The yen has also made big gains against the US currency.
The dollar fell from ¥120 at the end of January to ¥106 in early May, even though the Bank of Japan moved to a negative interest rate policy earlier this year.
The last couple of weeks, though, have seen the dollar regain some ground, with the euro falling back to around the $1.12 level and the dollar/yen rate rising to around ¥110.
The key driver of these currency movements has been changing market expectations in relation to US interest rates.
While both the ECB and BoJ cut rates this year, the moves were small.
The big changes year-to-date have been in relation to the expected future path of US rates, with large swings in market expectations in this regard.
The Fed hiked rates by 25bps in December to 0.375%. It indicated that it was likely to continue to hike rates at a steady pace in subsequent quarters.
However, very subdued inflation, a slowdown in the US economy, increased downside risks to global growth and fragile sentiment on financial markets made it difficult for the Federal Reserve to tighten monetary policy in recent months, despite its expressed wish to do so.
This resulted in a big scaling back of US rate hike expectations by the markets, to the extent that they believed it would be next year before the Fed would hike rates again.
This took its toll on the dollar, causing it to decline by around 5% on a trade-weighted basis over the spring.
However, the past week or so has seen hints from a number of senior Fed officials that US rates could rise as early as this summer.
Markets have changed their minds again and are now looking for the Fed to come with one rate hike in the second half of the year.
This has seen the dollar recover some lost ground during the past fortnight.
Much uncertainty, though, still surrounds the actual timing of Fed tightening.
The market is pricing in just one rate increase later this year.
However, the most recent projections from Fed officials in March, as well as their recent comments, point to at least two rate hikes over the remainder of the year.
Much will depend on the performance of the US economy, which appears to be regaining momentum after slowing in the last two quarters.
We have seen strong April figures published for retail sales, industrial production and housing.
Inflation looks to be on the rise also, with a pick-up in wage growth too.
Meanwhile, the jobless rate has fallen to 5% amidst strong growth in employment.
Given this backdrop and the recent comments from Fed officials, markets in our view are underestimating the potential for US rates to rise in the coming months.
It may be that the slowness of the Fed to hike rates over the past year has left the markets doubtful about whether it will follow through with rates hikes over the remainder of 2016.
However, Fed officials have been clear in their recent comments, stating that the latest data are lining up “to make a good case for rate increases” in the months ahead.
As we have seen already this year, rate hike expectations are a key driver of FX markets.
The dollar is likely to strengthen if US rates are hiked in the months ahead, as happened in the final quarter of last year, in the run-up to the Fed’s rate hike in December.
The pace of rate hikes in the US is likely to be modest so the currency will probably find it difficult to make substantial gains.
Nonetheless, we would expect to see the euro moving down towards last year’s low of $1.05.
The dollar should also recover some of the ground lost against the yen this year, rising to the ¥115 level or above before the end of 2016.