# log returns in finance

Why are log returns used in finance? For example to calculate a stocks performance. There are a lot of articles on that topic yet I don't find them very helpful. Could somebody please explain step by step? Maybe also with pros and cons.

It really is about compactness when devising models. The mathematical property of logarithms $$log(S_{t+n}/S_t)=log(S_{t+n})-log(S_t)$$ makes log returns more convenient for modeling than the traditional $$\frac{ S_{t+1}-S_t}{S_t}$$ because the former allow the modeler to think in terms of subtraction.