Perpetual Bond(en.wikipedia.org)
en.wikipedia.org
Perpetual Bond
https://en.wikipedia.org/wiki/Perpetual_bond
34 comments
> How's that work? Did the bondholder agree to new terms or did the issuer just unilaterally "change" them?
The government can always unilaterally change the terms. That’s the defining feature of a government, the monopoly on the legitimate use of force. See when the US went off the gold standard [1].
[1] https://www.history.com/this-day-in-history/fdr-takes-united...
The government can always unilaterally change the terms. That’s the defining feature of a government, the monopoly on the legitimate use of force. See when the US went off the gold standard [1].
[1] https://www.history.com/this-day-in-history/fdr-takes-united...
But it's not government issued (or at least not by any "federal" level agency).
Per https://news.yale.edu/2015/09/22/living-artifact-dutch-golde...
The bonds were issued by the Hoogheemraadschap Lekdijk Bovendams, a water board composed of landowners and leading citizens that managed dikes, canals, and a 20-mile stretch of the lower Rhine in Holland called the Lek. (Stichtse Rijnlanden is a successor organization to Lekdijk Bovendams.)
Per https://news.yale.edu/2015/09/22/living-artifact-dutch-golde...
The bonds were issued by the Hoogheemraadschap Lekdijk Bovendams, a water board composed of landowners and leading citizens that managed dikes, canals, and a 20-mile stretch of the lower Rhine in Holland called the Lek. (Stichtse Rijnlanden is a successor organization to Lekdijk Bovendams.)
Water boards are an actual layer of government in the Netherlands, they levy taxes and there are elections for them. I don't know their exact powers regarding contracts.
> Dutch water boards had relative financial autonomy, which protected them from falling fortunes of the central government and allowed the securities that they issued to survive. The lives of perpetual loans typically were “cut short by imprudent financing, government recall, or the misfortunes of wars and revolutions,” Rouwenhorst and Goetzmann write.
https://news.yale.edu/2015/09/22/living-artifact-dutch-golde...
https://news.yale.edu/2015/09/22/living-artifact-dutch-golde...
The rule of law applies to a government as well as any other body, organization, firm or person.
That's the most fundamental difference between a democratic country and authoritarian & tyrannical regimes.
You can sue the US government in US courts and to some extent in international courts.
Not that democratic governments don't abuse their power. They do quite regularly, but still: even their use of force is limited by the law.
That's the most fundamental difference between a democratic country and authoritarian & tyrannical regimes.
You can sue the US government in US courts and to some extent in international courts.
Not that democratic governments don't abuse their power. They do quite regularly, but still: even their use of force is limited by the law.
The TLDR for how a bond that continues to pay interest forever can be valued at less than infinity dollars is due to the "time value of money", which states that $X in the future is worth less than $X today. This makes sense intuitively if you consider that if you had that money today, you could invest it and earn interest on it.
So since money in your hands is worth more than that same amount of money in the future, you can actually calculate how much a future cash flow is worth today by discounting it to its present value ("discounted cash flow" aka DCF).
To bring it back to perpetual bonds, if you DCF all of the future cash flows to their present value, you actually get a finite number (due to the diminishing nature of the cash flows that are further and further in the future).
For those who want to learn this in more detail, I recommend MIT's OCW course "Finance Theory I" with Andrew Lo.
So since money in your hands is worth more than that same amount of money in the future, you can actually calculate how much a future cash flow is worth today by discounting it to its present value ("discounted cash flow" aka DCF).
To bring it back to perpetual bonds, if you DCF all of the future cash flows to their present value, you actually get a finite number (due to the diminishing nature of the cash flows that are further and further in the future).
For those who want to learn this in more detail, I recommend MIT's OCW course "Finance Theory I" with Andrew Lo.
Default risk (either outright or de facto) is also extremely present. Most countries (including the US, cf Roosevelt's abrogation of gold-denominated debt) have defaulted at various times.
> including the US, cf Roosevelt's abrogation of gold-denominated debt
How is Roosevelt abrogating America’s gold standard a counterfactual to default risk?
How is Roosevelt abrogating America’s gold standard a counterfactual to default risk?
You don't need the concept of "time value of money" to value a perpetual stream of payments.
Intuitively, only a sucker would pay $1,000,000,000,000 for the promise of $1 per year in perpetuity, even in the absence of discounted cash flows.
