Investors seem to think if there's a rate cut by the Federal Reserve, stocks will automatically rally. That may not be the case.

That's the message from UBS ahead of the Fed's policy decision on Wednesday. Traders are betting that the central bank would deliver an easing of monetary policy soon to provide the economy with some insurance and hence boosting stocks, but UBS believes such a move would do little to lift the market.

"When it comes to U.S. stocks, the Fed put is dead," UBS equity strategist Francois Trahan said in a note on Monday. "In the past 20 years, the so-called 'Fed Put' has failed to revive equities the way rate cuts did in the 1990s. The two easing cycles of this millennium took place amidst severe declines in equities."

The correlation between the S&P 500's price-to-earnings ratio and the fed funds rate has broken due to the long period of low rates since the early 2000s, UBS noted. When the Fed slashed rates in 2001 and 2008 to salvage the economy from recessions, U.S. equities did not rally following the rate reductions. In fact, the S&P 500 fell as much as 16% in the 12-month period after the cuts, the bank pointed out.

The market has been increasingly betting on a rate cut ever since Fed chair Jerome Powell said the central bank will "act as appropriate to sustain the expansion. " Traders are now pricing in a 20% chance of a rate decrease on Wednesday and a nearly 90% of at least one cut in the July meeting, while a September cut is almost a done deal, according to the CME FedWatch tool.

Meanwhile, stocks have fully come back from the May turmoil with the S&P 500 up more than 16% so far this year and about 1% from its all-time high hit in late April.

Unlike in the 1990s when the S&P 500 price to earnings responded to the interest-rate changes, now they are behaving "very cyclical," meaning being driven by leading economic indicators, UBS said.

"This does not bode well for equities as it suggests that P/Es will likely continue to compress as long as leading indicators of the economy continue to slow. Fed rate cuts are unlikely to change any of this in the near term," Trahan said.

Contrary to the market's expectations, UBS is in the no-cut camp as it doesn't think the economic data have been weak enough.

— CNBC's Michael Bloom contributed to this report.