Table 1. This table presents average (std) annualized excess returns, risk, and ex post information ratios of the portfolios of the MV optimized by the sample covariance matrix and several shrinkage estimators.
λ | 0.1 | 1.0 | 10.0 | 100.0 | 10000.0 | |
---|---|---|---|---|---|---|
α (%) | 20.38 (3.19) | 12.23 (1.90) | 2.09 (0.69) | 0.19 (0.23) | 0.00 (0.00) | |
Sample cov | (%) | 7.91 (1.09) | 5.36 (0.96) | 1.80 (0.29) | 0.49 (0.08) | 0.01 (0.00) |
IR | 2.59 (0.29) | 2.31 (0.32) | 1.16 (0.33) | 0.36 (0.43) | 0.31 (0.43) | |
α (%) | 20.47 (3.24) | 12.97 (1.90) | 2.09 (0.41) | 0.21 (0.04) | 0.00 (0.00) | |
Shrink-I | (%) | 7.93 (1.09) | 5.47 (1.00) | 1.12 (0.30) | 0.11 (0.03) | 0.00 (0.00) |
IR | 2.59 (0.29) | 2.40 (0.32) | 1.94 (0.37) | 1.93 (0.37) | 1.93 (0.37) | |
α (%) | 20.47 (3.27) | 14.48 (1.88) | 2.80 (0.57) | 0.29 (0.07) | 0.00 (0.00) | |
Shrink-SF | (%) | 7.96 (1.07) | 5.86 (1.03) | 1.44 (0.50) | 0.15 (0.06) | 0.00 (0.00) |
IR | 2.58 (0.30) | 2.51 (0.31) | 2.05 (0.36) | 2.00 (0.38) | 2.00 (0.38) | |
α (%) | 20.65 (3.26) | 14.83 (2.35) | 2.76 (0.58) | 0.28 (0.06) | 0.00 (0.00) | |
Shrink-CC | (%) | 7.94 (1.08) | 5.93 (1.03) | 1.38 (0.39) | 0.14 (0.04) | 0.00 (0.00) |
IR | 2.61 (0.30) | 2.53 (0.33) | 2.06 (0.36) | 2.04 (0.36) | 2.04 (0.36) | |
α (%) | 20.40 (3.26) | 13.03 (1.92) | 2.15 (0.43) | 0.22 (0.05) | 0.00 (0.00) | |
Shrink-NS | (%) | 7.93 (1.09) | 5.50 (0.99) | 1.16 (0.31) | 0.12 (0.03) | 0.00 (0.00) |
IR | 2.58 (0.29) | 2.40 (0.30) | 1.90 (0.33) | 1.88 (0.33) | 1.88 (0.33) |
Note: Standard deviation in parentheses.