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

30 Optimizing Optimization

The case with TO  30% is shown here in the same way as previously
shown in Figures 2.1 – 2.3 , and is shown in order to facilitate comparison with
the other TO cases.
In all three TO cases, portfolio performance is improved by adding the sec-
ond risk model constraint and making it as tight as possible without making
the primary risk constraint nonbinding.

4.0

2.2

1

X = Active asset bound (%)

Fundamental risk constraint not binding

Statistical risk constraint not binding

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2.4

2.6

2.8

Y

= Active statistical risk (% Ann.)

3.0

3.2

3.4

3.6

3.8

−8.26 to −8.20

−8.39 to −8.33

−8.52 to −8.46

−8.65 to −8.58

−8.78 to −8.71

−8.90 to −8.84

−9.03 to −8.97

−9.29 to −9.22

−9.16 to −9.10

−9.42 to −9.35

−9.54 to −9.48

−9.67 to −9.61

−9.80 to −9.74

Figure 2.3 The worst, monthly, active return (%) when both risk models are binding.
TO  30%.

4.0

Y

= Active statistical risk (%)

3.5

3.0

2.5

2.0

1.5

123

15% monthly TO

4567

150.4–152.0

147.2–148.8

144.0–145.6

140.8–142.4

137.6–139.2

134.4–136.0

131.2–132.8

128.0–129.6

124.8–126.4

121.6–123.2

118.4–120.0

115.2–116.8

112.0–113.6

10 1 2 3 4 5 6 7 10 1 2 3 4 5 6 7 10

30% monthly TO 60% monthly TO

X = Active asset bound (%) X = Active asset bound (%) X = Active asset bound (%)

Figure 2.4 The number of asset held versus asset bound and the statistical risk model
risk constraint for TO  15%, 30%, and 60%.