Optimal solutions for optimization in practice 71month off each historic return and repeat our analysis for our three optimiza-
tions, both 100%-constrained and 25%-constrained ( Tables 3.3 and 3.4 ).
The GLO (100%-constrained) excepts one asset class that is included by
both mean – variance optimizations owing to its negative skewness and higher
kurtosis. Otherwise, the results are broadly similar to those in Tables 3.1 and
3.2 ; emerging markets are only considered by 3.4.3.5.8 Squared losses
An investor whose disutility of a double unit loss is more than twice a single
unit loss might find a utility function that includes the square of expected losses
suitable. We also constrain property (IPD) to 10% in all cases ( Table 3.5 ).a. GLO: E [ U G (^) / (^) L ] E [ gains ] (1 l ) E [ losses ], l 1
b. GLO: E U E gains
l
[][] [()]GL/ E losses l
2
(^2) , 20
c. GLO: (^) E U E gains
l
[][] [()]GL/ E losses l
2
(^2) , 4
Table 3.3 Summary of optimization results: maximum holding 100%, trimmed EM
Mean% StdDev% Skewness Kurtosis Gain% Loss% Omega Probability
(a) G/L l 1 10.89 4.07 0.21 3.01 9.27 3.17 2.924 0.75
(b) M/V λ 2 18.17 14.39 0.53 2.85 28.24 14.87 1.900 0.67
(c) M/V λ 10 13.50 7.22 0.66 3.17 15.46 6.76 2.317 0.69
Table 3.4 Summary of optimization results: maximum holding 25%, trimmed EM
Mean% StdDev% Skewness Kurtosis Gain% Loss% Omega Probability
(a) G/L l 1 11.27 5.57 0.68 3.37 11.54 5.08 2.271 0.72
(b) M/V λ 2 14.48 11.70 0.96 3.70 21.69 12.01 1.805 0.70
(c) M/V λ 10 12.99 7.29 0.68 3.30 15.11 6.92 2.183 0.69