"If we don't want women living in their cars - and it will be women that this falls to in retirement - we need to address retirement adequacy," he said, speaking at a parliamentary inquiry on superannuation.

Liberal MP Craig Kelly, who said the rise in the compulsory superannuation contribution from 9.5 per cent to 12 per cent by 2021 would make it more difficult for young people to save for a house, and leave people relying on the aged pension.

"It's even more stark than that," Dr Fahy, Association of Superannuation Funds chief, responded. A couple with a mortgage-free house needed a lump sum of $640,000 for a "comfortable" income of $60,000 a year. A couple who had to rent needed $1.1 million.

Some government backbenchers have called for the superannuation contribution to be frozen at 9.5 per cent, but Dr Fahy said superannuation should not be conflated with housing affordability. There had been no change in the superannuation contribution in the past five years, but wages had remained flat and housing prices had boomed.

If the contribution increased as scheduled to 12 per cent, there was a very good chance that half of Australians were self-funded in retirement by 2050, taking account of longevity and costs of aged care and health care, he said.

The Productivity Commission highlighted the huge losses to people whose money is in the bottom performing superannuation funds in a report in January, and found a higher proportion of under-performing funds among retail funds (such as those run by banks and insurance firms) than among industry funds (run by unions and other industry groups). Labor MP Andrew Leigh pointed to a sustained 1.8 to 2 per cent better performance by industry funds.

In December the government will begin publishing a "heat map" to compare superannuation funds. But Dr Fahy said took issue with the methodology, urging politicians to think of it in terms of football fans.

Take a village where 100 people supported team "retail" and 100 team "industry". You measure them in 1997 and again in 2014 and find that team industry has grown 2 centimetres more, he said.

"The reality is of the 100 people who support the retail team, 80 of them were pensioners and there were 60 in 1997, and they're not interested in growing. They're worried about osteoporosis and they're not interested in protein because it gives them bowel cancer. They're in the preservation phase. The industry team have got 80 teenagers who are all up for carbs and growth and protein."

"The only conclusion you can draw is that there's a difference," Mr Fahey said, later adding, "Anybody who says they understand this issue clearly doesn't."

Labor MP Daniel Mulino seemed to understand his meaning: "I concede demographic differences might be part of it," he said.

Mr Fahy tried again, pointing to QSuper, a Queensland public service fund, which went from 49th performing fund to best in a matter of months. "That's like being two from the back in the Melbourne Cup halfway through the race, then winning," he said.

The Productivity Commission reported big differences in the performance of superannuation funds, saying someone aged 21 starting on a $50,000 salary would retire with $1.2 million in super if their money was in the top quarter of funds, and just $560,000 if they were in the bottom-performing funds, the equivalent of 13 years' lost income.

But Dr Fahy contested the finding, saying the $1.2 million result assumed that someone in the middle of the top-performing funds stayed there, receiving double-digit returns every year for 40 years, which was completely unrealistic.

Being in the bottom quartile of funds did not mean under-performance, Dr Fahy said, with those funds still returning three times more than term deposits and close to a median OECD pension fund.

One way to think about it was to consider James Ruse selective high school, NSW's top school, "where all the kids are smarter than average", he said. At James Ruse, the bottom quartile performed as well as a median student elsewhere.

"I wish people would stop talking about my high school," Dr Leigh responded. He didn't appear to be joking.

Dr Leigh questioned the value of the "tiddly wink funds", saying it was not obvious they were in the interests of members. Ninety-three funds had assets below $1 billion, he said.

But Mr Fahy cautioned against consolidation to the point that a small handful of dominant funds remained. Canberra fund Avsuper, whose members are aviation, was relatively small, at $2.8 billion, but was a strong performer and had the highest median balances of any fund, he said. In contrast some of the biggest funds had median balances below $50,000.

"So we have to be careful about drawing conclusions that small is bad and big is better," he said, comparing it to supermarkets, where sometimes you want to go to Woolies or Coles, but sometimes you want to go to your local store "because they know your name".