A comparison of results by Perks' approximate valuation methods with those by individual policy computer methods

Abstract

1. In papers submitted to the Institute in 1933 and 1945 (J.I.A. 64, 264 and 72, 377), Wilfred Perks put forward formulae based on uses of the '«-ages method' to enable liability valuations to be carried out by means of valuation records that did not need to contain any figures related to the valuation basis. Thus, not only was a change in valuation basis made a great deal easier actually to adopt, but the actuary was able readily to compare at any time the broad effects, for the main classes of business, of different bases, including 'bonus reserve' results, as against the net premium basis actually in use. 2. In the closing passages of the second paper he mentioned that for ordinary branch business a large office had been successfully employing the two-ages, two-terms method set out in the earlier paper and that, under wartime pressures, shorter methods, as described in the second paper, had been developed. Both kinds of method have continued to be used in that office, although not without concern about the possible effects, which proved difficult to estimate, of the considerable changes in the 'shape' of the business on the books resulting from the effects of inflation on the size of new policies. Fortunately A. E. Lacey, who had been Perks's principal assistant and collaborator on the techniques involved, was still in active employment at the office during this difficult time and his detailed examinations enabled the continued use of the methods by means of splitting up the business into groups of years of entry. 3. Both what were colloquially known in the office as the 'long method' and the 'short method' were based on punched cards that contained constants based on x . Sx and x2 . Sx for whole life assurances (x being the entry age and Sx the sum assured) and on n . Sn and SJn for endowment assurances (where correspondingly n is the term and Sn the sum assured). This punched card record was maintained independently of the office's premium collecting system and the inter-checking between the two served as a valuable piece of internal audit work. 4. Incidentally, the formulae employed were used separately for year of entry calculations and for year of birth and maturity calculations, again affording a valuable cross-check, and enabling the most suitable choices to be made for the purposes of actual valuation results. The 'short method' was, in practice, used on its own only for the less important classes of business. For the principal classes, VSA, VRB and VOP were taken from the 'long method', while NP and VNP were adjusted 'short method' results. Apart from the year-of-entry split mentioned above, the methods were