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

46 Optimizing Optimization

namely, higher transfer coefficient and lower tracking error. P1, however, has an
undesirably high tax liability.
In order to generate portfolios with lower tax liability, we modified the
objective function of the above strategy to minimize tax liability. Since we are

Portfolio P0

Summary statistic

Exp return

Transfer coef.

Active risk

Tax liability

Tu r n o v e r

0.2794%

0.6391

1.98%

$5,427.28

10.00%

Constraint

elasticities

Increase turnover

increase exp. return

Value

Turnover–tracking error

expected return heatmap Expected return–turnovertax liability heatmap

Turnover–tracking error

transfer coef. heatmap

Objective

hierarchy

Constraint

Increase turnover elasticities

decrease tracking error

Portfolio P1

Summary statistic

Exp return

Transfer coef.

Active risk

Tax liability

Tu r n o v e r

0.2736%

0.6650

1.84%

$6315.24

10.40%

Value

Portfolio P3

Summary statistic

Exp return

Transfer coef.

Active risk

Tax liability

Tu r n o v e r

0.2733%

0.6643

1.84%

$3616.29

13.00%

Value

Portfolio P2

Summary statistic

Exp return

Transfer coef.

Active risk

Tax liability

Tu r n o v e r

0.2700%

0.6577

1.85%

$4161.39

10.40%

Value

Figure 2.15 Flowchart.

Table 2.4 Portfolio P0

Summary statistic Value

Expected return 0.2794%

Transfer coefficient 0.6391

Implied beta 1.0107

Tracking error 1.98%

Tax liability $5,427.28

Turnover 10.00%

Realized short-term gains $13,409.61

Realized short-term losses $18,897.15

Net realized short-term gains/losses ($5,487.54)

Realized long-term gains $47,579.42

Realized long-term losses $5,910.04

Net realized long-term gains/losses $41,669.39