John Finlaison and the British Government's Life Annuity Issuance (1808-1829)

The aftermath of the British Government’s life annuity issuance of 1808 provides a colourful and historically important example of how the eighteenth- century foundations of mortality thinking were built upon and extended by some new and highly able actuarial thinkers in ways that prompted some disagreement with the earlier actuarial generation. This particular example of the changing of the guard of actuarial thought leadership involved some public controversy, prompted Cabinet-level political reaction and was accompanied by increasing personal animosity.

Some 120 years earlier, the British Government had experimented with the use of life annuities as a form of debt funding for its European wars. It found, somewhat peculiarly, that the scheme was both quite unpopular with investors and yet highly unprofitable for the government issuer, relative to simply issuing fixed long-term bonds. The government subsequently tried on occasion to use life annuities to raise debt funds over the course of the eighteenth century, but the issuances were very small in volume. For example, a life annuity was issued in 1779 with the aim of raising up to ?7 million, but only 133 annuities were sold raising a sum of only around ?150,000.[1] In 1808, in the midst of the Napoleonic wars and with Britain under serious threat of invasion, the government tried again with renewed vigour. The profitability to the issuer was similarly dismal to the 1692 issuance, but this time the market was better prepared to spot a bargain.

William Morgan, as the actuarial leader of the pre-eminent and dominant life assurance company of the age, advised the government on the mortality basis to be used for the pricing of these life annuities. His advice was to do what he did: use the Northampton table. The exact form of the advice that Morgan provided is not available, but with the benefit of hindsight his recommendations might appear surprising, or indeed rather odd. Morgan was well aware at this time that the Equitable’s mortality experience was significantly lighter than that implied by the Northampton table. He would have known that if the annuity purchasers had experienced mortality rates similar to those experienced at the Equitable, life annuities priced with the Northampton table would prove highly profitable for the annuitant investor and unprofitable for the issuer. However, Morgan’s view was steadfast and consistent throughout his entire career: he believed that the Northampton table was a fundamentally accurate description of the law of human mortality; and the lighter mortality experienced by the Equitable on its assured lives was due to the selection effects of its rigorous life assurance underwriting practices.

Even if Morgan’s belief was in fact correct, it ignored the self-selection effect that is inevitably to be observed in annuity experience: only the healthiest of lives would be nominated for annuity contracts, and this selection effect was likely to be even stronger than the impact of the underwriting safeguards that Equitable applied to its assured lives. The potential for annuity selection was exacerbated by the ability of the annuity purchaser to nominate the life on which the annuity is written—annuities were not considered as insurance in the context of the 1775 act that created the concept of insurable interest. In Morgan’s defence, however, it should be noted that the Equitable had been open for annuity business for many years and used the Northampton table as the premium basis throughout. This had hardly stimulated an overwhelming public demand for annuities (they consistently sold in tiny volumes compared to assurance business). Indeed, the Equitable had managed to sell such small volumes of annuities on the Northampton basis that there does not appear to be any record of an analysis of its profitability.

And so, in 1808, the government offered life annuities at prices based on the Northampton table, and this offer remained open for many years to follow. Ten years later, several million pounds had been raised by the annuity scheme, requiring annual annuity payments of ?640,000.[2] Around this time, a civil servant at the Admiralty named John Finlaison wrote a letter to the Chancellor of the Exchequer expressing his concern at the losses that he believed were arising from the overly generous annuity pricing basis. Finlaison estimated that losses of ?8,000 per month were being incurred as a result.

Finlaison would, in 1848, become the first President of the Institute of Actuaries. For an actuary of the period, he had an unconventional career and background. He never worked in a life office, and instead spent his entire career as a civil servant. He first made his mark in 1805 as the second clerk of the Commission of Revising and Digesting the Civil Affairs of the Navy. As noted in a recent history of the role of Britain’s civil service in the Napoleonic Wars: ‘Finlaison, born in Caithness, the son of a fisherman, had come to London after an education in Edinburgh; at this time only twenty-three, but already demonstrating a formidable logical brain and an immense capacity for work.’[3] He worked at the Admiralty from 1809 to 1822, where he joined the newly established Admiralty Record Office and was responsible for a much- improved parliamentary reporting of the naval accounts and expenditure. He then moved to the Treasury and was appointed the Actuary of the National Debt, a position he held for the next 29 years.

No action was taken by the chancellor in 1819 when Finlaison first raised his concerns about the pricing of the government’s life annuities. Empowered by his appointment as Actuary of the National Debt, he was eventually asked by the Treasury to provide a full analysis and he delivered a parliamentary report on 31 March 1829.[4] Finlaison’s report contained a comprehensive analysis of the mortality experience of the annuities and tontines written by British (or English) governments since 1693. His work was ground-breaking in many ways. Most pertinently, it showed that the view he had expressed to the chancellor ten years earlier was right: the mortality experience of the government life annuities was much lighter than the Northampton table that had been used in pricing them for the previous 20 years. This is illustrated by Fig. 3.2, which also shows Milne’s Carlisle table for comparison.

