Shares of the world's largest custodian bank plunged 7.8 percent in premarket trading on Wednesday.

The company said even though there was less chance of future hikes in interest rates, there has been no decline in competition for deposits.

"Competition for deposits is still high, and we expect that the rate paid on interest-bearing deposits will increase a little," BNY Chief Financial Officer Michael Santomassimo said during the bank's post-earnings conference call with analysts.

Earlier in the day, BNY reported a 20 percent drop in profit, missing estimates for the first time in two years, as lower client activity and a fall in assets under management pressured fee revenue.

(Reporting By Aparajita Saxena in Bengaluru; Editing by Shinjini Ganguli)