Stocks closed sharply higher in a broad rally Tuesday after data signaled a solid economy, but investors braced for volatile trading this week as voting was underway in an extremely tight presidential election.

The Institute for Supply Management said its nonmanufacturing purchasing managers index, a gauge of the services sector, accelerated to 56.0 last month, its highest since August 2022, from 54.9 the prior month and above the 53.8 expected by economists polled by Reuters.

The election outcome could take days to be finalized as the latest polls showed the race between Republican Donald Trump and Democrat Kamala Harris, which has affected markets in recent months, was too close to call.

The former president's odds improved on Tuesday in betting markets that many investors see as election indicators.

"The market continues to try and price for what is the outcome of this election," said Rob Haworth, senior investment strategist at U.S. Bank Wealth Management in Seattle.

"It's been so tight and even if we look at the price range we've been in, we've been in a tight price range, and so what's really moving us is marginal positioning for one result or the other."

"Both the bond market and the equity market are looking at Congress as important as well," he added. "Most base cases are for divided government, but this election is so close we could get any outcome. That's the challenge."

According to preliminary data, the S&P 500 gained 70.42 points, or 1.23%, to end at 5,783.11 points, while the Nasdaq Composite gained 259.19 points, or 1.43%, to 18,439.17. The Dow Jones Industrial Average rose 431.42 points, or 1.04%, to 42,227.74.

Volatility was more pronounced in government debt and currency markets. The benchmark 10-year U.S. Treasury note yield rose more than 10 basis points to a high of 4.366% before paring gains on a solid auction, and was last down slightly on the day.

Equity markets avoided Monday's volatility on expectations of a soft landing for the economy, bolstered by corporate earnings, lower interest rates and a resilient labor market.

Other economic data on Tuesday showed the trade deficit hit a 2-1/2 year high in September, as domestic demand draws in imports while concerns about higher tariffs under a Trump presidency have led to a front loading of imports by businesses.

Still, the CBOE Volatility Index, also known as Wall Street's "Fear Gauge," was slightly higher than its long-term average of 19.46, although it had eased from a near-two month high hit last week of 23.42.

Industrials and consumer discretionary led S&P 500 sectors higher.

Investors are also keeping an eye on congressional elections to determine the balance of power in Washington. Many analysts predict a split government, which would limit the ability of the president to enact significant policy changes.

Stocks viewed as proxies on a win for the former president experienced large swings, with Trump Media & Technology Group climbing as much as 18.64% and dropping as much as 8.42%, while also being halted for volatility multiple times.

Crypto stocks tracked bitcoin higher, with the cryptocurrency up roughly 4%, as Trump has positioned himself as an ally to the sector.

Palantir surged to a record high after the data analytics firm raised its annual revenue forecast for the third time.

The Federal Reserve will announce its latest policy statement on Thursday. Markets have almost completely priced in a 25-basis point interest rate cut, but the outlook for the path of future easing is less certain given the U.S. economy's strength.