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

Novel approaches to portfolio construction 49

or P1. However, P2 also has a lower transfer coefficient and lowest expected
return among the three portfolios P0, P1, and P2. This suggests that it might be
worthwhile exploring portfolios that are similar to P2 but have better transfer
coefficient and expected return.
Table 2.8 displays the elasticities of various constraints in the strategy
that was used to generate P2. Note that the tracking error constraint has a
very high elasticity, suggesting that portfolios with lower tax liability can be
obtained by increasing the tracking error bound. Since the PM is interested in
low-risk portfolios, we forgo this option and examine the trade-offs between
the next two most responsive constraints, namely the turnover constraint and
the expected return constraint. Figure 2.18 plots the minimum tax liability for
various combinations of turnover and expected return values. Evidently, port-
folios with higher expected return and lower tax liability can be obtained by
increasing the turnover value. Consequently, we increased turnover value to

Table 2.7 Portfolio P2

Summary statistic Value

Expected return 0.2700%

Transfer coefficient 0.6577

Implied beta 1.0099

Tracking error 1.84%

Tax liability $4,161.39

Turnover 10.40%

Realized short-term gains $11,687.70

Realized short-term losses $13,594.12

Net realized short-term gains/losses ($1,906.41)

Realized long-term gains $43,812.42

Realized long-term losses $14,163.38

Net realized long-term gains/losses $29,649.04

Table 2.8 Constraint elasticities (minimize tax liability strategy)

Constraint Elasticity

Tracking error 16.9601

Turnover 2.5490

Expected return constraint 1.9965

Industry bounds 0.6024

Style bounds 0.3178

Active beta 0.3089

Sector bounds 0.2160

Asset bounds 0.1505

Threshold holding 0.0163

Threshold trade 0.0121