Yale to Be Paid Interest on Dutch Water Authority Bond from 1648
bloomberg.com
bloomberg.com
I still consider the more 'recent' 19th century bonds he passed around in class to be the coolest show-and-tell item ever from a professor.
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.
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_...
The maturity, of course, is infinite.
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.
Christie's also gives background info on the bond, such as "While it was originally a requirement that the bond-holder send the original parchment to the Lekdijk Bovendams on 12 January to receive the annual interest, the successful bidder on this lot need only send the allonge, on which the payment will be neatly recorded by a responsible clerk of the Waterschap Kromme Rijn (successor to the monk and Secretary who sealed the document in 1634), as it has been for 302 years since 1698."
There are some corpora of handwritten digits (for OCR training) lying around the net, I guess I should check those to be sure.
Did a brief survey off people around me, results were inconclusive:
1x Upper Left
1x Upper Middle
1x Upper Right
Do you write Z with a line through it? My British family does.
Z with a line through it is quite common in mathematics in the US (to prevent confusion with the number 2.) Many people who do a lot of math carry the dash over to Zs in general.
So it's horizontally mirrored compared to the way you do it :-)
"Aan de noordzijde van de Lek was een dijk aangebracht van ruim 32 km lang en hij liep vanaf Amerongen (aan de rand van de Utrechtse heuvelrug) naar het Klaphek bij Vreeswijk, de Lekdijk Bovendams genaamd."
It was an bond ("obligatie") of 1000 guilders, given out by Hoogheemraadschap Lekdijk Bovendams (more recently merged into Hoogheemraadschap De Stichtse Rijnlanden). It returns 25 guilders (now 11,35 euros) interest per year. Yale bought it in 2003 for 24.000 euros. It was given out in 1648 to build a groyne ("krib") near the hamlet of Honswijk. Looking at Google Maps, you can see a system of multiple groynes there; I am not sure whether this bond paid for only one of them or for more: https://www.google.com/maps/place/3998+Honswijk,+Netherlands...
Original buyer of the bond was Niclaes de Meijer: http://www.zeit.de/2015/15/ewige-anleihen-kredit-geldanlage (German!).
In the first 50 years of the 17th century, Lekdijk Bovendams gave out 300.000 guilders of bonds to repair the dikes along the 8 km stretch it was responsible for. Stichtse Rijnlanden is nowadays responsible for the Lek dikes between Amerongen and Schoonhoven, as well as water management in most of the province of Utrecht.
Perhaps the bond was originally issued and in 1944 a companion document was issued with it? So now the single bond consists of two documents. It would make sense to issue a newer document that goes along with the original. I imagine some numbering scheme was introduced between the original issue and 1944. The 1944 document would provide a number in the modern scheme for the original bond.
Back then, inflation was probably less of a problem for investors.
For the record, in case there still are Ron Paul fans/goldbugs out there: moderate inflation is generally considered a good thing by economists today and inflation is probably too low at the moment.
One person described money as "sweat, distilled" and I find that definition incredibly attractive. I recognize that plenty of people making money not by sweating but thinking or whatever, but I still find it an excellent description. And I can't see how devaluing a person's effort over time is a viable strategy for building a lasting civilization. I think it leads inevitably towards the kind of throwaway society we have here in the US and virtually guarantees that we won't build infrastructure of long lasting value like exists elsewhere in the world. Well built stuff can last for hundreds or thousands of years. I wish money was the same.
I'll reword it for you:
'Encouraging money to be invested, by motivating people via inflation, is a good thing overall because it puts wealth to work creating jobs and stimulating economic activity.'
Thus, I think the idea that a dollar saved today can buy roughly the same amount of stuff in a decade is actually bad, because in a world where that's likely, that dollar was probably sitting useless in someone's purse for a decade.
Inflation, in my opinion, actually does the opposite of what you suggest -- because it encourages lending and investing in order to beat inflation, money is actually put to use for longer term projects such as infrastructure that can last years and years.
Because we all know banks put all the currency they receive in huge vaults filled with paper $100 bills, instead of, oh, lending it out (several times over one way or another).
Unless you're converting it all to gold, or stuffing it under a mattress, your savings are in institutions like banks which are not a sink where the velocity of your money goes to zero, outside of economic messes where they aren't willing to lend, or people are afraid to borrow. And your being encouraged to spend your money doesn't seem to help those situations.
Right?! Every bank vault is just huge piles of gold bars and ornery old men counting and recounting the money, hoarding it up and never loaning it out.
Inflation is currently bouncing between around 1.6% and 2% (but mostly towards the 1.6%). A 3 year CD at a decent bank is currently paying around 1.6%; a 5 year CD is paying around 2%. So if you're willing to commit to a 5 year deposit, you will probably beat inflation and realize a small, real return. Even an interesting-bearing checking account (with a sufficient balance...) pays close to 1.6%.
Granted, it's not the glorious 5%+ returns of yesteryear, but then, we're in a savings glut.
