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I’m seeing the first signs of a new relationship between stocks and the U.S. dollar.

Ever since Lehman Bros went into bankruptcy in the fall of 2008, the dollar and stocks have been negatively connected. When the dollar went up, stocks went down, as investors saw any hint of risk as a reason to sell stocks and buy dollars (and dollar-denominated Treasuries). When the dollar went down, stocks went up, as investors decided that risk had receded enough so they could buy stocks again (and sold dollars and dollar-denominated Treasuries to do so.)

For the last two months, however, the negative connection has been getting weaker and weaker with commodities and stocks, on the one hand, and the U.S. dollar, on the other, moving in the same direction.

So far in December, the negative connection has come apart completely, according to Bloomberg. Since December 1, the Dollar Index, which tracks the performance of the U.S. dollar against the euro, yen, pound, Canadian dollar, Swiss franc, and Swedish krona, has moved in sync with stocks on more than half of all trading days. For the first 11 months of the year the U.S. dollar and stocks moved in opposite directions on seven out of every 10 days.

The dollar and commodities have also moved in tandem recently. The Reuters/Jefferies CRB Index of commodities is up 2.1% from the end of October through December 18, Bloomberg reports. During that same period the U.S. dollar is up 1.8%.

The reason for the shift, I’d speculate, is a change in the way that investors view the U.S. economy in both absolute and relative terms.

In absolute terms the consensus after recent data is that the economy will grow strongly in 2010. Strong growth is good for stocks, of course, since more growth means higher sales and higher sales mean higher profits. Strong economic growth would also bring the Federal Reserve closer to ending current benchmark interest rates near 0%. Stronger economic growth and higher interest rates would both be good for the U.S. dollar.

If the economy looks strong enough that diminishes fears that higher interest rates or a strong dollar will significantly slow growth.

In relative terms the U.S. dollar and U.S. stocks are getting a boost from troubles in the Euro Zone and Japan. Soaring budget deficits in the PIIGS economies—Portugal, Italy, Ireland, Greece, and Spain—have increased worry about the euro and raised the odds that the Euro Zone economic recovery will be weaker than that in the United States.

 In Japan the economy has slipped back into deflation (see my post ) and could well be sliding toward recession again. GDP growth in Japan came in at an annualized rate of just 1.3% in the third quarter. That was down from an expected 4.8% growth rate. The country is looking at an estimated annual supply-demand gap of $390 billion, economists estimate. (That gap is the difference between what the economy can produce when running at full capacity and what it is producing now given what customers are actually demanding.)

A weak yen and the return of deflation means that the Japanese currency can step back into the carry trade as a replacement for the U.S. dollar. Traders can pay back dollars and liquidate their dollar loans but put the same bets on commodities and emerging market stocks on by borrowing in yen.

I wouldn’t put my kids’ college money at risk on a trend that’s less than a month old and where the pattern may be heavily influenced by end of the year profit-taking, it the potential shift is sure worth watching.