The stock market saw gains on Tuesday, propelled by strong bank earnings and a surprisingly positive inflation report. The Nasdaq Composite rose 0.9%, and the S&P 500 gained 0.4%. The Dow industrials saw a modest increase of less than 0.1%, dragged down by a significant drop in IBM shares, which fell approximately 25% following a profit warning.

Treasury yields declined as June inflation registered at 3.5%, lower than anticipated. Federal Reserve Chairman Kevin Warsh cautioned against premature celebration regarding inflation, noting that one month's improvement does not signify a completed mission. He is scheduled to testify before the Senate Banking Committee on Wednesday.

Earnings season intensifies with reports due Wednesday from companies including Johnson & Johnson and Morgan Stanley. Meanwhile, elevated oil prices persist as optimism for a swift resolution to the Iran-U.S. conflict wanes. Brent crude futures surpassed $85 a barrel, and U.S. crude benchmark prices edged higher.