* Stocks hit by doubts over Greece
* Wall Street set for losses
* Euro around one-year lows vs dollar
* "Peripheral" bonds under pressure
By Jeremy Gaunt, European Investment Correspondent
LONDON, May 4 (Reuters) - Optimism about the recovering U.S. economy was drowned out on financial markets by worries about the euro zone sovereign debt crisis on Tuesday, with stocks falling and the euro at a one-year low.
The premium investors demand to hold peripheral euro zone government bonds rose, despite the weekend's aid package for stricken Greece.
World stocks as measured by MSCI <.MIWD00000PUS> fell half a percent, dragged down by more than 1 percent losses in Europe <
>. Wall Street also looked set for losses.Investors remained highly sceptical about the efficacy of the weekend agreement among European countries and the International Monetary Fund to provide a 110 billion euro aid package to Greece.
The European Central Bank also agreed to take Greek assets as collateral, even though they are rated as junk.
In exchange, Athens has promised to carry out spending cuts and tax hikes worth 30 billion euros over three years, on top of belt-tightening measures already taken.
But doubts remain about whether this can be achieved.
"The package has finally arrived and ... the ECB is bending over backwards to be accommodative," HSBC strategist Phil Poole wrote in a note.
"But, unfortunately, these measures were not delivered early enough to prevent Greece from being priced out of financial markets and considerable damage being done which has made the longer-term adjustment even more difficult."
Moody's Investors Service official said the bailout does not mark the end of the country's fiscal crisis because the key is whether the country can adjust to meet the budget deficit targets it has agreed to.
Not for the first time in recent weeks, the concern about Greece and the euro zone overshadowed otherwise bullish news.
U.S. stocks staged a broad rally on Monday that drove the S&P 500 <.SPX> to its best day in two months after manufacturing, consumer spending and construction data all instilled confidence in economic recovery.
EURO PRESSURE
The euro hovered near one-year lows, pressured by the sovereign debt crisis within its borders.
Investment advisers at RGE suggested that clients build short positions on the currency on any sign of strength.
"First, the prospect of the Greek debt restructuring raises a question mark as to the euro's status as a key reserve currency," they wrote.
"Second, we believe the Greek crisis is only the tip of the iceberg. The debt sustainability problems in other euro zone countries are equally serious while the macroeconomic limitations are often more severe than in Greece."
Tom Levinson, currency strategist at ING, also voiced concern about the spread of the crisis to other vulnerable euro zone countries such as Spain and Portugal.
"There is disappointment on the Greek package and so many obstacles ahead still. Worries over the peripherals will continue to weigh on the euro," he said.
The euro was down half a percent at 0.2 percent at $1.3129 <EUR=>.
Benchmark euro zone government bonds were stronger as investor sought relative safety in the currency bloc's core. Two-year bond yields <EU2YT=RR> were down seven basis points at 0.782 percent, with 10-year yields down six basis points at 3.008 percent.
Spreads between benchmark Bunds and Portuguese and Italian bonds widened and the cost of insuring against a Greek default rose. (Additional reporting by Jessica Mortimer)