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

44 Optimizing Optimization

Table 2.5 displays the elasticities of various constraints in the strategy. Note
that the tracking error and turnover constraints have significantly higher elas-
ticities than the remaining constraints. Figure 2.16 plots the optimal expected
return for various combinations of tracking error and turnover values, while
Figure 2.17 plots the transfer coefficients of the respective portfolios. Since both
of these constraints have similar elasticities, the level curves of Figure 2.16 are
equally responsive to perturbations in the tracking error and turnover bounds.
In contrast, the level curves of Figure 2.10 are much more responsive to varia-
tion in the highly elastic tracking error constraint than to variations in the rel-
atively inelastic turnover constraint. Figure 2.17 suggests that portfolios with
higher transfer coefficients can be obtained by decreasing the tracking error
bound and increasing the turnover limits. By overlaying the expected return
heatmap ( Figure 2.16 ) over the transfer coefficient heatmap ( Figure 2.17 ), we
determined that increasing the turnover to 10.40% while decreasing the track-
ing error to 1.84% should yield portfolios with higher transfer coefficient and
comparable expected return. Table 2.6 gives the key characteristics of the result-
ing optimal portfolio, referred to as P1 in the sequel. While both P0 and P1
have similar expected returns, P1 has two additional desirable characteristics,

5.5

5.45

5.4

5.35

5.3

5.25

5.2

5.15

5.1

5.05

Tracking error

Tu r n o v e r

5

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

33

Color key

Value

1.061.09 Implied beta

Figure 2.13 Turnover — tracking error — implied beta heatmap.