Let the post-taper forex trading begin!

One effect of the Federal Reserve's scaling back its bond-buying program: a stronger U.S. dollar. It's already started, and the bullish calls are heating up.

Bank of America Merrill Lynch and Nomura strategists predict that the euro will weaken to 1.25 next year, while Morgan Stanley is projecting 1.24. That's an 8 percent to 9 percent decrease from current levels.

"We think that tapering pace will be picked up and tapering completed by July to Sept," Derek Halpenny, a currency strategist at Bank of Tokyo Mitsubishi, wrote in an email to me. "So we anticipate by Q2 short-term yields in the U.S. will become unanchored to a degree which will be the trigger for greater dollar strength."

If the dollar strength is a sustained trend in the 2014, the impact will be felt far beyond the currency market.

(Read more: Dollar extends rally after Fed, yen held back by BoJ)

It's a double whammy for the bottom line of some of America's most recognizable companies—the multinationals, whose overseas profits in foreign currencies become worth less when they're brought home.

On Friday, McDonald's Japan lowered its profit forecast for the year by nearly 60 percent, partly because of the weaker yen.

Dollar-yen to trend higher: Pro

Other companies with significant overseas exposure include Colgate-Palmolive, which generates almost 80 percent of its sales abroad; Yum Brands gets three-quarters of revenues overseas, and Tiffany a little more than half.

Companies hedge their foreign currency exposure to protect themselves from fluctuations, but it can be tricky with outsize moves in foreign exchange.

For instance, Philip Morris International said in November that it expects an earnings-per-share hit of 40 cents in 2014 because of yen hedges that didn't work in the company's favor.

The stronger dollar isn't all bad news for the stock market.

Tobias Levkovich, chief equity strategist at Citigroup, has looked at sector performance during historical periods of dollar strength and weakness.

He's found that it can create opportunities as well, including in health care, software and services, and retail.

—By CNBC's Sara Eisen