William Morgan and the Actuarial Management of with- Profit Business (1775-82)
Several developments important to the nascent life assurance industry occurred over the dozen years following the Equitable’s founding in 1762. Price’s Observations, with its new mortality tables and sound actuarial insights, brought actuarial thinking on the pricing of life contingencies to a new level of competence. The Equitable had established itself and its whole- of-l ife assurance product as successful features of the British life assurance industry. It had become the leading provider of life assurance, but the size of this market remained modest relative to other forms of insurance business. The Life Insurance Act of 1774 further improved the conditions for future growth in the industry. This act introduced the legal concept of insurable interest. Henceforth, life assurance could not be used as a means of speculative gambling, but only as a form of risk mitigation where the buyer had a real and legitimate exposure. This focused life assurance business on products that were generally most amenable to actuarial and statistical analysis. Thus the scene was set for the next step in the development of life assurance business and the actuarial practices required to make it sustainable.
William Morgan, nephew of Richard Price, and the actuary of the Equitable for a full 55 years from 1775 to 1830, played a most significant role in shaping this next stage of actuarial practice. Morgan was appointed assistant actuary in 1774, serving under John Pocock, who was elected actuary a month earlier following the death of John Edwards, the previous holder of this post. John Pocock had been in office less than a year when he died unexpectedly in early 1775. Morgan had distinguished himself sufficiently well during his short term as assistant actuary for him to be elected actuary in an uncontested election at a general court of the society in 1775. Morgan did not attend university but did receive some medical training as an apprentice at an apothecary prior to joining the Equitable. He was tutored in life assurance mathematics by Price in 1773 before being appointed assistant actuary. At this time, the actuary’s role in a life assurance business was not yet well defined. Edwards and Pocock had been book-keepers rather than statisticians. It would not have been viewed as essential for Morgan to demonstrate advanced mathematical learning, and the tutelage under Price would likely have carried some weight with the directors of the business.
At the start of Morgan’s tenure as actuary, there was an emerging interest in the distribution of the capital that was evidently accumulating in the business. A satisfactory way of assessing the appropriate level of reserves for in-force business had yet to be fully implemented (actuarial methodology and the computational burden of policy-by-policy valuation both had to be addressed). A rigorous and accepted means of determining how much of the visible asset accumulation could be considered as surplus available for distribution was therefore wanting. With Morgan still establishing himself in his new role, the directors looked to Price for guidance and he duly provided them with a number of recommendations. Price suggested the society should pursue three approaches to analysing the current adequacy of the accumulated capital fund: a comparison of the actual mortality experience to date with the mortality assumptions used in the premium basis; a comparison of the amount of premiums being received with the claims being paid (he suggested, as a rule of thumb, that around two thirds of premiums received in the early years of a whole-of-life policy would be required to adequately build up the reserve for the claims that would arise in its latter years); and a comparison of the accumulated assets of the society with a valuation of the liabilities.
In anticipation of a surplus being identified by the above methods, Price also provided some advice on the form of distribution of surplus to the participating policyholders. In particular, he advised against the payment of any cash dividends. Instead, he argued, if any distribution of surplus was deemed appropriate, it should be made by either increasing the sums assured or reducing the future regular premiums of the participating policies. Price’s advice was acted upon by Morgan and, like virtually everything else Price did in the field of actuarial science, his recommendations became part of standard actuarial practice for decades (or, as in this case, centuries).
The market value of the assets of the society at the end of 1773 amounted to ?33,000. Price surmised that a valuation of the liabilities might be around ?22,000, implying a surplus of ?11,000. It was Morgan’s job to perform the first rigorous valuation of the society’s liabilities and hence determine a reliable measure of the surplus. He and his small team of assistants valued each of the 922 policies in-force individually. Four months and several thousand manual calculations later the full results were ready to report. The results were even better than anticipated by Price. At the start of 1776, the assets were valued at ?41,928 (their market value) and the liabilities were valued (using the premium basis) at only ?16,786, implying a surplus of ?25,142. This startling result raised two fundamental questions: how did such a large surplus arise? And what should be done with it?
