Table 1 The values of portfolio expected return, variance risk, and sparsity ratio for different \(\beta _{1}\) with minimum guaranteed return ratio \(r=0.1\) and \(r=0.2\) under SEPO-\(\ell _{0}\) and standard MVO
From: Proximal linearized method for sparse equity portfolio optimization with minimum transaction cost
\(\beta _{1}\) | r = 0.1 | r = 0.2 | |||||||
|---|---|---|---|---|---|---|---|---|---|
SEPO-\(\ell _{0}\) | Standard MVO | SEPO-\(\ell _{0}\) | |||||||
E.R. | V.R. | Spar | E.R. | V.R. | Spar | E.R. | V.R. | Spar | |
0.1 | 0.6355 | 3.2835 | 0.58 | 0.6889 | 2.3603 | 0 | 0.7441 | 4.3108 | 0.72 |
0.2 | 0.6279 | 2.9577 | 0.61 | 0.5735 | 1.5138 | 0 | 0.6732 | 3.2822 | 0.66 |
0.3 | 0.5050 | 2.1304 | 0.47 | 0.4555 | 1.0320 | 0 | 0.5829 | 2.4655 | 0.58 |
0.4 | 0.5180 | 2.0288 | 0.53 | 0.3760 | 0.8114 | 0 | 0.5796 | 2.2333 | 0.64 |
0.5 | 0.4865 | 1.7976 | 0.51 | 0.3003 | 0.6689 | 0 | 0.5374 | 1.9056 | 0.64 |
0.6 | 0.4237 | 1.5684 | 0.39 | 0.2646 | 0.5785 | 0 | 0.4675 | 1.6193 | 0.52 |
0.7 | 0.3677 | 1.4070 | 0.30 | 0.2223 | 0.5324 | 0 | 0.4655 | 1.4800 | 0.59 |
0.8 | 0.3581 | 1.3248 | 0.31 | 0.2057 | 0.4930 | 0 | 0.4521 | 1.3289 | 0.63 |
0.9 | 0.3787 | 1.2635 | 0.44 | 0.1750 | 0.4704 | 0 | 0.4182 | 1.2149 | 0.56 |
1 | 0.3455 | 1.1802 | 0.40 | 0.1560 | 0.4501 | 0 | 0.4014 | 1.1204 | 0.56 |