38 Optimizing Optimization
A financial model provided as input to a strategy can only capture a portion
of the information available to a PM. Often, a PM has access to information
bits or “ market hunches ” that are difficult to model but nevertheless can be
useful in making an informed decision. Heatmap representations such as the
one shown in Figure 2.10 can be used to partially overcome this shortcoming.
The example that follows elaborates on this observation.
Consider a PM rebalancing his or her portfolio in view of an expected eco-
nomic downturn. Suppose the fund managed by the PM has traditionally held
long positions in entertainment and food products industries, and the strategy
used by the PM has tentative limits on the amount of exposure to each one
of these industries. As the economy turns sour, the demand for entertainment
and food products is likely to go down. For instance, people might want to
save money by cutting down on visits to entertainment theaters. Similarly, they
might reduce emphasis on environmentally conscious and ethically produced
food items (such as organic food) and replace them by regular food products.
However, as is well known in Economics, the demand for luxury goods such as
entertainment products is significantly more elastic with respect to variations
in average income than the demand for essential goods such as food products.
Despite being a well-known fact, the PM has very limited means of meaning-
fully incorporating this economic wisdom within his or her strategy. Ideally,
the PM would like to understand the impact on the optimal expected return
that results as he or she reduces his or her exposure to the more elastic enter-
tainment industry, and increases his or her exposure to the relatively inelastic
food products industry. Heatmaps such as the one shown in Figure 2.10 can be
tremendously helpful in depicting these kinds of trilateral dependencies involv-
ing expected return and exposures to a pair of industries.
Is there a good way of detecting pairs of constraints whose joint
variation has nontrivial impact on the overall model?
A strategy with k constraints has k ( k – 1)/2 pairs of constraints that can be
examined simultaneously to perform trade-off analysis discussed above.
Admittedly, only a small fraction of these pairs of constraints are likely to be of
practical interest, and identifying such pairs can be a difficult task. One could
argue that a PM can use his or her judgment to select pairs of constraints and
study the associated heatmaps. Such an approach has an immediate shortcom-
ing, namely, that it is strongly rooted in the PM’s preconceived view of the
portfolio construction process, and hence never surprises him or her. In other
words, such an approach deters the PM from examining combinations of con-
straints that are unlikely to yield interesting outcomes despite being perform-
ance bottlenecks of the strategy.
Furthermore , sometimes heatmaps obtained by jointly varying a pair of con-
straints are completely determined by variations in only one of the constraints.
For instance, consider the heatmap shown in Figure 2.11 obtained by jointly
varying the tracking error and sector bound constraints. Clearly, in this case,