ASX portfolio with different investment restrictions based on asymmetric DCC GARCH model estimated correlations_
| Consumer Discretionary | Consumer Staples | Energy | Health Care Index | Industries | Information Technology | Materials | Real Estate | Telecommunications Services | Optimal Portfolio Return | Portfolio Standard Deviation | Sharpe Ratio | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Investment weights (Equally weighted) | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 8.35 % | 16.57 % | 0.3528 |
| Investment weights (no short sell) | 0.00 % | 0.00 % | 30.56 % | 54.72 % | 0.00 % | 5.76 % | 8.96 % | 0.00 % | 0.00 % | 16.48 % | 14.76 % | 0.9474 |
| Investment weights (no short sell with max 50% in one sector) | 0.00 % | 0.00 % | 32.15 % | 50.00 % | 0.00 % | 7.81 % | 10.04 % | 0.00 % | 0.00 % | 16.43 % | 14.70 % | 0.9475 |
| Investment weights (no short sell with max 20% in one sector) | 0.00 % | 0.00 % | 20.00 % | 20.00 % | 20.00 % | 20.00 % | 20.00 % | 0.00 % | 0.00 % | 13.57 % | 13.72 % | 0.8069 |
| Investment weights (100% short sale) | -4.98 % | -10.89 % | 50.75 % | 49.93 % | 49.75 % | -5.65 % | 28.46 % | -50.08 % | -7.29 % | 43.40 % | 21.66 % | 1.8883 |
| Investment weights (100% short sale with max 50% in one sector) | -4.47 % | -10.90 % | 50.00 % | 49.82 % | 49.78 % | -5.59 % | 28.42 % | -49.93 % | -7.13 % | 33.38 % | 18.27 % | 1.8270 |
| Investment weights (100% short sale with max 20% in one sector) | 20.00 % | 20.00 % | 20.0 % | 20.00 % | 20.00 % | 20.00 % | 20.00 % | -60.00 % | 20.00 % | 23.24 % | 16.46 % | 1.4119 |
SSE portfolio with different investment restrictions based on asymmetric DCC GARCH model estimated correlations
| Consumer Discretionary | Consumer Staples | Energy | Financials | Health Care | Industrials | Materials | Telecommunications Service | Utilities | Optimal Portfolio Return | Portfolio Standard Deviation | Sharpe Ratio | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Investment weights (Equally weighted) | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 19.54 % | 14.69 % | 0.9213 |
| Investment weights (no short sell) | 0.00 % | 63.13% | 0.00% | 25.21 % | 11.66 % | 0.00 % | 0.00 % | 0.00 % | 0.00 % | 28.87 % | 16.24 % | 1.4080 |
| Investment weights (no short sell with max 50% in one sector) | 0.00 % | 50.00 % | 0.00 % | 29.43 % | 20.57 % | 0.00 % | 0.00 % | 0.00 % | 0.00 % | 28.03 % | 15.77 % | 1.3968 |
| Investment weights (no short sell with max 20% in one sector) | 13.97 % | 20.00 % | 20.00 % | 20.00 % | 20.00 % | 0.00 % | 5.69 % | 0.00 % | 0.52 % | 24.05 % | 16.32 % | 1.1776 |
| Investment weights (100% short sale) | -7.23 % | 97.01 % | 14.56 % | 42.33 % | 28.59 % | -28.70 % | -10.53 % | -18.09 % | -17.96 % | 39.69 % | 21.84 % | 1.5430 |
| Investment weights (100% short sale with max 50% in one sector) | -1.87 % | 50.00 % | 14.78 % | 41.74 % | 38.12 % | -15.09 % | -4.86 % | -12.50 % | -10.33 % | 32.62 % | 18.11 % | 1.4697 |
| Investment weights (100% short sale with max 20% in one sector) | 17.98 % | 20.00 % | 20.00 % | 20.00 % | 20.00 % | -7.55 % | 8.87 % | -3.83 % | 4.53 % | 24.43 % | 15.58 % | 1.1831 |
Nine sector indices equally weighted portfolio (out of sample)
| ASX in Australia | NSE in India | SSE in China | |
|---|---|---|---|
| Portfolio mean Annual return | 8.67% | 4.94% | -2.19% |
| Portfolio standard deviation | 9.47% | 1.17% | 11.69% |
| Sharpe ratio | 0.6521 | -1.7626 | -.7006 |
Summary statistics of sector indices – ASX, SSE, and NSE
| ASX Sector | Period | Observation | Mean | Variance | Skewness | Min. | Max. | Range |
| Consumer Discretionary | 2004/4/14-2012/4/13 | 2087 | -0.0062% | 0.0295% | -0.0895 | -14.3601% | 8.8923% | 23.2524% |
| Consumer Staples | 2004/4/14-2012/4/13 | 2087 | 0.0422% | 0.0267% | -1.1054 | -17.8561% | 9.6798% | 37.5360% |
| Energy | 2004/4/14-2012/4/13 | 2087 | 0.0615% | 0.0483% | -0.8292 | -19.8730% | 13.0450% | 32.9180% |
