MichaelStJules comments on Weighted Factor Models: Consider using the geometric mean instead of the arithmetic mean

MichaelStJules 21 Oct 2024 23:26 UTC
2 points
0 ∶ 0
Note that the logarithm of a positive weighted geometric mean is the weighted arithmetic mean of the logarithms:
$log ((x_{1}^{w_{1}} \dots x_{n}^{w_{n}})^{\frac{1}{w_{1} + \dots + w_{n}}}) = (w_{1} log (x_{1}) + \dots + w_{1} log (x_{n})) / (w_{1} + \dots + w_{n})$
So, instead of switching to the weighted goemtric mean, you could just take the logarithm of your factors.