Griffith Davies Tables of Life Continencies

Griffith Davies published Tables of Life Continencies, containing the Rate of Mortality among the Members of the Equitable Society, and the Values of Life Annuities, Reversions, etc computed therefrom: together with aa more extensive scale of Premiums for Life Assurances, deduced from the Northampton Rate of Mortality in 1825. The book consists of 26 worked examples and 22 tables. Below we give some information about the book including extracts and reviews. We have made use of information in 'Davies's Equitable Tables' in C Walford, The Insurance Cyclopaedia 3 (1874), 7-9.

Introduction to Tables of Life Continencies.

In offering this Tract to the attention of the Public, the Author deems it necessary to state, that the Rate of Mortality among members of the Equitable Society has been deduced from the accounts given by Mr Morgan, in his Addresses to the general Courts of that Institution, and in the Notes added by him to the latter editions of Mr Price's Observations on Reversionary Payments. In his address to the general Court, held on the 24th of April 1800, Mr Morgan stated, that the decrements of life among the members of the Equitable, for the preceding 30 years, had been to those expressed by the Northampton table ... And in the Notes added to Vol 1 of Dr Price's Observations on Reversionary Payments ... he states, that the same proportion between the decrements of life among the members of the Equitable Society and those expressed by the Northampton Table, had continued up to the year 1810, embracing a period of more than forty years. His Addresses delivered in December 1816 and March 1825, further confirm that the decrements of life had, up to those periods, still continued the same, or to bear the same ratio to those in the Northampton Table as he had previously represented. Granting these statements to be correct, it must therefore be concluded, that the rate of mortality among the members of the Equitable, for a period exceeding half a century, must have continued the same as that represented by Mr Morgan in the year 1800. ...
Comment about Tables of Life Continencies by: L G Chambers.
Griffith Davies (1788-1855), F.R.S. actuary, Transactions of the Honourable Society of Cymmrodorion (1988), 68.

These tables developed as a practical tool the actuarial technique of commutation columns, which is still in use in modern actuarial practice.
Example 1 from Tables of Life Continencies.

What is the present value of £50 annuity on a life of 40, estimating the interest of money at 4 per cent, and the average duration of human life by the rate of mortality among the members of the Equitable?
Example 6 from Tables of Life Continencies.

What is the present value of £120 annuity, payable during the joint lives and the life of the survivor of two persons aged 40 and 50; estimating the improvement of money at 5 per cent, and the rate of mortality by the experience of the Equitable?
Example 9 from Tables of Life Continencies.

What present payment should be required of a man aged 40, for the Survivorship Annuity of £50 to his wife, aged 35, in the event of her surviving him; estimating the interest of money at 3 1/2 per cent, and the rate of mortality by the experience of the Equitable?
Example 12 from Tables of Life Continencies.

Suppose a society of 500 persons of the age of 20 years, 700 of the age of 30, 900 of the age of 40, 800 of the age of 50, and 600 of the age of 60; it is required to determine the number of deaths which may be expected to happen in the year, according to the Northampton rate of mortality.
Example 15 from Tables of Life Continencies.

Suppose a person of 40 desirous of securing £1000 to his survivors at his death, whenever that event may happen, and not wishing to encumber himself with the payment of any premium after the age of 50; it is required to determine what annual premium payable for the next ten years (but subject to cease sooner if the life drop in the interval) should be required for such insurance; estimating the interest of money interest and the rate of mortality by the Northampton Table?
Example 18 from Tables of Life Continencies.

What annual premium should be required for the assurance of £2000 payable in the event of an assigned life aged 40, failing before another aged 50; estimating the improvement of money at 3 per cent, and the rate of mortality by the Northampton Table?
Example 20 from Tables of Life Continencies.

Suppose an Insurance for £100 effected 10 years ago, on a life then aged 40; it is required to determine the value of the Policy, supposing the renewal premium for the 11th year just paid, reckoning interest at 3 per cent, and estimating the rate of mortality by the Northampton Table?
Example 22 from Tables of Life Continencies.

Suppose an assurance for £100, effected 10 years ago, on a life then aged 40; and paid for by a single premium; it is required to determine the present value of the Policy, reckoning interest at 3 per cent, and estimating the rate of mortality by the Northampton Table?
Example 24 from Tables of Life Continencies.

Suppose a Policy for an assurance of £1000 to have been effected 15 years ago, on the joint lives of two persons, then aged 30 and 20, at an annual premium of £40 17s 6d; it is required to determine its present value, estimating interest of money at 3 per cent, and the rate of mortality by the Northampton Table?
Example 26 from Tables of Life Continencies.

Suppose a Policy, for the assurance of £5000, to have been effected 12 years ago, on a life then aged 30, against another life then aged 45, at an annual premium of £102 14s 2d; it is required to determine the value of the Policy, estimating interest of money at 3 per cent, and the rate of mortality by the Northampton Table?
Table 1 from Tables of Life Continencies.

Showing the Rate of Mortality among the members of the Equitable Society, from the year 1768 to 1825.
Table 2 from Tables of Life Continencies.

Showing the Value of the Annuities on Single Lives, according to the experience of the Equitable.
Table 3 from Tables of Life Continencies.

Showing the Value of an Annuity on a Single Life, allowing the Purchaser a given rate of interest on the Sum advanced, beside the Premium necessary to secure his Capital by a Life Assurance, according to the rates charged by the Equitable.
Table 6 from Tables of Life Continencies.

