Table 1.
The average and standard deviation of the (c)DCC parameter using six correlation methods targeting dimensions , with sample size .
Table 1.
The average and standard deviation of the (c)DCC parameter using six correlation methods targeting dimensions , with sample size .
N | DCC | DCC-LS | DCC-NLS | cDCC | cDCC-LS | cDCC-NLS |
---|
100 | 0.0506 | 0.0506 | 0.051 | 0.0498 | 0.0501 | 0.0503 |
| (0.0032) | (0.0033) | (0.0034) | (0.0028) | (0.0029) | (0.003) |
500 | 0.0497 | 0.0497 | 0.0498 | 0.0502 | 0.0501 | 0.0504 |
| (0.0011) | (0.0011) | (0.0015) | (0.0025) | (0.0027) | (0.003) |
1000 | 0.0496 | 0.0498 | 0.0501 | 0.0476 | 0.05 | 0.0501 |
| (0.0016) | (0.0013) | (0.0015) | (0.0017) | (0.0018) | (0.0018) |
Table 2.
The average and standard deviation of the (c)DCC parameter using six correlation methods targeting dimensions , with sample size .
Table 2.
The average and standard deviation of the (c)DCC parameter using six correlation methods targeting dimensions , with sample size .
N | DCC | DCC-LS | DCC-NLS | cDCC | cDCC-LS | cDCC-NLS |
---|
100 | 0.9279 | 0.9285 | 0.9287 | 0.9287 | 0.9284 | 0.9289 |
| (0.0048) | (0.0052) | (0.0054) | (0.0031) | (0.0034) | (0.0038) |
500 | 0.9282 | 0.9285 | 0.9292 | 0.927 | 0.9275 | 0.9283 |
| (0.0024) | (0.0024) | (0.0022) | (0.004) | (0.0046) | (0.005) |
1000 | 0.9278 | 0.9278 | 0.9277 | 0.9269 | 0.9271 | 0.9275 |
| (0.0021) | (0.0016) | (0.0018) | (0.0022) | (0.0025) | (0.0024) |
Table 3.
Average loss for (c)DCC estimators using six correlation methods targeting dimensions , with sample size . The unit is .
Table 3.
Average loss for (c)DCC estimators using six correlation methods targeting dimensions , with sample size . The unit is .
N | DCC | DCC-LS | DCC-NLS | cDCC | cDCC-LS | cDCC-NLS |
---|
100 | 8.60257 | 8.27205 | 7.47024 | 7.95906 | 7.6558 | 6.8779 |
500 | 23.04541 | 18.36612 | 14.55736 | 22.16638 | 18.07399 | 13.37496 |
1000 | 70.44232 | 24.46691 | 18.8293 | 63.24801 | 24.4935 | 15.29444 |
Table 4.
Annualized return, volatility, and Sharpe ratio for an MV portfolio using six methods for dimensions , with sample size . The out-of-sample period is from January 2000 to December 2015. In the rows labeled Sharpe Ratio, the largest number appears in bold. In the columns labeled DCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: *** denotes significance at the 0.01 level; ** denotes significance at the 0.05 level; * denotes significance at the 0.1 level. In the columns labeled cDCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: +++ denotes significance at the 0.01 level; ++ denotes significance at the 0.05 level; + denotes significance at the 0.1 level.
Table 4.
Annualized return, volatility, and Sharpe ratio for an MV portfolio using six methods for dimensions , with sample size . The out-of-sample period is from January 2000 to December 2015. In the rows labeled Sharpe Ratio, the largest number appears in bold. In the columns labeled DCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: *** denotes significance at the 0.01 level; ** denotes significance at the 0.05 level; * denotes significance at the 0.1 level. In the columns labeled cDCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: +++ denotes significance at the 0.01 level; ++ denotes significance at the 0.05 level; + denotes significance at the 0.1 level.
