7 ms·

Perpetual Bond

66 points by archielc 4y ago

OscarCunningham 4y ago
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'?
- OscarCunningham 4y ago
  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.
Animats 4y ago
"Never sell consols".
- fennecfoxen 4y ago
  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.
throwaway6745 4y ago
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.
- seoaeu 4y ago
  No, property is far more risky than that. However even if nothing goes wrong, revenue tracks local rents, not overall inflation
  - autosharp 4y ago
    (Local) rents track (local) inflation. So it does represent inflation.
    - ben_w 4y ago
      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.
      - autosharp 4y ago
        > 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.
bombcar 4y ago
Be perpetual bond (consul) Get redeemed anyway Surprised pikachu face Current “perpetual bonds” if issued would be inflated away eventually anyway.
rkagerer 4y ago
An example from the article of one of the oldest perpetual bonds still paying out: https://indroyc.com/2015/09/17/a-367-year-old-bond-still-paying-interest/ 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?
- barry-cotter 4y ago
  > 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-states-off-gold-standard https://www.history.com/this-day-in-history/fdr-takes-united...
  - rkagerer 4y ago
    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-golden-age-yale-s-367-year-old-water-bond-still-pays-interest 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.)
    - gpvos 4y ago
      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.
prionassembly 4y ago
Thus money and capital are different things with different cardinalities. (More: https://asemic-horizon.com/2021/07/31/zero-chroma-infinity/ https://asemic-horizon.com/2021/07/31/zero-chroma-infinity/ )
- skybrian 4y ago
  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.
  - karpierz 4y ago
    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.
    - deleted 4y ago
      [deleted]
    - joosters 4y ago
      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.
      - karpierz 4y ago
        Sure, I'm not trying to argue about how to appropriately price the rate; just that it's variable.
  - deleted 4y ago
    [deleted]
chillpenguin 4y ago
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.
- slavboj 4y ago
  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.
  - JumpCrisscross 4y ago
    > including the US, cf Roosevelt's abrogation of gold-denominated debt How is Roosevelt abrogating America’s gold standard a counterfactual to default risk?
    - milkshakes 4y ago
      https://en.m.wikipedia.org/wiki/Cf https://en.m.wikipedia.org/wiki/Cf.
      - JumpCrisscross 4y ago
        Whoops! Thanks!
- ohyoutravel 4y ago
  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!
zhenyakovalyov 4y ago
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).

66 points by archielc 4y ago

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'?

OscarCunningham 4y ago
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.

Animats 4y ago

"Never sell consols".

fennecfoxen 4y ago
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.

throwaway6745 4y ago

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.

seoaeu 4y ago
No, property is far more risky than that. However even if nothing goes wrong, revenue tracks local rents, not overall inflation
- autosharp 4y ago
  (Local) rents track (local) inflation. So it does represent inflation.
  - ben_w 4y ago
    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.
    - autosharp 4y ago
      > 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.

bombcar 4y ago

Be perpetual bond (consul) Get redeemed anyway Surprised pikachu face Current “perpetual bonds” if issued would be inflated away eventually anyway.

rkagerer 4y ago

An example from the article of one of the oldest perpetual bonds still paying out: https://indroyc.com/2015/09/17/a-367-year-old-bond-still-paying-interest/ 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?

barry-cotter 4y ago
> 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-states-off-gold-standard https://www.history.com/this-day-in-history/fdr-takes-united...
- rkagerer 4y ago
  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-golden-age-yale-s-367-year-old-water-bond-still-pays-interest 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.)
  - gpvos 4y ago
    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.

prionassembly 4y ago

Thus money and capital are different things with different cardinalities. (More: https://asemic-horizon.com/2021/07/31/zero-chroma-infinity/ https://asemic-horizon.com/2021/07/31/zero-chroma-infinity/ )

skybrian 4y ago
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.
- karpierz 4y ago
  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.
  - deleted 4y ago
    [deleted]
  - joosters 4y ago
    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.
    - karpierz 4y ago
      Sure, I'm not trying to argue about how to appropriately price the rate; just that it's variable.
- deleted 4y ago
  [deleted]

chillpenguin 4y ago

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.

slavboj 4y ago
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.
- JumpCrisscross 4y ago
  > including the US, cf Roosevelt's abrogation of gold-denominated debt How is Roosevelt abrogating America’s gold standard a counterfactual to default risk?
  - milkshakes 4y ago
    https://en.m.wikipedia.org/wiki/Cf https://en.m.wikipedia.org/wiki/Cf.
    - JumpCrisscross 4y ago
      Whoops! Thanks!
ohyoutravel 4y ago
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!

zhenyakovalyov 4y ago

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).