Whale Optimization Algorithm for Multiconstraint Second-Order Stochastic Dominance Portfolio Optimization

Table 3

The performance of the portfolio obtained by the various algorithms under δ = 0.10.

Indicators/algorithms	WOA		GWO		FOA		PSO		FA
	Mean	Optimal	Mean	Optimal	Mean	Optimal	Mean	Optimal	Mean	Optimal
Net return	0.1001	0.1182	0.08775	0.1097	0.05386	0.06503	0.05337	0.06692	0.04820	0.06993
Skewness	−0.08742	−0.07992	−0.1029	−0.05443	−0.1898	−0.1845	−0.1880	−0.1577	−0.1860	−0.1732
Kurtosis	0.9275	0.7266	0.8847	0.9680	0.7697	0.8485	0.7766	0.8309	0.7746	0.6532
Shannon’s entropy	3.9961	3.9906	4.0519	3.9914	4.2038	4.1722	4.2069	4.1627	4.2230	4.0865
Yager’s entropy	−0.8616	−0.8613	−0.8237	−0.8966	−0.7190	−0.7411	−0.7146	−0.7499	−0.7034	−0.8342
EMR	8.0891	8.8274	7.6398	8.4398	6.3660	6.7649	6.3501	6.8179	6.1376	6.9920
	−0.01349	−0.01368	−0.01350	−0.01398	−0.01337	−0.01329	−0.01089	−0.01110	−0.01088	−0.01086
	−0.01780	−0.01769	−0.01779	−0.01783	−0.01772	−0.01751	−0.01504	−0.01512	−0.01498	−0.01481
Downside deviation	0.2546	0.2480	0. 2471	0.2655	0.2327	0.2414	0.2262	0.2513	0.2251	0.2403
Sortino ratio	0.3190	0.3558	0.3103	0.3177	0.2746	0.2802	0.2811	0.2712	0.2732	0.2909
STARR ratio	−0.04543	−0.04989	−0.04295	−0.04731	−0.03593	−0.03863	−0.04220	−0.04507	−0.04095	−0.04718
Sharpe ratio	7.0194	9.0582	5.5788	8.0460	1.6596	3.0298	1.6079	3.2149	1.0754	3.5891
Information ratio	0.1808	0.1978	0.1767	0.1799	0.1624	0.1650	0.1650	0.1620	0.1613	0.1693
Times	34.1131	35.3522	34.3511	34.2063	33.9993	35.9620	31.3336	33.5159	38.0149	39.8047
Upper bound	0.07952	0.08456	0.07515	0.08125	0.05307	0.05465	0.05357	0.05872	0.05226	0.06554