We're getting ever so close to a new bull market. Another few days of gains for the S&P 500 could officially put the major index back in bull territory. But as the old saying goes, "Close only counts in horseshoes and hand grenades." There's no guarantee that the S&P will move the 4% or so higher needed. 

The good news for investors is that there are great stocks that aren't dependent on the S&P 500's gyrations. Here are three stocks that could soar whether there's a new bull market or not.

Axsome Therapeutics (NASDAQ: AXSM) stock more than doubled last year while the S&P 500 plunged. So far in 2023, though, it's a different story. Axsome's share price has fallen as the S&P rose. But don't read too much into this seemingly inverse relationship.

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Source Fool.com