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?