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Yale’s 367-year-old water bond still pays interest (2015) (yale.edu)
208 points by marc__1 on March 23, 2021 | hide | past | favorite | 127 comments


> In the 17th century, people sometimes issued perpetual debt. But it is very rare that there is an uninterrupted history when governments or other entities have not defaulted on those debts.

Ever see those banking website ads or financial planning brochures that tell you that you can become a millionaire by the time you retire if you sock away just $75 a month through the magic of compound interest? The math checks out, but the longer the time horizon the more likely it is that wars, bankruptcies, currency devaluations, revolutions, government confiscations, hyperinflationary periods, and other economic cataclysms will wipe out your investment.


Around the developed world, interest rates are at a historic low over the last 20 years or so. The EU borrows at 0%. Argentina issued a 100-year bond at 8%, for God's sake.

One way to tell this story is that investors have unprecedented trust in global stability. They rate the risk of wars, bankruptcies, revolutions, etc extremely low.

There are other interpretations: you can say that central banks keep interest rates artificially low through control of the money supply, or compel investors to buy government bonds at artificially high prices, and both are reasonable arguments. But treating a price as a function of both supply and demand, I think there's a lot of truth in the "peaceful, stable" interpretation.


I think there's "trust in global stability" and then there's "trust that none of this will matter anyways if the global economy destabilizes". It's too big to fail.

I worry that people's trust in the system also creates apathy about the things that can break it. The tragedy of the commons is alive and, well... tragic.


> none of this will matter anyway

That's a bit of a self-fulfilling prophecy.

What I mean is that the mindset that "none of this will matter anyway if <foo>" injects some measure of irrational optimism into the economy, causing the relative economic severity of the occasional inevitable blip to increase somewhat.

We'd all do well to rationally consider the (small) risk of widespread destabilization. Doing so may keep bubbles smaller, but that's a good thing insofar as they are bubbles relative to value.


Being too big to fail is a testament to a working beautocracy. Before, things would just fail no matter how precious.


It's not that investors have trust, it's just that there's no alternative.


People say this, but I didn't consider it worthy of being mentioned as a serious reason. You can invest in stocks or commodities or real estate or these days cryptocurrencies. They all have great historic returns but some people and some institutions instead lend their billions to the world's governments at such low prices. You can't say with a straight face that there are no other plausible investments.

You could tell the opposite story: bonds continue to be popular and pricy because the world fears instability: that any other asset class may be in a bubble and about to lose all its value. But even then, investors are saying that though companies and industries may rise and fall, the countries will survive and pay their debts.


Are they saying the countries will pay their debts, or are they saying that they know that they can turn around and sell their bonds to the Fed whenever they want?


No everyone knows the high yield Argentinian debt is trash. The investment managers and traders buying it today think they're smart enough to offload it to some sucker before the next default. Or they expect to move on to another job before that and just don't care about what happens long term.


Well, in either case, the valuations are based on the expectation that they can sell the bonds to somebody else, rather than the expectation that they will collect on the debt.


They’re talking about the institutional market. If you are a big holder of money, you basically have no place to park it other than bonds.


The central bank cannot actually stem the tide in a loss of market confidence, central bank actions all depend on people retaining confidence in the currency to begin with.

If a central bank wants to buy government bonds from all the sellers and government treasury, it is always purchasing by diluting the currency. Once the market gets tired of bagholding the currency then the central bank has outlived its utility and the government cannot sell any more bonds because all the sellers evaporated.


Trust hasn’t much to do with it, there are people with much capital and nowhere to put it accepting anything.


> investors have unprecedented trust in global stability

That's one way to spin it. Another is "investors have unprecedented low trust in traditional investment tools". (If you have extra money laying around and no way to put it to productive use then you just might dump it all into bonds, because it's the default option and you don't have much in the way of alternative anyways.)

The rise of "bockchain" corroborates.


Given rising debt loads, this view seems myopic. Presumably if the balance of foreign debt outweighs the risks of walking away from it - countries will eventually walk away from it.

It may simply be that revolution or other political instability will be required prior to countries walking away from the debt.

I’d doubt any major power could or would fight a debt war in the 21st century.


> Ever see those banking website ads or financial planning brochures that tell you that you can become a millionaire by the time you retire if you sock away just $75 a month through the magic of compound interest? The math checks out, but the longer the time horizon...

Those flyers depend on a high-interest environment. At 1% annual interest (0.083% monthly interest), accumulating $1,000,000 by saving $75 / month would take just over 3,000 months, or 250 years.

