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

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.