NEW YORK, SEPT. 10 -- Stocks rose for the second straight day today after a week of declines, and traders attributed the reversal to a strengthened dollar, an improved bond market and speculation that the trade deficit may have narrowed.

But they also said the relatively light trading volume suggested that many investors were reluctant to participate before knowing the July trade deficit figure, which will be reported Friday.

The Dow Jones average of 30 industrial stocks, which fell more than 173 points from its record high of 2722.42 set Aug. 25, advanced 26.78 to 2576.05, a more substantial increase than the indicator's 4.15 gain Wednesday. Broader measurements of stock prices also rose.

The market focused on the trade number because a bigger deficit would suggest the dollar will fall further, incite inflation, cause interest rates to rise sharply and discourage investors from buying stocks and bonds.

Conversely, a smaller deficit would help stabilize the dollar and encourage investments in U.S. securities.

Wall Street rallied early in the session, as did the dollar and bond markets on news that Japan's August trade surplus had narrowed significantly from a year earlier.

This indicated that the July trade deficit in the United States, Japan's biggest market, may have narrowed from the $15.7 billion June shortfall.

"I think the stock market was looking for a reason to have a nice technical bounce, but there still is a lot of cautiousness," said Philip C. Puccio, senior vice president and manager of institutional trading at Dillon, Read & Co. in New York.

Lawrence R. Helfand, manager of retail sales at Rodman & Renshaw Inc. in Chicago, said stocks had been extremely oversold since late August and it was premature to call today's improvement the start of a prolonged rise.

In New York Stock Exchange composite trading, advancing issues outnumbered declines by about an 11-to-5 margin.

NYSE volume totaled 179.79 million shares, compared with 164.91 million the previous session.

Among the most notable blue-chip gainers, Philip Morris rose 4 1/4 to 115, Alcoa rose 1 1/8 to 59 3/8 and Kodak rose 1 3/8 to 99 3/4.

The most-active NYSE issue was First City Bancorp of Texas, which fell 5/8 to 1 on 2.6 million shares. On Wednesday, the Federal Deposit Insurance Corp. announced a $970 million plan to rescue the troubled banking company.

The NYSE composite index measuring all listed issues rose 1.67 to 177.46. Standard & Poor's index of 400 industrials rose 4.38 to 371.10, and S&P's 500-stock composite index rose 3.21 to 317.13.

At the American Stock Exchange, the market value index rose 3.93 to 351.48.