Suppose we have 3 stocks following [GBM][1]s.

We are given the distribution of the **daily** log returns which is multivariate normal.

Suppose I want to sample the stock price tomorrow ($\Delta t = 1$ day), could I just sample a return vector from this distribution and then say that the stock price tomorrow is $S_0 \cdot \exp(r_\text{sample}\Delta t)$?

I've been arguing with my friend about this and he claims I should multiply by $\sqrt{\Delta t}$? I don't understand his argument.

Is there anything wrong with what I am doing here? 


  [1]: https://en.wikipedia.org/wiki/Geometric_Brownian_motion