Unless you are a Citigroup or JPMorgan Chase, your bank is pretty safe from the turmoil in Greece and China, right?

Think again.

The threat of a Greek default and the Chinese stock market plunge will exert downward pressure on interest rates, and global insecurity could encourage the Federal Reserve to delay a rate hike, experts say. That could translate into even tighter margins and delay relief for the many banks starved for revenue growth.

Yes, investors likely will react by demanding safe assets that U.S. banks hold and trade, which could be a small silver lining. But there are doubts that flight to quality would spur a boomlet in mortgage refinancings as optimists might hope.

Perhaps the biggest problem is that it adds uncertainty at a point in the year — and the long recovery from the financial crisis — when banks thought things would be getting better.

Instability from international crises like these can cut both ways for banks, said Kevin Jacques, a finance professor at Baldwin Wallace University and former Treasury Department economist specializing in systemic risk.

"It's very difficult to tell what the effect of volatility will be, because it spills over from one market to the next," he said. "But sometimes volatility can be beneficial."

The good news is that U.S. banks lack much direct exposure to either crisis, observers say. The Greek debt crisis, which intensified after a dramatic vote against austerity on Sunday, has played out for more than five years, giving banks plenty of time to clear off any exposure to their risk.

The crisis in China has unfolded more swiftly, with the Shanghai Composite Index losing more than a quarter of its value over the last month. But, of course, U.S. banks do not hold Chinese stocks, and there is relatively little new U.S. investment in China, which reduces the likelihood of contagion.

An important area for banks to watch will be foreign-exchange rates, said Tim Yeager, a finance professor at the University of Arkansas and former economist at the Federal Reserve Bank of St. Louis.

"With the volatility in the Chinese yuan and euro, people will be more likely to put their money in dollars," he said. "You're likely to see some pressure on interest rates, but they're already so low that the impact will be small."

Scott Buchta, head of fixed-income strategy at Brean Capital, thinks the effect could be more dramatic, even though U.S. markets have "priced in" an orderly Greece exit.

"We could see rates move sharply lower from here should conditions continue to deteriorate in Greece," Buchta said.

The turmoil in Greece and China is coming just as the Fed was poised to raise interest rates for the first time in nearly 10 years. Many observers had all but assumed a modest rate increase late in the year, but the Fed may hold off until the uncertainty is resolved.

Additionally, a stronger dollar versus the euro and yuan would hurt American exports, with negative economic consequences that could further encourage the Fed to delay a rate rise, Jacques said.

Peter Donisanu, a global research analyst at Wells Fargo Wealth Management, said the key risk for a Fed rate increase may come from emerging Southeast Asian financial markets and their response to China's stock market sell-off.

Many countries and companies have heavy dollar-denominated external debt.

"As the Fed starts raising rates, that increases the financing costs for those countries and companies that have borrowed in dollars," Donisanu said. "If we continue to see a deterioration in confidence, that could spill over into other Asian markets and could be a factor that weighs on the Fed's decision to hold off raising rates until December."

Continued low interest rates might spur another refinancing boom, but the effect so far is not strong enough to move the needle. Mortgage rates would have to drop below 3.75% to see a significant pick-up in refinancing activity, Buchta said.

Rates are currently hovering around 4.06%, up from 4.14% a week earlier, according to HSH.com, a publisher of mortgage and consumer loan information.

Even if rates fell below 3.75%, the refi outlook is unclear.

On the one hand, the volatility in rates late last year and in January upended the view that borrowers with 30-year fixed rate mortgages at 4% or so would never refinance again. Mortgage rates fell 37.5 basis points from September to December, and dropped by the same amount in January, sparking significant prepayment activity before rates reversed course again in February.

On the other hand, many observers question whether much pent-up demand still remains — in other words, maybe all those who would refinance have done so already.

Cliff Rossi, the chief economist at mortgage insurer Radian Group, said the Fed is unlikely to change course unless there is a further softening of the U.S. economy.

"Any contagion effect associated with Greece is very, very remote," Rossi said. "If the [Greek crisis] goes on for a protracted period of time and U.S. investors start to react by losing confidence, then it could have an effect on the stock market. But the stock market has been rallying so long that at some point it has to run out of steam, and investors have known we were due for a correction."

Whatever its effect on the Fed's rate deliberations, the crises are likely to make investors more hungry for safe, high-quality assets like U.S. government-backed bonds. This "flight to safety" may already be pushing down rates on government-backed bonds.

The yield on 10-year Treasuries has dipped as the Greek drama played out over the last month, down 20 basis points, to 2.30%, as of Tuesday.

Lower rates arguably could help banks — which hold a lot of these securities — increase their trading revenue. Banks with large portfolios of Treasuries or agency-backed bonds could find their holdings becoming more valuable due to investor demand.

"To the extent that bond prices are pushed up, there could be some increased capital gains, but I don't anticipate that the effect is going to be very noticeable," Yeager said.

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