That's a nonsensical statement when the central bank is fully in control of the money supply, and thus, the interest rate.
That's like saying "well my computer has a billion copies of funny cat gifs on it, so there's a funny cat gif glut". It doesn't make any sense. You control how many copies of funny cat gifs are on your computer. If there are too many, it's because you made too many copies. If there are two few, it's because you made too few. Pretending that market action had anything to do with something that you are ultimately in control of makes zero sense.
The interest rate is low (or zero) because the central bank decided it should be, not because all the people in the world collectively don't have any real preference for a dollar today versus a dollar tomorrow.
The return from consumer savings accounts being near inflation / a near-zero real rate of return is because of the savings glut.
The two are related but not the same thing.
The interest rate is supposed to be the price of money. There's going to be a bid/ask spread on that because of the cost of accepting money and bundling it together, along with the cost of keeping up with the book-keeping and various other things that are costs for loans. So the rate you get paid in interest should always be less than the rate that you pay in interest. This I understand.
But if the interest rate is low, then the interest rate is low. The interest rate is determined by the aggregate supply and demand for money. If there is a lot of supply, relative to demand, then the interest rate is low. If there is a lot of demand relative to supply, then the rate is high. And given that people have a nearly infinite desire for money today versus in the future, the rate is really determined by the supply.
The Fed is in control of the supply by creating or destroying money as needed. That means that they fully and truly do set the rate, because they can do literally whatever is needed to move the needle.
The idea that everyone's individual actions to save is somehow what created the tremendous amount of expansion in the money supply (and thus the very low interest rate) is utter nonsense. The Fed created a lot of extra money which expanded the supply of loans, thus pushing down the rate.
Australia also still has a 2% official rate vs near 0 in the US.
I think the idea that a dollar today buys just as much in a decade IN NO WAY precludes people from investing their money to earn a return. It just eliminates the stupidity tax that some people pay for not understanding how things work.
In a non-inflationary environment nearly all people would still invest their money and put it to work. It's just that they wouldn't be taxed for not doing so.
Inflation doesn't encourage lending, it encourages borrowing. It's smart to pay back with dollars that are worth not as much as the dollars you borrow. Inflation actually discourages lending because you now have to find borrowers who can pay you back higher than the interest rate.
Of course, all this is predicated on a real market in interest rates which we don't have in the US because the Fed sets the rate through various means.
I might not care too much if it was $0.50 or $1 per month. But quantitative differences eventually become qualitative ones, and at this point it's not just some tiny abstract amount of money, it's real consumption that a person has to forego every month (or day!) for the sake of not getting financially ruined the first time a big unexpected expense comes up.
When I see, oh, normal genre 300-500 page paperbacks going for Amazon prices from 8-11 USD, mid '80s official inflation adjusted prices of ~$3.65-5, and lower actual prices from a quick check of my library, my response to the higher end is not no, but hell no, and I'm not going to buy the lower end new for all but the most exceptional titles.
Many economists think deflation causes people to hoard their money, since an item bought tomorrow will cost less (assuming your form of storage survives, $N in a bank that goes bust before the FDIC was established is worth $0), and the reverse for inflation. I think it's a lot more complicated than that.
When the interest rate you pay is 4%, the inflation rate is 2% and the interest that you earn is 0.25% quantitative changes become qualitative ones at numbers that seem very innocuous.
I do understand that for double-digit losses and gains things are nonlinear, in other words a 50% loss means that you need a 100% gain to offset it, and a 90% loss needs a 1000% gain to offset. But in the single digits, this is very close to linear. If you lose 5%, then gaining back 5% leaves you very close to even.
If 2% compounded deflation is the end of society, how can 2% compounded inflation be the savior?
The reason is that ~90% of the money that exists needs to be continuously rolled over into new loans to maintain the total supply (and it actually needs to increase a bit [ie. inflation]). At any given time, only a small fraction (~10%) of the total supply is available to make the upcoming interest & principal payments. If new loans don't roll out in time (to replace the money destroyed by the principal payments), you can enter a situation where there is no legally manifestible currency (banks are completely insolvent) without some seriously disturbing hackery and deception.
You begin to hit serious problems (many individual actors will fail due to 0 flow) before you even get to that point. This is just the ultimate fate of our economy.
Edit: What we really need are accurate and accessible simulations of our economy so that everyone has a chance to understand it.
The money isn't destroyed. It's back in the hands of the lender, available to do whatever they'd like with it. Perhaps they'd invest it into a factory or a business that they own, instead of just loaning it out. That would mean it'd be spent on real things in the real world, thus meeting the criteria of not being destroyed and being spent.
What? How does that have any bearing on reality? The values of mortgages a bank has on its books aren't a reflection of how much reserves it has, it's a reflection of the dollar values attached to the loans.
