The assessment of ordinary shares is at present the subject of intense activity. A full-scale professional analysis of a particular share can, however, be a most formidable document and one which does not produce the answer to the question ‘What long term return can I expect from my investment?’ On the other hand a simple statement of dividend cover and dividend yield at the current price is clearly insufficient to decide on the merits of a share.

This paper describes a method of assessing ordinary shares in terms of ‘expected yield’, i.e. the compound interest return which a long-term buyer would expect to obtain from his investment, and includes a note on a simple way of adjusting a company's published rates of dividend and earnings to produce a consistent growth record suitable for use in estimating the expected yield.

The census taken in this country last April will still be fresh in everybody's minds, so that the present time seems very suitable for a discussion on census-taking. The subject is of particular interest, as considerable developments have taken place throughout the world in the 16 years since the war ended, and more developments are likely in the years to come. In these notes, therefore, I have tried to set the British census against the background of census-taking as it is practised in the rest of the world at the present time.

It is first necessary to consider why with-profit pensions schemes have been introduced. Three reasons emerge. The first is protection for the office; the second is a desire to be equitable to the policyholder, and the third is competition—from other offices and from private funds.

These reasons are now amplified.

Pension schemes are the longest form of liability undertaken by the office; further, existing benefits can be purchased by level premiums guaranteed to pension age (as in individual contracts) with an underlying rate of interest of the order of 4¼%. It is therefore desirable to have protection against both improvements in mortality and against the office's not earning an average of 4¼% on the premiums and interest which it has to invest each year.

1. Kennedy & Howroyd (1956) have discussed the application of the Lagrangian multiplier technique to actuarial problems. This technique permits the analytical solution of constrained optimization problems, where both the function to be optimized and the constraints must satisfy stringent analytical conditions. In particular, the first derivatives of all functions must exist.

When constraints comprise inequality as well as equation restrictions, as is the case in linear and non-linear programming, then the conditions required for the Lagrangian multiplier technique do not hold. It was therefore found necessary to develop a new body of techniques, known as mathematical programming techniques, for the solution of constrained optimization problems involving inequality constraints.