Your deposits would only total about $225,000 over that time, so the "magic" of compound interest is still apparent, but it doesn't make for a compelling sales pitch.

"Quintuple¹ your money in just 250 years!

¹ Almost."


To a reasonable approximation, no financial planner is telling anyone to sock away their money exclusively in a low-interest savings account. Stock historical yields are well in excess of 5%, which changes the math substantially. Even the 3-4% "secular stagnation" fearmongering that was all the rage five years ago improves the math substantially over the 1% figure you've chosen.

$75/mo is definitely too low for a realistic time horizon, though. $500/mo at ~5% for 45 years (e.g., working 20 to 65) gets you >$1mil, with 270k basis.[0]

[0]: https://www.investor.gov/financial-tools-calculators/calcula...


For what it's worth, a spare $500/mo is never going to happen. I think I was 33 before I had an extra $500/mo.


$500/mo is $6k/year. There are definitely people for whom that is not possible, but there are a lot of people for whom that is possible. If you work in software, odds are pretty good you're in the latter category, even at the start of your career. $1M as a target is chosen arbitrarily, and often people save less earlier and more later; it's a simplistic model. (As financial advice: you should still save, even if you can't save $500/mo.)

"Never going to happen" is probably overstating it.


If you had reduced your latté consumption by just 5 lattés per day you'd have had that spare $500.


That means I have to make and sell 4 lattés per day, which doesn't seem probable.


You just need to invest in an automatic espresso maker to have your 5 lattes a day at a reasonable price.


But this is all thinking from an American perspective. Plenty of other countries with higher interest rates in the range of 7 to 9 percentage from banks and double digit from the share market.

I do wonder why don't more people move in to the third world from the West, it makes a lot of sense I think, especially if one is looking for financial independence. In third world, generally the same amount of money goes much longer than in the West.


> In third world, generally the same amount of money goes much longer than in the West.

There are some things that just cannot be purchased in the third world, though. Stability, a well educated population, a fair court system, confidence in the institutions that supply infrastructure (roads, trains, bridges, water, electricity, etc.), low perceived corruption, confidence that property rights will be upheld, high trust low friction transactions, and so on.

There's definitely variance between the different first and third world countries, and all countries have their pros and cons, but some things can definitely not be purchased with money.


> Plenty of other countries with higher interest rates in the range of 7 to 9 percentage from banks

Technically, only interest rate above inflation is interesting though. Might be 8 pct at high inflation still wins out, though.

> and double digit from the share market.

I'm curious about this - we're are these emerging markets? I suppose the Asian Tigers have slowed down a bit? Parts of Africa and South/Latin America?


My original comment was in dollars in response to a comment in dollars; we've been talking American perspective the whole time.

I don't think it's as reasonable to make 45-year compounding interest models for retirement in 3rd world economies. There's just a lot more going on as far as stability, interest rates, personal safety, etc. You can still do it, but I don't know if the numerical result tells you anything.


Well they've gone from using their savings accounts in the calculations to just putting everything into the stock market, usually the S&P 500.

Its a win-win - they get to charge higher transaction fees and management fees if its their own product, and the recent bull market makes the customer think they're going to get 7% returns forever. Just as long as they don't need to withdraw their money during a recession.


The worst-ever 20-year return for the S&P 500 index was +6.4% per year. It’s not the recent bull markets convincing investors that 7% returns will come forever. It’s a long history of such returns.

https://www.thebalance.com/rolling-index-returns-4061795


(Obligatory remark about the Nikkei's last 30 years)


Exactly. We are fooling ourselves if we think that the S&P 500 is immune to being in a bear market.


That data looks at January 1979 to present. I believe ever includes the rest of the 20th century as well...

There was certainly a negative return over 20-year periods including the Great Depression.

And negative real returns during the 1970s stagflation.


It's also only looking at the US, cherry-picking a country that has had an unusually good run of stability for the past few centuries.

Ask Germans or Russians what the worst rate of return for a 20-year period was in their country.


The S&P 500 just didn't exist before 1957, so it can't say anything about back then. Remember S&P 500 is actually a specific (actively-managed!) large cap index.

I'm not sure what the return on all US stocks is since then, but Japan's market has only just returned to the level it was at in its 80s bubble.


