Interest rates are now negative, below zero, for a growing number of borrowers, mainly in the financial markets. It means in effect they are being paid to borrow someone else's money. So what on earth is going on?
Perhaps the first thing worth stating is that negative interest rates are probably not coming to a High Street near you in the near future.
It is a phenomenon that has had economists scratching their heads. In fact there is a well-known (to economists) term for the idea that interest rates shouldn't go below zero. It's the "zero lower bound".
It has been breached. There is probably a limit to how much further we can go in that direction. But at the very least recent developments show the zero lower bound is not as rigid as it was widely thought to be.
One point worth spelling out is that we are not talking about negative real interest rates. That is where you have an interest rate that may be above zero but it is lower than inflation. That means that a borrower's total repayments have less purchasing power than the amount they first borrowed.
That is not so unusual. As long as there is at least moderate inflation, central banks can get real rates below zero to stimulate economic recovery and there have been many episodes of that.
No. We are talking here about what economists call nominal interest rates below zero, making no allowance for rising (or falling) prices.
The reason it is so strange is this: normally a potential lender can choose not to lend and just sit on the funds. That is equivalent to getting a nominal interest rate of zero. Not great, but surely better than an interest rate of less than zero. That is the basic idea behind the concept of the zero lower bound.
So why do we have negative rates at all?
Some examples are central bank policies. In the eurozone, in Denmark, Sweden, Switzerland and Japan, central banks have decided to have a negative rate on commercial banks' excess funds held on deposit at the central bank. In effect, private sector banks have to pay to park their money.
In the case of Sweden, the central bank has gone below zero on the rate it lends money to the banks, its main policy tool.
The aim in the eurozone is to stimulate economic growth and to raise inflation, which is also below zero and even further adrift of the European Central Bank's target of below but close to 2%. In Sweden too, it is about raising inflation.
In Denmark and Switzerland the immediate objective has been to prevent the currency rising too much. The idea of lower and negative interest rates is to discourage investors from buying the local currency, which tends to push its value up.
These policy decisions are not the most surprising examples. They are the actions of central banks whose job is to keep inflation under control and to support economic growth and employment. If they judge that their economic policy objectives are best pursued by negative official interest rates, why not?
Betting on currencies
It gets slightly stranger when the lender is a private sector firm, which you would normally expect to try to maximise its profits.
In fact it is possible in some circumstances that a negative interest rate might be profitable, if you think currencies are going to move in your favour. Take the case of Switzerland, where, earlier this month, the government borrowed money for 10 years in the financial markets at an interest rate slightly below zero.
It's a safe investment. The chances of the Swiss government not repaying are negligible. You can't get high returns on such a safe investment anywhere just now.
If you are an investor in, say France, you might think that the Swiss franc will rise enough against the euro that you can make money by the time you bring your investment home - enough to compensate for the negative interest rate.
Something similar has been going on with Germany. The possibility that the eurozone might break up lingered after the worst of the crisis and arguably has still not entirely gone away.
If it did disintegrate, a holder of German government debt would presumably be repaid in German marks, which would probably gain in value. That has helped keep some of Germany's government borrowing costs below zero.
Now that doesn't explain why some Spanish rates are below zero (though not by as much as Germany's).
There are some other possible factors. First, for banks any excess funds parked at the central bank involve paying the ECB's negative deposit rate. Buying a government bond might be less costly, even if there is a negative return.
That is part of the reason some banks are lending to each other at negative interest rates - including some of the rates known as Libor, in euros, Swiss francs and yen. It may be preferable to lend money to another bank or a government rather than pay to keep it at the central bank.
In addition some types of investment funds essentially have to buy government debt, so there is a certain amount of what has been called passive investment going on, despite the poor returns. It's a practice that reflects the days when safe government debt did yield some money.
Low interest rates are of course unwelcome news to savers. Negative central bank rates have started to lead to some bank customers being charged a negative rate on their accounts, mainly businesses with large balances.
How low could rates go?
These are some of the factors that help explain how we get from extremely low positive interest rates to negative levels.
But it's worth recalling the reasons we were so close to the supposed zero lower bound in the first place.
It reflects the persistent weakness of many developed economies in the aftermath of the financial crisis. Central banks have kept their policy interest rates very low to stimulate economic growth and more recently to get higher inflation.
Investment (as a share of national income) is below its pre-crisis levels in the great majority of rich countries, by a hefty amount in some cases. If there is less demand for money to fund new investment, the cost of borrowing tends to be lower.
So will interest rates go even further into negative territory? Most that are negative are between zero and -1%
As things stand, anyone who doesn't want a negative interest rate on their bank account does have an alternative in the shape of hard cash. That does involve a cost: perhaps a fee for storing it somewhere safe or the risk of burglary if you keep it under the mattress.
A bank account is more convenient, which is why many people would, grudgingly perhaps, pay for one. But as it gets more expensive some probably would shift more towards hard cash, which means there is likely some limit on how far below zero rates can go.
There are some radical ideas about how to address this. Willem Buiter of Citigroup, formerly of the Bank of England, has produced a list of options, the most striking being the abolition of cash. He does have answers to some obvious objections, though views will vary on whether they are good enough and it is not part of any realistic political agenda at present.
The point is that allowing interest rates to go even further below zero could, he suggests, make central bank policies more effective in a situation of weak growth and very low inflation.
If those problems persist then perhaps negative interest rates will turn out to be a long-lasting feature of the economic landscape.