In theory, negative yields are impossible. Why would you buy something that pays you back less than what you paid? However, this is exactly what is happening across Europe. Almost a dozen European countries now have bonds with a negative yield. What does that mean and how does that come to exist?
WHAT IT MEANS
The yield is the return received by a bond investor expressed as a percentage of the purchase price. For the sake of simplicity, assume a bond maturing in x years has no coupon and $100 principal, i.e. the bond gives the investor $100 after x years.
If you pay <$100 for this bond, then you will receive a + yield.
If you pay exactly $100, then you get a 0% yield.
If you pay >$100, then you get a - yield.
In effect, a negative yield means you lend someone MORE than $100 with the expectation of only receiving $100 back.
HOW IT COMES TO EXIST
In theory, this bond should never exist. Why would you ever lend more to someone than s/he will pay back? You can keep the cash under your mattress and get a better yield (of 0%) with zero risk! However, this bond DOES exist, and in fact, it is estimated that there is over $2 TRILLION of negative-yield bonds today. For example a 2 year German "bund" (which is Deutsch for bond) has an almost -0.30% annual yield, so you are effectively losing 30 cents annually for every $100 you invest. In fact, Germany, France, Netherlands, Belgium, Finland, Austria, Switzerland, Sweden and Denmark all have negative-yield 2y bonds.
Here is a list of four reasons that I can think of (which is certainly not exhaustive) to justify this situation:
1. RESERVE REQUIREMENTS (RR) and INTEREST ON RESERVES (IOR)
Banks are required by financial regulation to hold a percentage of their assets as reserves with the central bank (you can think of a CB as a bank for banks). Banks can keep their reserves with the CB either in 1) cash deposits or in 2) gov't bonds. So why not keep it all in cash? In normal times, banks receive some interest on their reserves (IOR), just as you would receive interest in your checking/savings account with your bank. However, here's the catch: now some central banks such as the ECB (European Central Bank), SNB (Swiss National Bank), Sweden's Riksbank and Danish National Bank have negative IOR, which is effectively a fee on cash deposits. To a bank that's being charged to hold cash in their reserve accounts, holding negative-yield bonds instead doesn't look so bad.
2. FX REDENOMINATION and CURRENCY BETS
If the Eurozone monetary union breaks up, there will be 19 new currencies. Countries with stronger economic and fiscal positions will almost certainly have their new currencies appreciate. For example, in this breakup scenario, German bunds, instead of paying you Euros (EUR) which would no longer exist, would probably pay out in newly created Deutsche Marks (DEM). Since DEM would significantly appreciate against EUR, the negative yield would be more than compensated. This is a popular idea for journalists to write about in the media, but since the chances of this are insignificant and the mechanics of this FX redenomination is uncertain (the contracts on which these bonds are written have no clause on the possibility of redenomination), this has the least explanatory power out of the four theories here. Still, it is worth mentioning and it's a cheap bet to take (you pay 0.30% annually for a 2y bund but you have a chance, albeit low, of making double-digit returns if the Eurozone falls apart).
A similar thing is playing out in Switzerland and Denmark, which are not part of the Eurozone, but have historically maintained currency pegs with EUR. When the SNB removed the Swiss Franc (CHF) peg, it immediately appreciated by 20% against EUR in one day. Investors who believe that Denmark will do the same thing with its Danish Krone (DKK) peg can purchase Danish negative-yield bonds for a similar bet.
3. "PONZI BORROWERS" or GREATER FOOL THEORY
If you hold a bond to maturity and there is no default, your total return will be exactly the yield at which you purchased the bond. For a negative yielding bond, this means that you are guaranteed a negative total return by holding to maturity. However, if you sell the bond before maturity, your total return will also be determined by your sale price. If your sale price is higher than your purchase price, you will have a positive total return.
An investor who borrows money to purchase an asset with the expectation to sell at a higher price before maturity was termed by economist Hyman Minsky as a "Ponzi borrower". Due to the inverse price-yield relationship of bonds, this means that Ponzi borrowers who purchase bonds must have the expectation that yields will go down. For negative yielding bonds, that means that Ponzi borrowers are expecting them to become even more negative! This might not be so ridiculous, especially if central banks cut their deposit rates even further into negative territory.
Although buying negative-yield bonds may be foolish, there may be even greater fools who are willing to buy them from you later. Hence, the Greater Fool Theory.
4. (LACK of) SUPPLY and (TOO MUCH) DEMAND
Finally, the central banks themselves are buying these bonds in large size. The ECB has committed to buying over $1.2 trillion of assets over the next 1.5y, most of which will be Eurozone gov't bonds. It is willing to buy bonds with yields as negative as -0.20%. Furthermore, there is little sign that gov'ts will pick up bond issuance in any size, keeping supply very tight, as gov'ts aim for deficit targets mandated by Eurozone treaties. Denmark has actually completely stopped issuing new gov't bonds.
Ponzi schemes end when there are no more new investors willing to pay ever-increasing prices to existing investors. This inevitably happens with all Ponzi schemes. However, when the perpetrator of the scheme controls both supply (through official fiscal constraints on gov't borrowing) and demand (through bank regulatory requirements as well as direct outright purchases by the central bank), the scheme can be perpetuated for much longer than you'd think.