# Geometric and aritmetic index disparities

Geometric Indexes. We have seen the importance of geometric returns through time. A geometric index is formed across different stocks at a particular point in time, such as a day. Constructing a portfolio 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 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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Both of these indices assume equally weighted positions, or equal dollar amounts, invested into many stocks. For both the VLA's and the VLG's construction, we first compute the ratio of each stock's closing price today to the close on the previous trading day. For the VLG, we then multiply all of these ratios together, while for the VLA, we would add them just as if finding a typical "average." The difference in how these indices are created is the reason for their ...

#### Solution Summary

Value Line Arithmetic Index vs Value Line Geometric Index; reasons for their divergence