Based on your financial expertise, provide your response or viewpoint on the given financial question or topic. The response format is open.

When to use geometric vs. arithmetic mean? Why is the former better for percentages?
JoeTaxpayer nailed it.  Here's another way to look at it: Generally, we invest in something, then might leave it there for a few years, then take it out, but don't touch it in between.  In that case, to get the final amount X(N), we need to take the initial amount, then multiply by growth in the first year, then multiply by growth in the second year, etc. So, for three years, we have: X(3) = X(0) * G(1) * G(2) * G(3) = X(0) * "average annual growth" ^ 3 So, here, we see that we want the average annual growth to the power three equal to the product of the annual growth rates, thus, geometric mean: geometric mean = (G(1) * G(2) * G(3)) ^ (1/3) On the other hand, consider a situation where I have three investments X,Y,Z over one year. Now I have, after one year: X(1)+Y(1)+Z(1) = X(0)*G(1,X) + Y(0)*G(1,Y) + Z(0)*G(1,Z) = ( X(0)+Y(0)+Z(0) ) * "average annual growth" Now, in this case, if we assume X(0) = Y(0) = Z(0) = 1, i.e. I put equal amounts in each, we see that the average annual growth rate we want in this case is the arithmetic mean: arithmetic mean = (G(1,X) + G(1,Y) + G(1,Z)) / 3 (if we had unequal amounts at the beginning, it would be a weighted average). TL;DR: