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History: An Equitable life

William Morgan was born on 26 May 1750 in Bridgend, Glamorgan, to William Morgan (1702-1772), a physician of Bridgend, and Sarah (1726-1803), the sister of Dr Richard Price, a well-known philosopher of the time. At the age of 18 he relocated to London to practice medicine at St Guy’s Hospital, returning to his hometown in 1772 after the death of his father.

On arriving back in London, he approached his uncle, Dr Price, for help in finding employment. Price had recently consulted with a newly formed society that was considering providing life assurance for the whole of life at a level premium dependent on age at entry. It was through this connection that Morgan was appointed clerk to the Equitable Society for Lives and Survivorships. In 1774, after a short time studying, he became sufficiently proficient in mathematics to be appointed assistant actuary.

On 16 February 1775, he was promoted to actuary of the society following the death of his predecessor, John Edwards. This would be one of Morgan’s greatest achievements: managing a life assurance company at the tender age of 25. The Equitable offices at Chatham Place, near Blackfriars Bridge, became his home for the first seven years of his career and he received a salary of £120 a year.

Career highlights
William Morgan spent the majority of his life working for the Equitable Society. One of his first assignments as actuary in 1776 was to compare the number of assured people that died with the number of assured people that ‘should have died’ according to Dobson’s Table. This enabled him to provide the first real estimate of the mortality experience of a life office. This estimate was then recalculated using Dr Price’s Northampton Tables based on the church registers of death from All Saints, Northampton. Morgan would continue to carry out this analysis annually.

Morgan made his first valuation of the society in 1776 in order to decide whether there were sufficient funds to meet future liabilities. With over 2000 policies, each requiring four calculations, it took exactly one year to complete. He undertook similar valuations at irregular intervals thereafter, each one taking longer than the last due to the increasing number of policies.

In 1779, Morgan published his Doctrine of Annuities and Assurances on Lives and Survivorships in which he detailed the methods and underlying theory of his calculations. The importance of this paper was in the appreciation that the premiums charged for any assurance cover must be calculated with reference to statistical experience. Morgan used a hypothetical table for his paper, in which, of 86 births, there was one death every year until the age of 86 (de Moivre’s Hypothesis — see box page 29).

In the years 1788-1800, Morgan produced a series of papers on the evaluation of survivorships using the actual probabilities of life. These papers were a valuable contribution to the subject of actuarial science and, in recognition of this, he was awarded the Copley Medal by the Royal Society in 1789. He was elected fellow of the Royal Society in 1790 and served twice on the council.

Bonus distribution
In 1800, Morgan created a fair method of distributing bonuses to policyholders that was dependent on the premiums they were paying. He found that if he did this at regular intervals, allocating only a certain proportion of the surplus, then the system would be sustainable.

In the same year, he also advocated the adoption of three by-laws on valuations:
>> 1 An investigation into the value of each policy must be undertaken every 10 years

>> 2 No addition to claims or any other method of distribution without such a valuation

>> 3 The addition made to claims must not exceed two-thirds of the surplus of the Society.

These by-laws meant that surplus funds could only be distributed every 10 years. Morgan felt that, up to this point, distributions were being made too frequently and, as the Society was growing, valuations would take longer and longer to complete, so 10 years was a suitable period. One-third of the surplus was to be kept as a reserve in case of times of increased mortality. It is believed that Morgan had a reason for this figure, but it was never disclosed.

Upon realising that the profit margins of the Society were decreasing, Morgan restricted the number of assurances that shared in bonuses to 5000. It would now normally take approximately five years before a new policy would become eligible for a share in the bonus. New members who survived this waiting period would then be entitled to the full bonus — both declared and to be declared, in respect of past, as well as future premiums. The only people who would lose out would be new members with early claims — however, these were the members who would do well from a life assurance policy.

William Morgan (1791-1819), the eldest son of William and his wife Susannah, became a member of staff at the Equitable Society in 1809. Morgan often confided in him, in the hope that one day his son would succeed him as actuary to the Society. However, this was not to be, as William died at the premature age of 28. His death, and that of another member of staff, made way for the appointment of Arthur Morgan (1801-1870), William Morgan’s youngest son, as assistant actuary.

William Morgan had always enjoyed the support of Equitable’s directors and could have continued in his role indefinitely, but decided to retire in his late-70s due to ill health. His son Arthur was elected on 2 December 1830 to take his place. Between them, father and son would control the Society for 95 years. William Morgan died shortly after his retirement at the age of 83.

Morgan’s legacy
William Morgan is considered by many to be the father of actuarial science and was the driving force behind the initial success of the Equitable Society for Lives and Survivorships. He made a considerable contribution to actuarial science through his publication of the Equitable’s experience, and his introduction of life office valuations. These ideas have since been developed and have played a part in shaping the profession as we know it today. His long life allowed him to make an impact on subjects unrelated to his profession and he is also recognised as an accomplished scientist, having been credited as the first to record the ‘invisible light’ produced when a current is passed through a partly evacuated glass tube: the first X-ray tube.

Without pioneering actuaries like William Morgan, the profession would not have advanced to its current status as a science in its own right, dealing with not only life assurance, but also general insurance and pensions. The actuarial profession owes much to William Morgan and, as such, will continue to evolve for many years to come, based on the foundations he constructed.

Laura MacDougall is a final-year student at the University of Glasgow studying Mathematics

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Further reading
1 Ogborn, M.E. (1962), Equitable Assurances, London: Allen and Unwin.
2 Elderton, W.P. (1933), William Morgan FRS, 1750-1833, Journal of the Institute of Actuaries 64: 364-365.
3 Elderton, W.P. (1931), William Morgan FRS, 1750-1833, Transactions of the Faculty of Actuaries 14: 1-20.
4 Anderson, J.G. (1945), William Morgan and X-Rays, Transactions of the Faculty of Actuaries 17: 219-221.
5 Hald, A. (2003), History of Probability and Statistics and their Applications before 1750, New Jersey: Wiley.

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De Moivre’s hypothesis
That every person has an equal chance of living the average time of people their age. He assumed that the probability that someone aged x survived for a further t years was where the maximum age, w, was 86.