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

Staying ahead on downside risk 157

approach tends to underweight the asset compared to mean – variance. Once
again, the main differences are found for the S & P and FTSE indices. By adopt-
ing a mean – EVaR criterion instead of mean – variance, we end up overweighting
the UK index, for the reason explained above: The S & P 500 has experienced

Table 6.5 Actual returns observed for December 2008 and sample moments of the

100 simulated alpha vectors

spx dax nky ukx

Return in December 2008  2.20% 1.51% 3.70% 1.54%

Simulated alphas:

Mean  0.74% 0.45% 1.08% 0.40%

Standard deviation 2.08% 2.84% 2.88% 1.97%

80

60

40

20

0

80

60

40

20

0

Frequency

80

40

50

30

20

10

0

Frequency

E-VaR

overweight

Mean variance

overweight

–40 –20 0 20

dax ukx

nky spx

Pct points Pct points

Pct points Pct points

40 60 80 –40 -20 0 20 40 60 80

Frequency

35

25

30

20

15

5

10

0

Frequency

–40 –20 0 20 40 60 80 –40 –20 0 20 40 60 80

Figure 6.5 Difference between mean – variance and mean – EVaR allocation.