Portfolio Optimization of Equity Mutual Funds—Malaysian Case Study

Table 3

Investment proportions with different levels of 𝛼 for maximizing return.

𝛼-level	Upper bound of	Return intervals	Investment	Proportion
	variance	(Z)	X2	X3
𝛼=0	𝑀≥44.915	[0.035,0.237]	[0,0]	[1,1]
	𝑀=40	[0.035,0.237]	[0,0.056]	[0.944,1]
	𝑀=35	[0.035,0.237]	[0,0.118]	[0.882,1]
	𝑀=32	[0.035,0.237]	[0,0.5]	[0.5,1]
	𝑀≤31	NFS	—	–
𝛼=0.25	𝑀≥40	[0.0600,0.2120]	[0,0]	[1,1]
	𝑀=35	[0.0597,0.2120]	[0,0.060]	[0.940,1]
	𝑀=30	[0.0594,0.2120]	[0,0.130]	[0.870,1]
	𝑀=15.1	[0.0581,0.2120]	[0,0.390]	[0.610,1]
	𝑀≤15	NFS	—	—
𝛼=0.5	𝑀≥35	[0.086,0.187]	[0,0]	[1,1]
	𝑀=32	[0.086,0.187]	[0,0.033]	[0.967,1]
	𝑀=25.1	[0.084,0.187]	[0,0.145]	[0.855,1]
	𝑀≤25	NFS	—	—
𝛼=0.75	𝑀≥32	[0.111,0.161]	[0,0]	[1,1]
	𝑀=25	[0.110,0.161]	[0,0.070]	[0.930,1]
	𝑀=22	[0.109,0.161]	[0,0.128]	[0.872,1]
	𝑀≤21.9	NFS	—	—
𝛼=1.0	𝑀≥25	0.136	0	1
	𝑀=22	0.135	0.034	0.966
	𝑀=10	0.128	0.356	0.644
	𝑀=5	0.123	0.565	0.435
	𝑀=3	0.120	0.695	0.305
	𝑀≤2	NFS	—	—