| DCC | DCC-LS | DCC-NLS | cDCC | cDCC-LS | cDCC-NLS |
---|
N = 100 |
Return [%] | 8.08 | 8.23 | 8.29 | 7.82 | 8.09 | 8.62 |
Volatility [%] | 16.40 | 16.41 | 16.36 | 16.20 | 16.16 | 16.18 |
Sharpe Ratio | 0.49 | 0.50 | 0.51 | 0.48 | 0.50 | |
N = 500 |
Return [%] | 9.80 | 9.65 | 9.71 | 9.81 | 9.74 | 10.09 |
Volatility [%] | 17.15 | 17.16 | 17.00 | 16.92 | 16.93 | 16.90 |
Sharpe Ratio | 0.57 | 0.56 | 0.57 | 0.58 | 0.58 | |
N = 1000 |
Return [%] | 9.25 | 9.50 | 9.97 | 9.66 | 9.64 | 10.05 |
Volatility [%] | 16.61 | 16.63 | 16.37 | 16.23 | 16.17 | 16.15 |
Sharpe Ratio | 0.56 | 0.57 | 0.61 | 0.59 | 0.60 | |
Table 5.
Annualized return, volatility, and Sharpe ratio for an MV portfolio without short-sales constraints (MVS) using six methods for dimensions , with sample size . The out-of-sample period is from January 2000 to December 2015. In the rows labeled Sharpe Ratio, the largest number appears in bold. In the columns labeled DCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: *** denotes significance at the 0.01 level; ** denotes significance at the 0.05 level; * denotes significance at the 0.1 level. In the columns labeled cDCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: +++ denotes significance at the 0.01 level; ++ denotes significance at the 0.05 level; + denotes significance at the 0.1 level.
Table 5.
Annualized return, volatility, and Sharpe ratio for an MV portfolio without short-sales constraints (MVS) using six methods for dimensions , with sample size . The out-of-sample period is from January 2000 to December 2015. In the rows labeled Sharpe Ratio, the largest number appears in bold. In the columns labeled DCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: *** denotes significance at the 0.01 level; ** denotes significance at the 0.05 level; * denotes significance at the 0.1 level. In the columns labeled cDCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: +++ denotes significance at the 0.01 level; ++ denotes significance at the 0.05 level; + denotes significance at the 0.1 level.
| DCC | DCC-LS | DCC-NLS | cDCC | cDCC-LS | cDCC-NLS |
---|
N = 100 |
Return [%] | 10.54 | 10.63 | 9.43 | 10.14 | 10.18 | 11.57 |
Volatility [%] | 22.65 | 22.54 | 20.90 | 15.19 | 15.12 | 15.08 |
Sharpe Ratio | 0.47 | 0.47 | 0.45 | 0.67 | 0.67 | |
N = 500 |
Return [%] | 9.48 | 9.27 | 7.41 | 9.37 | 9.33 | 11.09 |
Volatility [%] | 12.64 | 12.47 | 13.90 | 11.63 | 11.40 | 11.12 |
Sharpe Ratio | 0.75 | 0.74 | 0.53 | 0.81 | 0.82 | |
N = 1000 |
Return [%] | 6.01 | 6.52 | 6.98 | 6.26 | 7.78 | 9.30 |
Volatility [%] | 9.96 | 8.95 | 9.16 | 10.56 | 8.99 | 8.21 |
Sharpe Ratio | 0.60 | 0.73 | 0.76 | 0.59 | 0.87 | |
Table 6.
Annualized return, volatility, and Sharpe ratio for an RP portfolio using six methods for dimensions , with sample size . The out-of-sample period is from January 2000 to December 2015. In the rows labeled Sharpe Ratio, the largest number appears in bold. In the columns labeled DCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: *** denotes significance at the 0.01 level; ** denotes significance at the 0.05 level; * denotes significance at the 0.1 level. In the columns labeled cDCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: +++ denotes significance at the 0.01 level; ++ denotes significance at the 0.05 level; + denotes significance at the 0.1 level.
Table 6.
