LONDON -- Shares in the U.K.-focused high-street banks, Lloyds Banking (LLOY -2.62%), Royal Bank of Scotland (NWG -2.38%) (NWG) and Barclays (BARC -2.13%) (BCS -0.22%), were hit this week following the EU bail-out of Cyprus and the accompanying raid on savers' deposits.

It's a salutary reminder how vulnerable U.K. banks are to mishaps in the eurozone. But while markets shudder, it's worth thinking about the long-term trajectory for bank shares.

Governor spies recovery
The Governor of the Bank of England, Mervyn King, said last week that he thought an economic recovery would 'come into sight' during 2013. That's no reason to open a bottle of champagne, but it's a reminder that the economy is heading upwards, not downwards.

The Governor pointed out that GDP statistics were distorted by problems in North Sea oil construction and production. If it hadn't been for those, the U.K.'s economy would have grown by 1.5% last year.

Banks are highly sensitive to the economies in which they operate, and share prices generally anticipate future developments. So the banks' shares should start to reflect expectations of a strengthening economy.

Bad debts
Economic growth translates into a healthier corporate sector, which is more credit-worthy and borrows more.

A healthier economy reduces the incidence of bad debts, alleviating concerns that banks might need to raise more capital. Only recently, shareholder-consultants PIRC calculated that if the old-style U.K. GAAP accounting rules still applied, RBS would need to make an additional 9.4 billion pounds of provisions for bad debts. The hit at Barclays and Lloyds would be 7.3 billion pounds and 2.5 billion pounds respectively.

Investment
Finally, economic growth should feed through into the personal sector.

It looks as if RBS shares the Governor's optimistic view. It's going to invest 700 million pounds over the next three years to revamp its U.K. bank branches. Meanwhile, Barclays has identified U.K. mortgages, wealth management and Barclaycard as business areas to invest in. You never know, competition might hot up between the lenders.

With Lloyds and RBS on the path to privatization and Barclays reinvigorated with a new management and strategy, the trio's shares should react quickly to signs of economic recovery. But the impact of Cyprus's bail-out shows they remain vulnerable to the eurozone crisis.

If you already own banks but are looking for a growth story with a lower risk profile, I suggest you look at this company. It hasn't made a capital call on its shareholders for more than 70 years, and has increased or held its dividend every year since at least 1988.

Its earnings per share have risen by 44% since 2009, and there could be considerable value that isn't reflected in the share price. That's why it’s "The Motley Fool's Top Growth Stock for 2013."

You can learn more by downloading a free report from the Motley Fool -- just click here.