Right, there was an index in place during the Great Depression for sure. From wikipedia: https://en.wikipedia.org/wiki/S%26P_500

History

In 1860, Henry Varnum Poor formed Poor's Publishing, which published an investor's guide to the railroad industry.[20]

In 1923, Standard Statistics Company (founded in 1906 as the Standard Statistics Bureau) began rating mortgage bonds[20] and developed its first stock market index consisting of the stocks of 233 U.S. companies, computed weekly.[1]

In 1926, it developed a 90-stock index, computed daily.[1]

In 1941, Poor's Publishing merged with Standard Statistics Company to form Standard & Poor's.[20][21]

On March 4, 1957, the index was expanded to its current 500 companies and was renamed the S&P 500 Stock Composite Index.[1]


1929-1948 gave investors a +0.6%/year, which I think is the lowest nominal return. 1962-1981 was +0.8%/year.

As you allude, there were 20-year periods spanning the 1970s where Treasuries outperformed large-caps, but that’s fairly rare (and with the printing presses running three shifts, something we’re in extremely little danger of right now).


You just need to freeze yourself for 1,000 years..

https://www.youtube.com/watch?v=g9Z4d5EOjGs&t=27s


The biggest threat to interest compounding is inflation. Every time you see someone saying that by saving $X each month you can get $1M in 50 years, the question to answer is: what's gonna be the real value of $1M 50 years from now?


Only because you're talking about a bond with fixed payments. Operating companies (stocks) handle inflation better because they can raise prices.


But with companies you're not dealing with interest compounding, you're dealing with a company's growth prospects, which are largely unrelated to interest rates.


I've not seen a context where people where strict about saying compound interest is exclusive to interest payments. Reinvested dividends and reinvested earnings also compound.


You'll have a hard time finding companies that pay decent dividends and at the same time have high growth prospects.


He isn't saying that you'd have both at the same time. He's saying that high company growth is also compounding. And reinvesting dividends is yet another form.


This bond still yielding is an anomaly though. Instability will often manifest as inflation, but not always. Any idea which current countries have not experienced revolution, hyperinflation, annexation, and more intense events than just low or moderate inflation?

https://upload.wikimedia.org/wikipedia/en/8/88/The_Hanke_Kru... is a good starting point.

I started making a list of countries where you could reasonably be expected to have lost all your monetary savings at some point in the last 100 years. Not a full list yet, but quite impressive already. It's at https://imgur.com/a/gczjp4y .


This would be even better if the cause as well as the time period for each country was included as well.


I'm not sure that math actually checks out. By my math, you'd need to save more like $600 a month starting at age 22 to accumulate $1 million by age 65 (assuming 5% annual returns after inflation).


When was the last time a single cataclysm affected every financial market at the same time? We have a greater ability to diversify now than anyone did 100 years ago.


In practice diversification has actually gotten harder for most investors. The correlation coefficient between all major asset classes during periods of high volatility has increased across the board. Investors have had to move into riskier illiquid assets in pursuit of uncorrelated returns.


And the internet is constantly making it easier to access illiquid assets, making them more liquid.

When you say correlation coefficient, I assume you mean the positive one?


The correlation coefficient is in the range -1 to 1.

The Internet hasn't really made it much easier to invest in the types of illiquid assets that would interest large institutional investors. Those investments are still largely based on personal relationships and negotiations, often facilitated by brokers or bankers.


Yes but if they're negatively correlated and everything is tanking then they won't impact your returns as much than if they're positively correlatd.


The problem is that almost every asset class now becomes positively correlated during economic crises. It's very difficult to find negatively correlated or uncorrelated returns in those situations.


The events OP is talking about are not normal market fluctuations:

> wars, bankruptcies, currency devaluations, revolutions, government confiscations, hyperinflationary periods, and other economic cataclysms

Those are primarily political risks. Not independent events, of course, but very different than correlations between asset classes.


So what? Regardless of the cause, the point is that there will be occasional "black swan" events when all major asset classes fall together and diversification becomes less effective.


Zoom out farther. Markets regularly take major hits and then recover, but someone only invested in local markets in 1914 France or Venezuela today is starting from scratch. OP was talking about the events that leave people with nothing. Those are political events and diversification is about which governments one is exposed to.


A year ago?


It's not a cataclysm when markets recover in 6 months. OP is talking about getting wiped out.


Just wait for the (hyper?)inflation.


Tom Scott has an excellent short video about just this topic if you're interested in further information about it. https://www.youtube.com/watch?v=cfSIC8jwbQs Quite an interesting video, definitely worth a watch!


You can really see how much inflation has impacted this.

Th note was written for "1,000 Carolus Guilders of 20 Stuivers a piece." I believe the Carolus Guilder was a copy of the Golden Florin, which was 3.5 grams of gold. A gram of gold is about $50 today, so that would make the value of the note $175,000.

