so I have closing prices for 2 different stocks and I want to analyze the covariance between their yields. The first thing I did was figure out the yields so I can compare those.
Now I can use the arithmetic mean to calculate the covariance between, but shouldn't I be using the geometric mean when analyzing yields? I've tried both, and both lead to almost exactly the same result (about 2.4% difference). Which one should I use in my paper?
I'm leaning towards the geometric mean as it seems more correct to me, but I couldn't find anyone else having done the same so far.
(If I take the first closing price I have and multiply it by the geometric means to the n-th power, n being the trading days up until the last closing price I have, I get the exact closing price on that day, as I should. If I do the same with the arithmetic mean, I get an error of almost 70€. That's why I'm leaning toward the geometric mean even for things like variance and covariance.)
Best regards, and thanks in advance!
Edit: Regarding the yields: I have a bunch of closing prices, say for example,
and I calculated their daily yield as the closing price divided by the closing price of the previous day, minus 1. (e.g. 6754.20/6764.83-1 = -0.00157..)