Although we have followed convention in using the arithmetic mean of returns, for returns data, the geometric mean is often – and more correctly – used.

The geometric mean g is defined implicitly by the formula:

In other words, it is the constant return that would compound up to exactly the same terminal amount as the observed sequence of returns x1, x2 ....xN.
Comparative returns data are used extensively by the research firms that compile fund rankings. For such purposes, which do you think is the more correct measure—the arithmetic mean or the geometric mean?

(1+g) = (1+x, )( 1 + x, )....( 1 + xy ) "N