At the reduced interest rate of 2.5%, the coupon should be $4375 per year. Instead they got $153 for 12 years of interest, a devaluation of 343x.


As other responders have pointed out, the interest should be 2.5% x 1,000 Guilders, not 2.5% of the amount of gold that was in 1,000 Guilders in 1,648.

Its worth going through the math: 2.5% x 1,000 Guilders = 25 Guilders. The Netherlands replaced the Guilder with the Euro in 2002, with an exchange rate of 2.20371 Guilders per Euro. If we interpret the contact as being due in Euros, then the interest should be €11.34/year, or at today's exchange rate, $13.44/year.


Really the problem is the lack of reinvestment of dividends.

If they'd reinvested their 2.5% every year, in a similar bond paying 2.5%, then they'd now be collecting dividends of something like $600,000/year... absolutely crushing holding Gold.

The fact that this is a perpetual bond is interesting, but rolling an investment through shorter-dated bonds paying 2.5% over the centuries would have achieved a better result.


Could you explain a bit more please? If the annual interest rate was supposed to be 2.5% of the value of 1000 pieces of 3.5g gold coins, which works out to 0.025 x 1000 x 3.5 = 87.5g of gold per year, why aren't they receiving 87.5g of gold or the equivalent of $4375 a year?


The loan wasn’t denominated in gold, it was denominated in guilders. At the time, guilders happened to be made of gold, but that’s somewhat irrelevant. The interest is 2.5% of the initial value of the bond in guilders, which has almost certainly deflated drastically, and will continue to do so.

Put another way, the loan will continue to pay out 14 Euro per year 100 years from now, when that will likely be the cost of one can of soda.


In other words, inflation wipes out debt. No wonder all governments issuing debt like crazy.


No, because interest on debt compounds and the rates are frequently higher than inflation.


Lol what.

I haven't been able to buy government bonds/gilts with an coupon rate hire than inflation for years.

At least my equities return when everyone deflates the value of money.


Note that the Dutch water boards (waterschappen) are effectively a separate layer of government, apart from the national, provincial and municipal governments. We have elections for them. They raise taxes. Their borders generally do not correspond with provincial or municipal borders.


Wikipedia confirms that the Dutch water boards are indeed a highly significant form of local government...

> Punishments meted out by water boards were fines for misdemeanors such as emptying waste in the nearest canal; however, according to various historical documents, the death penalty was used more than once for serious offenders who threatened dike safety or water quality


I’ve heard of this before, but I’m still puzzled by the logic of a loan that never gets paid off. Was this just a bad idea, or does this still happen and there’s a good reason for it? Could the water authority pay the loan back to close it out?

Just asking questions to the air, but if anyone knows the answer I’d love to know!


> I’ve heard of this before, but I’m still puzzled by the logic of a loan that never gets paid off. Was this just a bad idea, or does this still happen

It sounds weird but it's not a bad idea, no. In essence an infinite set of future payments has a finite present value, due to inflation.

i.e., suppose inflation is 100%, this means prices will double every year, and the real value of a nominal amount will halven every year. So $100 today, will be worth $50 (in today's money) in a year from now. A year later (2 years), a $100 then will be worth $25 in today's money. Another year later (3 years) it'd be worth $12.5. And so on.

As you can see, a nominal future payment, say $100 in 300 years, will start to approach zero.

Of course interest rates aren't quite that high, but it's just to get the point across. The interest rate is essentially a discount rate, which lets you value a future amount of money, in today's prices. In the above example, $100 in 3 years would be worth 100 / 2^3 = 12.5

This means that an infinite series of payments (perpetuity) can be calculated as well by simply taking the payment divided by the interest rate to discount it with. So at an interest rate of say 5%, a $100 per year infinitely, would be worth $2000 today.

In other words, in a world with 5% interest rates, you'd be indifferent to receive $2000 today, or $100 ad infinitum. They have the same present value.


> It sounds weird but it's not a bad idea, no. In essence an infinite set of future payments has a finite present value, due to inflation.

Is it really due to inflation?

Even without inflation, wouldn't there still be interest on loans to compensate the lender for not having the use of their money and for the risk that the loan will not be paid back. The present value of a future payment would thus still be discounted, and a stream of payments under a fixed interest rate would still lead to a convergent geometric series for the present value of the total stream.


Yes it's due to the interest rate, which is loosely connected to inflation. But you're right, even with no inflation, you'd discount by future interest rates, leading to a finite number.


You're right. I should've just stuck to 'discount rate' instead of interest or inflation. But that's a little too abstract for some.

