234 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 7.3 Risk/reward relationships for various portfolios according to modern
portfolio theory
Figure 7.3 shows all of the available portfolios under a given study. If
you hold Portfolio C, you would be better off with Portfolio A, as you would
have the same return with less risk, or Portfolio B, where you would have
more return with the same risk.
In describing this, Markowitz described what is called theefficient fron-
tier.This is the set of portfolios that lie on the upper and left sides of the
graph. These are portfolios where the yield can no longer be increased
without increasing the risk and the risk cannot be lowered without lower-
ing the yield. Portfolios lying on the efficient frontier are said to beefficient
portfolios.
Portfolios lying high up and off to the right and low down and to the left
are generally not very well diversified among very many issues. Portfolios
lying in the middle of the efficient frontier are usually very well diversified.
Which portfolio a particular investor chooses is a function of the investor’s
risk aversion, his willingness to assume risk. In the Markowitz model, any
portfolio that lies upon the efficient frontier is said to be a good portfolio
choice; where on the efficient frontier is a matter of personal preference
(later on, we’ll see that there is an exact optimal spot on the efficient
frontier).