true or false: the risk-neutral measure is useless in this situation

Example 2 of this Wiki article on the risk-measure describes how a stock price $$S_t$$ that is modeled with Geometric Brownian motion with drift $$\mu$$ $$dS_t = \mu S_t dt + \sigma S_t dW_t$$ can be rewritten in a risk-neutral way so that the drift is the risk free interest rate $$r$$:

$$dS_t = r S_t dt + \sigma S_t d \tilde{W}_t.$$

My question is this:

if I am an investor who is only buying/selling $$S_t$$ (no bonds, no derivatives, etc.), why should I care about this at all? How would this have any impact on my investment decisions?

• The risk-neutral one is only for the valuation of derivatives by arbitrage. So no, if you are not working with derivatives you don't need to know about that one. May 11 '20 at 20:23