Many investors have short memories. Make an argument based on a trend over the last year or two, and they'll happily assume that the trend will last indefinitely.

One such trend that has gained a lot of attention lately is the relationship between the U.S. dollar and the stock market. On an increasingly frequent basis, whenever the dollar has gone up, stocks have fallen, and vice versa. But if you think that puts the U.S. in a no-win situation in which investors have to choose either another lost decade for stocks or continuing devaluation in the dollar's value, there's another alternative you may not have considered: the trend may come to an end.

The theory behind the dollar-stock relationship
Look around the financial world, and you'll find plenty of explanations for why stocks and the dollar have gone their separate ways. One popular theory involves the carry trade, in which international investors borrow U.S. dollars at the currently prevailing extremely low interest rates, then exchange them for higher-yielding assets denominated in foreign currencies. But the problem with that theory is that it hasn't held true for the other major carry-trade currency: the Japanese yen. Over the years, few currencies have gone up as much as the yen, despite rock-bottom interest rates that have prevailed throughout much of its 20-year economic doldrums. And while the Japanese stock market hasn't risen nearly as much as the S&P 500 over the past couple of years, it hasn't gone down.

On a narrower scale, the idea that dollar weakness creates stock strength for certain companies makes quite a bit of sense. For Yum! Brands (NYSE: YUM), Heinz (NYSE: HNZ), and Philip Morris International (NYSE: PM), which rely on the international popularity of their consumer brands for the majority of their total revenue, strength in the dollar only reduces the value of their foreign business, while a falling dollar makes their foreign currency earnings that much more lucrative. Similarly, technology companies including Qualcomm (Nasdaq: QCOM), Texas Instruments (NYSE: TXN), and Intel (Nasdaq: INTC) also rely on overseas sales for the vast majority of their overall business.

All good (and bad) things come to an end
The best argument against the dollar-stock relationship, however, is what experience tells you: Historically, you haven't always seen it. Over the long haul, the dollar and stocks have moved in tandem for years at a time, only to delink during other periods. Moreover, the shift between negative, positive, or no correlation can happen extremely quickly.

For investors, that has clear ramifications. Perhaps the most important is not to get too wedded to the idea that you can use stocks and the U.S. dollar as hedges for each other. You might think, for instance, that an anti-dollar currency ETF like CurrencyShares Euro Trust (NYSE: FXE) would track in the same direction as stocks, given that the currency ETF should rise when the dollar falls. But those who believe that stocks can't fall as long as the dollar is weakening will be in for a big shock if the next financial crisis brings with it a breakdown in that relationship.

Nevertheless, once an explanation for a market trend gains a following, it can become a self-fulfilling prophecy. Therefore, if you want to keep your eyes open for a possible reversal of the dollar-stock relationship, watch out for U.S. interest rates to rise. Higher rates could signal the end of the carry trade, giving the U.S. dollar a huge boost as speculators rush to pay off dollar-denominated loans.

Take the long view
Many investors pay a lot of attention to short-term trends, because they can be quite lucrative in short periods of time. Their problem, though, is that they only last until they don't -- and often, it's impossible to predict exactly when they'll break down.

While keeping an eye on those short-term trends is a smart move, you should always keep the bulk of your attention focused on what's happened over longer periods of time. That way, you can avoid making any silly mistakes just because of a temporary lapse of reason in the financial markets.

International stocks are another investment that would like to see the dollar continue to weaken. Learn which international fund makes the cut in The Motley Fool's free report, 3 ETFs Set to Soar During the Recovery. To read the whole thing, click here.

Fool contributor Dan Caplinger always wanted to be a mythbuster. He doesn't own shares of the companies mentioned in this article. Philip Morris International is a Motley Fool Global Gains pick. Heinz is a Motley Fool Income Investor selection. The Fool owns shares of and has bought calls on Intel, which is a Motley Fool Inside Value recommendation. Motley Fool Options has recommended buying calls on Intel. The Fool owns shares of Philip Morris International, QUALCOMM, Texas Instruments, and Yum! Brands. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Fool's disclosure policyis no myth.