NEW YORK (CNN/Money) - There are two parallel universes in the financial realm, stocks and bonds, and unfortunately the denizens of one or the other could be burned badly in the months ahead.

The bond market remains on fire, with yields dropping to levels that seem almost impossibly low, setting up the possibility of a nasty snapback -- unless the fears of disinflation and deflation have more credence than most economists give them. If that's the case, then stock market bulls, who have bid the Dow up 8 percent since March in anticipation of recovery, should be the ones worrying.

The latest catalyst for the bond rally is remarks from the head of the Bank of Japan, Toshihiko Fukui. This is the Alan Greenspan of Japan.

According to the Japan Times, Fukui said Friday, "the world's major economies are on the verge of accelerated disinflation as deflationary pressures grow on a global scale."

Here's a direct quote the Bank of Japan chief from the article: "I think world price movements are about to trigger accelerated disinflation." And he said this at a news conference so there's no doubt that this is the message he intended to deliver.

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Seeing this, bond market bulls, who must be drunk with speculative fever by now, bought more bonds. The yield on the benchmark 10-year U.S. government bond got down to as low as 3.29 percent on Friday, 3.29 percent, a fresh 45-year low, and set a new-record low for the 30-year yield of 4.24 percent.

And it's not just here -- European bonds are in rally mode as well. Today in Germany came news that the inflation rate could drop below 1 percent. And there are some big brokerage analysts talking about the possibility not only of deflation in Germany, Europe's biggest economy, but also in France, the continent's third-biggest.

Now, anyone who follows markets knows that when a market gets the bit in its teeth there's just no stopping it -- markets overshoot, the trend is your friend, don't step in front of a speeding train, etc.

And there's no doubt that a large part of the reason for the big move in bonds is the bet by speculators that the Fed may have to start buying up notes and bonds to push money into the economy. In fact, speculators don't even have to be correct that the Fed actually does that, they just have to be correct that other people will buy bonds in anticipation of such Fed action. And then the speculators have to time their departure.

But a cautious investor takes heed of all the signals he or she can. And right now bonds are telling you that the world economy is under heavy downward price pressure with economies sluggish, a lot of excess capacity holding business investment down, and consumers made cautious by job losses.

If bond bulls are right, and economies stay weak and companies can't raise prices or, worse, they have to cut them, then we're not living in a universe that's good for corporate profits. And that can't be good for stocks.

Whichever universe you inhabit, keep watching the other dimension.

Kathleen Hays anchors The FlipSide, airing Monday to Friday on CNNfn. As part of CNN's Business News team, she is also a regular contributor to Lou Dobbs Moneyline.