The government life annuity mortality experience and Northampton and Carlisle tables

Fig. 3.2 The government life annuity mortality experience and Northampton and Carlisle tables

Finlaison’s analysis evidenced the profound differences between the government annuity mortality experience and the mortality rates assumed in the Northampton table: for example, at age 60, the Northampton table was implying a mortality rate that was fully double that experienced by the government annuitants! The Carlisle table provided a significantly closer guide, but still overestimated the mortality rate experience (which could be explained by annuity anti-selection effects and by life expectancy improvements in the decades between the two sets of observations). Finlaison’s analysis implied that the government annuity prices should be increased by around one quarter. His report had an immediate impact: an Act of Parliament was passed in 1830 which upwardly revised the government life annuity prices in accordance with his recommendations.

Even under the revised annuity pricing basis, scope for anti-selection was still significant, especially at older ages: a 90-year-old life could obtain an annuity rate of 62 % (payable in quarterly instalments). Francis’ 1853 book provides amusing tales of the creative anti-selection speculation that this generated:[5]

The shrewd gentlemen of the Stock Exchange immediately saw and seized the advantage. Agents were employed to seek out in Scotland and elsewhere robust men of ninety years of age, to select none but those who were free from the hard labour which tells on advanced life ... Wherever a person was found at the age of ninety, touched gently by the hand of time, he was sure to be discovered by the agents of the money market ... The inhabitants of the rural districts of Scotland, of Westmoreland, and of Cumberland, were surprised by the sudden and extraordinary attention paid to many of their aged members. If they were sick, the surgeon attended them at the cost of some good genius; and if they were poor, the comforts of life were granted them. In one village the clergyman was empowered to supply the wants of three old hale fishermen during the winter season, to the envy of his sick and ailing parishioners. In another, all the cottagers were rendered jealous by the incessant watchful attention paid to a nonagenarian by the magnate of the place. It was whispered by the less favoured that he had been given a home near the great house; that the cook had orders to supply him with whatever was nice and nourishing; that the laird had been heard to say he took a great interest in his life, and that he even allowed the doctor twenty-five golden guineas a year, so long as he kept his ancient patient alive.

Clearly there was still much to learn about annuity market behaviour! Nonetheless, the new pricing basis undoubtedly brought the cost of servicing new government life annuities closer to that of long-dated gilts.

William Morgan resented and resisted the implication that his advice had unnecessarily cost the government huge sums of money, commenting:

By the assistance of these tables (Finlaison’s tables of the government annuity mortality experience), the notable discovery has been made of the loss sustained by the public of many thousands every week ... With the least knowledge of the subject, it might easily have been seen that the use of the Northampton table could not possibly be attended by such a loss, and that the extent of any loss (if it really existed), instead of six years, did not require as many hours to ascertain it.

Finlaison and Morgan also adopted opposing views on other actuarial debates of the time. Whilst Morgan argued that selection was the primary factor explaining the discrepancy between the Equitable’s experienced mortality and the Northampton table, Finlaison’s position was ‘that there is very little if any advantage at all in favour of selection’.[6] Whereas Morgan argued for the use of statistical rates of sickness in friendly societies, Finlaison argued that ‘life and death are subject to a known law of nature, but that sickness is not, so that the occurrence of the one event may be foreseen and ascertained, but not so the other’.[7] On these other points, history proved Morgan the more accurate. The following section will discuss how selection effects were measured by actuaries using techniques developed over the nineteenth century that showed them to be highly material. The estimation of rates of sickness was also developed into an increasingly reliable science by actuaries over the course of the nineteenth century, culminating in the Manchester Unity sickness tables that were published in 1903 and remained in use through much of the twentieth century.[8]

Beyond the impact it had on government policy, Finlaison’s report was an important milestone for actuarial thought. It was noted in Chap. 1 that a government annuity mortality experience analysis was first performed by the Dutchman Johannes Hudde in the 1660s. Finlaison noted that Kersse (again in Holland) and Deparcieux (in France) had performed analysis of government annuity and tontine experience in the 1740s. But the scale and rigour of Finlaison’s analysis was of a different order to these earlier works. His study also provided the era’s most comprehensive analysis of how British mortality behaviour varied by sex. The chronological span of Finlaison’s analysis provided insight into how mortality rates had decreased over the eighteenth century. It was commonly understood that life expectancy had improved substantially over this period, but Finlaison was able to provide greater detail of how mortality rates had changed differently across ages. He also noted that this had implications for how historical mortality observations should be used in constructing forward-looking estimates:

If the diminution (in mortality rates) had been doubtful, or very slight in degree, it would follow as a matter of course, that a combination of all the facts observed upon would have formed the proper basis for life annuities and insurances; but this being quite otherwise, there was no choice but a combination of two or three observations, the latest in point of time.

Finlaison also applied a smoothing or graduation technique to the fitting of the tables derived from mortality experience. Graduation was starting to emerge as an important topic in mortality table construction at this time and Finlaison was a pioneer of its real-life application. More generally, Finlaison’s detailed work with experience data rather than population data anticipated and perhaps partly motivated the next important development in life office mortality modelling.

  • [1] Leeson (1968), p. 9.
  • [2] Francis (1853), p. 203.
  • [3] Knight (2013), p. 325.
  • [4] Finlaison (1829).
  • [5] Francis (1853), Chapter XII.
  • [6] Finlaison (1829), p. 19.
  • [7] Parliamentary Papers (1825).
  • [8] Watson (1903).
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