SYDNEY, March 14 (Reuters) - The Australian dollar eased on Tuesday on souring risk appetite, while bonds posted their biggest rally in more than a decade as markets priced out any chance of further rate hikes from the nation's central bank and even wagered on a cut in April. The Antipodean slid 0.5% to $0.6636 as tanking share markets, gripped by contagion fears from the collapse of Silicon Valley Bank and Signature Bank, shattered confidence. It surged 1.3% on Monday to as high as $0.6717.

Three-year bond futures jumped a total of 43 ticks since Friday when SVB collapsed, reaching 97.008, in their biggest three-day rally since 2011.

Investors are now expecting the RBA will most likely pause its tightening cycle in April, leaving the cash rate unchanged at 3.6%. There was even a 7% probability that the central bank would even cut interest rates by 25 basis points to 3.35%.

Just a week ago, markets were wagering that rates might have to peak at 4.2%.

That followed moves in the U.S. markets, as traders drastically pared back expectations for the Fed funds rate to peak at 4.8% now, compared with about 5.5% previously, and even priced in a whopping 70 basis point cut by the end of the year.

Fallout from the collapse of U.S. lenders SVB and Signature Bank deepened overnight, despite government efforts to shore up investor confidence. Heavy selling of U.S. regional bank stocks extended to Asia on concerns that banks worldwide could be exposed to similar risks.

"While the Fed's move to backstop uninsured deposits will likely prevent further banking runs, a potential banking crisis threat trumps high inflation any day of the week," said Tony Sycamore, analyst at IG Group.

"As noted in recent months and in wider financial circles, the Fed has historically continued tightening until something breaks."

New Zealand two-year swap rates plunged 33 basis points to imply an interest rate of 5.0% on Tuesday, compared with 5.5% just last week.

The kiwi also slid 0.2% to $0.6206, having jumped 1.4% to as high as $0.6263. It faces resistance at $0.6275.

U.S. inflation data due later in the day is likely to inject more volatility, even if investors see the Federal Reserve prioritising financial stability.

Ben Powell, APAC Chief Investment Strategist, BlackRock Investment Institute, expects the SVB collapse to complicate the Fed's job in fighting inflation.

"We think that rates are not going to come down as quickly as the markets now imply ... We think the Fed would be highly reluctant to change their tune and the policy settings that they have been warning us for and have been delivering now for coming up to a year." (Reporting by Stella Qiu Editing by Shri Navaratnam)