Intuitively, only a sucker would pay $1,000,000,000,000 for the promise of $1 per year in perpetuity, even in the absence of discounted cash flows.
Thanks for the explanation, I saw the formula in the OP for pricing it and it seemed like using that simple formula, the price should be infinity. I came to ask about that and your comment answered the would-be question. Thanks!
> seemed like using that simple formula, the price should be infinity
Deriving the value of a perpetuity is simple but revealing [1].
[1] http://fahmi.ba.free.fr/docs/Courses/2012%20HEC/FBA_FE_Chap1...
Deriving the value of a perpetuity is simple but revealing [1].
[1] http://fahmi.ba.free.fr/docs/Courses/2012%20HEC/FBA_FE_Chap1...
there is nothing scary in the concept of perpetuity when it comes to bonds. the experts may correct me, but I would think that a comparable instrument to this would be a preferred stock: you do not have voting rights, you agree to receive a fixed rate until the issuer buys back or goes bankrupt.
where they may differ - liquidation preferences (I would assume that bonds pay first) and taxation on proceeds (depends on your country of residence).
where they may differ - liquidation preferences (I would assume that bonds pay first) and taxation on proceeds (depends on your country of residence).
Property giving rent is behaves a inflation adjusted bond - in the long run the rent will increase along with inflation, while the coupon payment of perpetual bond stays constant (reduces in value due to inflation over time). Both perpetual bonds and property price will increase when interest rates fall.
No, property is far more risky than that. However even if nothing goes wrong, revenue tracks local rents, not overall inflation
>> No, property is far more risky than that. However even if nothing goes wrong, revenue tracks local rents, not overall inflation
Nothing truly "tracks inflation" because inflation itself is a highly debated figure which depends on who calculates it and how it is calculated. It isnt some scientific constant to which we can track.
Nothing truly "tracks inflation" because inflation itself is a highly debated figure which depends on who calculates it and how it is calculated. It isnt some scientific constant to which we can track.
(Local) rents track (local) inflation. So it does represent inflation.
To an extent, but not immediately and not perfectly — I’m a landlord, the rent I get from my property in the UK actually went down recently despite UK inflation being 7%. (FWIW this is probably a good thing for the UK as a whole even if it’s not so good for me: “rent extraction is bad” is one of the things where Adam Smith agrees with Karl Marx).
More relevantly if you want to use it as a passive source of income, in the long term you need to worry about war or terrorism destroying your property, even if your property is in a powerful nation. For example, my dad was born just before the British joined WW2 and was temporarily relocated to Wales, my mother was born during it and her earliest memory was using the kitchen table as an air raid shelter — and the British Empire was still a genuine world power back then. (And yes, both were British).
Likewise, governments and businesses may follow economic policies that reduce the economic productivity of the area in of the property: in the UK, there is the Welsh town of Merthyr Tydfil, which went from a wealthy steel producing area at its peak to one of the poorest areas with the cheapest homes in the UK in the late 2000s. Even if you’d lived in Merthyr Tydfil from its best days to its worst and therefore influenced by the local (as opposed to national) inflation rate, you’d have been made worse off by its decline.
Such booms and busts from economic shifts can be found worldwide and throughout history, just as outright destruction from war.
More relevantly if you want to use it as a passive source of income, in the long term you need to worry about war or terrorism destroying your property, even if your property is in a powerful nation. For example, my dad was born just before the British joined WW2 and was temporarily relocated to Wales, my mother was born during it and her earliest memory was using the kitchen table as an air raid shelter — and the British Empire was still a genuine world power back then. (And yes, both were British).
Likewise, governments and businesses may follow economic policies that reduce the economic productivity of the area in of the property: in the UK, there is the Welsh town of Merthyr Tydfil, which went from a wealthy steel producing area at its peak to one of the poorest areas with the cheapest homes in the UK in the late 2000s. Even if you’d lived in Merthyr Tydfil from its best days to its worst and therefore influenced by the local (as opposed to national) inflation rate, you’d have been made worse off by its decline.
Such booms and busts from economic shifts can be found worldwide and throughout history, just as outright destruction from war.
> in the long term you need to worry about war or terrorism destroying your property
True, although in that case you continue to own the land.
On the other hand, countries also default. So the question is which one is more common. E.g. Argentina used to be a serious economic force with 5% of world GDP. Owning property there (even with all the violence) may have been safer going through the series of government defaults. Greece, Cyprus, Russia, too.
