Key benchmark indices Sensex and Nifty were trading flat in early session on the last trading day of 2020 with IT and FMCG stocks cancelling out gains made by financials and energy shares.
After opening on a negative note, the 30-share BSE Sensex was up by 17.84 points or 0.04 per cent at 47,764.06 in morning session on Thursday.
The broader Nifty of NSE edged up by 2.25 points to 13,984.20 with 30 of its constituents trading in green.
Among major gainers, ONGC was up by 1.55 per cent, ICICI Bank by 0.87 per cent, HDFC by 0.36 per cent and Bajaj Finserve by 0.58 per cent.
On the other hand, TCS , Infosys, M&M, Ultratech Cement, HUL, NTPC and SBI dropped.
Markets were volatile due to the expiry of derivatives series on Thursday.
The Sensex and Nifty had raced to fresh record highs on Wednesday on the back of gains in financials, auto and cement counters.
Although the market is at its most expensive valuation level, FPIs continue to pump in funds and roll the Indian market higher on a daily basis, analysts said.
Among other Asian markets, Hong Kong benchmark rose by by 0.26 per cent while Chinese shares gain 1.45 per cent. Australian shares dropped 0.80 per cent due to fresh curbs to control COVID-19 cases.