Former Prime Minister Sir John Key may be forced to resign from one of his banking roles over concerns of a potential conflict of interest.
Sir John is the chairperson of ANZ New Zealand and sits on the board of its parent bank in Australia. He has held both roles since late 2017.
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Orr, the former chief executive of the New Zealand Superannuation Fund, told RNZ trans-Tasman roles like the one held by Sir John and BNZ chairperson Doug McKay could be unfair.
"My biggest concerns with boards is in whose interests are they working? Are they working for the parent shareholder, or the subsidiary shareholder... that's a real critical challenge," he said.
Orr used the hypothetical example of a New Zealand bank whose Australian parent was in trouble and the director was on both boards. If the Australian bank wanted to bring money back from New Zealand it would be difficult for the director to act in the best interests of both boards at the same time.
The Reserve Bank has already suggested ANZ will be under greater scrutiny, asking for two reports from the local unit of the bank to prove it was operating in a prudent manner in June.
The first report will cover ANZ NZ's compliance with RBNZ's current and historic capital adequacy requirements and the second will assess the effectiveness of ANZ NZ's director's attestation and assurance framework, focusing on internal governance, risk management and internal controls.
It came after the Reserve Bank revoked ANZ's local licence to calculate its own operational risk capital and raising minimum capital requirement towards the end of June.
ANZ said at the time it would work with the Reserve Bank to commission a third party to look at its compliance with capital adequacy requirements.
An internal review released in April revealed ANZ was not using the operational risk model the Reserve Bank had approved.
The Reserve Bank has already proposed raising top banks' capital ratio to 16 percent, meaning the country's top four banks, including ANZ, could collectively have to raise NZ$20 billion ($A19 billion) in new capital over the next five years.
The banks have suggested the change could force up borrowing costs, or cause companies to pull money out of the New Zealand market.