50 Optimizing Optimization
13% and the lowest allowable expected return to 0.2733%, and reoptimized
the resulting model to obtain the P3 portfolio whose key characteristics are
reported in Table 2.9. Note that P3 has significantly lower tax liability even
though its expected return, tracking error, and transfer coefficient are compa-
rable to that of P1. Furthermore, P3 has higher realized long-term losses and
lower realized long-term gains as compared to P1. In other words, P3 uses the
additional 2.6% turnover to harvest losses that in turn are used to offset gains
thereby reducing the overall tax liability.
This entire exercise can be viewed as a systematic attempt to improve the opti-
mal portfolio P0 derived from the original strategy. At various stages of this exer-
cise, we used the concept of elasticity to select pairs of constraints whose joint
perturbations was most likely to impact the optimal objective value. Heatmaps
associated with such pairs of constraints were used to gain insights about the
optimal portfolio terrain, and also to determine the most appropriate perturba-
tion values. The final portfolio P3 has better transfer coefficient, tracking error,
and tax characteristics than P0 despite having almost the same expected return.
13.52
13.208
12.896
12.584
12.272
11.96
11.648
11.336
11.024
10.712Tu r n o v e rExpected return10.4
10.088
9.776
9.464
9.152
8.84
8.528
8.216
7.904
7.592
7.280.2560.2570.2580.2590.260.2610.2620.2630.2640.2650.2660.2670.2680.2690.270.2710.2720.2730.2740.2750.276Color keyValue4000 7000Tax liabilityFigure 2.18 Expected return — turnover — tax liability heatmap.