Stocks' strength was largely due to solid earnings reported before the opening bell, though some strategists are forecasting shares will continue rallying as the dollar's relative value declines.
"Weakness in the dollar and strength in equities is really the key inner market theme that's going on right now," Oppenheimer technical analyst Ari Wald said Monday on CNBC's "Power Lunch."
"The dollar is trading off the perceived changes in global monetary policy. In 2014, it was the divergent policy, a tighter Fed and an accommodative ECB causing a surge in the dollar, and that's really what caused a lot of destructions underneath the surface when commodities collapsed and [market] breadth really narrowed," he said, referring to a measure of how many stocks are rising at a given time.
As the European Central Bank has moved to unwind its years of quantitative easing, the dollar has depreciated against the euro, Wald noted on Monday. In addition, it now looks like the Federal Reserve will be less aggressive in raising rates than some had previously anticipated. The next clue about Fed policy will come on Wednesday, when the central bank releases a policy statement.
The euro's strength against the dollar is likely to continue, said Marc Chandler, global head of currency strategy at Brown Brothers Harriman. But he likes American stocks over European names at this juncture. He believes the equity market has gotten "way ahead of itself on Europe."
"The thing we've been pointing out to our clients is that so far this year, despite these fund managers and analysts liking European stocks on an unhedged basis, that the S&P 500 has actually done better, about 4 percentage points better than the Dow Jones 600 in Europe. So, I think, as this continues, I think we'll see people beginning to move back into the U.S., afraid of missing the returns," Chandler said Monday on "Power Lunch."
"The USD has sold off and U.S. yields are lower as markets see diminishing prospects for legislative dealmaking in Washington. As we go into August, our key forecasts are generally unchanged but risks around those targets are growing," Bank of America Merrill Lynch foreign exchange strategist John Shin wrote Tuesday in a note to clients.
Though Shin noted its recent pressure, he forecasts upside by the end of the year, with a euro-dollar target of 1.08, as compared with its current level near 1.17. The dollar index, which measures the greenback's strength against a collection of foreign currencies (mostly the euro), has declined over 8 percent year to date.