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

Novel approaches to portfolio construction 47

interested in portfolios whose expected return is similar to that of P0 and P1,
we added a constraint to the strategy limiting the expected return to be at least
0.27%. Table 2.7 gives the characteristics of the resulting optimal portfolio,
referred to as P2 in the sequel. Clearly, P2 has a lower tax liability than P0

Table 2.5 Constraint elasticities

Constraint Elasticity

Tracking error 0.1687

Turnover 0.1563

Industry bounds 0.0978

Style bounds 0.0784

Sector bounds 0.0323

Active beta 0.0256

Asset bounds 0.0162

Threshold holding 0.0013

Threshold trade 0.0000

2.2

2.18

2.16

2.14

2.12

2.1

2.08

2.06

2.04

2.02

Tracking error

Tu r n o v e r

2

1.98

1.96

1.94

1.92

1.9

1.88

1.86

1.84

1.82

1.8

9

9.19.29.39.49.59.69.79.89.9^10 10.110.210.310.410.510.610.710.810.9^11

Color key

Value

0.27 0.28

Expected return

Figure 2.16 Turnover — tracking error — expected return heatmap.