GLOBAL MARKETS-Grimmest of years ends with touch of hope

* Asian shares gain for 3rd day; post worst year on record

* Oil falls on global econ worries; challenging year ahead

* Dollar hit by rate outlook; sterling near record low

* Government bonds end year as outperformers

By Rafael Nam

HONG KONG, Dec 31 (Reuters) - Asian shares rounded out their worst year ever on Wednesday, down 50 percent after 12 months of financial market and economic turmoil, but optimism that 2009 will be an improvement lifted stocks for a third straight session.

Government bond yields held near their lowest in decades, oil prices dipped further below $40 a barrel and the U.S. dollar extended its recent falls as it heads into 2009 in a position of weakness due to the near-zero interest rates in the world's largest economy.

Yet some remain optimistic after a year of shattered milestones, as policy makers worldwide respond to the worst financial crisis in decades with antidotes that combine slashing interest rates, rescuing whole sectors and boosting spending.

"It has been a shocking year, hardly anything was spared in the market carnage," said Michael Heffernan, senior client adviser and strategist at Austock Group in Australia.