Usage of Cholesky Decomposition in order to Decrease the Nonlinear Complexities of Some Nonlinear and Diversification Models and Present a Model in Framework of Mean-Semivariance for Portfolio Performance Evaluation

Table 3

Data for examples.

Mean Covariance	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
	1.737	1.074	1.543	1.791	1.033	1.463	1.368	1.367	0.985	1.165	1.303	1.349	1.411	1.114	1.385	1.659	1.51	0.735	1.145	1.479	1.619	1.169	0.979	1.215	0.85	1.145
	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23	24	25	26
1	54.33	45.82	45.2	47.19	41.19	45.19	42.06	37.58	27.88	36.13	42.37	37.79	46.37	34.26	43.4	40.77	37.94	41.59	37.22	45.8	44.45	41.58	42.07	35.37	41.06	30.94
2	45.82	61.66	40.77	42.69	39.41	42.86	37.51	33.48	25.45	32.69	39.39	34.3	39.51	32.7	35.46	34.06	34.47	36.49	33.08	42.01	38.93	37.76	36.42	32.14	37.98	31.58
3	45.2	40.77	44.25	42.32	38.25	41.51	37.72	32.73	24.73	32.14	38.33	32.41	41.7	31.22	36.7	37.3	34.06	39.42	33.29	41.08	39.53	37.51	38.41	30.57	37.34	28.5
4	47.19	42.69	42.32	45.58	39.22	42.63	40.38	35.33	26.74	34.76	39.59	34.92	42.82	32.69	39.49	37.89	35.87	40.23	35.97	42.51	41.01	39.71	39.72	33.42	38.22	29.91
5	41.19	39.41	38.25	39.22	38.51	39.9	35.65	31.93	24.07	30.9	35.1	30.97	37.88	30.64	34.77	33.81	32.13	36.54	31.49	38.8	36.84	35.38	34.95	29.06	34.62	28.47
6	45.19	42.86	41.51	42.63	39.9	45.71	38.4	34.73	25.81	33.48	38.63	33.25	41.33	32.7	38.34	36.94	34.86	40.31	34.53	42.12	40.08	38.82	38.51	31.46	37.39	30.01
7	42.06	37.51	37.72	40.38	35.65	38.4	42.65	31.99	23.87	32.89	34.95	30.87	38.71	30.53	35.54	34.38	32.63	35.53	32.68	37.68	37.21	35.86	36.25	29.51	34.23	27.29
8	37.58	33.48	32.73	35.33	31.93	34.73	31.99	31.74	22.2	28.18	31.44	28.09	34.19	27.24	31.44	30.57	29.21	32	29.45	33.93	32.54	31.72	31.59	27.29	30.7	24.65
9	27.88	25.45	24.73	26.74	24.07	25.81	23.87	22.2	18.99	21.16	23.88	21.94	25.77	21.34	22.74	22.78	21.99	24.38	21.89	25.45	25.44	23.66	23.79	21.11	22.86	19.14
10	36.13	32.69	32.14	34.76	30.9	33.48	32.89	28.18	21.16	29.87	30.5	27.34	33.6	26.62	31.44	29.4	28.49	30.81	28.37	33.34	32.36	30.94	31.66	26.33	29.83	23.67
11	42.37	39.39	38.33	39.59	35.1	38.63	34.95	31.44	23.88	30.5	37.64	31.26	38.14	29.31	34.6	34.09	31.9	36.53	31.35	38.3	36.52	34.82	35.32	29.74	34.67	26.79
12	37.79	34.3	32.41	34.92	30.97	33.25	30.87	28.09	21.94	27.34	31.26	31.01	34.06	26.27	30.95	29.92	28.27	30.72	28.04	33.13	32.96	29.99	30.58	27.32	29.97	23.52
13	46.37	39.51	41.7	42.82	37.88	41.33	38.71	34.19	25.77	33.6	38.14	34.06	43.37	31.92	38.89	37.54	34.56	39.23	34.43	41.07	40.81	37.89	38.6	31.93	37.46	28.66
14	34.26	32.7	31.22	32.69	30.64	32.7	30.53	27.24	21.34	26.62	29.31	26.27	31.92	29.63	28.27	27.84	27.05	31.15	27.13	31.49	31.21	28.39	29.79	25.29	28.89	24.6
15	43.4	35.46	36.7	39.49	34.77	38.34	35.54	31.44	22.74	31.44	34.6	30.95	38.89	28.27	40.74	33.47	31.95	34.97	31.76	38.65	37.77	35.09	35.29	29.64	33.58	25.34
16	40.77	34.06	37.3	37.89	33.81	36.94	34.38	30.57	22.78	29.4	34.09	29.92	37.54	27.84	33.47	36.33	30.61	34.51	30.21	35.97	36	33.56	34	28.42	33.74	25.67
17	37.94	34.47	34.06	35.87	32.13	34.86	32.63	29.21	21.99	28.49	31.9	28.27	34.56	27.05	31.95	30.61	30.55	32.01	29.45	34.99	33.21	32.27	32.44	27.3	31.37	24.54
18	41.59	36.49	39.42	40.23	36.54	40.31	35.53	32	24.38	30.81	36.53	30.72	39.23	31.15	34.97	34.51	32.01	43.03	32.42	38.35	37.37	35.97	36.37	29.22	34.57	27.06
19	37.22	33.08	33.29	35.97	31.49	34.53	32.68	29.45	21.89	28.37	31.35	28.04	34.43	27.13	31.76	30.21	29.45	32.42	30.9	34.05	32.69	32.02	31.78	27.19	30.61	24.38
20	45.8	42.01	41.08	42.51	38.8	42.12	37.68	33.93	25.45	33.34	38.3	33.13	41.07	31.49	38.65	35.97	34.99	38.35	34.05	45.08	39.49	38.05	38.38	31.64	37.38	28.68
21	44.45	38.93	39.53	41.01	36.84	40.08	37.21	32.54	25.44	32.36	36.52	32.96	40.81	31.21	37.77	36	33.21	37.37	32.69	39.49	41.48	36.27	37.11	30.91	35.46	28.02
22	41.58	37.76	37.51	39.71	35.38	38.82	35.86	31.72	23.66	30.94	34.82	29.99	37.89	28.39	35.09	33.56	32.27	35.97	32.02	38.05	36.27	38.18	35.71	29.18	34.12	26.46
23	42.07	36.42	38.41	39.72	34.95	38.51	36.25	31.59	23.79	31.66	35.32	30.58	38.6	29.79	35.29	34	32.44	36.37	31.78	38.38	37.11	35.71	38.34	29.57	34.32	26.37
24	35.37	32.14	30.57	33.42	29.06	31.46	29.51	27.29	21.11	26.33	29.74	27.32	31.93	25.29	29.64	28.42	27.31	29.22	27.19	31.64	30.91	29.18	29.57	27.33	28.68	22.8
25	41.06	37.98	37.34	38.22	34.62	37.39	34.23	30.7	22.86	29.83	34.67	29.97	37.46	28.89	33.58	33.74	31.37	34.57	30.61	37.38	35.46	34.12	34.32	28.68	36.26	26.34
26	30.94	31.58	28.5	29.91	28.47	30.01	27.29	24.65	19.14	23.67	26.79	23.52	28.66	24.6	25.34	25.67	24.54	27.06	24.38	28.68	28.02	26.46	26.37	22.8	26.34	24.69