Should arithmetic or geometric mean be used in CAPM?

In estimating parameters in CAPM, some prefer to use geometric mean because it represents a more accurate measure in estimating long term expected return. [1] This is an accurate observation. 

However,  variance is calculated from arithmetic mean. Hence the Markowitz theory is built on arithmetic mean. From theoretical perspective, arithmetic mean, instead of geometric mean, should be used in CAPM.

Kelly and Latane's investment theory is built on geometric mean. 

1. Copeland, Koller, Murrin, McKinsey & Co (1994) Valuation, Second edition p. 257-267, John Wiley & Sons