1.1 A paper about the Appointed Actuary is essentially a paper about prudential supervision of life insurance companies. The system which has operated in the UK since the mid-1970's is only partly one of Government supervision. Through the professional role of the Appointed Actuary, it also contains elements of a system of self-regulation with the Institute and Faculty of Actuaries standing in place of SRO's. Unlike the self-regulatory arrangements of the Financial Services Act, though, this second part of the system has grown up by custom and practice and in certain respects it is not codified. However it enables the Insurance Companies Act to be operated successfully.

The two approaches to modelling aggregate claims—the individual and the collective models—have been regarded as arising by considering a portfolio of policies in different ways. The individual risk model (IRM) is derived by considering the claims on individual policies and summing over all policies in the portfolio, while the collective risk model (CRM) is derived from the portfolio as a whole. This is sometimes held to be the main difference between the IRM and the CRM. In fact the IRM can be derived in exactly the same way as the CRM and can be regarded as a compound binomial distribution. This makes a unified treatment of risk models possible, simplifies the calculation of the mean and variance of the IRM, and facilitates the calculation of higher moments.

1. In a recent article in this Journal, Professor Wilkie gave an account of the determination of the rate of interest in a Fisher–Hirshleifer model. In his analysis of a production economy (§§3–7), he appeared to take as intuitively reasonable, not to say axiomatic, the existence of an inverse monotonic relation between the value of investment and the rate of interest. ‘A reduction in the auctioneer's rate of interest will stimulate capital investment.’ (p. 290) Now one of the conclusions to emerge from the capital theory debates in economics of the 1950s and 1960s is that the value of investment is not in general an inversely monotonic function of the rate of interest (see, for example, Harcourt). The purpose of these Notes is to alert actuaries to the existence of this conclusion and discuss some of its implications. To achieve the first objective, I shall need to construct a simple model—this is done in §2. I devote §3 to the analysis of the relation between the value of investment and the rate of interest. I discuss wider implications and draw some conclusions in §4.

1.1 In the paper ‘Improving the Performance of Equity Portfolios’ by Clarkson and Plymen the authors concluded that Modern Portfolio Theory methods made no contribution whatever to improving the performance of equity portfolios and suggested that attention should be paid instead to the application of fundamental analysis, which—if carried out by skilled and experienced analysts—should lead to higher expected returns. The only practical application of techniques related to Modern Portfolio Theory appeared to be in the area of Index Funds, where it is desired to track the performance of a chosen index as closely as possible.

p. 388, line 6: add ‘not’, so that the sentence becomes:

That is not necessarily a bad thing.