Stocks fell deeper into bear market territory on Tuesday as fears over the Federal Reserve's aggressive rate-hiking campaign impacted market sentiment. The S&P 500 fell into a bear market on Tuesday, while the Dow Jones Industrial Average fell over 100 points and the Nasdaq Composite closed up 0.25%.

Here's how the market settled on Tuesday:

S&P 500 Index (SPY  ): -0.21% or -7.75 points to 3,647.29

Dow Jones Industrial Average (DIA  ): -0.43% or -125.82 points to 29,134.99

Nasdaq Composite Index (QQQ  ): +0.25% or +26.58 points to 10,829.50

At closing, the S&P 500 is now 24.3% below its record set in January, while the Dow is 21.1% below its all-time high. The tech-heavy Nasdaq has also fallen more than 33% since its last record high in November.

Stocks were initially higher on Tuesday following comments from Chicago Fed President Charles Evans that he remained "cautiously optimistic" that the U.S. economy can avoid a recession despite the central bank's current aggressive strategy to tame surging inflation.

"Again, I still believe that our consensus, the median forecasts, are to get to the peak funds rate by March - assuming there are no further adverse shocks. And if things get better, we could perhaps do less, but I think we are headed for that peak funds rate," Evans said in an interview with CNBC's "Squawk Box Europe."

However, those morning gains were short-lived as market participants anticipate the Fed will raise interest rates by one percentage point by the end of the year to keep in line with their funds rate projections.

On the economic front, home prices cooled at the fastest rate on record in the history of the S&P CoreLogic Case-Shiller Index, according to a report on Tuesday, but cooled from June's gains.

Home prices nationally rose 15.8% over July 2021, slower than the 18.1% gain in the previous month. Moreover, the 10-City Composite climbed 14.9% year-over-year, down from 17.4% in June, while the broader 20-City Composite gained 16.1%, from from 18.7% in the previous month. July's annual gains were lower compared with June in each of the cities recorded in the index.

"As the Federal Reserve continues to move interest rates upward, mortgage financing has become more expensive, a process that continue to this day," said Craig Lazzara, managing director at S&P DJI, in a press release. "Given the prospects for more challenging macroeconomic environment, home prices may well continue to decelerate."