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Faculty Viewpoints

What is a long life worth?

A document from 1787 Holland lists the names of girls whose income from government annuities was pooled and securitized, allowing investors to essentially bet that the girls would live a long time. Yale SOM Professors Will Goetzmann and Geert Rouwenhorst discuss how this novel financial device functioned and how it fits in the story of the development of more and more sophisticated securities.

  • William N. Goetzmann
    Edwin J. Beinecke Professor of Finance and Management Studies & Director of the International Center for Finance
  • K. Geert Rouwenhorst
    Robert B. and Candice J. Haas Professor of Corporate Finance & Deputy Director of the International Center for Finance

Q: For the uninitiated, this type of security can seem downright weird. People create a fund based on the long life expectancy of well-to-do girls. Can you explain how this security works?

GR: To understand it, you should understand how governments borrowed in the 18th century. It was often done in the form of annuities. These were securities with a flexible maturity. The government would borrow from you, and they would pay you an annuity for the rest of your life — or more precisely, the life of the person named on the security, who could be someone different from you. However, when these annuities were introduced, the mathematics of life expectancy hadn't really developed very well, so governments didn't quite know how to price them and, as a matter of fact, they offered the same terms to everybody, regardless of age. Because younger persons have higher life expectancies, the promised payouts to the young should be lower than the payouts to the old. But since the government didn't differentiate, the bonds could be much more valuable for a young person than the old. Not surprisingly, what happened is that people would show up at city hall to buy annuities in the names of their children or grandchildren.

But here is where things get interesting. Despite the higher life expectancy, there was still, of course, a chance that the child would die young. Enter the investment bankers. First in Switzerland, and later in Holland, bankers set up funds which pooled these annuities on the lives of young girls who had already survived smallpox, and sold fund shares to the public. So now, as a shareholder in that fund, you would hold a diversified portfolio of annuities, and the risk of any of the girls dying young would be diversified away, and you would almost lock in this mis-pricing of the annuities by the government. Why girls? I am not sure. It was probably a tradeoff between the risks associated with childbirth and the risk of having to go to war.

Q: It sounds like a great idea. But were there any drawbacks?

GR: Not really. The potential drawbacks were merely psychological. Holding a portfolio of such annuities means that your cash flows would diminish over time as the nominees decease. There is not a lump-sum payment at the end where you get your money back. The bankers fixed this by initially holding back some of the income from the securities and reinvesting it in the fund. Say that the annuities were going to be paid at 5%. Then the dividends passed along to shareholders would be about 4%. The capital would build up in the fund to compensate for the fact that these securities themselves would, one by one, disappear. So at the end of a 25-year term, there still would be enough capital to give people their initial investment back.

WG: Is that not almost a pure use of the Central Limit Theorem?

GR: Yes it is. It is really trying to diversify idiosyncratic risk.

WG: Jacob Bernoulli basically developed the Central Limit Theorem around the end of the 1600s and the beginning of the 1700s, where he argued that he could specify the probability that a random event would fall outside of a certain number. And these securities are examples of the application of that concept.

Bernoulli's work began to appear just after 1700, especially his proof of the Law of Large Numbers. People in Basel — he had relatives in Basel — knew about it at that time. He demonstrated that, for a large enough number, n, the proportion of black and white balls in a given urn will converge to a measurably close approximation to the actual proportion. So, when you look at this security, the idea is to get a large n, right? And then if some of the people are going to be long-lived and some are going to be short-lived, you're going to converge to a predictable age. So this is a really revolutionary structure. This shows that people were tied into this mathematical knowledge which says, "How big does a sample have to be in order for the number to converge to the predictable proportion?"

Q: Tell us about the document itself. How is the fund put together?

GR: If you look at the document you can see clear patterns emerge. The person who created the fund had to be able to verify that each girl was still alive, so he had to know them. So you've got two Nepveus here, Elizabeth and Marguerita. Here's an Akhout. Here's another Akhout. Here, this is Clausina Elizabeth Voomberg. Voomberg was a very prominent financial family, involved in organizing the depository receipt market in the 19th century. Here's another Voomberg, Johanna Elaida Voomberg. Here's a Kleinpenning, there is a Kleinpenning. There is a Nobel here. So you see? They're all between three and eight years old. They're all from prominent Amsterdam families who know each other. In a way, it's a type of social registry.

Q: How many girls were in the fund?

GR: There were sixty names in all, but one of the girls — Elizabeth Judith de Freese — died just before they started selling shares in the fund. Kind of sad, don't you think?

Q: It seems that once governments figured out how to price annuities based on the age of the person, this type of fund loses its appeal. But this idea of betting on the length of human life — are there any analogies today?

WG: As a matter of fact, there is now a big trend, among not-for-profit institutions, for them to buy life insurance on members of their board. They make the periodic payments themselves and then they reap the rewards when the person dies. But, again, it's borrowing a human life to contract on, to create a financial instrument. There's this tie-in to the uncertainty of the duration of human life, and the willingness to bet on survival is alive and well.

Q: This security is Dutch. What was the financial environment like then?

