was to provoke discussion and the discussion we have had this evening is, I think, very gratifying indeed. It was also an aim of ours to make some constructive suggestions, and in doing so we were aware that there may be a welter of criticism. We have not been disappointed.

The opener mentioned that he favoured the net premium valuation, and he also mentioned 7.2 where we say “ There can be little doubt that for a published valuation, the liabilities are to be determined in accordance with the proposed valuation regulations.” Perhaps we are mistaken but we seem to have just taken the legislation which appears in 7.1 at its face value, and if it is not the case that the ” published valuation ” has to be in accordance with the proposed valuation regulations, then we are very pleased to hear so. The discussion about whether the net premium valuation, or gross premium valuation, is suitable seems to have concentrated largely on annual premium business. It is said that the net premium valuation does not take account of future bonus loadings and also that when interest rates go up then, roughly speaking, there is an allowance for expenses that becomes greater, and that this is appropriate because at a time of higher interest rates there may also be the prospect of higher expenses in the future, but it does seem to me that the paradox with the net premium valuation is that the weaker the valuation result is, the greater the proportion of the

192 Valuation Standards office premium that appears to be reserved for future bonuses and expenses. But, if we leave aside annual premium business for the time being and consider single premium business, then surely an allowance has to be made for expenses ; there must be a means of determining the rate of interest, and if it is with-profit business some sort of allowance must be made for future profits. This leads to either a bonus reserve valuation which could result in a lower rate of interest in effect being used or what might be called the corresponding net premium valuation which is very much the same. So the two seem to overlap when single premium business is considered.

There have also been one or two speakers who have mentioned surrender values and what is a justifiable surrender value. In particular, Mr. Stewart asked this question, and I regard this as slightly unfair, if I may say so, because our concept of “ justifiable ” is based on the word “ reasonable ” which is contained in the legislation, and if we know what is “ reasonable ” then we will be able to say what is “ justifiable “. But I will reply to this question and I would say that a surrender value can be justified if it can be shown that, after taking account of the expenses and the costs of life cover, and any depreciation of assets, etc. it is somewhere near the figure that would result. I think that is sufficiently precise. Mr. Stewart also asks the direct question as to how the treatment of surrender values should differ from an office that has unrelieved expenses and one that has not. Based on what I have just said is justifiable, the office that has unrelieved expenses can justifiably give a somewhat lower surrender value for that reason.

Mr. Shedden referred to Appendix C end he considered that our technique was a little too complicated and could be simplified, and I think the difficulty arises there from the fact that we were working from the constraint of having to use market values.

Miss Allanach mentioned the problem of having one valuation standard that was to satisfy questions of solvency or adequacy, and also at the same time to allow an equitable emergence of surplus. There is no answer to this one as she suggests, and surely all we can do is have a valuation method that satisfies questions of solvency or adequacy and does not interfere with equitable emergence of surplus, that surplus and distribution of surplus being determined by an internal valuation.

Concerning the principles of valuation in Section 13, it was asked why negative reserves should be eliminated, and the answer to that is that in Appendix C where the reserve is negative we associate no assets with it, but it still needs to be eliminated. In the principle for a gross premium valuation standard No. 4 (rate of bonus reserved for) we do state “ not less than two-thirds ” and we do state that this is rather arbitrary. One or two speakers have suggested that the full rate of bonus should be used but I cannot see that this would be appropriate as we have not allowed for increasing dividends when considering the valuation position of the assets.

Finally, Mr. President, Mr. Stewart suggests that a fixed reinvestment rate of interest is likely to be specified, and perhaps I could respond to this by asking whether this is also to be the rate of interest at which disinvest- ment takes place, and whet allowance for matching, or immunisation, will be included?

The President :—A number of the speakers contributing to the discussion have remarked on how important a part valuation plays in the life of an actuary, we are therefore, I must say again, very grateful to the authors for bringing this paper before us tonight. It has provoked an admirable discussion and that, and the authors’ replies to it, will greatly enrich our

Valuation Standards 193 Transactions. I have much pleasure now in proposing formally a vote of thanks to the authors.

