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

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Robust portfolio optimization using second-order cone programming 21


their goal. However, there is a question as to whether this is a fair method of opti-
mization from the point of view of the individual managers. Suppose that instead
of both managers in the above example having a minimum portfolio alpha require-
ment of 5%, one of the managers decides to target a minimum portfolio alpha
of 6%. If they are still both constrained to have a maximum individual tracking
error against their own benchmark of 2%, it can be seen from Figure 1.16 that the
tracking error for the overall fund against the overall benchmark will increase.


2.5

3

3.5

1.5

0.5

0

Overall
benchmark

only

Tracking error (%)

Constrain both

to 3%
Constrain both

to 2%
Constrain both

to 1%
Constrain both

to 0.85%
Constrain fund

1 to 0.85%
fund 1 to 0.8%Combined, minT E on each

1

2

Benchmark for Fund 1
Benchmark for Fund 2

Overall benchmark

Figure 1.15 Tracking errors with constraints on risk for each fund.


Fund 1 alpha = 5%,
Fund 2 alpha = 5%

Fund 1 alpha = 5%,
Fund 2 alpha = 6%

Tracking error (%)

1.76
1.74
1.72
1.7
1.68
1.66
1.64
1.62
1.6
1.58
1.56

Figure 1.16 Tracking error with different alpha constraints on Fund 2.

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