The stock market hit a new high on Wednesday as BSE Sensex crossed the 62,585 level for the first time in its history and hit a new lifetime high at 65,588. However, the National Stock Exchange (NSE) Nifty index missed the opportunity to hit a new record high as it recoiled from its intra-day highs of 18,875, which is only 12 points from its record high level of 18,886.