Rent doesn't have to be all from buildings. You can combine with farm and forest to be even more resilient. Low leverage also adds to your ability to recover.
> Even if you’d lived in Merthyr Tydfil from it’s best days to its worst and therefore influenced by the local (as opposed to national) inflation rate, you’d have been made worse off by its decline.
I promise you that back then, people spent between 10% and 50% of their income on rent, as they have done forever, and continue to do today.
You happen to track a declining area. If the area had seen 10x more development, rents would have developed by that order of magnitude.
True, although in that case you continue to own the land.
On the other hand, countries also default. So the question is which one is more common. E.g. Argentina used to be a serious economic force with 5% of world GDP. Owning property there (even with all the violence) may have been safer going through the series of government defaults. Greece, Cyprus, Russia, too.
Rent doesn't have to be all from buildings. You can combine with farm and forest to be even more resilient. Low leverage also adds to your ability to recover.
> Even if you’d lived in Merthyr Tydfil from it’s best days to its worst and therefore influenced by the local (as opposed to national) inflation rate, you’d have been made worse off by its decline.
I promise you that back then, people spent between 10% and 50% of their income on rent, as they have done forever, and continue to do today.
You happen to track a declining area. If the area had seen 10x more development, rents would have developed by that order of magnitude.
> I promise you that back then, people spent between 10% and 50% of their income on rent, as they have done forever, and continue to do today.
We agree on this.
I’m just saying that that the economy immediately surrounding the property isn’t necessarily the one driving the landlord’s costs or lifestyle. It certainly isn’t in my case.
We agree on this.
I’m just saying that that the economy immediately surrounding the property isn’t necessarily the one driving the landlord’s costs or lifestyle. It certainly isn’t in my case.
"Never sell consols".
Eh. Take a look at the antique bond on goatskin parchment that financed a whole dike, now paying a mere €11.35 a year, valued only as a curiosity.
Value it based on the discounted future income stream like everything else. Sell if offered a price above that. Buy if offered a price below. It’s great to avoid reinvestment risk but inflation risk is real.
Value it based on the discounted future income stream like everything else. Sell if offered a price above that. Buy if offered a price below. It’s great to avoid reinvestment risk but inflation risk is real.
Thus money and capital are different things with different cardinalities. (More: https://asemic-horizon.com/2021/07/31/zero-chroma-infinity/ )
That's just confusion about discount rates.
Money in the future is worth less than money in the present, so an infinite sequence can have a finite sum when it's priced in today's money.
Money in the future is worth less than money in the present, so an infinite sequence can have a finite sum when it's priced in today's money.
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That is true, but the pertinent question is: how much less?
If the world is ending tomorrow, then much less. If we discover immortality tomorrow, then much more.
If the world is ending tomorrow, then much less. If we discover immortality tomorrow, then much more.
How does immortality affect the discount rate? Just because you or I will die, doesn't stop our heirs (or companies) from collecting income from assets.
I'd suggest that discovering immortality might have the opposite effect, it would only bring more uncertainty about the future.
I'd suggest that discovering immortality might have the opposite effect, it would only bring more uncertainty about the future.
Sure, I'm not trying to argue about how to appropriately price the rate; just that it's variable.
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It's a shame they don't still sell these. They're so much simpler than a bond with a coupon and principal. Was the reason they stopped just because people mistakenly thought that they were 'infinite debt'?
Actually, consols were more complicated than I imagined. They were 'redeemable at the option of the government'. So they're not just a simple income flow; they're some form of option.
Be perpetual bond (consul)
Get redeemed anyway
Surprised pikachu face
Current “perpetual bonds” if issued would be inflated away eventually anyway.
Get redeemed anyway
Surprised pikachu face
Current “perpetual bonds” if issued would be inflated away eventually anyway.
https://indroyc.com/2015/09/17/a-367-year-old-bond-still-pay...
It's written on goat skin and must be physically presented in the Netherlands to collect interest of 11.34 euros per year.
Yale University bought it in 2003 for 24,000 euros.
One part I don't understand:
According to its original terms, the bond would pay 5% interest in perpetuity, although the interest rate was reduced to 3.5% and then 2.5% during the 18th century.
How's that work? Did the bondholder agree to new terms or did the issuer just unilaterally "change" them?