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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.

Thanks in advance.

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Why are log returns used in finance?

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.

The only "con" for using log returns is that logarithms are more difficult to compute or approximate "by hand" than a subtraction and division. However, with our widespread access to computers, that is not really a drawback for practical purposes.

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