Optimizing Optimization: The Next Generation of Optimization Applications and Theory (Quantitative Finance)

94 Optimizing Optimization

● Identification of risk regimes, which partitions historical returns into subsamples
representing quiet and turbulent periods; and
● Full-scale optimization, which directly maximizes expected utility, however it is
defined, from the full sample of returns.

4.2 Multigoal optimization

4.2.1 The problem

Sophisticated investors employ optimization to determine a portfolio’s asset allo-
cation. Some investors care about absolute return and risk, while others focus on
relative return and risk. Many investors, however, are sensitive to both absolute
and relative performance. Typically, they address this dual concern by constrain-
ing the asset weights in the optimization process. This approach is inefficient.

4.2.2 The WPA solution

In the years following the introduction of portfolio theory by Harry Markowitz,
the investment community, at first reluctantly and then gradually, embraced his
prescription for constructing portfolios, but with an important caveat. To the
extent that the recommended solution departed from industry norms or prior
expectations, investors typically imposed constraints to force a more palatable
solution. For example, an investor might instruct the optimizer to find the com-
bination of assets with the lowest standard deviation for a particular expected
return subject to the constraint that no more than 10% of the portfolio is allo-
cated to foreign assets or nontraditional investments and that no less than 40%
is allocated to domestic equities. The reason for such constraints is that inves-
tors are reticent to depart from the crowd when there is a significant chance
they will be wrong, in the sense that they lose money. The matrix shown in
Figure 4.1 illustrates this point.
If we accept the notion that investors care not only about how they perform in
an absolute sense but also about how their performance stacks up against other
investors or a popular benchmark, there are four possible outcomes. An investor
achieves favorable absolute returns and at the same time outperforms his or her
peers or the benchmark, which would be great as represented by Quadrant I.
Alternatively, an investor might beat the competition or benchmark but fall
short of an absolute target (Quadrant II). Or an investor might generate a high

Absolute

performance Favorable Unfavorable

Favorable I. Great II. Tolerable

Unfavorable III. Tolerable IV. Very unpleasant

Relative performance

Figure 4.1 Wrong and alone.