In finance interest rates are typically used for the discount rate. But discount rates can be something else that's not directly related to interest rates, too.

For example, suppose I buy gold and it appreciates in value by 10% per year. You could in a way call that inflation (inflation of the price of gold, typically due to inflation of the money supply). And if you were to calculate the value of x amount of gold in one year, in this case you'd use the inflation rate of 10% to discount it to the present value.

I should've said discount rates, and in general discussions it's fine to speak of interest rates. Should not have mentioned inflation as it's confusing and often different from the discount rate.


> In essence an infinite set of future payments has a finite present value, due to inflation.

Inflation counts, but this would still be true in the presence of strong deflation. A set of future payments has a finite present value due to the fact that the same amount of purchasing power is worth less in the future than it is right now, "time discounting".


Wait, that doesn't make sense now, does it? Deflation means precisely that money will be worth more in the future than it is now, so a future payment stream will correspondingly also be more valuable than cashing out right now. (Which is also why economists often regard it as a bad thing, because it entices people to hold off on spending/investing, thereby slowing down the economy).

Now I agree that as such money now is somewhat more valuable than money later in nominal terms simply due to the uncertainty of the future, and it's probably unwise to bet on everlasting strong deflation, but at least in the short or medium term I'd say strong deflation could certainly overcome even these built-in inflationary tendencies.


> Wait, that doesn't make sense now, does it?

Yes, it does.

> Deflation means precisely that money will be worth more in the future than it is now

Deflation means that $X in the future will have more purchasing power in the future than $X has now.

It does not mean that the money will be worth more in the future than it is worth now; these are different concepts. You'll note that my comment says "the same amount of purchasing power is worth less in the future than it is right now". By the same token, more purchasing power in the future may still be worth less than less purchasing power right now.

People like to slam the intrinsic value of gold by saying "you can't eat gold". But even in the sense in which you can eat gold, you can't eat gold you don't have. The uncertainty of the future is one reason why money in the future is worth less than money in the present, but the bigger reason is option value. You can hold present money and spend it in the future. You cannot pre-realize future money and spend it in the present.


in a perfect world, we'd have neither inflation or deflation, as we'd be able to perfectly predict what friction is needed with every transaction to keep the world in balance. but because that's practically impossible and because we have only one or two coarse knobs on the economy, we've settled on a relatively high inflationary policy being better than any deflationary one.

i'd conjecture that we could increase the number of economic friction knobs appropriately to easily get the real inflation rate under 1%, but we don't because that would lessen the advantage the already moneyed and their political appendages have with the current system.


Yes and no. In the case of true deflation, interest rates can become negative, such that money in the future has more value than money today. In that case, the value of this loan would diverge towards infinity.


You're making an unfounded assumption about the rate of time discounting.


Help me explain where my unfounded assumption is. If the interest rate is negative, that explicitly means that money in the future is worth more than money today. That's the definition of a negative interest rate.


Well we have a constant rate of inflation in modern times, how true was that 300 years ago?


> constant

Yeah about that..


> simply taking the payment divided by the interest rate to discount it with

Looks right, but do you have a proof?


We have an infinite series such as:

S = sum from (i=1) to infinity of [a^i]

we can then multiply by a on each side:

aS = sum from (i=1) to infinity of [a^(i+1)]

Simplify/cancel out to:

aS = S - a

a = S(1 - a)

S = a / (1 - a)

where a = 1 / (1 + R)

so $100 perpetuity with R = 5%:

a = 1 / (1 + 0.05) = 1 / (1.05)

$100 x (1/1.05) / (1 - (1/1.05)) = $100 x 1 / (1.05 - 1) = $100 / 0.05

= $100 / 5%

= $2000


I've always thought this was the most useful equation I learnt at school -

S = P (1+i)^n

P - Principal

S - Sum

i - interest rate p.a.

n - the number of years


I always liked 58008


Do you know what website you're on? You should have used $128 or $256.


Real hackers are not limited to numbers that are powers of two.


Real hackers maintain their ability to hack decimal architectures.[0]

[0] https://en.wikipedia.org/wiki/IBM_7070


In addition to what others have said, from a historical perspective such bonds were the functional equivalent of stock. That is, these particular bonds effectively represented equity, not debt. Joint-stock, limited liability corporations are relatively recent, especially in terms of market liquidity and legal norms. Whereas the laws regarding bonds and bond payments are much older and were (and in many ways remain) much more consistent across all of Europe and, today, the world.

