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

Table 1

The performance of the portfolio obtained by the various algorithms under δ = 0.05.

Indicators/algorithms	WOA		GWO		FOA		PSO		FA
	Mean	Optimal	Mean	Optimal	Mean	Optimal	Mean	Optimal	Mean	Optimal
Net return	0.06737	0.08801	0.05907	0.08540	0.04590	0.05707	0.05327	0.06190	0.05043	0.06266
Skewness	−0.1925	−0.1958	−0.1940	−0.1787	−0.2118	−0.1719	−0.1819	−0.1533	−0.1801	−0.1017
Kurtosis	0.7343	0.8044	0.7090	0.6122	0.6726	0.8385	0.7681	0.9286	0.7851	0.8488
Shannon’s entropy	4.1047	4.0839	4.1639	4.0754	4.2235	4.2332	4.2087	4.2044	4.2213	4.1845
Yager’s entropy	−0.7950	−0.8218	−0.7589	−0.8384	−0.7075	−0.6827	−0.7142	−0.7639	−0.7040	−0.7360
EMR	6.9164	7.7089	6.5942	7.6058	6.0903	6.4979	6.3322	6.6825	6.2200	6.6440
	−0.01334	−0.01331	−0.01334	−0.01393	−0.01330	−0.01357	−0.01333	−0.01325	−0.01330	−0.01346
	−0.01770	−0.01790	−0.01764	−0.01787	−0.01760	−0.01773	−0.01770	−0.01785	−0.01766	−0.01777
Downside deviation	0.2306	0.2316	0.2257	0.2040	0.2232	0.2384	0.2252	0.2269	0.2273	0.2512
Sortino ratio	0.3004	0.3327	0.2930	0.3728	0.2732	0.2725	0.2817	0.2945	0.2746	0.2644
STARR ratio	−0.03905	−0.04305	−0.03737	−0.04253	−0.03458	−0.03663	−0.03577	−0.03742	−0.03521	−0.03737
Sharpe ratio	3.2811	5.7412	2.3138	5.3432	0.7703	2.0340	1.5921	2.6265	1.3023	2.6582
Information ratio	0.1759	0.1921	0.1722	0.2060	0.1635	0.1617	0.1647	0.1695	0.1616	0.1536
Times	32.1304	33.7750	34.3511	34.2063	31.3813	31.3803	30.7534	32.6466	37.2835	36.3269
Upper bound	0.04997	0.05000	0.04931	0.04977	0.04689	0.04954	0.05335	0.05662	0.05260	0.06131