The most profound event of the past week for investors may not have been either the on-off referendum plans in Athens or the machinations of the Group of 20 in Cannes, but a comment from Ben Bernanke in Washington.

The Federal Reserve chairman essentially pledged to take more action -- if necessary -- to make the U.S. economy stronger.

Looked at from one standpoint, this was like saying to investors that if the euro zone crisis starts dragging Europe into recession, the Fed is there to help bail out world growth and maintain flows into riskier assets.

Conversely, if the euro zone does manage to contain its Greek problem then investors will be able to continue the risk rally that began in the lead up to the latest bailout agreement.

That's better news than not, but we have to be cautious, said Karen Olney, head of European Thematic Research at UBS.

The U.S. will probably be one of the stronger pockets of growth in the developed world over the next year or so. The euro zone seems to be the swing factor.

A surprise interest rate cut from the European Central Bank, along with a confident performance from new president Mario Draghi, will have helped risk appetite in the otherwise crisis-ridden euro zone.

It is mainly the improvement in the U.S. economy, however, that may allow for investors to salvage something out of the rest of the year.

Jobs data on Friday was disappointing, but it did show growth and employment is known as a lagging indicator.

The week ahead brings the latest take on U.S. consumer sentiment, which should give some idea of whether the better data is trickling down to the man and woman in the mall.

GREECE

It is, meanwhile, a brave person who can predict what will happen in the euro zone crisis, particularly when it comes to Greece.

The referendum debacle -- a call for a vote that could have destroyed the whole bailout agreement, then a sharp reversal in the face of EU and domestic anger -- has undermined what residual investor confidence there was in Athens.

More significantly, perhaps, it led to the ditching of a taboo. Greece's possible exit from the euro zone is now spoken of publicly by European leaders for the first time.

If there are further signs that Greece will not live up to its commitments then planning for a euro zone exit will have to gear up.

The regular meeting of euro zone finance ministers on Monday may provide hints. But even if not, investors are keen to get more details about the bailout plans that have already been agreed.

Franz Wenzel, senior investment strategist at AXA Investment Managers in Paris, said one key would be plans for private investors to accept a 50 percent cut in the face value of Greek bonds.

The issue is whether this can be done without triggering credit default swaps, insurance policies on the debt.

We want clarity on that, he said.

Investors will also be wary of any further spreading of the crisis to bigger economies, notably Italy, despite the ECB's bond-buying efforts.

Under fierce pressure from financial markets and European peers, Rome has agreed to have the International Monetary Fund and the EU monitor its progress with long delayed reforms of pensions, labour markets and privatisation.

Such a move may be taken positively by investors, but it does underline the size of the problem.

The pressure from the G20 ... will surely help to make Italian policy makers understand there is a sense of urgency, said Giorgio Radaelli, chief strategist at wealth manager BSI, adding that the parliamentary difficulties in Italy were not that different from those in Greece.

Elsewhere, some emerging market investors may be on their toes in the coming week over Ukraine. The IMF left Ukraine after its latest visit without a deal to start re-lending.

(Editing by Mike Peacock)