Fernholz and Karatzas have published various papers about so called stochastic portfolio theory. Basically they say that the return to be expected from a portfolio on the long run is rather the growth rate $$ \gamma = \mu - \frac12 \sigma^2 $$ than $\mu$, where $\mu$ is the drift coefficient of the price process $S_t$ which solves the following SDE: $$ dS_t = \mu S_t dt + \sigma S_t dB_t. $$
One can argue with Ito's lemma, with the geometric mean of a lognormal random variable and similar - but what is the intuition behind this?
As references see Stochastic Portfolio Theory and Stock Market Equilibrium by Fernholz and Shay for the first paper on this and Does a Low Volatility Portfolio Need a “Low Volatility Anomaly?” by Meidan as a more recent reference.
If I am not mistaken then the above SDE would look like this $$ dS_t = (\mu-\sigma^2/2) S_t dt + \sigma S_t \circ dB_t $$ in Stratonovich form and one sees the "correct" growth rate... which is another link. But what is the big picture of all this?