explored. The broad pattern observed in his accounts is that of slow accumulation of very secure government bonds. However, although he was not a frequent trader, he did engage in some complicated moves that would require more work to understand. No attempt is made in this article to explicate those, or to evaluate his entire investing career. Instead, two cases are examined in which he did risk-free arbitrage. These examples demonstrate that even in the world’ s most sophisticated market of the time, opportunities for such arbitrage did surface— often the result of financial innovations by the government— and that there seemed to be some reluctance on the part of ordinary investors to take advantage of them.
Financial Innovations and Unsophisticated Experts
Novel financial instruments often surprise their inventors with the ways they end up used and abused. This is true today, and it was true centuries ago. The only difference is that the level of sophistication of both the securities and the people dealing with them were lower in earlier times.
Richard Price was a famous philosopher, mathematician and demographer of the late 18th century. However, the Sinking Fund( which repurchased in the market government bonds) and his faulty Northampton Tables of Mortality led to substantial losses to tax-payers. Those losses were not stopped until the late 1820s.
In 1829, the British government restarted sales of life annuities, using correct mortality tables. The new tables were sound, but the pricing of the life annuities did not take into account adverse selection. The rules allowed for the purchase of annuities for the life of any person— even individuals unrelated to those purchasing the policy— and up to the age of 90. Therefore, some enterprising people purchased annuities for the lives of elderly individuals who were in excellent shape and lived in healthy parts of the country. Reportedly, in many cases, they even provided extra care for the nominees, to prolong their lives. This led to substantial losses to the taxpayer and— although the government periodically tightened the rules— investors found ways to keep profiting.
A related government mispricing led to Turner’ s gains. In November 1829, as the government started selling the new life
Self-portrait of Joseph Mallord William Turner, oil on canvas, 1798.
annuities, it also offered investors terminable annuities. Today, the actuarial term for these is“ annuities certain,” and they consist of a fixed number of equal payments in return for an initial lump sum. At that time, the GDP of Great Britain( so excluding Ireland) was approximately £ 400 million, with a population of about 16 million. The national debt was around £ 800 million, so about twice the GDP( or somewhat less if we include Ireland); almost all of it consisted of perpetual annuities. Those could not be cashed in by investors, only sold on the open market, but the government could call them in at their par value. The largest of those were the famous Consols, and they formed about half of the total debt. Paying just the interest on all the annuities consumed about half of the national budget.
In 1829, in addition to Consols and other perpetual annuities, there were the aforementioned life annuities and some terminable annuities. The largest of the latter were the long annuities( LA). They paid interest twice a year, on April 5 and October 10, through October 1859, with a final quarter-year payment on January 5, 1860. In 1829, paying them cost the government £ 1.36 million per year. £ 1 per year of LA was valued in the market at about £ 19, so LA in total were worth about £ 25 million, or roughly 3 % of the national debt.
On Monday, November 23, 1829, the government started selling new terminable annuities. Those annuities could be for essentially any number of years, and they paid interest on the same dates as LA. In particular, they could be bought for 30
years, with the last payment due on October 10, 1859, and they will be referred to here as TA. They were to expire at almost the same time as LA, except that LA had that final £ 0.25 payment coming on January 5, 1860, a payment that was worth about £ 0.10 in 1829. The £ 0.10 was about 0.5 % of the LA price in 1829, so this made a nontrivial difference, although not enough to destroy the rationale for the arbitrage to be described. As is shown by the ledger C73 / 14 in the Bank of England Archive( which is the basis for most of the evidence for this article), practically all of the new terminable annuities sold through January 5, 1830 were TA. And almost two-thirds of them were purchased by exchanging LA for them.
The intention of Parliament was that the new terminable annuities would be purchased primarily by exchange from perpetual annuities. This resulted from an almost universal( but fallacious) notion prevailing at that time that the best way to force Parliament to reduce the gigantic national debt was to move from perpetual to terminable annuities.
Although the intention was to sell the new annuities in exchange for perpetual ones, the published rules allowed them also to be sold by exchanging LA for them. Further, the interaction of LA market prices and the price tables meant that there was a clear gain by swapping LA for TA. On the first date of sales, Monday, November 23, 1829, there were three purchases of the new annuities— all of TA, and all by exchanging LA for them. All three buyers were members of the London Stock Exchange. One of them exchanged £ 289 per year of LA for £ 300.15 per year of TA, so a gain of 3.86 % nominally, as was usually reported in the press, but really more like 3.4 % if one takes into account that stub payment of £ 0.25 that was due on LA on January 5, 1860.
This was a totally risk-free exchange, one stream of payments from the British government for another, almost identical, and did not require any fees. All an investor had to do was to appear in the appropriate office, sign the papers, walk two blocks to the Bank of England to carry out the transfer of LA to the government and then go back to complete the transaction. The next day, The Times of London reported this exchange with some incredulity, as a rumor that was hard to believe. But the next day it confirmed that there was, in fact, free money to be had.
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