Showing the Present Value of a Deferred Annuity of £1 on a Single Life, according to the rate of mortality among the members of the equitable, reckoning Interest at 3 1/2 per cent.
Table 9 from Tables of Life Continencies.

Showing the Average Value of £1 to be received at the end of the year in which an Assigned Life may fail, estimating the rate of mortality by the experience of the Equitable.
Table 15 from Tables of Life Continencies.

Showing the Value of the Annuities on Two Joint Lives, according to the Northampton rate of mortality.
Table 18 from Tables of Life Continencies.

Showing the Premium required, for a given number of Payments, to secure £100 at the extinction of a Single Life, according to the Northampton rate of mortality, at 3 per cent.
Table 21 from Tables of Life Continencies.

Showing the Premium required to secure a Sum payable on the death of A, provided he dies before B, according to the Northampton Table, at 3 per cent.
William Morgan addresses the Select Parliament Committee on Friendly Societies 1827.

Q. Have you any reason to think that the tables calculated by Mr Griffith Davies from the Experience of the Equitable Office are correctly deduced from the data that they furnish?

W M. I do not think the data were sufficient to compute any table from; I am sure they were not.

Q. State your reasons more particularly.

W M. I will give my reasons. We insure no lives hardly to the under 30, so that the number is too small to be depended upon with regard to the probability of life under that age. Those tables begin in early life, and a great deal must be assumed in giving a table where there is no data to go from; besides, I find the probability of life approaching nearer to the Northampton Table in our office than it used to be in the later periods of life; for the Northampton Table gives the decrements of life as high as most tables in old age.
From the paper by: John William Lubbock.
On the comparison of various tables of annuities, Transactions of the Cambridge Philosophical Society (1830), 321-341.

In a recent publication Mr Morgan admits that he was not aware of the great number of instances in which there are several policies on one and the same life, and he sys that this circumstance very materially affects Mr Davies's calculations. Such statements as those appear to me too vague to be made the basis of calculations, although the experience of the Equitable Society would be most valuable, if we were acquainted with all the details concerning it.
From the book by: J Finlaison (ed.).
Tables for the use of Friendly Societies (Shaw and Sons, London, 1847).

Tables computed by Mr Griffith Davies

1. Showing the Monthly Contributions to be required till Death, for Allowances in Sickness during Life.

2. Showing the Monthly Contributions to be required till the Age of Sixty-five, for Allowances in Sickness, to cease at that Age.

3. Showing the Monthly Contributions to be required till the Age of Sixty-five, for Pensions. to commence at that Age, and to be continued Payable during the remainder of Life.

4. Showing the Monthly Premiums to be required during Life for Sums to be paid on Death.

5. Showing the Monthly Premium required till the Age of Sixty-five, for Sums to be paid on Death.
From a paper by: John Adams Higham.
On the Value of Selection as exercised by the Policy-holder against the Company, Assurance Magazine 1 (3) (1851), 179-202.

The preference I have elsewhere expressed for Mr Davies's tables as a basis or the calculation of premiums is confirmed by the present extended observation. It agrees very nearly throughout with the values of lives at the time of selection which those observations furnish. But if it agreed exactly, it would be a false table for every other purpose than that of determining the premium. All subsequent calculations affecting the policy ought to be made from classified tables ... At the moment of entry, Mr Davies' tables represent (I think) most correctly the value of life for an office whose business is of the best class; after a considerable period of assurance the Northampton values will be most correct ...
From a book by: Alexander Glen Finlaison.
Report and Observations on Tontines and Life Annuities (1860).

The first table mentioned, famed by the late Mr Griffith Davies, an actuary of profound science, is derived from what may be called a factitious experience of the Equitable Society, disclosed by the late Mr W Morgan in his edition of dr Price's works. ... This factitious experience consisted merely of a statement of the ratio which the decrements of life in the Equitable experience bore to certain ages to those decrements which are given in the Breslau tables of Mortgages. Mr Griffith Davies raised an immense superstructure of calculation, in the tables of the values of single and joint life annuities at many different rates of interest on this small foundation; but these computations, which, notwithstanding their origin, make near approach to the truth, and form, for some purposes, a highly useful system of tables based on a combination of the two sexes.
From the Institute of Actuaries.
Catalogue of the Institute of Actuaries Centenary Exhibition 1848-1948 (1948), 8.

Griffith Davies (1788-1855)

(a) Values of assurances by Northampton 3 per cent. MS. 1820
lent by the Commercial Union Assurance Company Ltd.

(b) "Tables of life contingencies" 1825.

(c) "An investigation of the bases for calculating life contingencies, of the profits on life assurances, and of an equitable method of apportioning those profits by way of bonus among those assurers" Twenty-four reports by Griffith Davies MSS., 1822-1831 Probably (in part) original lent by the Guardian Assurance Company Limited.

The tables of 1825 gave the first full commutation columns published in Great Britain. Davies was Welsh and born of poor parents. He set up as a teacher of mathematics and became the first Actuary (1822-1854) of the Guardian Assurance Company. He was also Actuary of the Reversionary Interest Society from 1823. His interest in reversions may have suggested the preparation of the table based on the experience of the Equitable Society. This should not be confused with Arthur Morgan's table. Davies computed his by reference to the Northampton table on the basis of the proportions of actual to expected deaths given by William Morgan. Davies showed how, in capable hands, good results may be obtained from very scanty data. The "investigation" was for the use of the Guardian who also have a set of tables prepared by him.

Last Updated July 2022