The federal government is expecting a lot of interest in the upcoming privatisation of Medibank.

The share sale process for the nation’s largest private health insurer – covering almost four million Australians – begins today with a government campaign to get mum and dad investors to pre-register their interest.

The prospectus, which will indicate the price per share, will be available in the second half of October with the enterprise due to list on the domestic stock exchange by December.

The offer will preference registered policyholders, who will be able to get a greater share allocation than non-policy holders.

Finance Minister Mathias Cormann said the government anticipated a “large amount of interest” in the sale, which could raise about $4 billion for the federal coffers.

The proceeds would be invested in productivity boosting measures, he said.

AMP chief economist Shane Oliver said it wasn’t surprising policy holders would get preferential treatment.

“It’s consistent with what happened in the past with privatisation – where policy holders get preference,” he told AAP on Sunday.

“Even AMP, when it demutualised, its policyholders got shares initially.”

Dr Oliver said at an expected $4 billion, the initial public offering (IPO) was one of largest seen in Australia for some time.

“Along with other capital raisings and IPOs in the next few months, this means quite a lot of money will be drained out of the market,” he said.

People wishing to register for the share sale can go to: medibankprivateshareoffer.com.au.

The IPO will also be open to domestic and foreign institutional investors.

The coalition is hoping to offload 100 per cent of Medibank Private, saying there is no reason why the federal government should be involved in the health insurance market.

It has often said there is a conflict of interest in the commonwealth being both the regulator and the largest market participant in the sector.

Senator Cormann said Medibank Private would perform better in private hands, but denied privatisation would lead to higher insurance premiums.

“Medibank Private … will continue to have to compete for customers with 33 other health funds and that of course will put a natural limit on Medibank’s capacity to lift premiums beyond what is competitive,” he told reporters in Melbourne.

The finance minister refused to say how much the government hoped to raise from the float, slated for December.

“The best possible net return for taxpayers – that’s what our objective is with this sale,” Senator Cormann said.

Senator Cormann said the privatisation of Medibank would see it perform better as a business.

“Medibank Private is already performing very well as a business, but there are obviously some restrictions that come with being government owned and we believe that in private ownership, that Medibank private will be able to perform even better,” he told reporters.

He said the public would get first access to buy shares, before the sell-off proceeds into the institutional phase.

But he said no buyer could own more than 15 per cent of the company.

Medibank chairman Elizabeth Alexander welcomed the announcement.

“We’re excited for this new opportunity for Medibank and what it may bring and we are pleased to be proceeding with this next step that will lead us to our debut on the Australian stock exchange,” she said

She assured Medibank customers that they can expect the same service after the sell-off.

“The Medibank you have trusted for years is the very same Medibank that will continue to look after your health well into the future.”