Investors on Wednesday eagerly snatched up a new two-year German bond with a zero-percent coupon, meaning investors were willing to pay to loan money to Europe's strongest economy when expected inflation is factored in. The yield ended at 0.07 percent.

In what Der Spiegel magazine called a remarkable feat, demand outpaced available supply of the bond as investors shoveled €4.56 billion ($5.77 billion) into Germany's central bank, a symptom of deep concern over the future of the euro zone.

We are observing a flight into safety in the markets. Many investors are putting their money only in places where there is a high probability that of getting it back. Investors are forfeiting returns in exchange for a higher level of security, Commerzbank analyst Alexander Aldinger told the Berliner Morgenpost.

The yield on U.S. two-year bonds is 0.29 percent and the same bond from Japan is giving up 0.1 percent. The German Ministry is keeping mum on whether more zero-percent bonds will be issued.  

Meanwhile, the euro hit a 21-month low against the dollar ahead of an informal meeting of European leaders in Brussels, the staging ground for preparations for the official June meet.

The time has come to put more emphasis on the measures more directly linked to encouraging growth and jobs . . . and to discuss in the most constructive manner innovative, or even controversial, ideas, European Council President Herman Van Rompuy said Wednesday in a statement to European Union heads of state.

Pre-meeting jitters also sent the benchmark German 10-year bond yield down six basis points to 1.41 after three days of losses.

Conditions remain very fragile, Daphne Roth, the head of ABN Amro Private Banking in Singapore, told Bloomberg Television. There is a strong likelihood that Greece might exit the euro zone. Even if it stays, going forward there will be a lot of volatility.

The only way yields would fall further... is if people pay Germany to look after their money for them, Gary Jenkins, director at Swordfish Research, told Reuters.

In other words, negative yields.

Some analysts says a Greek bailout is more likely than a Greek exit, but that German bonds are likely to continue to be in high demand.

We believe there is a shortage of safe havens in this environment and we think they (Bunds) are likely to perform extremely well over the next six months, Stuart Thomson, chief market economist and fixed income fund manager at Ignis Asset Management, told Reuters.