The surplus primarily arose from the much lighter mortality experienced to date than that assumed in the premium basis. This was especially true in the non-profit business, where, as discussed earlier, the premium basis was more expensive than the premium basis applied to with-profit policies. But even the with-profit experience was very substantially better than assumed in its premium basis. Morgan himself noted that the 1776 investigations had concluded ‘the probabilities of life in the Society had been higher than those in Mr Dodson’s Table, from which its premiums were computed, in the proportion of three to two’.[1]
This substantial mortality margin had several contributory factors. The premium basis used Dodson’s recommended London Bills of Mortality basis. This was based on mortality data from 50 years prior at a time when life expectancies were improving significantly due to medical developments and improvements in economic and social conditions. The period on which the bills were based included 1740, a year of weather-induced food shortages that resulted in mortality almost as severe had been experienced in bouts of the plague. The bills were based on the experience of London, which was probably the least healthy place in the country; and they were based on the full breadth of the London population, not the emerging middle class that was buying the Equitable’s whole-of-life assurance policies. Furthermore, the business had an active approach to underwriting, with every new life assured being reviewed and approved by a director.
There were other factors beyond the mortality basis that also contributed significantly to this accumulation of surplus. A number of somewhat arbitrary additional loadings were applied on top of the premiums implied by Dodson’s tables. These included loadings for larger assurances, young lives and females (sex-specific mortality tables were not in use at this time). And then a final 6 % margin was additionally applied to all premiums. Furthermore, wars in Europe and America had resulted in significant increases in government bond yields, and much new money was therefore invested at yields well in excess of the 3 % assumed in the premium basis.
These profits were amplified by the gearing effect whereby the surplus generated by non-participating short-term business was left to be shared amongst the remaining participating policyholders. A decade later, in an analysis of the surplus that had emerged between 1768 and 1787, Morgan concluded that more than half was due to profits made on temporary (and non-participating) assurances.
Finally, there was another source of surplus that was important during this period. Of the whole-of-life assurances written during the society’s first twenty years, less than half ultimately resulted in claims. The vast majority of those policies that did not result in claims were forfeited without any compensation. The society did have a policy of offering fair surrender values, but it may have been that many policyholders never actually applied to surrender their policy but merely forfeited them when they chose not to make any further premium payments. Furthermore, the surrender basis used by the Equitable was based on a form of net premium valuation rather than an asset share-based calculation. This prospective approach to assessing the surrender value was highly sensitive to the mortality basis used in the valuation. When the Equitable moved its premium basis to the Northampton table in 1780 (discussed further below), it meant that many of the regular premium whole-of-life contracts written on the old premium basis were worth very little on this prospective basis, or even had a negative value to the policyholder![2] So the surrender values were much lower than the accumulated value of the assets that the surrendered policies had contributed (even after deducting the cost of the life assurance that had been provided over the duration of the policy to date).
What to do with the surplus? A series of meetings of the general court of the society in 1777 determined that a 10 % reduction in all future premiums should be effected. Moreover, the in-force with-profit policyholders would have this reduction back-dated: it would be calculated for all the premiums they had paid to date, and this would be offset against their next regular premium. To the extent that the refund was greater than the next regular premium, the remainder would be paid to the policyholder in cash. So the back-dated element was essentially a one-off cash dividend.
The premium reduction and refund of 1777 was a temporary stop-gap measure that alleviated the building pressure from participating policyholders. But a more fundamental review of pricing and surplus distribution was called for. As usual, the intellectual impetus was provided by Richard Price. In 1780, he advocated a change in the underlying mortality tables that were used in the premium basis. Dodson’s London Bills of Mortality premium basis was still in use, and this was clearly generating premiums that were much larger than was reasonable. Indeed, it is interesting that the business could continue to generate significant new business at these rates. This perhaps reflects the lack of (credit-worthy) competition in the life assurance market of the time. It may also suggest that policyholders increasingly viewed the whole-of-life with-profit policy not merely as an insurance product, but as an investment product (with likely future participation somehow in the surplus). Price recommended using a mortality basis derived from the Northampton or Norwich tables that he published in Observations. The directors, as usual, followed this recommendation and decided upon the Northampton table. Price updated this table to include Northampton Bills of Mortality data up to 1780 (so the table was based on data from 1735 to 1780). The directors opted to add a 15 % loading to the premiums implied by this table. Even Price, whose advice to the society tended to be universally prudent and frugal, referred to this loading as ‘exorbitant’.
This new premium basis would be applied to new business. It did not address if and how to distribute the surplus that had accrued to date to existing policyholders. How much of the surplus should be distributed to the existing with-profit policyholders, and what form should this distribution of surplus take? The directors recommended that an addition should be made to with-profit policyholders’ sums assured of 1.5 % of the sum assured for each annual regular premium paid (hence a policy that had been in-force for the full 19 years since the founding of the society would obtain a 28.5 % proportional increase in their sum assured). The proposal was approved by the members, and the first with-profit reversionary bonus was thus paid in 1781.
