LONDON—The dollar fell again on Tuesday, while risk-sensitive currencies such as the British pound gained and the Australian dollar recovered from an overnight drop. After falling nearly 5 percent in January, world equities started February slightly firmer and currency markets have also changed course. After hitting a 19-month high last week, the U.S. dollar index fell on Monday and on Tuesday was down 0.3 percent on the day at 96.395 at 0811 GMT. The change follows slight caution from four U.S. Federal Reserve policymakers about how many interest rate hikes will follow an expected first one in March. The dollar also fell against the Japanese yen, with the pair at 114.990. The Australian dollar dropped sharply overnight after the Reserve Bank of Australia (RBA) pushed back against expectations for near-term rate hikes until inflation is higher. But the “risk-on” tone in markets meant that the Australian dollar soon recovered and …