How to play a stronger dollar

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The assets most likely to benefit from the U.S. dollar's march higher may not be stateside, with analysts looking to Europe and other regions.

"It's a positive for European equities," said Pascal Blanque, chief investment officer at Amundi Asset Management, which has over $1 trillion under management.

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"[Europe's] the region in the world where the big companies are the most global," he said. "To an extent, this offsets the lower growth of Europe, especially when the euro is going down."

A weaker euro means earnings in other currencies, especially the U.S. dollar, will flatter corporate bottom lines after conversion.

The dollar's strength has certainly given the euro a beating, with the common currency shedding more than 6 percent against the greenback since the end of June. More broadly, the dollar index is sitting at its highest levels since summer 2010, up more than 6 percent since the end of June.

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Economists say the greenback's new fans are reacting to growing confidence in the U.S. economy, especially compared with the less-than-rosy outlook in Japan, Europe and China.

Asia could benefit

Some expect Asian assets will benefit as the U.S. dollar advances.

"A stronger U.S. dollar today means stronger growth in the U.S. economy relative to global gross domestic product (GDP) six months down the line," Citigroup said in a note Monday. "The beneficiary in particular of this stronger growth is Asia within emerging markets," it said.

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Traditionally, a stronger U.S. dollar was considered a negative for emerging markets, but Citigroup noted that fewer countries are pegging their currencies to the greenback. In addition, the emerging market corporate sector has become more international, it said.

But not all emerging markets will benefit from a stronger buck, largely due to commodity prices, which are denominated in dollars.

"A stronger U.S. dollar tends to be unfriendly for commodity exporters but friendly for commodity importers - a negative for EMEA (Europe, Middle East and Africa) and Latin America, but a positive for Asia," Citigroup said.

US stocks left behind?

But there's one region that may not get much of a leg up from a stronger greenback: U.S. stocks.

The S&P 500 has outperformed since 2009 amid dollar weakness, Barclays said in a note Monday. Since the end of 2009, the S&P 500 has climbed nearly 80 percent.

"Easy Federal Reserve policy has led to a weaker dollar, but has also fuelled earnings, boosting behavior such as equity buybacks," Barclays said.

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"We would not conclude that dollar strength will necessarily lead to yet more outperformance of U.S. equities," it added. "At the very least, a significant shift in the trend of net equity outflows is needed, which may be a challenge, given that U.S. valuations are already a little stretched."

It noted that foreign funds have been pulling out of U.S. equities this year, while U.S. purchases of foreign equities are on the rise.

In August, $1.6 billion flowed out of U.S. diversified equity funds, the fifth consecutive month of redemptions, according to data from Lipper.

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To be sure, some think expectations the dollar will continue to rise could boost foreign investment in U.S. stocks.

"You have more incentive to go there," as the stronger greenback will boost returns when they are converted back into the home currency, Beat Siegenthaler, chief strategist at UBS, told CNBC earlier this month. He noted that recently funds have flowed out of European equities and into the U.S. in the wake of the Russia-Ukraine tensions.

—By CNBC.Com's Leslie Shaffer; Follow her on Twitter @LeslieShaffer1