The authors subsequently wrote :-A great many points were raised in the discussion and we feel we can only ask for space to reply to those which seemed the most fundamental. The most general point was in connection with Principle No. 4, that the minimum rate of bonus to be reserved for should not be less than two-thirds of the rate being currently declared. This minimum rate was derived from observation of the practices of offices employing bonus reserve systems of valuation. Certainly, we would expect any office which reserved for the full rate of reversionary bonus to find itself able to increase its rate of bonus quite substantially in the short term. The underlying reason appears to be that for most normal types of office, if fixed interest securities are attributed to the non-participating liabilities, then the ratio of equity and property investments to the participating liability becomes very high. Also the participating business will, unless the constitution of the office provides otherwise, enjoy its share of the profits made on the non-participating business. On the question of surrender values, we do not agree with Mr. R. K. Stewart that long term business should be redefined to exclude any contracts providing a guaranteed surrender value within the first ten years freely upliftable by the policy holder. From some points of view it is more dangerous to guarantee surrender values at longer durations where funnels of doubt will have expanded more widely. A large outflow of surrender values would weaken an office whether these values were guaranteed or not, because the most readily realisable investments would be sold to meet the cash outflow and this would be likely to damage the overall quality of the investment portfolio of the fund. It is true that net premium valuations take credit in the case of participating business for a lower proportion of the premium than gross premium (bonus reserve) valuations. However, the partitioning between the net premium and the bonus loading is not fixed, neither even is the partitioning between net premium and expense loading. For example, a certain office using a net premium valuation basis at one valuation date implicitly reserved 30% of with profit assurance premiums for expenses and profits and 6% of without profit premiums. Three years later, in vastly different financial conditions, when rates of interest had risen to un- precedented heights, it so reserved 51% of with profits and 45% of without profit premium; In the case of annuities the relevant percentages at the earlier date were 32% and 6% and at the later date 64% in both cases. This pattern does not appear to indicate specific provision for the “ reasonable expectations ” of-policyholders, although there was no shadow of doubt of the adequacy of the office’s reserves on either date. The bonus reserve method would have made specific provision for future bonuses in both cases and any variation in the proportions of premiums reserved for expenses would have depended on current costs plus the relevant allowance for inflation (Principle 3) not on the accidental relationship between the (historic) interest content of the aggregate actuarial model and the current rate of interest based on market values at the valuation dates. Miss Allanach puts forward the elegant suggestion of a net premium valuation taking credit for net premium bonus loadings. However, we feel that there would be logical grounds for limiting the net premium plus net premium bonus loading to a maximum percentage of the office premiums and we feel that this method would be likely to become in practice a gross premium bonus reserve method. Mr. C. M. Stewart asked how the American contribution method of bonus declaration would fit into our principles. We

194 Valuation Standards think that it could be accommodated by performing a gross premium valuation taking credit for office premiums less an allowance for expenses and less the appropriate proportion under Principle 4 of the scale of bonuses currently being declared. Mr. J. M. MacLaren raised the problem of quantifying the probability of insolvency. From observation in the U.K. this appears to have, to all intents and purposes, a nil value most of the time but then to acquire a small but definite positive value every 100 years or so. The size of this positive value depends a lot on whether it is measured by the number of offices getting into difficulties divided by the total number of offices in business at the time, or whether one takes the amounts of business of the offices as numerator and denominator instead. We cannot agree with Mr. MacLaren that the liabilities can be valued entirely divorced from the assets. Regarding his remarks on the “ Bubble Office “, this example was constructed in such a way that it could have appeared that the office was distributing surplus in a correct manner although in fact it was distributing over-generously. Mr. MacLaren seems to be moving towards Miss Allanach’s “ net premium bonus reserve valuation ” in his method of tackling the problem. On the general problem of the practic- ability of the method in Appendix C, we hope to be given the opportunity to provide an illustration of its working as an actuarial note.

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