288 THE HANDBOOK OF PORTFOLIO MATHEMATICS
FIGURE 9.1 Conceptual view of the old framework,left, with the new,right
Why This New Framework Is Better
For nearly four decades, portfolio construction was envisioned in a two-
dimensional plane, where return made up the vertical axis, and risk—
actually, some surrogate measure of risk—was the horizontal axis. The basic
notion was to get as great a return for a given level of risk, or as low a level
of risk for a given level of return, as was possible on this two-dimensional
plane (see Figure 9.1).
The new framework to be presented is an altogether new way of view-
ing portfolio construction, different than looking at portfolios in a two-
dimensional, risk-competing-with-return sense.^2 There are a number of rea-
sons to opt for the new framework over the old.
The new approach is superior because the inputs are no longer along
the lines of expected returns and (the rather nebulous) variance in expected
returns, or some other ersatz measure of risk. The inputs to this new model
are differentscenariosof different outcomes that the investments may take
(a more accurate approximation for the real distribution of returns). Now,
rather than estimating things like expected returns and variance in those
expected returns, the inputs are much closer to what the investment man-
ager may be thinking (e.g.,ay%chance of anx% gain or loss, etc.). Now,
(^2) In Chapter 12 we will see, however, how to take the portfolio constructed from the
methods outlined in this chapter, juxtaposed to its respective drawdown and thus
truly maximize return for a given level of “risk.”