Bullish investors are starting to worry that the US stock markets are turning in their favor, after a downbeat first half of the year.

Fundstrat's Tom Lee has argued that prices for equities have reached the bottom and say the summer rally on the major US benchmarks is on the road and will reach all-time highs before the end of 2022.

The S&P 500 surged 17%, and the tech-heavy Nasdaq has added over 20% over the past two months, as of this writing. 

However, Wall Street's biggest names have another opinion about it. Prominent bank analysts have argued that stocks' current rebound is just a classic bear market rally — when equities soar but just for a short time before resuming a long-term decline.

"Stocks are still not inexpensive, despite the bear market," Bank of America's Savita Subramanian, an equity and quant strategist, said in a recent research note.

"In fact, they are more expensive after the S&P 500's 17% rally from its June low, driven by a drop in the cost of equity."

According to analysts like Subramanian and UBS' Jason Draho, now is not the time for investors to try to time the bottom, and disappointing economic data could send stocks through the mayhem.

"Becoming more optimistic in the current highly uncertain environment does make the markets more vulnerable to negative news," Draho, the head of Americas asset allocations at the Swiss bank, said.

Morgan Stanley's Mike Wilson has cautioned investors not to bet on a rate-hike pause in the upcoming months. The bank's CIO noted that July's strong labor market report — which showed the US adding 528,000 jobs — would be a motivation for the Fed to continue tightening aggressively.

"While inflation appears to be peaking, it's not likely to come off at a pace fast enough to spur the type of sustained Fed pause the equity market is already discounting," Wilson said in a recent research note.