• The S&P 500 has picked up more than 3% since the Fed's June meeting, at which it raised rates by 75 basis points.

• But the broad-market index could see a muted gain, if any, after Wednesday's Fed meeting, said Bespoke Investment Group.

• Investors widely expect the Fed to hike rates by another 75 basis points.

The S&P 500 has largely been advancing as the market approaches Wednesday's Federal Reserve meeting, and that could result in a lackluster gain for stocks after policymakers announce their next interest rate move, according to Bespoke Investment Group.

The S&P 500 has picked up roughly 3.5% since June 15, when the Federal Open Market Committee raised its key interest rate by 75 basis points — the largest rate hike since 1994 — to combat hot inflation.

The advance marks a "major difference" in the S&P 500's direction compared with five consecutive inter-meeting declines.

"[Fed] days in which the S&P 500 has been down more than 5% between meetings have usually seen stronger gains on the Fed day itself whereas gains have been more muted when it heads into a meeting in the green," said Bespoke, an independent market research firm, in a note published Tuesday.

While there are no guarantees the broad-market index will rise on Wednesday, Bespoke noted the S&P 500 has rallied in response to FOMC actions over its past few meetings. Since the latest rate-tightening cycle began in March, the S&P has risen by 2.24%, 3%, and 1.46% respectively on each of those Fed days.

"[Those] have been stronger (market) reactions to the Fed than most others since 1994. In fact, the 3% rally in May ranked as the fifth best Fed day on record (out of a total of 228) while the March meeting's 2.24% rally ranks tenth."

As well, "the moves to the upside in response to the FOMC have been a sight to behold," when zeroing in on the reaction in the stock market after the Fed's rate decisions starting in March.

The "S&P 500 has fallen into the red right around the time Fed Chair [Jerome] Powell has taken the podium each time, but then the index staged massive rallies in the late afternoon, hitting at least a 2% gain at some point in the afternoon," said Bespoke.

The CME FedWatch tool indicated expectations for a Fed rate hike of 75 basis points at Wednesday's meeting were at 75% as of late Tuesday. That would put the Fed funds rate at a range of 2.25% to 2.5%. Meanwhile, a key recession indicator for the Fed has been flashing a warning that traders want the central bank to ease off rate hikes.

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