Today, there exists roughly $4.6-trillion worth of negative-yielding government bonds around the world.

Indeed, we’ve now entered a fifth dimension, beyond that which is known to most investors… A dimension where bank deposit rates are negative, purchasing power is constantly destroyed, and risk can exist without return.

In last week’s episode of the Fixed-Income Twilight Zone, the European Central Bank (ECB) announced its highly anticipated bond-buying program, or quantitative easing (QE). Each month until at least September 2016, the ECB will purchase 60 billion euros’ worth of bonds issued by euro-area central governments and agencies.

The ECB also confirmed that its purchases would include negative-yielding bonds. The German yield curve is negative out to four years, and France’s is negative out to three years.

Of course, buying negative-yielding bonds won’t do much to help the approximately 7.5 million Europeans between the ages of 15 and 24 who are neither employed, nor in education or training…

Nonetheless, when economies are facing deflation, central banks ramp up stimulus.

Japan, which has been on monetary morphine for years, has a yield curve below 0.1% all the way out to six years.

Now, some institutional investors, pension funds, and insurance companies in Japan and Europe may have to hold ultra-low-yielding bonds in order to adhere to mandates or track benchmarks.

But we’re under no such requirements.

That’s why U.S. investors should avoid a group of international bond funds with sizable exposure to ultra-low-yielding government bonds.

The Vanguard Total International Bond Index Fund (VTABX, VTIBX) has $27.6 billion in assets under management – three-quarters of which are government bonds. It has a 22.0%, 11.5%, and 9.5% allocation to Japan, Germany, and France, respectively. A similar ETF version of this fund, the Vanguard Total International Bond ETF (BNDX), has a lower allocation to Japan, but higher allocations to the U.K., Italy, and Spain.

Another mutual fund, the American Century International Bond Fund (AIDIX, BEGBX), holds 94% government bonds and has a 25% exposure to Japan.

Finally, a pair of State Street ETFs are stinkers, as well. The SPDR Lehman International Treasury Bond (BWX) should have been sold in mid-2014. Mathematically, I’m not even sure how a government bond fund would lose over 8% on a total-return basis in the past six months, but this fund did it. The SPDR Barclays Short Term International Treasury Bond ETF (BWZ) has such a low yield that it’s not worthy of consideration.

From a risk-return standpoint, there’s really no reason to own any of these funds. Basically, bond portfolios loaded with Japanese government bonds, German bunds, and French OATs have a huge weight around their necks.

I wouldn’t underestimate QE’s ability to artificially boost European financial asset prices (corporate bonds and stocks) and support excessive risk-taking, just as has occurred in Japan. Just make sure your bond funds don’t have significant exposure to the government bond markets in either region.

As I predicted, U.S. rates have declined, following global rates lower. Treasuries are virtually “high yield” compared with bonds in many other developed nations. The U.S. 10-year is currently at 1.82%.

And just imagine how far yields will fall if we get some real fear in the U.S. equities market.

Yet traders are still hugely short Treasuries, aggressively betting on higher rates for some reason. Don’t make the same mistake as them… There’s no telling what could happen in the fixed-income fifth dimension.