Indian rupee hovered close to its all-time low on Tuesday. The currency was at 84.0725 against the USD at 11:20 am (IST). The currency had slipped to an all-time low of 84.0750 in the previous session. The dollar index was at 103.3 on Tuesday, its strongest level in over two months. Other Asian currencies were down between 0.1% and 0.8%.