Portfolio Optimization of Equity Mutual Funds—Malaysian Case Study

Table 4

Investment proportions with different levels of 𝛼 for minimizing risk.

𝛼-level	Minimum fuzzy	Variance	Investment	Proportion
	return	intervals (Z)	X2	X3
𝛼=0.25	𝐿≥0.059	NFS	—	—
	𝐿=0.058	[0.842,39.579]	[0,0.889]	[0.111,1]
	𝐿=0.057	[0.842,17.855]	[0.333,0.889]	[0.111,0.667]
	𝐿=0.056	[0.842,5.456]	[0.667,0.889]	[0.111,0.333]
	𝐿≤0.055	[0.842,2.246]	[0.889,0.943]	[0.057,0.111]
𝛼=0.5	𝐿≥0.083	NFS	—	—
	𝐿=0.082	[1.086,34.242]	[0,0]	[1,1]
	𝐿=0.081	[1.086,26.250]	[0.125,0.916]	[0.084,0.875]
	𝐿=0.080	[1.086,19.395]	[0.250,0.916]	[0.084,0.750]
	𝐿=0.079	[1.086,13.677]	[0.375,0.916]	[0.084,0.625]
	𝐿≤0.074	[1.086,2.016]	[0.916,0.941]	[0.059,0.084]
𝛼=0.75	𝐿≥0.133	NFS	—	—
	𝐿=0.133	[1.425,6.510]	[0,0.418]	[0.582,1]
	𝐿=0.13	[1.358,5.671]	[0.463,0.953]	[0.047,0.537]
	𝐿=0.12	[1.358,3.458]	[0.612,0.953]	[0.047,0.388]
	𝐿=0.11	[1.358,2.142]	[0.761,0.953]	[0.047,0.239]
	𝐿≤0.1	[1.358,1.723]	[0.953,0.905]	[0.047,0.095]
𝛼=1.0	𝐿≥0.137	NFS	—	—
	𝐿=0.136	23.569	0	1
	𝐿=0.135	21.567	0.043	0.957
	𝐿=0.13	12.989	0.261	0.739
	𝐿=0.12	2.988	0.696	0.304
	𝐿≤0.1	1.554	0.934	0.066