Novel approaches to portfolio construction 37
portfolio optimizer returns a solution with expected return of 3%. Suppose
there exists an alternative solution with expected return of 3%, tracking error
of 4.5%, and turnover of 22%. While this solution is infeasible to the PM’s
original strategy, it is still of interest to him or her; the alternative solution
offers the same level of expected return at a lower tracking error although it
entails a small increase in the turnover.
Traditional portfolio optimization techniques restrict the vision of a PM to
only those portfolios that strictly satisfy all the constraints in his or her strat-
egy. We believe that marginally infeasible solutions such as the one presented
above can play a crucial role in guiding the decision-making process of a PM.
For the sake of illustration, consider the heatmap representation of optimal
expected returns for various combinations of tracking error and turnover val-
ues as depicted in Figure 2.10. Such a representation is insightful and can help
a PM discover opportunity pockets, i.e., attractive combinations of tracking
error and turnover values that cannot be discovered by tools geared toward
generating just one solution. In principle, all of these trade-offs could theoreti-
cally be considered in an objective with appropriate weights to capture the eco-
nomic benefit. However, choosing the correct weights is difficult and subject to
trial and error, limiting the overall usefulness of such an approach.
5.5
5.45
5.4
5.35
5.3
5.25
5.2
5.15
5.1
5.05Tracking errorTu r n o v e r5
4.95
4.9
4.85
4.8
4.75
4.7
4.65
4.6
4.55
4.5
27
27.327.627.928.228.528.829.129.429.7
30
30.330.630.931.231.531.832.132.432.7
33Color keyValue
0.8 0.88Expected returnFigure 2.10 Turnover — tracking error — expected return heatmap.