Michael St Jules 🔸 comments on Weighted Factor Models: Consider using the geometric mean instead of the arithmetic mean

[Michael St Jules 🔸]

Note that the logarithm of a positive weighted geometric mean is the weighted arithmetic mean of the logarithms:

$$\log ((x_1^{w_1}\dots x_n^{w_n}{)}^{\frac{1}{w_1+\cdots +w_n}})=(w_1\log (x_1)+\cdots +w_1\log (x_n))/(w_1+\cdots +w_n)$$

So, instead of switching to the weighted geometric mean, you could just take the logarithm of your factors.

EDIT: Well, the weighted geometric mean is easier than taking logarithms, but it can be useful to remember this equivalence. With a weighted arithmetic mean, you might want your factors to be able to go arbitrarily negative, corresponding to the logarithms of values close to 0 in the geomean.