# Question regarding calculating Geometric Standard Deviation

I know GSD can be calculated by taking exponent of standard deviation of log return. My question is whether 1 should be subtracted from exp or should 1 not be subtracted ie exp(stdev of log returns)-1 or exp(stdev of log returns).

Thanks.

• Usage is different in Statistics and Finance. In Statistics a logarithmic transformation of a variable is used. In Finance "logreturn" does not mean "log of return" but "log of return plus 1" i.e. $l=\ln(r+1)$ therefore to convert in the opposite direction you subtract 1: $r=\exp(l)-1$. I would suggest doing the same for GSD. Aug 17, 2022 at 10:10
• Thanks nbbo2 for the clarification! Looks like my question is answered. Aug 17, 2022 at 10:17
• @nbbo2 Can I annualize the standard deviation of log returns (by multiplying the stdev by square root of 12) and apply the formula exp (annualized standard deviation of log returns)-1 to get Annualized GSD or should I not annualize the standard deviation of log returns? Aug 17, 2022 at 18:59