“Those who cannot remember the past are condemned to repeat it,” warned George Santayana (Reason in Common Sense 1905, p. 284). Moshe Milevsky wants us to remember a small bit of forgotten history precisely because he thinks we should repeat it.

The history he resurrects concerns the seventeenth- and eighteenth-century form of sovereign debt known as the tontine, named after its champion in the court of Louis XIV, Lorenzo de Tonti. Back then kings had to borrow to finance their wars. They might issue bonds that paid interest or sell annuities that promised higher annual payments but that would end when the lender died. Tonti's scheme was a twist on the life annuity. The interest payment on a tontine loan was paid, not to the individual subscribers, but to the subscribers as a group. That sum was divided each year among the group's surviving members. Heirs of those expiring had no claim on the payments. As a result, the annual payment to each recipient grew over the years as the number of survivors inevitably shrank. The last survivor received the entire annual interest payment due on the original loan. At the last death the principal reverted to the state.

The French, Dutch, and English governments used tontine loans multiple times in the seventeenth and eighteenth century to raise money. These schemes became famous for the large sums received by the last survivors (Kent McKeever, “A Short History of Tontines,” Fordham Journal of Corporate and Financial Law 15 no. 2 (January 2010): 491–521).

There are two ways to look at the public's attraction to tontine debt instruments. Adam Smith suggested that the tontine appealed to the gambling instinct; “from the confidence which every man naturally has in his own good fortune, the principle upon which is founded the success of all lotteries, [the tontine] annuity generally sells for something more than it is worth” (The Wealth of Nations, 1776, Volume 2, Book 5, Chapter 3, p. 548). Moshe Milevsky prefers to emphasize the advantage to the purchaser of the implicit longevity insurance—insurance against the risk of living too long (pp. 9–11). By either argument (and they are not mutually exclusive) the tontine will cost the treasury less. Tonti's scheme also had the advantage that the debt would be self-extinguishing. When the last participant died, the king had no further debt obligation.

Milevsky, a finance professor at York University (Toronto), is an expert on life-cycle finance (retirement, annuities, and such) and the author of several textbooks in the field. He is also an unabashed enthusiast for “tontine thinking.” The main point of his book is that tontine arrangements are an attractive way to spread longevity risk in modern retirement plans. They can be both efficient and fair. Milevsky also admits to a didactic purpose, educating the reader on such technical topics in finance and demography as present value, portfolio diversification, amortization, annuitization, option pricing, Monte Carlo simulation, Bernoulli utility functions, life-cycle models, probability density functions, mortality plateauing, and (in an appendix) the Gompertz law of mortality. All of these topics he [jokingly?] bundles into the self-christened science of “tontinomics” (p. 16).

Milevsky's specific contribution to the history of the tontine is to tell the story of King William III's tontine of 1693, better known to historians as the “Million Act,” after the sum it was intended to raise. MIlevsky provides an extended discussion of the mechanics, rationale, and arithmetic of tontine instruments (which I suspect will be essential background for many readers). For the most part these technical details are clearly and patiently explained, the best and most complete effort that I have seen. Chapters 3 through 6 trace the history of tontines and tontine-like financial instruments in the eighteenth and nineteenth century winding up with an “around-the-world tour” of modern tontines. Only three twentieth-century plans are described, those organized on Israeli Kibbutzim (pp. 130–34), the National Defined Contribution plan in Sweden (pp. 134–37), and the Glasgow Tontine Society (pp. 114–18). The latter is offered as an example of a private tontine loan syndicate. Milevsky waits until the final two chapters to offer his financial advice for future retirees.

The intricate details of King William's tontine of 1693, complete with a full list of the nominees and their ages, are based on Milevsky's research in British archives and described in rich and clear detail. He thinks they will prove “intriguing to anyone with a passing interest in finance or economics” (p. 60). They will no doubt be of interest to those curious about royal finances in the seventeenth century. Descriptions of other early tontine schemes are cribbed from secondary sources. For the French tontines and the biographical note on Lorenzo de Tonti, Milevsky relies on Robert Jennings and Andrew Trout (The Tontine: From the Reign of Louis XIV to the French Revolutionary Era, Richard D. Irwin 1982). A paper that I published with my colleague Roger Ransom is Milevsky's source on tontine insurance policies introduced in the United States by the Equitable Life Assurance Society (“Tontine Insurance and the Armstrong Investigation: A Case of Stifled Innovation, 1868–1905,” this Journal 47 no. 2 (1987)).

