5 ms·

Perpetuities are a great idea. One of their advantage is that new debt issues are fungible with old debt issues (provided the coupon payment dates debt align).

Perpetuities are a great idea. One of their advantage is that new debt issues are fungible with old debt issues (provided the coupon payment dates debt align). The downside of that is that the duration of such a bond is fixed and depends on the prevailing interest rates. However, one can issue a perpetuity where the coupon is set to decrease (or increase!) geometrically over time. Different issue of such bonds are still fungible (provided they use the same rate of exponential decay), but their duration can now be tuned at will, by changing the characteristic time of the exponential. Why does this matter? There is a large market in government bonds (particularly in the US) and this market places a large premium on the latest issued bonds, or "on-the-run". This is because these bonds enjoy the most liquidity and can be used as alternatives to cash. The premium disappears as the bond is replaced with a new issue. Real economic value is being destroyed because the bonds aren't fungible. Perpetuities with exponentially decreasing coupons would immediately solve that problem in one fell swoop.

rjdevereux 11y ago
You've obviously never had to build a system that tracks bonds when their original currency no longer exists. ;)
- brador 11y ago
  How would you do that?
  - boxy310 11y ago
    When a currency disappears on a planned basis (like the Deutschmark) the government issues a recall of the currency in banks at a set exchange rate: e.g. for the Deutschmark it was set by law at 1.95583 DM = 1 euro (source: https://en.wikipedia.org/wiki/Deutsche_Mark https://en.wikipedia.org/wiki/Deutsche_Mark) When a currency disappears entirely (like with Zimbabwe), there's a much more chaotic basis as it switches to separate sovereign currencies, which often have different inflation rates baked in. As this can be much more unexpected than a planned currency transition, the market often doesn't incorporate the expected changes in real interest rates, and often the exchange rate needs to keep floating for a while to account for ongoing inflation. More info on Zimbabwe's abandonment of their currency: https://en.wikipedia.org/wiki/Zimbabwean_dollar#Abandonment_and_demonetization https://en.wikipedia.org/wiki/Zimbabwean_dollar#Abandonment_...
  - abduhl 11y ago
    Seems like the easiest way would be to tie the payment to the cost of a basket of goods at the time of the issuing of the debt or at the cessation of the currency, whichever paid less (assuming you are the person paying) and then converting that to dollars at the date of the cessation of the original currency and then paying that amount.
- murbard2 11y ago
  I'm glad I never had to, but that edge case doesn't obviate the advantage of issuing perpetuities.
  - exelius 11y ago
    I wouldn't say it's an edge case; it eventually will happen to any perpetuity.
    - ghshephard 11y ago
      Well, if the payment is specified in gold, it will be a very long time before that medium is not available.
      - exelius 11y ago
        Then it's just a futures contract; and nobody in their right mind would sell a futures contract on a perpetuity. Currency is a useful abstraction for a lot of reasons.
        murbard2 11y ago
        No, it's absolutely not a futures contract: you collect coupons over time.
    - tome 11y ago
      Yes, but also the issuer of any perpetuity will go out of existence.
      - exelius 11y ago
        Not if they're the Dutch government, apparently.
tdees40 11y ago
Do you mean the duration is infinite in the bond-market sense of the word (i.e. sensitivity of cash flows to interest rates)? In that case, a perpetuity still has finite duration. The maturity, of course, is infinite.
- murbard2 11y ago
  You are absolutely correct. I initially wrote maturity then changed to duration, and forgot to correct the sentence. I now have.
murbard2 11y ago
If you're thinking: this is fascinating, what other schedules can we use, besides exponentially increasing or decreasing the coupon over time? Assume we have a market with n different perpetuities: p1,p2...,pn. When we shift the coupon schedule of any of these securities in time, we would like the resulting security to be expressible as a linear combination of the n perpetuities. p1...p2 should be the basis of a vector space of coupon schedules which is stable for time shifts. As it turns out, any vector space with such a property will be the sum of spaces spanned by { exp(lambda t) t^k | k < K } or { exp(lambda t) t^k cos t, exp(lambda t) t^k sin t | k < K } for lambda real. So for instance, we could have the following set of coupon schedule, and it would be stable: {1, exp(-0.03 t)} But so would: {1, t, exp(-0.03 t)} or even {1, cos t exp(-0.05 t), sin t exp(-0.05 t)} etc.

rjdevereux 11y ago

You've obviously never had to build a system that tracks bonds when their original currency no longer exists. ;)

brador 11y ago
How would you do that?
- boxy310 11y ago
  When a currency disappears on a planned basis (like the Deutschmark) the government issues a recall of the currency in banks at a set exchange rate: e.g. for the Deutschmark it was set by law at 1.95583 DM = 1 euro (source: https://en.wikipedia.org/wiki/Deutsche_Mark https://en.wikipedia.org/wiki/Deutsche_Mark) When a currency disappears entirely (like with Zimbabwe), there's a much more chaotic basis as it switches to separate sovereign currencies, which often have different inflation rates baked in. As this can be much more unexpected than a planned currency transition, the market often doesn't incorporate the expected changes in real interest rates, and often the exchange rate needs to keep floating for a while to account for ongoing inflation. More info on Zimbabwe's abandonment of their currency: https://en.wikipedia.org/wiki/Zimbabwean_dollar#Abandonment_and_demonetization https://en.wikipedia.org/wiki/Zimbabwean_dollar#Abandonment_...
- abduhl 11y ago
  Seems like the easiest way would be to tie the payment to the cost of a basket of goods at the time of the issuing of the debt or at the cessation of the currency, whichever paid less (assuming you are the person paying) and then converting that to dollars at the date of the cessation of the original currency and then paying that amount.
murbard2 11y ago
I'm glad I never had to, but that edge case doesn't obviate the advantage of issuing perpetuities.
- exelius 11y ago
  I wouldn't say it's an edge case; it eventually will happen to any perpetuity.
  - ghshephard 11y ago
    Well, if the payment is specified in gold, it will be a very long time before that medium is not available.
    - exelius 11y ago
      Then it's just a futures contract; and nobody in their right mind would sell a futures contract on a perpetuity. Currency is a useful abstraction for a lot of reasons.
      - murbard2 11y ago
        No, it's absolutely not a futures contract: you collect coupons over time.
  - tome 11y ago
    Yes, but also the issuer of any perpetuity will go out of existence.
    - exelius 11y ago
      Not if they're the Dutch government, apparently.

tdees40 11y ago

Do you mean the duration is infinite in the bond-market sense of the word (i.e. sensitivity of cash flows to interest rates)? In that case, a perpetuity still has finite duration. The maturity, of course, is infinite.

murbard2 11y ago
You are absolutely correct. I initially wrote maturity then changed to duration, and forgot to correct the sentence. I now have.

murbard2 11y ago

If you're thinking: this is fascinating, what other schedules can we use, besides exponentially increasing or decreasing the coupon over time? Assume we have a market with n different perpetuities: p1,p2...,pn. When we shift the coupon schedule of any of these securities in time, we would like the resulting security to be expressible as a linear combination of the n perpetuities. p1...p2 should be the basis of a vector space of coupon schedules which is stable for time shifts. As it turns out, any vector space with such a property will be the sum of spaces spanned by { exp(lambda t) t^k | k < K } or { exp(lambda t) t^k cos t, exp(lambda t) t^k sin t | k < K } for lambda real. So for instance, we could have the following set of coupon schedule, and it would be stable: {1, exp(-0.03 t)} But so would: {1, t, exp(-0.03 t)} or even {1, cos t exp(-0.05 t), sin t exp(-0.05 t)} etc.