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. 2019 Aug 5;47(4):642–652. doi: 10.1080/02664763.2019.1648394

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 σa (%) 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 σa (%) 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 σa (%) 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 σa (%) 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 σa (%) 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.