The U.S. greenback broke above the key 100 yen mark for the first time in over four years earlier this month and yen hit a low of more than 103 last week. On Monday, the dollar traded near its best level in more than six weeks against the euro but gave up some ground against the yen.
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"I'm not expecting a full-scale bull run for the dollar, but we may see it appreciate against other currencies for the next quarter or two," said Bryan Novak, director of trading at Astor Asset Management. "[But] if global growth starts to pick up, then you'll see some stabilization in the dollar."
Stocks, meanwhile, have continued to push upwards, with the Dow and the S&P briefly touching fresh all-time highs and the Nasdaq crossing above 3,500 Monday. The Russell 2000 index broke above the 1,000 level for the first time.
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"Much depends on the Federal Reserve and on the economic data," said Krosby. "If economic data are to get stronger, even modestly, then the U.S. dollar can continue to strengthen and it could also be good for stocks—especially the domestically-focused equities and it will help curtail rising commodity prices."
In recent years, weakness in the U.S. dollar was a positive for the stock market because it cheapened exports and increased the fortunes of multinational firms.
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The dollar also moved in the opposite direction of risk assets, and would move higher during the years since the financial crisis mainly when investors were seeking a safe haven. But now, it is moving higher on the view that the U.S. economy, while not vibrant, is the better place to invest.
"For some time, the minute the dollar strengthened against the euro, you saw the market having trouble gaining traction because the gain was a manifestation of worries in the euro zone," said Krosby. "Now, the rising dollar is sort of like a positive cushion for rising commodity costs, which is ultimately helping manufacturing and consumers and that's perceived as a major positive."
Still, Krosby warned that the stronger dollar could be a headwind for some mega-cap companies with large international exposure.
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"While the stronger dollar will help bring down commodity costs, the companies that are hurt have a bigger global presence," said Krosby. "You've already started hearing about it during this earnings season."