The S&P 500 had a strong Monday, gaining 1.18% to close at 7,440.43, and now prediction market traders are cautiously betting that momentum will carry into Tuesday's opening bell. Polymarket's June 30 contract implies a 61% probability that the benchmark index will open higher, though betting has been volatile throughout the session.

Monday's rally was driven by a couple of big catalysts. First, the U.S. and Iran agreed to halt hostilities and allow commercial vessels to move freely through the Strait of Hormuz, easing fears about energy supply disruptions. That geopolitical thaw gave investors a reason to be more optimistic. Second, semiconductor stocks staged a sharp rebound. Alphabet (Alphabet (GOOGL)) gained nearly 5% in its debut as a Dow component, while the VanEck Semiconductor ETF (SMH) climbed more than 3%, reversing earlier losses. The Dow Jones Industrial Average even closed above the 52,000 level for the first time.

But it's not all smooth sailing. Investors are also balancing this newfound optimism with lingering concerns about whether the artificial intelligence spending boom is sustainable. That tension is likely to keep markets on edge.

Looking ahead, there's more data to digest. Investors will be watching May's JOLTS job openings report, June's Chicago PMI, and consumer confidence data for fresh clues on the strength of the U.S. economy. S&P 500 futures were marginally down 0.03% early Tuesday, suggesting a cautious start.

For context, Monday's Polymarket bet on the S&P 500 open resolved "Up" after the index opened at 7,391.88, above Friday's close of 7,354.02. That contract saw about $191,102 in traded volume before settling. So traders have been right recently, but as always, past performance doesn't guarantee future results.