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?



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

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  • 3
    $\begingroup$ Arithmetic returns is $a_t = S_t/S_{t-1}-1$. Log-return is $r_t = \ln(S_t/S_{t-1})$. So $r_t = \ln(a_t+1)$ $\endgroup$ – Quantuple Sep 6 at 16:18

Transmuting one to the other is pretty straightforward without the underlying sequence of prices.

To go from log to simple:

$R = exp(r) - 1$

To go from simple to log:

$r = log(R+1)$


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