GR: The 17th and 18th centuries were an amazing time for financial innovation in the Netherlands. Many of the financial structures that we know today, basically, emerged from the 17th-century Netherlands, among which are mortgage-backed securities, mutual funds, and depository receipts, which were actually a little bit later. They were developed in the early 19th century.

What people learned how to do was to securitize, to create liquid securities from illiquid claims. For example, the mortgage-backed securities came about through the financing of the slave trade, a dark period in world history. Merchant bankers in Amsterdam would make mortgages to the plantations in the West Indies, and as their return — as part of the triangular trade which involved the slaves — planters would essentially send their products to Western Europe to be sold. Rather than put up their own money to finance these mortgages, these merchant bankers, who were truly merchants and bankers, would issue securities in the Dutch capital markets that were backed by payments on these mortgages in the West Indies.

Turning again to this document, it shows that during this period people discovered how to increase the scope of capital markets. The range of investments increased, and people learned how to diversify. The prospectus of one of the early mutual funds literally stated that it is not prudent to allocate all your capital to a single security, and that it would be unlikely for all securities in a fund to cease payment at the same time. All these things happened in the 18th century, in Holland. So it was, in many ways, a very remarkable time in the history of the capital markets.


Will Goetzmann and Geert Rouwenhorst discuss other types of historical securities they've studied.


Rouwenhorst: Tontines are annuities issued to groups. They're named after Lorenzo di Tonti, an Italian who was an advisor to the French court in the 17th century. In a tontine, the government borrows from a group and makes interest payments to the group until the last person dies. And the group gets to divide the interest on the capital among the surviving members. As people in the group die, the payout to each remaining individual goes up. Fewer members of the group equals more money for each. That's why tontines feature in crime novels. Tontines were also organized privately by individuals to pool assets and insure each other against outliving their means. In this way tontines are a predecessor of life insurance and modern pension funds.

The Perpetual Bond

Rouwenhorst: A perpetual bond is one that theoretically pays interest to the bearer forever. But there are very few perpetuities around, since at one time or another most governments that issued them defaulted on the payments.

We have a perpetuity from Holland that was issued in 1648 and is still paying interest. It was issued by a water board, which is a semi-public organization in Holland. They were instituted for water-management reasons and their origins back to at least the 13th century. Because state boundaries don't necessarily overlap with the flood-plains of rivers, states would get together with provinces and towns to set up organizations that managed the dikes. There were hundreds of them, which over time merged into a few large ones. These boards had many of the powers of the state, in the sense that they had a power of taxation and they could borrow. And they could draft people into an army, called the dike army — in the case of a break of a dike, you were drafted to work to repair the dike.

Normally this maintenance would be paid out of the taxes that were levied on the people protected by the dike. But in very unusual circumstances, if there was a large breach, the organization itself would borrow and would issue bonds. And we have one of those bonds that was issued in 1648, when there was an unusual amount of flooding in that particular area. It's a 1/8th kilometer section of dike somewhere south of Utrecht.

Water boards never go to war, so as entities they survived a lot longer than most governments. So the securities have survived. I bought this bond in 2003 at an auction on behalf of Yale. When I picked it up, we realized the interest had not been collected since 1975, so I made arrangements with the auctioneer that he notify the water board of my intention to collect interest on the security. The security was originally for 1,000 Carolus guilders, at 5% per year, so that would be 50 guilders per year. The Carolus guilders became gold-coin guilders which became guilders and eventually became Euros, and in the meantime there had been a partial adjustment of the interest rate to 2.5% so, to make a long story short, my 25 guilders per year became 11 Euros per year. So multiplying it by about 28 years that I went back, I collected something about 300 Euros from the water board on behalf of Yale.

Forced Loans

Goetzmann: The remarkable thing that set Europe apart from other parts of the world was the existence of capital markets, very early on.

Venice was constantly at war with Genoa and Pisa and Byzantium, and it had to mount fleets all the time. The way they financed those fleets was by forcing their citizens to buy bonds. The citizens had to lend money. These were forced loans. The richer you were, the more you had to loan. The government paid you back at 5% per year interest. These were perpetuities. And they allowed people to trade the bonds. So a market developed right at the Rialto bridge in the middle of Venice. Right at the base of the bridge is a little campo, with a church and everything, surrounded by money exchanges and bankers. This started in the late 1100s, and by the middle of the 1200s it was a very well-developed market, where you could buy bonds, you could sell bonds, you had banking services where you could keep money in a bank and say "pay my dividends into my bank account." This allowed the middle class to have a form of wealth that was not tied to land, and a form of wealth that was not really tied to being an entrepreneur and having to be an active participant in a business venture.

All the Italian city states saw what Venice and also Pisa were doing and realized they needed to do the same thing. It was like an arms race, only it was a financial arms race. All these cities created, in essence, a permanent debt, just like the United States has. That's where the idea came from. And it meant that there had to be a permanent market for all of that debt that went along with the financing. When you think about the 1100s, 1200s, 1300s, they became a period of growth out of feudalism, and the creation of a free people who were able to live in a city. This created social mobility, because you could amass this kind of wealth. A new form of society appeared because governments were weak and had to borrow money. This shifted power to the people and the markets.

View more historical financial documents at the International Center for Finance.

Interviewed by John Zebrowski

Department: Faculty Viewpoints