LONDON (Reuters) - How strong is the euro really? Despite European policymakers’ alarm over its run to 2-1/2-year highs against the dollar, several factors governing exchange rates imply the single currency’s bout of strength is far from over. European Central Bank boss Christine Lagarde said on Thursday the bank was closely watching the euro, which surged 9% last year to above $1.23, its biggest annual gain in four years.. The currency’s strength is a headache for the ECB which is struggling to somehow get inflation towards the 2% mark and saw it stay below 0% in December for the fifth straight month. It’s a headwind for exporters too as companies in Germany’s DAX index derive 70% of their sales outside Europe. Lagarde’s comments, reiterating all instruments could be adjusted to ensure inflation moves towards target, were interpreted by some as a warning -- if traders don’t stop pushing the euro higher than levels that suit the central bank, interest rates could be cut, even from current -0.5% levels. “The ECB is joining the ranks of those central banks who – because domestic tools have largely been used up – discover the exchange rate as a monetary policy ‘tool’,” Commerzbank told clients. For a graphic on ECB to rein in euro?: But euro strength may in reality be overstated, and the ECB’s wiggle room limited. Indeed, a median estimate of a Reuters poll predicted the euro/dollar exchange rate to rise to $1.25 by end-year. For a graphic on Euro during the coronavirus crisis: Vasileios Gkionakis, head of FX strategy at Banque Lombard Odier & Cie is even more bullish with a $1.27 forecast. As to whether the euro is too strong, he points out its gains of late were primarily at the expense of the U.S. dollar. A wider euro index -- measuring the exchange rate against 42 trade partners’ currencies and watched by the ECB -- is indeed near 10-year highs but its gains have been slowed since August as emerging market currencies and the yuan rebounded. Euro-dollar, meanwhile, strengthened 6% in this period. There is another euro-supportive factor -- ten-year interest rate differentials adjusted for inflation between the euro zone and the United States are currently at levels last seen in early-2014, when the euro was around $1.37. For a graphic on EURUSD rate differentials: Higher U.S. yields could narrow or eliminate that differential but Federal Reserve officials’ recent comments suggest they are in no mood to allow borrowing costs to rise even as inflation expectations rise. And whether the ECB could actually respond with a rate cut remains debatable. With European banks facing growing volumes of pandemic-linked bad loans, the ECB will balk at hitting the sector with even lower interest rates. “Put simply, the bar for more policy easing to stem currency gains is very high,” Lombard Odier’s Gkionakis said.