The Geometry of Mean Variance Portfolios 267
FIGURE 8.2 The efficient frontier with/without reinvestment
In Figure 8.2 you can see the efficient frontier corresponding to the
arithmetic average HPRs as well as that corresponding to the geometric
average HPRs. You can see what happens to the efficient frontier when
reinvestment is involved.
By graphing your GHPR line, you can see which portfolio is the ge-
ometric optimal (the highest point on the GHPR line). You could also
determine this portfolio by converting the AHPRs and Vs of each port-
folio along the AHPR efficient frontier into GHPRs per Equation (3.04)
and see which had the highest GHPR. Again, that would be the geo-
metric optimal. However, given the AHPRs and the Vs of the portfolios
lying along the AHPR efficient frontier, we can readily discern which
portfolio would be geometric optimal—the one that solves the following
equality:
AHPR− 1 −V= 0 (8.05a)where: AHPR=The arithmetic average HPRs. This is the E
coordinate of a given portfolio on the efficient
frontier.
V=The variance in HPR. This is the V coordinate of a
given portfolio on the efficient frontier. This is equal
to the standard deviation squared.