The historical chapters are breezy, written in a pell-mell style, and garnished with attempts at light humor (the emotionally detached and hyper-logical Mr. Spock is introduced to design the “optimal” tontine). There are pop references dating to the 1970s (M∗A∗S∗H, ABBA, The First Churchills, Barney Miller), and several arresting anecdotes. In one such aside, Milevsky suggests—with some support from the experts—that William Shakespeare was the recipient of a life annuity from a private tontine that grew from age 17 on, bestowed in gratitude for his performances as a “player” in a wealthy lord's household (pp. 39–40). Milevsky even speculates that Shakespeare was the last surviving member of the tontine class when he died at 52. The annual income from this pension began at two pounds a year and rose to £16.13s.4d for the last survivor. This handsome stipend, by Milevsky's account, financed the writing of the Merchant of Venice and the other plays and sonnets attributed to the Bard.

The effect of these stories when combined with Milevsky's obvious enthusiasm and voluble prose is to induce some cautionary skepticism. For example, almost every facet of Shakespeare's life is controversial. Consistency with the historical record, if the Bard's tie-in to the tontine is accurate, requires that Shakespeare was secretly Catholic, hired when still a teenager as a private tutor by Alexander Hougthton of Lancaster, and while in that employ went by the name of William Shakeshafte. This speculation, while intriguing, remains speculation. After some research, however, I am inclined to believe it. For me, the tale becomes even more fascinating and gains resonance from the banter of two of the players in Midsummer Night's Dream [act 4, scene 2]:

Six pence a day was (can it be a coincidence?) the distribution received by the antepenultimate survivor of Lord Hougthton's tontine. (On this topic see Stephen Greenblatt, Will in the World: How Shakespeare became Shakespeare, Norton 2004: 104–106; and Robert Bearman, “ ‘Was William Shakespeare William Shakeshafte?’ Revisited.” Shakespeare Quarterly 53 no. 1 (Spring, 2002): 83–94).

Milevsky's colloquial style might be off-putting to some and his attempts at broad humor often fall flat (or worse), at least for me. King Charles II, with a dozen mistresses and twenty illegitimate children, is described as the Bill Clinton of the late seventeenth century (p. 2). Israelis living on Kibbutzim are described as routinely “sharing spouses and lovers” as well as their wealth. This is irrelevant, even if true. Yet the claim is repeated three times in an effort to amuse or titillate (p. 131 and twice on p. 133).

Milevsky explains what he is trying to achieve with his spirited romp through history.

The tontine's reputation, he fears, needs rehabilitation. Previous accounts denounced the immorality of gaining from another's death. But, of course, anyone who receives a bequest by will or probate benefits from another's death, so that argument seems lame. Others have claimed tontines were an inducement to murder. Certainly a lucrative tontine has served as a plot device for many writers including Robert Lewis Stevenson (The Wrong Box, with Lloyd Osbourne, 1889) and Agatha Christie (What Mrs. McGillicuddy Saw! [US Title], 4:50 from Paddington [UK title], 1957). Crime novels aside, Milevsky insists that he “couldn't find any story or account of nominees in a tontine pool trying to murder another member of the pool” (p. 81). Other critics have sided with Adam Smith and denounced them as “lotteries.”

For modern-day retirement schemes Milevsky proposes an investment pool that shares longevity risk. All members are to be close in age and in comparable health. The payments of income from the investments are made to the pool to be distributed to survivors as in the classic tontine. But these payments are designed to decline over time in such a way that—if the actuarial assumptions prove accurate—the payment to each surviving member would be constant over the years. The declining investment payments would closely offset the rising “mortality credit” as the group inherits the shares of those who die. Since the annual income of recipients is roughly constant, there is no incentive to murder. The scheme would have an agreed life—say twenty years. Before that closing date is reached the fund would also begin to liquidate and distribute the principal, but still in such a way that the total payouts would remain relatively constant. There would be no dramatic payments to the last survivors, eliminating any lottery effect.

His scheme is similar, as Milevsky generously notes, to proposals that others have made to pool and share longevity risk while avoiding some of the problems and optics that make straight annuities unattractive. Milevsky prefers his proposed arrangement because it makes the mortality credit visible and linked to protecting the members' retirements. It frontloads the return on the members' investment. The principal is not captured by an insurance company (or the government) at their death. These arguments are persuasive. The scheme has much to recommend it, yet surprisingly Milevsky has little to say about how to, or who would, implement it. He is content to advise readers to wait patiently. Apparently, the invisible hand will unclench it in short order.