There is a big difference between a bond with a negative yield to maturity than a bond with a negative coupon rate. Many in the market conflate the two.
We are searching for bonds that pay a negative coupon rate. Rare, but some do exist.
Here is a good clarification.
Because of the complexity of having a negative coupon, it is common on negative-yielding issues to sell the bonds at a cash price higher than par. This means the issuer pays back less than the amount borrowed, removing the need to figure out how to organise reverse coupon payments.
This is one of the reasons negative yields on bond issues remain a rarity and off limits to many investors.
In the corporate bond world, the likes of Deutsche Bahn have issued negative-yielding bonds in the past, and this month Merck sold three tranches of debt, the shortest of which held a negative yield. – Reuters
But they do exist
France issued its first-ever 10-year bond at a negative borrowing rate on Thursday, meaning investors pay, rather than receive, interest for the privilege of owning French sovereign debt, said the state debt management agency, AFT.
AFT said in a statement that it issued 9.996 billion euros ($11.3 billion) in long-term bonds, with just under half — or 4.972 billion euros — in the form of 10-year bonds at a rate of -0.13 percent. – France 24
This is an interesting one.
Copenhagen | In the world’s biggest covered-bond market, a Danish bank says it’s now ready to sell 10-year mortgage-backed notes at a negative coupon for the first time.
It’s the latest record to be set in a world that’s being dragged down by ever lower interest rates. In Denmark, where Jyske Bank will offer 10-year mortgage bonds at a fixed rate of minus 0.5 per cent, average Danes will borrow at rates far lower than those at which the US government can sell its debt. – Financial Review
Global Macro Monitor 
Excellent of a complex subject. John porter, Mendocino
Gary, excellent explanation . I posted a comment. John
On Thu, Aug 8, 2019 at 5:50 PM Global Macro Monitor wrote:
> macromon posted: “There is a big difference between a bond with a negative > yield to maturity than a bond with a negative coupon rate. Many in the > market conflate the two. We are searching for bonds that pay a negative > coupon rate. Rare, but some do exist. Here is a go” >
But negative interest rates and negative yields have turned bond investing into a casino where buyers keep waiting for the “greater fool” to come along.
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“at a rate of -0.13 percent”
Is that the coupon rate or YTM? It isn’t clear at all from the article that it’s the coupon that’s negative.
YTM. I have yet to see any bond with a negative coupon rate. Don’t think one could ever be issued. Negative yields are the result of unmoored financial markets and monetary policies coupled with trading bots without context and momentum traders. When say France issued a bond with a negative yield, the coupon was north of 2 percent but the issue price was north of say, 150.
Yeah that makes sense, pay enough for any bond and you’ll push the traded yield down below 0.
Still, even if you bought a bond with a negative coupon rate, and even if you held it to maturity, you could end up with a positive return if interest rates rose enough later on for the reinvestments to offset it.
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@macromon
The Jyske Bank 10 bonds do have a negative coupon and are issued at a price below 100, like all Danish mortgage bonds have to. The trick is that they are annuities, so the negative coupon is just subtracted from the quarterly principal payment. So it is in some ways not a real negative coupon.
This article has a bit more detail:
http://news.coveredbondreport.com/2019/08/annuity-structure-allows-jyske-negative-coupon-milestone/
Intereresting… Can you get an intererest only negative coupon? Or a 10-year bullet negative coupon? I haven’t seen it anywhere?