A bond is a type of negotiable instrument, and laws regarding negotiable instruments--which also include checks, letters of credit, mortgages, etc--go back to at least the Medieval period in their literal terms, and in general terms to the Lex Mercatoria (i.e. merchant laws of the Mediterranean trading nations, including the Roman Empire, that were organically preserved through the Medieval period and even up to today). Other commercialized civilizations also had substantially similar laws. Bonds are a relatively safe investment for more than the reasons commonly recited today--e.g. hedging market volatility, etc.


The UK government used to issue consols, which are perpetual bonds. Over the centuries, they bought them all back. https://en.wikipedia.org/wiki/Consol_(bond)


Whenever you read in Regency to Victorian books that so-and-so has an income some pounds per year it is usually referring to these.


They often refer to rents paid by tenants on the estate.


I know nothing about finance but kept thinking in this.

There is a wiki on it which says “ Perpetual bond, which is also known as a perpetual or just a perp, is a bond with no maturity date. Therefore, it may be treated as equity, not as debt.”

However the wiki notes that they have no voting rights so aren’t as good as equity.

https://en.m.wikipedia.org/wiki/Perpetual_bond


Aka « preferred shares », but they often have rules about being redeemed for par value.

But in bankruptcy, they get paid after other creditors. The payments are dividends which may have tax advantages/disadvantages.


There are some practical and legal difference between the two, but this "water bond" is more akin to a modern stock certificate. The interest payments are derived from an ownership stake in the a series of dykes and canals, which are managed by a water board.

Replace water board with board of directors and interest payment with dividend and nobody would bat an eye at the perpetual aspect.

The big difference is that stock certificates usually don't have dividend entitlements outlined on them, while bonds do. However, historically, stock certificates could have either face values or distribution entitlements listed directly. Especially stocks in railways.


These sorts of bonds used to be more common and in the US. The closest more common semi-equivalent thing today is perpetual preferred stock. Most of it is callable, meaning the issuer can pay it off after a designated period. As for what is used for— it’s cheap capital to run your business with.


So a perpetual bond has both major advantages and disadvantages. The advantage is liquidity - all the different issuances are interchangeable like common stock, so instead of N different markets for each of N times the company raised money via selling bonds, there's one market.

The disadvantage is that bonds do not just entitle you to periodic coupon payments, but also give you rights according to the face value of the bond in bankruptcy proceedings. Selling bonds far from the "par" you are theoretically owed in bankruptcy has big problems - either the bond is trading above par and you risk not being made "whole", or it is below par and the company is selling bankruptcy liabilities on their assets for pennies on the dollar. The movement of interest rates over time guarantees that one of these situations will eventually hold, so either issuers or buyers will want to adjust the nominal yield (and thus par value), resulting in the loss of interchangeability.

Notably, the US government has zero risk of being able to pay its nominal obligations, so is a prime candidate for issuing perpetuals in a way that corporations cannot. Currently, if you buy a new 20-year treasury bond and wait 2 years, you end up with an off-the-run bond that is difficult to efficiently trade. It'd be much better if these instruments did not "expire" as such, and the increased usefulness to investors would wind up reflected in lower financing costs for the government. Theoretically, the entire US treasury bond structure could be replaced with a zero-duration overnight interest account, a perpetual that pays a $1 coupon per day, and an inflation-linked perpetual that pays the CPI as coupon.


If they expire you have to manage the rolling over (creating debt to pay off other debt). If the interest rates have gone up since the original loan, you pay more.

This is often forgotten when people say 'but the state can get 0.01% interest loans!'. Sure, true, but if the rate goes to 5%, that 3xGNP loan becomes quite cumbersome to service.

At 2.5% fixed forever perhaps it's interesting to keep. Also, I suppose that there are not many bonds that survive 367 year. So a lot of the debt 'disappears' as time goes on.


My mortgage does not need to be re-financed in 25 years, since it’s designed to be paid off by then. Since that’s been my main interaction with debt to date, I assumed that’s how it always works. I’m starting to suspect from the comments here that was a bad assumption


Most debt at this level works with coupons. The debtor simply pays the interest every year and at the end returns the principal


I believe the water authority could offer to purchase the bond (and then write it off once they own it). It would be up to the current owner to decide if they are willing to sell.


The price of the bond itself is at least 100x the value it would have to pay for eternity


100x the annual yield would be assuming a 1% interest rate, so I'm guessing it's worth quite a bit less than that. Long-term government bonds give 2+% returns and fixed term annuities/MYGAs are giving ~4% returns, as far as I know. So I would expect a value more like 30–50 times its eternal annual payments. Heck, inflation is around 2%, so eventually this will be worthless.


