* Graphic: World FX rates in 2020 tmsnrt.rs/2egbfVh * Graphic: Trade-weighted sterling since Brexit vote tmsnrt.rs/2hwV9Hv (Updates prices, adds comment) LONDON, Feb 16 (Reuters) - Sterling hit two-and-a-half-year highs against the dollar on Tuesday and set a nine-month high to the euro as investors stuck to bets that rapid COVID-19 vaccinations would set Britain up to recover from its biggest drop in output in 300 years. The pound rose to $1.3955 against the dollar - its highest since April 2018 - in Asian trading, paring some of those gains to trade 0.1% lower on the day at $1.3891 by 1558 GMT. Against the euro, it reached 87.06 pence, its highest since May 2020, last trading 0.2% higher at 87.06 pence per euro. Speculators have increased their long positions on the pound - bets that the currency will appreciate against the dollar - for a second consecutive week in the week up to last Tuesday, CFTC data showed. Britain’s coronavirus-ravaged economy suffered its biggest crash in output in more than 300 years in 2020 when it slumped by 9.9%, data showed last week. Still, sterling is the best-performing G10 currency so far this year, up 2% against the dollar, and 2.5% against the euro. The pound’s outperformance against the euro is attributed by analysts to a slower vaccine roll-out in other European countries. “While the UK is currently in lockdown and growth this quarter will be negative, the full-year macro-economic backdrop remains strong and inflation contained,” said Caroline Simmons, UK Chief Investment Officer, UBS Global Wealth Management. Expectations of large fiscal stimulus in the United States and an overall negative outlook on the dollar have also boosted the pound/dollar exchange rate - known by traders as “cable”. Investors betting on a rebound in global growth - known as the reflation trade - have also contributed to sterling’s gains as the currency is considered correlated with growth and risk sentiment. “Sterling continues to push ahead as the dividend of rapid vaccination and the currency’s relative high beta among the three majors (USD, EUR and JPY) both help in the current reflationary environment,” ING strategists said in a note to clients. “We expect the EUR/GBP medium-term valuation gap to continue closing (we estimate EUR/GBP medium-term fair value at 0.82, based on our BEER model) this year and next. “But with the GBP showing signs of a modest overvaluation based on our short-term financial fair value model, the pace of near-term appreciation may slow from here.”