Stocks finished an uninspiring session mixed yesterday as investors kept a wary eye on near-record oil prices and debated the prospect of...

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NEW YORK — Stocks finished an uninspiring session mixed yesterday as investors kept a wary eye on near-record oil prices and debated the prospect of a Social Security package without private investment accounts.

The Dow Jones industrial average fell 9.44 to 10,599.67.

Microsoft, one of the 30 Dow stocks, added 4 cents to close at $25.15 a share. Boeing, also a Dow stock, fell 89 cents to $62.78. Broader stock indicators were narrowly mixed. The Standard & Poor’s 500 index was down 2.49 at 1,213.61, and the Nasdaq composite index gained 2.94 to 2,091.07.

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One day after reaching record highs, crude-oil futures fell below $59 per barrel, but the historically high prices were still weighing on investors’ enthusiasm for stocks. A barrel of light crude settled at $58.90, down 47 cents, on the New York Mercantile Exchange.

Some analysts were cheered that stocks have yet to sell off despite higher oil prices, though there are growing worries about whether the market will be able to sustain its gains from May and June should oil prices remain at these levels.

“What we’ve seen yesterday and today is some hesitancy, some skepticism … ” due to high oil prices, said Ken Tower, chief market strategist for Schwab’s CyberTrader. “It’s tough to generate a lot of enthusiasm.”

Investors were also concerned about the state of proposed changes in Social Security after President Bush encouraged Republicans in Congress to introduce a plan that did not include private accounts favored on Wall Street.

“You’re seeing some bond movement, which kind of brings a little bit of movement to stocks, but really, there’s not much going on,” said Bryan Piskorowski, market analyst with Wachovia Securities. “There’s no real economic data, not a lot of earnings, nothing really here to guide us aside from oil.”