The Compilation of Price Index Numbers and Yield Statistics Relative to Stock Exchange Securities

Synopsis

Reference is made in the introductory remarks to the appointment of Investment Research Committees by the Faculty and Institute of Actuaries to undertake, in the first instance, the compilation of a comprehensive service of Index Numbers relating to British Stock Exchange Securities which will be suitable for Insurance Companies, Trust Companies, and so on. The Committees have been at work for some time, and it is hoped that publication of the results will be commenced at an early date. The Paper discusses the purposes of such indexes and the most suitable form of index numbers for the purposes decided upon. The difficulties arise from two sources ; the variety of uses for which the index must cater, and the requirement that the results must be comparable between any two dates in the series.

At every point in compilation the objects of the results must be carefully kept in view. These objects are divided under three headings : (a) uses directly connected with current investment activities ; (b) investigation of the effect of economic financial and political events on the level of security prices ; and (c) assistance in measuring approximately changes in the value of a portfolio of investments. It is suggested that securities should be divided into homogeneous classes, and a separate index calculated for each class. The wide groups “Fixed Interest” and “Variable Dividend” are not suitable for the purposes involved. The weighting system should approximate to the distribution likely to be found in an Insurance or Trust Company's investments.

Within each class companies' holdings will tend to approximate more nearly to equal amounts of money in each security than to any other distribution for which a system of varied weights would cater. Simple weights are accordingly advocated.

Various methods of averaging are discussed and reasons given for preferring the geometric average of price ratios to other methods. The dangers of adopting the arithmetic average—where the resulting figures are always dependent on the base prices—are illustrated in Table I. The geometric results are independent of base. Even using the geometric average great care must be exercised in applying the results to valuation purposes in groups where individual price movements show wide divergencies. The “error” involved by the geometric method, however, is always in the same direction. Capital appreciation is never overstated and depreciation never understated.

The foregoing remarks refer to price indexes. To obtain maximum utility from the results yield statistics also are required. The very different nature of the problem of yields is stated and an arithmetic average of individual yields in each group is advocated. While the price index should be related to 100 at the starting-point it is obviously preferable to publish actual yield averages.