Asian shares turned higher on Tuesday, reversing earlier losses on the back of gains in Hong Kong and China, while the dollar extended highs scaled in holiday-thinned trading in the previous session. MSCI’s broadest index of Asia-Pacific shares outside Japan rose 0.5 percent, after eking out a late gain in the previous session. Hong Kong’s Hang Seng index (.HSI) jumped 1.5 percent, flirting with seven-year highs, on expectations of more money inflows from the mainland following Beijing’s fresh moves to expedite cross-border investment.