# Convert arithmetic returns to log returns [closed]

I have a series of arithmetic returns and I need log returns. I do not have the underlying prices. How do I convert?

All the posts I have found explain why using one versus the other is appropriate but how do I get from one to the other without the underlying data?

Thanks

## closed as off-topic by Quantuple, byouness, Daneel Olivaw, Bob Jansen♦Sep 8 at 13:12

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "Basic financial questions are off-topic as they are assumed to be common knowledge for those studying or working in the field of quantitative finance." – Quantuple, byouness, Daneel Olivaw, Bob Jansen
If this question can be reworded to fit the rules in the help center, please edit the question.

• Arithmetic returns is $a_t = S_t/S_{t-1}-1$. Log-return is $r_t = \ln(S_t/S_{t-1})$. So $r_t = \ln(a_t+1)$ – Quantuple Sep 6 at 16:18

$$R = exp(r) - 1$$
$$r = log(R+1)$$