Don't relax just yet, euro-dollar parity's still on its way

The euro rallied on Wednesday after the U.S. dollar tumbled, following weaker-than-expected U.S. retail data and spikes in German and U.S. government bond yields, which have rattled markets and pushed investors to reconsider their short bets on the single currency.

Having touched lows of around $1.04 in March after the launch of the European Central Bank's massive trillion-euro bond-buying program, the euro has climbed against the dollar as European government bond yields have edged higher and a resolution to debt talks between Greece and the euro zone have proven elusive.

Read MoreDollar-euro parity: What a one-to-one exchange means

An employee counts euros and U.S. dollar notes in a currency exchange store in Lisbon, Portugal.
Mario Proenca | Bloomberg | Getty Images

The dollar hit a more-than three-month low against a basket of major currencies after U.S. retail sales data missed expectations, helping to support expectations that the U.S. Federal Reserve will hold off on raising rates.

But longer-term, fund managers invested in U.S. markets are still expecting the dollar to return to strength from current levels of around 1.13 against the euro. This would leave euro-dollar parity, or a one-to-one exchange rate, still very much on the cards.

While the ECB has only just starting its quantitative easing program, the Fed is in the process of trying to wind its measures down, a move which has helped support the year-long rally in the dollar against a number of currencies.

Read MoreWhy rising European yields are a worry for stocks

But as the Fed is expected to hike rates later this year, with most analysts eyeing September, some investors are anticipating further dollar strengthening.

Looking at historical moves in the dollar, the currency tends to move over three- of four-year cycles, where 20-30 percent appreciation is normal. All this points to the recent 15 percent appreciation in dollar against a number of other currencies has more room to run, according to chief investment officer of real return and asset allocation at PIMCO, Mihir Worah.

"We think there is another 5 to 10 percent appreciation left in the dollar. Clearly if the dollar moves too fast, it impacts what the Federal Reserve does, but to put numbers on it - we see parity versus euro and 125 versus the yen. So another 5 or 7 percent from here wouldn't change what the Fed is likely to do from here," Worah said, speaking at the Morningstar investment conference in London.

In light of the euro's recent strength, a number of analysts have reconsidered the consensus long dollar, short euro trade after some weaker economic data from the U.S. pushed back expectations of a Fed rate hike.

Global chief investment officer of UBS wealth management, Mark Haefele said while his base case is still for further euro depreciation, with a forecast of $1.08 on a six-month view, he closed the underweight position in the euro relative to the U.S. dollar last week.

UBS wealth management have moved back to neutral euro dollar position as some of the major drivers for the underweight euro position, including strong economic growth, the prospect of interest rate hikes in the U.S., and QE in the euro zone have "played out successfully."

But head of U.S. equities and fund manager at Artemis, Cormac Weldon, said the 20 percent surge in the greenback, or the "dollar shock" will continue as interest rates in the U.S. are set to go up later in the year.

Read MoreGreenspan: Get readyfor another taper tantrum

"I think it depends how far and how fast interest rates go up. We think a (U.S.) rate rise will be relatively gentle but by the end of next year perhaps they could be over 100 basis points. So yes, we do believe it is more likely to have further dollar strength. Against the euro, we think so, against the pound, not sure," Weldon said, also speaking from the Morningstar conference.

Analysts at Deutsche Bank agree. The sell-off seen in European bond yields, which followed softer-than-expected economic data in the U.S. in the first quarter helped the dollar to weaken, according to fixed income analyst at the bank, Dominic Konstam.

But as U.S. data picks up, expectations of a Federal Reserve rate hike and possible further easing from the ECB and the Bank of Japan (BOJ) come through, bond yields in Europe will fall again, which will support the dollar.

"We reckon that either (expectations of) Fed tightening or ECB /BOJ easing could re-strengthen the dollar and start the chain of events resulting in the need for more European QE, pushing bund yields back toward the deposit rate lower bound. The probability of one or both of these occurring is reasonably high," Konstam said.