Annualized return, volatility, and Sharpe ratio for an RP portfolio using six methods for dimensions , with sample size . The out-of-sample period is from January 2000 to December 2015. In the rows labeled Sharpe Ratio, the largest number appears in bold. In the columns labeled DCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: *** denotes significance at the 0.01 level; ** denotes significance at the 0.05 level; * denotes significance at the 0.1 level. In the columns labeled cDCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: +++ denotes significance at the 0.01 level; ++ denotes significance at the 0.05 level; + denotes significance at the 0.1 level.
| DCC | DCC-LS | DCC-NLS | cDCC | cDCC-LS | cDCC-NLS |
---|
N = 100 |
Return [%] | 6.95 | 6.97 | 7.16 | 7.01 | 7.01 | 7.06 |
Volatility [%] | 19.39 | 19.39 | 19.45 | 19.60 | 19.60 | 19.56 |
Sharpe Ratio | 0.36 | 0.36 | 0.37 | 0.36 | 0.36 | 0.36 |
N = 500 |
Return [%] | 9.46 | 9.35 | 9.76 | 9.82 | 9.81 | 9.68 |
Volatility [%] | 18.26 | 18.30 | 18.41 | 18.59 | 18.57 | 18.48 |
Sharpe Ratio | 0.52 | 0.51 | 0.53 | 0.53 | 0.53 | 0.52 |
N = 1000 |
Return [%] | 10.41 | 10.54 | 10.55 | 10.54 | 10.52 | 10.52 |
Volatility [%] | 16.88 | 16.93 | 17.07 | 17.23 | 17.19 | 17.07 |
Sharpe Ratio | 0.62 | 0.62 | 0.62 | 0.61 | 0.61 | 0.62 |
Table 7.
Annualized return, volatility, and Sharpe ratio for an MD portfolio using six methods for dimensions , with sample size . The out-of-sample period is from January 2000 to December 2015. In the rows labeled Sharpe Ratio, the largest number appears in bold. In the columns labeled DCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: *** denotes significance at the 0.01 level; ** denotes significance at the 0.05 level; * denotes significance at the 0.1 level. In the columns labeled cDCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: +++ denotes significance at the 0.01 level; ++ denotes significance at the 0.05 level; + denotes significance at the 0.1 level.
Table 7.
Annualized return, volatility, and Sharpe ratio for an MD portfolio using six methods for dimensions , with sample size . The out-of-sample period is from January 2000 to December 2015. In the rows labeled Sharpe Ratio, the largest number appears in bold. In the columns labeled DCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: *** denotes significance at the 0.01 level; ** denotes significance at the 0.05 level; * denotes significance at the 0.1 level. In the columns labeled cDCC and cDCC-NLS, significant out-performance of one of the two portfolios over the other (in terms of the Sharpe ratio) is denoted by asterisks: +++ denotes significance at the 0.01 level; ++ denotes significance at the 0.05 level; + denotes significance at the 0.1 level.
| DCC | DCC-LS | DCC-NLS | cDCC | cDCC-LS | cDCC-NLS |
---|
N = 100 |
Return [%] | 7.06 | 7.07 | 7.06 | 7.00 | 7.04 | 7.02 |
Volatility [%] | 20.48 | 20.49 | 20.49 | 20.49 | 20.49 | 20.49 |
Sharpe Ratio | 0.35 | 0.35 | 0.34 | 0.34 | 0.34 | 0.34 |
N = 500 |
Return [%] | 10.13 | 10.13 | 10.12 | 10.12 | 10.12 | 10.12 |
Volatility [%] | 19.64 | 19.64 | 19.64 | 19.64 | 19.64 | 19.64 |
Sharpe Ratio | 0.52 | 0.52 | 0.52 | 0.52 | 0.52 | 0.52 |
N = 1000 |
Return [%] | 10.63 | 10.63 | 10.63 | 10.66 | 10.66 | 10.63 |
Volatility [%] | 18.66 | 18.66 | 18.66 | 18.66 | 18.66 | 18.66 |
Sharpe Ratio | 0.57 | 0.57 | 0.57 | 0.57 | 0.57 | 0.57 |