Richard Price, 'Observations on the proper method of keeping the Accounts [at] the Society for Equitable Assurances ...', 1774
Richard Price, 'Observations on the proper method of keeping the Accounts, and determining from year to year the state of the Society for Equitable Assurances on Lives & Survivorships’, 1774. This is one of the key documents in the history of actuarial science. Richard Price introduces a number of ideas including that of the valuation of life policies; he indicates how the calculations should be made and how to use the results to ascertain the financial position of the society.
The report, which is addressed to the Society’s directors, develops methods for carrying out an investigation into the state of the Society from time to time. At this period the Society had no idea of whether it was making a profit or loss.
The first part of the report derives some approximate “rule of thumb” methods, including a comparison of actual and expected mortality. The latter part sets out:
- the method by which the data should be tabulated for each year of the period over which the investigation is to be made and
- a recommendation that the present value of each policy in force at the valuation date should be calculated by subtracting the present value of future premiums from the present value of the sum assured (using methods developed by Thomas Simpson, with corrections from Price’s own treatise). Price says he is aware that the computations will take up much time, but it is a work of particular importance. If done once, it will not be difficult to do subsequently, and it will not be necessary to repeat it every year.
The report states that the surplus at the valuation date can be calculated by taking the total value of all the policies in force, calculated as above, and subtracting this total from the Society’s “stock”, i.e. the (market) value of the assets. In addition the report gives an approximate method for analysing the profit or loss that has arisen in each year. Subject to further investigation, it appears from a cursory glance at the early valuations in the Society’s archives, that the tabulation and valuation methods shown were actually adopted in practice.
(Richard Price’s report is discussed briefly by M E Ogborn, Equitable Assurances (1962), pages 103-104. He concludes: “Richard Price’s observations were the first to show how the business of a life office should be arranged and valued.” The report does not appear to be in Price’s normal handwriting that he used for letters, so it may be a contemporary copy prepared for one of the directors. Ogborn says that the report was considered by the directors when they met at the President’s home on January 27, 1775.