Some $16 trillion of global debt, including corporate and sovereign bonds, now yield less than 0%, up from almost $13 trillion in early July.

Investors, desperate to grab any yield, have rushed into longer-dated bonds: U.S. 30-year borrowing costs are down 60 basis points in August, set for their biggest monthly decline since the 2011 euro debt crisis.

Long-dated Japanese bond yields have also hit three-year lows and are set for their biggest monthly declines in more than three years.

"The bond market is sending a clear message that it expects low economic growth and low inflation," said Neil MacKinnon, global macro strategist at VTB Capital in London. "It is saying: secular stagnation, here we come."

Biggest monthly fall in 30-year USTs since 2011 - https://fingfx.thomsonreuters.com/gfx/editorcharts/MARKETS-MILESTONES-FACTBOX/0H001QESK83L/index.html

Here are a few milestones charted by bond markets as the great yield collapse of 2019 unfolds:

1/INVERTED!

A key part of the U.S. Treasury yield curve, a closely tracked recession indicator, inverted in mid-August for the first time in 12 years and further still in recent days.

The curve, measured by the gap between two- and 10-year U.S. bond yields, has inverted before every recession in the past 50 years and sent a false signal just once.

No wonder that the warning signal from the world's most important bond market has rippled out. Britain's bond yield curve briefly inverted this month. The German curve is at its flattest since the global financial crisis.

"Given there hasn't been a single lead indicator as good as the yield curve at predicting U.S. downturns in the past 70 years, the inversion has to be taken very seriously," said Deutsche Bank strategist Jim Reid.

U.S. yield curve inverts for first time since 2007 - https://fingfx.thomsonreuters.com/gfx/mkt/12/5333/5285/Annotation%202019-08-28%20150328.png

2/THE NEGATIVE CURVE CLUB

Sovereign bond yield heatmap - https://fingfx.thomsonreuters.com/gfx/mkt/12/5334/5286/bondmarketmilestones.png

In early August, 30-year German and Dutch borrowing costs fell below 0%, bringing the two countries into a club of developed countries, whose entire sovereign bond yield curves pay negative yields. Finland now joined them.

The group already included Denmark and Switzerland. It was briefly joined in mid-August by Sweden, which saw yields on its longest-dated bond, a 20-year maturity, drop below 0% for the first time.

Japan could be the next to join, with bond yields out to 15 years below 0%.

With investors willing to pay governments to hold their debt, pressure is rising on the likes of fiscally prudent Germany to use unprecedented market funding conditions to ramp up spending and fight weak growth.

3/ AND THE U.S. TOO?

Technically speaking, the United States also now has negative-yielding bonds. Of late, yields on 10-year Treasury Inflation Protected Securities (TIPS), securities offering protection against inflation, have pushed into negative territory.

The yield on a TIPS security essentially is the yield on a plain-vanilla Treasury bond, minus expected inflation. Given 10-year TIPs now yield minus 0.07%, it means the equivalent Treasury bond is paying less than the expected inflation rate.

U.S. TIPS yield - https://fingfx.thomsonreuters.com/gfx/editorcharts/USA-BONDS-TIPS/0H001QES982T/eikon.png

4/PAID TO TAKE A MORTGAGE

Jyske Bank this month became the first in Denmark to offer a negative rate on a mortgage, in effect paying customers 0.5% to borrow money for 10 years.

The borrowers would still make monthly payments towards the initial amount they borrow, but they would eventually pay back less than the original amount.

While rare, the move in Denmark is part of a broader trend in tumbling mortgage rates globally. Borrowing costs on U.S. 30-year and 15-year fixed-rate mortgages have fallen to their lowest since November 2016.

5/FIRST SIGN OF TROUBLE?

There are some signs that investors' willingness to hold negative-yielding debt is being sorely tested. Last week, Germany auctioned a 30-year government bond at negative yields. But the euro zone's benchmark bond issuer sold just 824 million euros, versus a 2 billion-euro target.

That's a sign some private investors are being driven out of the higher-rated euro debt markets by negative yields. The new 30-year Bund had a 0% coupon, which means investors who hold the bond to maturity get nothing back.

Germany sells first negative-yielding 30-year bond - https://fingfx.thomsonreuters.com/gfx/editorcharts/MARKETS-MILESTONES-FACTBOX/0H001QESN83W/index.html

6/ NOT ALL BONDS ARE EQUAL

Not all bonds are partaking in the rally. Since President Mauricio Macri lost an Aug 11 primary election round to populist-leaning opposition candidate Alberto Fernandez, the tumble on Argentine dollar bonds has hit many investors, including some big-name asset managers such as Franklin Templeton.

Argentina's 100-year dollar bond, issued in 2017 at par, has been hard hit, too, falling more than a third in five days. The price, which lurched even lower after the government said on Aug. 28 it would launch a debt reprofiling plan, currently trades at 43 cents in the dollar.

Tale of two centuries - https://fingfx.thomsonreuters.com/gfx/editorcharts/MARKETS-MILESTONES-FACTBOX/0H001QESP83Z/index.html

(Reporting by Dhara Ranasinghe and Tom Arnold in London; additional reporting by Richard Leong in New York; graphics by Ritvik Carvalho; editing by Sujata Rao and Larry King)

By Dhara Ranasinghe, Ritvik Carvalho and Tom Arnold