I think they were referring to the historical value of the bond itself makes it worth far more than its strict monetary value over time. So even if its 'worth' 30-50 times more when you do the math, a collector maybe be willing to pay 500 time more due to its rarity.


I bought some shares in our local coop when they were building a new store to move into. Each share gives 3% interest with no expiration and I can sell it back if I want.


The 2nd mortgage on my house is a perpetual loan, so it very much is still a thing.

Some context: I could only go 5% down but wanted to avoid PMI, so the other 15% for 20% down on the first mortgage was taken from a 2nd mortgage, which had the perpetual terms. It's more commonly known as an interest-only payment loan. The interest rate is adjustable and I only pay the monthly accumulated interest.


Conceptually, it seems similar to a royalty.

I give you money to be a part of something, and collect a royalty into perpetuity.

Or, it's even more like buying land under a building.

I sell the land under my building to get some quick cash. And in turn agree to lease the land back from the new owner permanently.

Depending on how badly I need the money, it may be my best and only choice...


NPVs tend to converge even on a perpetuity. simple measure of whether the seller will underwrite it, and will there be a market for purchase.


Inflation.

As long as the perpetual interest are lower than the inflation, then it make sense.

I'd imagine all debt so marked in German marks before the German hyperinflation in 1920s gets essentially wiped this way.


Isn't it practically investment?


Here's one way of thinking about it:

Let's say I need $1000 now. I'd like to borrow it, and I'm willing to pay some amount of money back over time to obtain it. Money now is more valuable than money later, so I know the payments will sum to more than $1000. You have some cash on hand right now, and you'd like it to be larger; you're willing to lose access to it for a while in order to get more money later. Let's say I'm a SUPER trustworthy borrower, and that SUPER trustworthy borrowers generally borrow at 2% per year right now.

Here are some options that we would expect I (as the borrower) and you (as the lender) would find fairly equivalent:

1. You give me $1000 now, I give you $1,040.78 in 2 years.

2. You give me $1000 now, I give you $20 every month, and $551.46 in 2 years.

3. You give me $1000 now, I give you $17.53 every month for 5 years.

4. You give me $1000 now, I give you $9.20 every month for 10 years.

5. You give me $1000 now, I give you $1.67 every month for 10 years, and $1000 in 10 years.

6. You give me $1000 now, I give you $5.06 every month for 20 years.

7. You give me $1000 now, I give you $1.93 every month for 100 years.

Excel has all these functions build in; provide all but one of the rate, the number of periods, the present value (aka PV, here, $1000), the future value (aka FV, the final payment at the end), and the periodic payment size, and it's simple math to calculate the missing value.

Note that these all have, at least in theory, an equivalent value. Less money sooner, versus more money later, with the tradeoff defined by the rate (here 2%). If you, as a borrower, look that that and go "I'd really prefer a shorter term" that means the correct rate (for you) should be higher, but if 2% is the right rate, all 7 options will seem about the same.

Modern bonds often have the same value for PV and FV (that is, you pay the face value back at the end), but every combination you can imagine exists in the real world, and much financial activity involves people with a payment stream structured one way getting it transformed into one structured another way.

One thing you might have noticed: As the period gets longer, the amount you'd need to pay each period gets smaller and smaller, but it's asymptotic to a value. If $1000 now is "worth" $1.93 a month for 100 years, it'd be "worth" $1.67 a month over 500 years. Or indeed, over 1000 years.

Turns out, the payment per period works out to the PV times the interest rate. 12% APR is ~0.1667% per month, and $1000 * 0.1667% = ~$1.67 per month.

That's the finance 101 calculation, at any rate. In the real world, there's always risk in various forms.

One other point: Did you notice that the interest payment on the perpetuity was $1.67, same as for the "standard" 10 year bond? (And note, bond term doesn't matter here; it's the same for 1 year, 5 years, or 20 years.) That's not a coincidence, because they're economically equivalent (ignoring risk, liquidity, etc.). In fact, consider that as practical matter, most bonds issued by national governments will never, ever really be paid off. Instead, as they come due, they are "rolled". The principle for one lot of bonds is paid off by the issuing a new lot. But consider the math: Today I get $1000 by selling you a 5 year bond. Then every month for 5 years I pay $1.67 in interest. Then at the end of 5 years I issue a new bond for $1000 (which, let's say, you ALSO buy), and I use the proceeds to pay off the first bond. Then for 5 years I pay $1.67 in monthly interest, before we do it again. Ignoring the $1000 payments every 5 years, since they cancel out to $0, this borrowing deal is "I get $1000 now, then I pay $1.67 forever", which is...a perpetuity.

