The aim of this paper is to examine and document a scientific approach to establishing an estimate of the economic value or range of possible economic values of a life assurance enterprise.

This is essentially a practical paper which provides a ‘practitioner's guide’ to performing an actuarial appraisal of a life assurance company rather than providing a rigorous theoretical derivation of the methods. There is, however, a philosophical issue, that of an appropriate risk rate of return, which cannot be completely side-stepped in a paper on appraisal values. This issue is briefly covered in Section 3. It should be noted, however, that an entire paper could be devoted to this subject.

The paper finishes on a potentially controversial note, that of UK Generally Accepted Accounting Principles (UK GAAP) for life assurance companies, suggesting that the appraisal value techniques outlined in this paper could play a major part in formulating UK GAAP.

It is proposed to discuss the actuarial problems associated with the management of long-term sickness and invalidity benefits. The emphasis is on benefits provided by social security schemes (with particular reference to National Insurance benefit in the UK), but the main points are relevant to private sector benefits including permanent health insurance (PHI).

The plan of the paper is as follows. We describe in Section 2 the nature of long-term invalidity benefit provided by the British social security system and then consider in Section 3 the problems associated with defining disability. A discussion of the differences between the incidence of morbidity and the making of an insurance claim leads to consideration of selection and moral hazard (Section 4). We then examine in Section 5 the methodology for analysing costs and estimating future costs with particular reference to the development within the Government Actuary's Department (GAD) of a model based on an incidence and survivorship approach to invalidity benefit and the debate aroused by CMI Report No. 7 on the same topic5. The paper then presents an analysis of recent trends in disability claim rates (Section 6) and incidence and termination rates (Sections 7 and 8) based on invalidity benefit within the British social security system, as well as PHI and the experience of other countries. Attempts are then made in Section 9 to explain these trends and the upward trend in financial costs for disability benefits experienced by many social security systems. The paper concludes with an examination of two areas of current interest, viz. sex differences in morbidity rates and claim rates (Section 10) and the relationship between claim rates and the prevailing level of unemployment (Section 11).

8.1 This paper is concerned with the selection of investment portfolios to meet specified criteria which involve the liabilities of a long term investing institution such as a pension fund or a life office. In Part 1 (5) I showed a certain relationship between, on the one hand, portfolios selected according to a criterion of pure matching to the liabilities and, on the other hand, portfolios selected according to a more general criterion of ‘efficiency’. This connection points to a particular actuarial approach to the selection of portfolios, which is now further examined in Part 2.

8.2 Writing Part 2 separately presents an opportunity to re-state the main ideas. The next few paragraphs recapitulate the basic points with a view to reducing, within the subsequent discussion, the amount of cross-reference to Part 1, and to the three preceding papers on which the study is based.

The purpose of this short note is to explain a simple method of constructing a life table, given an explicit function for the force of mortality, μx, for all x. A similar method can be applied to the construction of multiple decrement tables, given explicit functions for the separate forces of transition, μbx, μcx, etc, from one ‘active’ status (a) to various ‘dead’ statuses (b, c, etc) for all x.

Although numerical results for the examples discussed in this note could be calculated equally well by more direct methods than the ones described herein, results for more complicated examples involving multiple status tables, in which transition back and forth between statuses is possible, cannot in general be calculated by such direct methods, and our methods provide a practical way by means of which numerical results for these more complicated cases can be calculated.

1.1 A number of papers have been written in recent years that discuss the valuation of the business of a life office, examples of these are Burrows and Whitehead (1987) and Bunch (1986). These papers recognize the need to use a risk adjusted discount rate in the calculations. Burrows and Whitehead devote a section of their paper to the determination of such a rate. In their abstract they state that “…an entire paper could be devoted to this subject”. This latter point is supported by the existence already of a number of papers in the finance literature on the very topic of determining risk adjusted discount rates e.g. Robichek and Myers (1966), Fama (1977).

1.2 This paper outlines some results of the theory of determining risk adjusted discount rates and the valuation of risky cash flows as developed in the finance literature, and discusses the application of this theory to the determination of life office appraisal values. Some comments are made on Section 3 of the Burrows and Whitehead paper.

Bias in estimates of the initial decremental rate q and the central decremental rate m is considered for several survival functions. It is first shown that the central rate estimate is unbiased when the survival function is an exponential curve; is similarly unbiased when the survival function assumes the Balducci shape. The evidence presented here also indicates that the proportional bias (the bias divided by the true value) is approximately twice as great for as for when the survival function is a straight line.

Life tables in common use in the United Kingdom are, however, concave at ages arising most frequently in actuarial calculations, while none of the above curves is concave. In order to investigate the bias properties of general survival functions a quadratic is chosen, with a parameter indicating the extent of curvature. For this particular class of survival functions, one can show that bias is approximately minimized when exposure to risk is symmetric about the middle of the rate year.