* CBA will not pass on variable rate cuts to home loan customers

* Fixed home loans trimmed to record lows, lower SME rates

* Westpac, NAB & ANZ follow suit

* Not cutting variable loans saving up to 5 bps of banks' NIMs-JPM

SYDNEY, Nov 4 (Reuters) - Australia's four major banks said on Wednesday they would not cut rates for a majority of their home loan customers, even after the central bank pledged to keep rates near zero for about three years, as the lenders attempt to safeguard profits.

Instead, the so-called "Big Four" lenders - Commonwealth Bank of Australia, Westpac Banking Corp, National Australia Bank and Australia and New Zealand Banking Group - said they would cut interest rates for small- and medium-sized businesses and lower fixed rates for mortgage holders to record lows.

By not passing the rate cut to the majority of their home loan customers, the banks are saving between 3 to 5 basis points on their net interest margins, JPMorgan analysts said, which have shrunk from more than 3% in early the 2000s to below 2% now.

The Australian central bank on Tuesday cut its cash rate to 0.1% to prop up the economy from the country's worst downturn in a generation, vowing not to raise it for at least three years.

The four banks, which hold about 80% of the country's mortgages, already have more money that they can use amid weak demand for credit.

Lower rates, therefore, hurt them.

CBA first announced a 100 basis point cut in its four-year fixed rate home loans for owner-occupied customers to 1.99% a year, its lowest ever, and trimmed rates for businesses. Westpac and NAB then followed suit.

ANZ was the last of the four banks to announce that it would slash its fixed home loan rates across one- to five-year terms by between 0.2% and 0.4% per year.

Shares of CBA and Westpac each ended 2% lower on Wednesday, underperforming the broader market, which closed down 0.1%. NAB fell 1.1% and ANZ finished 0.9% weaker.

"We are in an extraordinary period with the official cash rate at a historical low and unconventional monetary policy measures in place," said Richard Burton, head of Westpac's consumer division.

"It is critical we carefully manage interest rate changes."

Up to 40% of the funding of Australia's Big Four banks is rate insensitive, meaning it doesn't benefit from rate cuts, according to JPMorgan.

A number of smaller non-bank lender competitors, which fund themselves through capital markets and therefore benefit directly from the rate cuts, have passed on the full rate cuts to home loan customers. (Reporting by Paulina Duran in Sydney and Anushka Trivedi, Rashmi Ashok and Nikhil Kurian Nainan in Bengaluru; Editing by Sherry Jacob-Phillips and Jacqueline Wong)