Conversely, if I did sell you a perpetuity, you could just sell it in 5 years. You'd expect to get $1000 when you sell a perpetuity on those terms, if interest rates haven't changed, so the cash flows for you buying and later selling a perpetuity is identical to buying a bond and holding it to maturity.

So in short: Not a bad idea, still happens ALL THE TIME, we just package it differently for various practical reasons.


Thanks for breaking this down in a clear way, it shows how a share of a dividend-paying stock is basically indistinguishable from a perpetual bond from a financial perspective.


While none have been doing it for 367 years -- and they can stop paying it, or change the terms, at any time so it's not quite like a bond--there are companies who have paid stock dividends continuously for long periods of time. For example Coca-Cola (KO) has paid a dividend since 1920, and Colgate-Palmolive since 1895.


The corporate history of AT&T is a bit complicated, but it's paid a dividend every quarter since 1893 (https://investors.att.com/stock-information/historical-stock...). At least if you view the current AT&T, which is "really" the old SBC, as the successor of the old AT&T, which the current AT&T would really like you to do.


I mean, companies still sell corporate bonds too, even. They're typically for terms of years, but you can always just buy a new one at the end and it's practically the same thing.


A person upthread mentions that sometimes these bonds are also long term – Disney and Coca Cola have issued 100 year bonds.


What actively used financial instrument today has the longest time horizon? 100 years?

* sports stadium construction loans UC Berkeley $443 million by 2112

https://www.bloomberg.com/news/features/2017-01-04/college-f...


There have been instances of 1000 year (millennium) bonds, such as Danish energy company Orsted in 2017, Canadian Pacific Corporation in 1883(!), etc.

100 year (century) bonds are a bit more common - Disney issued a century bond in 1993, for instance. Argentina (!) issued a century bond in 2017, which it defaulted on last year, leaving creditors with around 55 cents on the dollar.

In general, long term (implicitly high risk) bonds become attractive in low yield environments such as we had been in for a couple of years up until the absolutely humongous amount of stimulus triggered by the current pandemic.


Most equity/preferred shares are considered perpetuities (i.e as long as the company is in business)

There are many many perpetual bonds still being issued today however they tend to be 'callable' at the option of the issuer ...most after 5/10/30 years, if they aren't called then they maybe called on the same date every 5yrs or so (so I don't really count them as they aren't really 'forever'.

Oxford and Cambridge Universities in the UK have recently issued 100 year 'Century' bonds in GBP. Thats the longest i've seen recently (I cover EUR/GBP bond markets at work)


I see Orsted bonds announced 2/10/2021 with maturity on 2/18/3021. That’s got to be the current winner.

Prospectus (PDF): https://orstedcdn.azureedge.net/-/media/www/docs/corp/com/in...


> It is a bearer bond, meaning anyone who presents the addendum to the issuing authority can collect the interest. The water board kept no register of ownership of the bond.

These types of bonds seem so interesting to me as they seem fraught with risk of theft,fire, and other harm. Why would I as an investor prefer this over some form of registration? Is it just to provide anonymity?

Wikipedia[0] only states that benefit but then the US Treasury issued them until a few decades ago.

If the only purpose is anonymity and illegal stuff, then why would a government issue them? It doesn’t seem like the demand is so high that they couldn’t issue similar debt that wasn’t bearer. Does this mean there’s some illicit gain that an issuer gets? I suppose that the percent that gets lost or destroyed would make them more attractive?

It would be comical if an unscrupulous issuer actively sought out the bonds to destroy.

[0] https://en.wikipedia.org/wiki/Bearer_bond


Just shooting from the hip here, maybe bearer bonds were a lot easier to sell back in the era before universal telegraph/telephone service? And then maybe they just took a while to go away, as old financial institutions often do?


This reminds me of the story[0] of a French annuity from 1738 that yields 1.20€ per year.

[0] https://news.ycombinator.com/item?id=26559687


For those who enjoy podcasts, 99% Invisible talked about this in an episode last year.

https://99percentinvisible.org/episode/mini-stories-volume-8...

It’s an excellent show covering a broad swatch of topics. I generally learn things from their reporting. The episode on Froebel blocks was captivating to me. I’m awaiting my niece’s third bday to buy her a set (choking hazard).


CUSIP?


If only there was a temperature clause so when the gulf stream fails the bond is void.




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