The managing director of KiwiSaver plan Simplicity is calling for an explanation from ANZ over transactions and personal expenses of outgoing chief executive David Hisco.
Hisco has been temporarily replaced by Antonia Watson, who had been filling in for him while was on sick leave.
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ANZ said its board had concerns "about the characterisation of certain transactions following an internal review of personal expenses".
Hisco's spending included the use of wine storage and corporate cars.
It was revealed Hisco had been spending about $1200 per day for the past eight years. It's also since been revealed his wife purchased their Auckland family home from ANZ for less than its capital valuation.
Simplicity managing director Sam Stubbs told The AM Show an independent inquiry needed to happen.
"This needs a proper, Government-funded Royal Commission of Inquiry.
"The reason for this is most KiwiSavers own shares in ANZ, or most of them are invested in ANZ - this is the country's biggest bank, and most profitable company.
"What they do really, really matters."
ANZ board chairman Sir John Key told The AM Show last week a case could be made for the wine storage, but the bank was most concerned about the use of the cars.
"These are the same companies who have been found to do so much wrong in Australia," Stubbs said on Monday.
The AM Show host Mark Richardson said he couldn't see the problem.
"We're getting value out of them," he said. "They just had to do this type of stuff to get their man, who was quite successful for them."
Stubbs replied: "That says doing something illegal is okay as long as you make money".
"There's too many questions, we need to have a proper look at this," he said.
"There may be a perfectly reasonable explanation for all of this."