The AI Journal

When the New York legislature’s Armstrong Investigation finished examining the life insurance industry in 1905, one of its clearest and most durable results was a ban: the sale of new tontine policies was prohibited outright, and none of the three companies at the centre of the inquiry, Equitable, Mutual, and New York Life, ever sold one again. A century later the verdict reads as settled. Tontines were a swindle dressed as insurance, killed off once regulators finally looked closely enough.

A tontine policy worked like this. A buyer paid ordinary life-insurance premiums for a fixed term, usually fifteen or twenty years. Instead of paying annual dividends out as they accrued, as a conventional policy did, the insurer accumulated them in a shared fund. Anyone who died during the term, or who let the policy lapse by missing a payment, forfeited their claim on that fund; what remained at the end of the term was divided among the policyholders who were still alive and still paying. The incentive the arrangement created, a direct financial interest in other people’s deaths and defaults, supplied the folklore that still attaches to the word, including the plot device that crime fiction has never tired of. Introduced in the United States in 1868, tontine insurance was within fifteen years the dominant form of ordinary life insurance the large companies sold (Ransom & Sutch 1987).

The economic-history reassessment of this episode is unambiguous about where the fault lay, and it is not where the folklore puts it. Roger Ransom and Richard Sutch, reworking the Armstrong-era evidence with the tools of actuarial analysis, found that tontine insurance was actuarially sound: the fund that financed it was correctly priced against the mortality and lapse experience the companies actually observed, and it functioned as an attractive form of life-cycle saving for the people who held it to term. Their conclusion is blunt: prohibition was probably unnecessary (Ransom & Sutch 1987). What Armstrong’s investigators actually documented was something narrower and, for the companies, more damaging: the surplus the tontine funds generated sat on company books for decades, undistributed, while management used it to finance expansion, pay inflated commissions, and misstate in sales illustrations what a policy was actually likely to pay out. The fraud Armstrong exposed was concealment and self-dealing in the administration of the fund. It was not a defect in the fund’s arithmetic.

That the whole episode is remembered as a verdict on the tontine as such obscures how recent and how narrow a slice of the device’s history it is. The mechanism is two centuries older than any American insurance company, and for most of that history it was a tool of sovereigns, not of salesmen. Lorenzo de Tonti, a Neapolitan banker, proposed the scheme to the French crown in the 1650s as a way to borrow cheaply: subscribers lent their capital in exchange for a share of a life-annuity fund, divided into age classes whose survivors received a rising income as fellow subscribers died, the whole arrangement extinguished when the last member of a class died. France used the device heavily through the following century; England adopted a version of it in 1693, under the Million Act, to help finance William III’s war against Louis XIV (Milevsky 2015). David Weir’s comparison of the two countries’ experience found that France leaned on tontines far more heavily than England did, and that the French crown paid, in effect, an above-market rate to borrow this way, a genuine cost to the issuing government, but a different cost from any of the ones that later sank the American product (Weir 1989). As a private instrument rather than a government one, the tontine had still another life: Kent McKeever’s history finds it operating as a respectable and widely used vehicle for private investment and civic development in the United States from roughly 1780 through the 1850s, well before the large insurance companies took up the structure and, as McKeever puts it, turned it into a sales gimmick and eventually a cover for fraud (McKeever 2009). Three different centuries, three different uses, and it is the last one, the shortest and least representative, that now stands in for the whole run.

The mortality-pooling logic that the American episode supposedly discredited has, in any case, had a long and serious second career. Moshe Milevsky’s history of the 1693 English tontine argues explicitly that its design logic, stripped of any insurance company sitting between the pool and its members, deserves reviving for retirement income today, precisely because a mutualised pool of survivors carries no counterparty whose balance sheet can fail the way an annuity guarantor’s can (Milevsky 2015). Milevsky and Thomas Salisbury worked out the underlying mathematics directly, modelling a fund that redistributes its own realised mortality experience among the living and comparing its performance against a loaded life annuity (Milevsky & Salisbury 2015). That a paper doing this kind of work exists, in a mainstream actuarial-science journal, is itself evidence that nothing about pooling survivors’ claims is inherently irrational. Nobody builds an optimisation model around a mechanism they consider a swindle.

Here the case needs narrowing, because Milevsky and Salisbury’s own result cuts against a stronger version of this argument. Their model shows that the classical design, no stated interest, pure pro-rata division among survivors, exactly the form King William’s government and the nineteenth-century American insurers both sold, is not the efficient choice for most savers. A loaded life annuity gives higher expected lifetime utility across most reasonable levels of risk aversion; the classical tontine only becomes the better bet in the limit as an individual’s fear of outliving their savings goes to infinity. Soundness, in other words, is not optimality, and nothing here licenses the claim that the historical product was the best available instrument for the people who bought it.

But that is a different claim from the one Armstrong’s legacy is actually built on, and the two should not have been merged in the first place. Actuarial soundness, in the sense that matters for a fraud inquiry, means a fund pays out what it collects, correctly priced, without the custodian skimming the difference; it says nothing about whether that fund is the wisest choice for a particular saver’s portfolio. Ransom and Sutch’s finding and Milevsky and Salisbury’s finding sit comfortably together: a tontine can be exactly as fair as its tables say and still be, for most people, a worse bet than an annuity. What ended the American product in 1906 was concealment of the first kind of fact, not failure of the second kind of judgement. Tellingly, every modern optimal-tontine design keeps the one feature the Armstrong investigators never actually impugned, a transparent pool whose own survivors divide its own experience, and discards the one feature they did impugn: a company standing between the pool and its members, free to misstate what the pool contained. The 1906 ban did not retire a bad idea. It retired a bad custodian, and left the idea waiting for someone willing to open the books.