The U.S. financial sector is gradually severing its links with an increasingly troubled Europe, but the pace probably isn’t fast enough to prevent contagion if things go terribly wrong.

The money-market funds that hold about $1.5 trillion in U.S. savings would be among the first to suffer if Europe's sovereign-debt problems bring down its banking system. That's because the funds have invested heavily in the debt of European banks -- a fact Federal Reserve Chairman Ben Bernanke has publicly noted in assessing the potential repercussions of a European meltdown.

The managers of money-market funds recognize the risk, and have been paring their European exposure. Fitch Ratings estimates that as of September, 37.7 percent of all money-market assets were invested in European banks, down from 51.5 percent in May.

Still, that leaves the funds' exposure to Europe at more than $500 billion. Even a small loss on such an amount could force a fund to "break the buck," bringing the share price below $1 as the Reserve Primary Fund did after the bankruptcy of Lehman Brothers Holdings in September 2008. That, in turn, could trigger a run on the funds by investors, crippling short-term lending markets on which companies rely for such everyday activities as buying supplies and paying their workers.

In other words, the U.S. and other countries outside Europe still have a lot to lose if European leaders don’t resolve their crisis.

(Mark Whitehouse is a member of the Bloomberg View editorial board)