How many loans a bank can write in a month is of course dependent upon how much money the bank has sitting around in excess of the reserves it is required to keep. But again, that doesn't dictate the dollar values on the loans. Those were fixed at signing and in the absence of problems, get smaller at a predictable rate. What do reserves have to do with the loan equations?
There's no symmetry between inflation and deflation. Your incredulity is unwarranted.
Money is an accounting method to enable easy trade. Ordinarily, it's worthless, which makes it available to be used in transactions. Under deflation, money gains an inherent value -- you can multiply your worth by holding on to the money you have now. This means that much less trade occurs, because the gains from that trade are less than the gains from holding on to your cash while it appreciates. But the gains from cash appreciation are in an important sense hallucinatory -- on a system level, they don't exist -- and the gains from trade are real, so the economy just ends up being crippled.
The other thing to consider is that any decision to wait has an opportunity cost, and the baseline opportunity cost is captured by the interest rate. Since nobody is going to stop charging interest to borrow money - even in sharia finance you pay a rental cost for money that is very very similar to interest - it would seem as if price inflation was an unavoidable characteristic of any system involving credit or loans.
Gold as currency had lots of really negative effects, read up on the populist movement in the late 19th century U.S. and the background of the "Wizard of Oz" story.
Generally speaking though, bonds are fixed income securities and are not explicitly inflation adjusted. The price you'd pay to buy a given bond fluctuates in part based on market expectations of future inflation.
Some bonds are, but with a moderate, low-volatility year-over-year inflation in the modern period its not that important (reasonably good inflation expectations exist and are factored into market prices), and before modern independent central banking -- governments weren't exactly inclined to surrender the power to monetize debt (when they were convinced to largely curtail that power, it was through independent central banking rather than through inflation-adjusting bond interest.)
Inflation adjusting bond yield -- if done generally so that it significantly affect debt service costs -- also creates substantial incentives to systematically manipulate official inflation measures; if you don't trust the issuing government to manage inflation within a reasonably predictable range so that it can effectively be priced-in to the bond purchase, do you trust them to accurately measure inflation when they have a substantial near-term financial incentive not to?
> Very long timespans such as these really devalue any interest payments, do they not?
Well, sure, they reduce the real (though not nominal) value of the annual income from a perpetuity, and those over time the real (though not nominal) value of the bond itself.
I'm not sure this is a bad thing inherently; why shouldn't bonds tend to have reduced real value over time?
Why should the real bond value reduce over time, though? Sorry to answer your question with another question, but I don't really see a reason why they should. After all, isn't some degree of predictability/fixed value the point?
One major issue with these is that the inflation adjustment typically lags by 6+ months, so they are not a good short-term hedge. But they are very popular.
As a side note, that's about half the entire GDP of Ethiopia last year. That's a country of 100m people.
From their small base, GDP has tripled in ten years. They've seen 11 straight growth years. The prior two years both saw around 10% growth, while inflation has been relatively low.
Life expectancy at birth has climbed from 50 to 64 in 20 years.
The poverty rate has fallen from 45% to about 25% in 20 years.
The infant mortality rate has fallen from 140/100k in 1980, to around 40 today, falling by 50% since 2000. It's expected to continue to fall.
They're actually generating wealth faster than any other comparable nation in Africa:
http://www.theguardian.com/world/2013/dec/04/ethiopia-faster...
Even in the article it states that some dont know where the money came from... I err on the side of corruption...
Per capita wealth in Ethiopia is close to $500, with 94 million people. They have around $45-$50 billion in wealth.
Fascinating. Yet they still require their students to pay tens of thousand of dollars each year in tuition. They should do what Stanford did and make education free for students whose families earn less than $125k.
"Yale does not require students to take out loans for their education. Instead, Yale meets 100% of demonstrated need for all admitted students with a financial aid package consisting of need-based scholarships, term-time employment, and a student income contribution."
http://admissions.yale.edu/financial-aid-prospective-student...
So...Yale does what Stanford does already...
http://admissions.yale.edu/financial-aid
Families don't have to pay if they make less than 65k.
Stanford's program is similar. Their 125k threshold is for not paying tuition, but a family making 125k is expected to pay for room and board.
Even if they had done 200 years, it likely wouldn't have diminished the bond's value too heavily (at purchase), and would have put a stop to this.
I guess they figured that they would eventually buy back all of the bonds, but missed a few or never had the money.
http://articles.latimes.com/2012/may/05/business/la-fi-0506-...
At least, from AA's perspective, that ends when the holder dies so there's light at the end of the tunnel.
I was hoping the answer would be in perpetuity. Sadly, it seems that the longest you can draw it out is until the death of one's surviving spouse.
Imagine how glorious it would be if you could stow away about $5k of post tax income every year and invest it in some stock index fund if you could give it to someone upon death. Of course, it wouldn't be a retirement account anymore though.
http://www.financeformulas.net/Perpetuity.html
Whether it was a good idea or not depends on whether the pier generated enough revenue to exceed the amount that's been paid in interest over the last 367 years.