272 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 8.5 AHPR, GHPR, and their CML lines
not) the same. The only time that these portfolios will be the same is when
the following equation is satisfied:
RFR=GHPROPT− 1 (8.10)
where: RFR=The risk-free rate.
GHPROPT=The geometric average HPR of the geometric
optimal portfolio. This is the E coordinate of the
portfolio on the efficient frontier.Only when the GHPR of the geometric optimal portfolio minus 1 is equal
to the risk-free rate will the geometric optimal portfolio and the portfolio
tangent to the CML line be the same. If RFR>GHPROPT−1, then the
geometric optimal portfolio will be to the left of (have less variance than)
the tangent portfolio. If RFR<GHPROPT−1, then the tangent portfolio will
be to the left of (have less variance than) the geometric optimal portfolio. In
all cases, though, the tangent portfolio will, of course, never have a higher
GHPR than the geometric optimal portfolio.
Note also that the point of tangency for the CML to the GHPR and for
the CML to the AHPR is at the same SD coordinate. We could use Equation