Australia's largest home loan lender last week reported a net profit of $3.66 billion in the six months to December 31, up one per cent on the same period in the previous year.
While the Reserve Bank of Australia (RBA) cut the cash rate by 125 basis points to three per cent in calendar 2012, Commonwealth Bank of Australia's (CBA) standard variable mortgage rate was cut by just 90 basis points to 6.4 per cent.
Despite the difference, Mr Narev said the bank was highly profitable for several reasons.
"If you dissect the result, the input of margin here overall, I think margin went up 4 basis points, that's a contributor but by no means the big driver of the profit," Mr Narev told ABC's Inside Business on Sunday.
He said there was a difference with institutional markets and with the markets business, which had nothing to do with rate cuts.
"You've got improvement in productivity, that's got nothing to do with rate cuts, you've got a big improvement in the wealth management business, 6.5 billion dollars of funds flowing and that's got nothing to do with the rate cuts, so I certainly wouldn't categorise the performance being driven by rate cuts."
CBA's better than expected profits last week pushed the bank's shares to a record high, and put the bank on track for another record full year profit near $7.6 billion.
Mr Narev said CBA's retail home lending income was up about 15 per cent but deposit income was down 11 per cent so it was important to look at margins on a net basis.
"We've seen a period where deposit competitions remain strong and in fact our retail banking margins are about, I think from memory, 30 or 40 basis points below where they were in 2006, so by no means are we sitting on a real bonanza of retail banking margin at the moment," he said.
Wholesale funding costs were going up because new funding was still more expensive.