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

Table 2

The performance of the portfolio obtained by the various algorithms under δ = 0.07.

Indicators/algorithms	WOA		GWO		FOA		PSO		FA
	Mean	Optimal	Mean	Optimal	Mean	Optimal	Mean	Optimal	Mean	Optimal
Net return	0.09664	0.1111	0.08346	0.1095	0.05426	0.06662	0.05378	0.06588	0.05123	0.06484
Skewness	−0.0962	−0.0389	−0.1058	−0.0841	−0.1906	−0.1097	−0.1858	−0.2220	−0.1854	−0.1634
Kurtosis	0.9434	0.9932	0.9227	0.9654	0.7533	0.9873	0.7582	0.6570	0.7525	0.9273
Shannon’s entropy	4.0016	3.9905	4.0554	3.9967	4.2113	4.2082	4.2105	4.1913	4.2097	4.1701
Yager’s entropy	−0.8672	−0.8648	−0.8357	−0.8910	−0.7124	−0.7182	−0.7105	−0.7131	−0.7156	−0.7534
EMR	8.0035	8.5137	7.5014	8.4974	6.3716	6.8292	6.3506	6.8817	6.2507	6.7399
	−0.01333	−0.01361	−0.01329	−0.01343	−0.01330	−0.01301	−0.01248	−0.01247	−0.01243	−0.01214
	−0.01780	−0.01782	−0.01769	−0.01791	−0.01763	−0.01782	−0.01636	−0.01623	−0.01634	−0.01641
Downside deviation	0.2414	0.2496	0.2434	0.2390	0.2267	0.2268	0.2263	0.2090	0.2247	0.2305
Sortino ratio	0.3317	0.3410	0.3091	0.3554	0.2814	0.3012	0.2812	0.3291	0.2787	0.2922
STARR ratio	−0.04496	−0.04776	−0.04238	−0.04742	−0.03613	−0.03833	−0.03881	−0.04238	−0.03823	−0.04106
Sharpe ratio	6.6455	8.2492	5.1370	8.1545	1.7145	3.1584	1.6535	3.1410	1.3999	2.9601
Information ratio	0.1860	0.1897	0.1762	0.1955	0.1654	0.1693	0.1647	0.1891	0.1637	0.1693
Times	36.1142	37.3528	37.9714	38.7565	34.0302	35.6235	30.8553	30.7140	37.0023	39.2392
Upper bound	0.06627	0.07000	0.06516	0.07000	0.05363	0.06101	0.05348	0.04946	0.05294	0.05344