We have seen the importance of geometric returns through time. A geometric index is formed across different

Question:

We have seen the importance of geometric returns through time. A geometric index is formed across different at a particular point in time, such as a day. Constructing a that exactly replicates a geometric index is thus impossible. Given this, why would you want to use a geometric index? In other words, what does a geometric index measure? Now consider the Value Line Arithmetic Index (VLA), which is equally weighted, and the Value Line Geometric Index (VLG). On February 1, 1988, both indexes were set to a value of 210.75. As of the close of the market on January 4, 2008, the VLA was at 2,118.61 and the VLG was at 414.98. Why would you expect to see such a disparity in the two index levels?

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