No explicit historical explanation is available, but it is likely that the size of the reversionary bonus was chosen to distribute a targeted portion of the surplus. What drove Price’s preference for distributing surplus through increases in sums assured rather than cash dividends? It was perhaps because retaining the assets within the society for as long as possible fitted with his vision of a long-term growing business of increasing influence and scale. In Ogborn’s outstanding history of the Equitable,[3] he suggested that the increase in government bond yields that occurred in the period of 1770-1780 may also have played a part. The American War of Independence had placed considerable strain on the British Government’s finances, and long-term government bond yields had increased from around 3 % in 1770 to around 6 % by 1780.[4] Most of the assets of the society were invested in long-term government bonds, and there may have been a reluctance to be forced to sell at these deflated price levels to fund a cash distribution (the assets, however, were valued at these market values in Morgan’s surplus analysis). The society had also recently started to invest a significant portion of its assets in mortgages. The illiquidity of these assets might also have tempered the directors’ enthusiasm to distribute significant amounts of cash (particularly if it created the expectation that more might be follow).
A further reversionary bonus of the same form was made in 1792, this time of 2 % of the sum assured for each regular premium paid. This same level of bonus was added again in 1800 when the surplus was calculated to be ?484,000 (and the bonus was calculated to reduce this surplus to ?225,000). The bonus system established by Morgan proved highly attractive to prospective policyholders. Furthermore, it was not a system that could be quickly replicated by competitors.
Despite spending much of the period at war, between 1781 and 1800 the British economy grew rapidly as the early stages of the industrial revolution gathered momentum. Increases in overseas trade and substantial population growth fuelled impressive economic growth.[5] For the emerging salaried middle class, the whole-of-life with-profit policy was a highly compelling composite of a short-term life assurance and a long-term savings vehicle. The Equitable was perfectly positioned to take advantage of this demand. The business of the Equitable exploded in scale over this period: between 1776 and 1800, the assets of the Equitable grew from ?42,000 to over ?1 million.[6]
The greatest challenges facing Morgan in the following decades were related to managing the consequences of this remarkable success. In particular, he was occupied with determining how to limit the number of new policyholders being admitted to the society so as to avoid ‘carpet-bagging’; ensuring an equitable distribution of surplus between the ‘old’ and ‘new’ members; and, more generally, managing the expectations of policyholders as to the amount of surplus that it was reasonable to distribute over time. In 1800, the society introduced two safeguards to over-distribution of surplus: bonuses would only be distributed once every ten years; and the present value of the size of the bonus should not exceed two thirds of the surplus assessed at that point in time. A further, rather more controversial safeguard was put in place in 1816: bonuses would only ever be applied to the oldest 5,000 policies of the society at the date of the bonus distribution. At the time of its implementation there were around 9,500 policies in-force.[7] This created a ‘waiting period’ for new policyholders before they were entitled to participate in any bonus distribution. Morgan expected at the time of the rule’s implementation that, based on historical discontinuance rates, this waiting period would be around five years. Whilst controversial at the time of its inception, this rule remained in place until 1893.
Thus, by the start of the nineteenth century, much of the actuarial ethos of with-profit management had fully emerged: Dodson, Price and Morgan had envisioned, analysed and implemented a financial product—the whole-of-life with-profit policy—that had radically reshaped life assurance as a product, business and important element of the financial sector. With William Morgan as the first role model, the actuary had emerged as a person of considerable power in a life assurance company: his considered judgement and detachment from short-term commercial pressure was required to determine equitable and prudent distributions of the surplus of a with-profit fund. Morgan was almost a caricature of this role: in later years, he would face much criticism for his near pathological prudence, resisting pressure from managers and members to reduce premiums or increase surplus distributions. Indeed, he felt compelled to defend his actions in a book that he published a year before retiring from his position as actuary in 1830, explaining in its Introduction:
It is indeed much against my inclination that I have engaged in the present work; but my anxious desire to justify the conduct of a Society for whose welfare I have laboured so many years, has impelled me to notice some of the misrepresentations with which it has been assailed, and, as the best refutation of them, to give a short history of the Society.[8]
Morgan’s time was many years before the introduction of financial regulators and statutory capital standards. There was perhaps less need for them when men like him were in the chair.
