For many years it has been fashionable to assume that a published Net Premium Valuation is merely a piece of window-dressing designed to reproduce the results obtained by an internal Bonus Reserve Valuation carried out for the information of the office only. It may be as well, therefore, to start by giving some of the reasons which make it desirable to re-examine a few of the problems which arise in a Net Premium Valuation, viz.:

(1) The Examiners require our students to have a thorough knowledge of the Net Premium Valuation Method, both as regards the technique of its application and the results which it can be expected to produce.

(2) A Net Premium Valuation probably forms the main instrument for measuring the surplus to be distributed to policyholders in Industrial Funds.

(3) Even if the Net Premium Valuation were no more than window-dressing, the published results have to agree with those obtained by the internal Bonus Reserve Valuation and a thorough understanding of the method is necessary to ensure this.

The conclusion reached from a consideration of Table 1, that ‘in a perfectly stationary fund…the bonus for which the premium scale is loaded will emerge from a net premium valuation whatever margin is allowed between the experience and the valuation rate of interest’, is difficult to accept without a more detailed investigation.

At first sight it appears to be supported by the incontrovertible argument that if the premiums are loaded to allow for a £2 % bonus and the experience is exactly that assumed in the calculation of the premiums, the profit made must be sufficient to pay a level bonus of £2 % per annum irrespective of the valuation basis. In a stationary fund, therefore, it might be argued that the valuation basis cannot affect the surplus brought out each year.

The standard deviation of the distribution of sickness is a statistic that appears to have been ignored by British Actuaries, with the exception of Sir G. F. Hardy who derived an approximation in his well-known Essay (J.I.A. Vol. XXVII, 1889, p. 245). By considering the graduated results of the A.O.F. Experience 1871–75 he concluded that the mean deviation of expected sickness was approximately 2√(expected weeks of sickness).

This note has arisen from some investigations being made into the statistics of non-life business, from which it appeared that the results obtained could be used to place the derivation of the standard deviation of expected sickness on a more satisfactory basis, and it is being put forward in the hope that some member with access to the necessary statistics will be able to make a more detailed study of this problem.

In 1923, lack of capital in Germany led to a system of financing house-building which later conquered large parts of central and south-eastern Europe. The ‘Gesellschaft der Freunde’ (in translation ‘Society of Friends’, but entirely unconnected with the body commonly known under that name in this country) was the first Continental Building Society that worked on the following principle:

Members entering the society pay an entrance fee E and undertake to pay periodically thereafter amounts a per annum. All payments of a member are accumulated at a certain rate of interest and credited to his individual account. Whenever there is enough money in the pool to pay an amount of 1, say, then the member next on the list, in the order of entry, receives this amount and becomes a debtor for the difference between unity and the accumulated amount of his previous payments. He undertakes to pay from then on b, say, per annum until all his payments E, a and b, reach unity, when he is released from all obligations and ceases to be a member of the community.

Consider a continuous probability distribution of a variable x measured from its mean in units of its standard deviation, and suppose that deviations from the mean are taken irrespective of sign; let px represent the ordinate applicable to x (this ordinate is, of course, the sum of the original ordinates at + x and — x). We then have

, and we write .

With the present high rates of income tax and low yields, redemption yields are frequently outside the range of bond value tables and even of the more accessible interest tables. The following approximate method of estimating yields has been found satisfactory in practice:

For a bond bought at ɪ + k paying g per annum half-yearly redeemable in n years at ɪ the yield i convertible half-yearly can be written

where at rate ½i.

Practical use of (ɪ) depends upon the accuracy with which we estimate θ. Successive approximation will give a correct result, but the formula is not in a form when this method can be easily used. Successive approximation can be more easily effected by choosing θ and then estimating the error.