Assuming the change in stock price P from one period (t1) to the next (t2) is small, we can calculate returns using either:(Pt2 - Pt1)/Pt1-or-ln (Pt2/Pt1)For small changes, either method outputs the same values. This I have verified empirically. I understand that if x is log normally distibuted, then log(x) is normally distributed. And we would like to work with normal distributions in our analyses. Given all of the above, what exactly is the meaning fof "Log Returns"? We're not taking the logarithm of returns above, are we? We're calculating the returns by taking either the logarithm of Pt2/Pt1 -or- logarithm of (Pt2 - Pt1)/Pt1, both of which happen to give the same values at very small changes in the price. However, we're not taking the logarithm of the return itself, are we? Is the term "log returns" misleading -or- am I missing something? Isn't the distribution of (Pt2 - Pt1)/Pt1 distributed normally anyway (with fat tails may be), even without needing to apply any logarithm?Thanks in advance.

Pt2 - Pt1 = absolute return(Pt2 - Pt1) / Pt1 = relative returnln Pt2/Pt1 = log return, this is just terminologyin the limit Pt2-Pt1 -> 0, \int_P1^P2 dP / P = ln P2/P1, this is independent of the distribution. If log( ) transforms your input into a normal variable is a completely different thing, it may be, it may also not. Also absolute returns may be asummed normally distirbuted etc. etc.-- cross post ...

Thanks to both responses!