|Johan de Witt - The first calculation on the valuation of life annuities||MacTutor Index|
(An important contribution to insurance mathematics)
It is debatable whether or not de Witt was correct in promoting life annuities as his favoured finance instrument.
On the one hand, he was right in pointing out several advantages of such annuities, both to buyers and sellers. Buyers could rely on a steady income of money over an undetermined span of time, they faced advantageous rates compared to other financing options, and the income from annuities was non-taxable (de Witt, 1672). For the government, it was an uncomplicated and timely way of raising funds, and the obligation to pay ended completely at the time of the life's death.
However, de Witt fails to point out any disadvantages of life annuities. For the buyer, it came with an obligation to prove that the life was still alive. The only accepted form of proof was an "attestatie de vita", which had to be obtained from the city hall in exchange for a fee (Bovers, 2009). In addition, should the buyer want to transfer the annuity to a different annuitant, a transfer tax applied (Dormans, 1991). This, along with the required proof of life, made annuities rather illiquid (Weir, 1989). This also meant that there was no lively secondary market for life annuities like the one that existed for redeemable annuities and bonds (Gelderblom et al., 2011). This was in the interest of the government, which could retain more direct power on the life annuities market, but more tradable and liquid instruments were generally preferred by the public. The return of the annuity was dependent on the life span of the person it was written on, which was subject to several exogenous factors and meant that the principal payment was not necessarily returned in full. On the other side, it could also be the case that effectively more than the initial payment was returned. As mentioned before, inflationary effects also played a role for the value of the annuity to the buyer.
It should be acknowledged that annuity holders chose this particular instrument for various reasons. For the majority of buyers, it was a financial investment that was intended to maximise profits and generate optimal income flows. This group of annuitants generally selected young lives to increase the likelihood of survival, and rarely self-selected. In the Seven Provinces, less than 20% of nominees were older than 20 years old, demonstrating that buyers were generally aware of higher survival chances for younger ages (Poitras, 2000). Geographically, Hup (2011) analysed that urban areas generally invested smaller amounts, mainly due to income disparities between city and countryside. He also points out that urban areas like Amsterdam and The Hague buy annuities for profit-maximising and investment motives more so than rural areas. In non-urban areas of the Provinces, self-nomination was more common, which presents a buy motive other than profit-maximisation. This group of buyers was looking for a steady income with an insurance aspect at older age, instead of riskier investment on other nominees (Rothschild, 2003). Interestingly, in the data analysed for his paper, Hup (2011) finds that most self-nominating annuity holders were female, contrasting the general market trend. Another finding about self-nomination is the age gap of nominees. Lives written on annuities were of an average age of 12 years, whereas self- appointed nominees averaged 34 years (Hup, 2011). Hup finds that life annuities excluding self-nomination lasted for around 42 years before expiring, while self-nominated ones only did so for 29 years.
This leads to a crucial point of consideration. The length of time that annuities ran for and hence signified periodical government expenses in the period, show how costly annuities were for the state. For the data analysed in his thesis, Hup (2011) concludes that more than 87% of annuities had a negative net present value with an average loss of almost 800 guilders, while the ones with positive net present value only averaged slightly more than 1100 guilders. Even the self-nominated annuities with shorter running times resulted in a loss of nearly 50% for his data.
It is interesting to see that de Witt did not point at any of these considerations. His calculations were a significant starting point for the valuation of life annuities, and an analysis of the actual gains and losses for the state would have been a natural extension of his mathematical considerations. Whether he had this in mind or not, it also needs to be made explicit that for a government, profits do not always play a dominant role. At the time of his presentation in front of the state ministers, there was a need for a rapid and sizeable acquisition of a war budget, and annuities were a very convenient way to achieve this objective. The immediate needs of a nation might have been of more significance than future investment strategies with the aim of a profit. Hence, it ought to be distinguished between the aims and motives of private investors as opposed to public ones. Even though registers of life annuity holders and the length of their acquisitions were kept, a comprehensive analysis of their profitability was unbeknownst. It is likely that the state was simply not aware of its losses through this financial investment, may it be due to uncontested belief in its advantages, or diluting effects of inflation, or a time horizon too long to uncover dramatic shortcomings.
Nevertheless, de Witt's advances cleared the way for considerations as the ones above, since such an analysis would have simply not been feasible before.
(An important contribution to insurance mathematics)