| ASX 200 Health Care Index | 2004/4/14-2012/4/13 | 2087 | 0.0573% | 0.0286% | -0.7165 | -13.9715% | 8.8720% | 22.8434% |
| Industries | 2004/4/14-2012/4/13 | 2087 | 0.0193% | 0.0298% | -0.8702 | -15.8409% | 8.4423% | 24.2832% |
| Information Technology | 2004/4/14-2012/4/13 | 2087 | 0.0498% | 0.0454% | 0.4556 | -15.8558% | 12.6206% | 28.4764% |
| Materials | 2004/4/14-2012/4/13 | 2087 | 0.0508% | 0.0554% | -0.6826 | -16.1608% | 11.7786% | 27.9394% |
| Real Estate | 2004/4/14-2012/4/13 | 2087 | -0.0118% | 0.0411% | -1.1577 | -18.4891% | 10.1560% | 28.6451% |
| Telecommunications Services | 2004/4/14-2012/4/13 | 2087 | 0.0006% | 0.0298% | -0.7163 | -13.2126% | 8.2886% | 21.5012% |
| SSE Sector | Period | Observation | Mean | Variance | Skewness | Min. | Max. | Range |
| Consumer Discretionary | 2005/1/4-2012/4/13 | 1898 | 0.0653% | 0.0438% | -0.6002 | -10.1840% | 9.2418% | 19.4258% |
| Consumer Staples | 2005/1/4-2012/4/13 | 1898 | 0.1040% | 0.0375% | -0.3588 | -10.0824% | 8.6832% | 18.7656% |
| Energy | 2005/1/4-2012/4/13 | 1898 | 0.0733% | 0.0504% | -0.1526 | -9.7384% | 9.2123% | 18.9506% |
| Financials | 2005/1/4-2012/4/13 | 1898 | 0.0835% | 0.0461% | -0.1012 | -9.4742% | 9.5227% | 18.9968% |
| Health Care | 2005/1/4-2012/4/13 | 1898 | 0.0857% | 0.0419% | -0.5047 | -9.9085% | 9.2736% | 19.1821% |
| Industrials | 2005/1/4-2012/4/13 | 1898 | 0.0453% | 0.0392% | -0.4705 | -9.6167% | 9.5346% | 19.1513% |
| Materials | 2005/1/4-2012/4/13 | 1898 | 0.0612% | 0.0480% | -0.4250 | -9.5166% | 8.2052% | 17.7218% |
| Telecommunications Services | 2005/1/4-2012/4/13 | 1898 | 0.0460% | 0.0533% | -0.2445 | -10.4016% | 9.5988% | 20.0004% |
| Utilities | 2005/1/4-2012/13 | 1898 | 0.0443% | 0.0358% | -0.5564 | -10.2425% | 8.1968% | 18.4393% |
| NSE Sector | Period | Observation | Mean | Variance | Skewness | Min. | Max. | Range |
| Automobile | 2004/4/14-2012/4/13 | 2087 | 0.0484% | 0.0508% | -0.1788 | -13.5417% | 17.2685% | 30.8102% |
| Banking | 2004/4/14-2012/4/13 | 2087 | 0.0543% | 0.0565% | -0.1451 | -15.3694% | 19.8858% | 35.2553% |
| Energy | 2004/4/14-2012/4/13 | 2087 | 0.1203% | 0.0691% | -0.1176 | -19.5035% | 18.2817% | 37.7852% |
| Financial | 2004/4/14-2012/4/13 | 2087 | 0.0823% | 0.0421% | 0.1709 | -9.9427% | 13.4082% | 23.3510% |
| Fast Moving Consumer Goods | 2004/4/14-2012/4/13 | 2087 | 0.0603% | 0.0220% | 0.1068 | -6.8357% | 9.2418% | 16.0775% |
| Information Technology | 2004/4/14-2012/4/13 | 2087 | 0.0414% | 0.0421% | -0.0185 | -13.9893% | 14.6993% | 28.6886% |
| Midea | 2004/4/14-2012/4/13 | 2087 | 0.0847% | 0.0633% | 0.2265 | -11.9898% | 20.0595% | 32.0492% |
| Metal | 2004/4/14-2012/4/13 | 2087 | -0.0602% | 0.0989% | 0.3840 | -44.3656% | 44.0013% | 88.3669% |
| Pharmaceuticals | 2004/4/14-2012/4/13 | 2087 | 0.0467% | 0.0209% | -0.4688 | -9.1241% | 12.6615% | 21.7857% |
NSE portfolio with different investment restrictions based on asymmetric DCC GARCH model estimated correlations_
| Automobile | Banking | Energy | Financial | Fast Moving Consumer Goods | Information Technology | Midea | Metal | Pharmaceuticals | Optimal Portfolio Return | Portfolio Standard Deviation | Sharpe Ratio | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Investment weights (Equally weighted) | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 11.11 % | 15.74 % | 13.60 % | 0.6428 |
| Investment weights (no short sell) | 0.00 % | 0.00 % | 39.86 % | 28.82 % | 14.48 % | 0.00 % | 16.83 % | 0.00 % | 0.00 % | 28.34 % | 15.61 % | 1.3678 |
| Investment weights (no short sell with max 50% in one sector) | 0.00 % | 0.00 % | 39.86 % | 28.82 % | 14.48 % | 0.00 % | 16.83 % | 0.00 % | 0.00 % | 28.34 % | 15.61 % | 1.3678 |
| Investment weights (no short sell with max 20% in one sector) | 0.00 % | 0.00 % | 20.00 % | 20.00 % | 20.00 % | 0.00 % | 20.00 % | 0.00 % | 2.00 % | 23.21 % | 12.70 % | 1.2492 |
| Investment weights (100% short sale) | -9.15 % | -5.89 % | 50.28 % | 49.87 % | 49.87 % | -5.80 % | 28.53 % | -50.36 % | -7.33 % | 49.81 % | 23.11 % | 1.8526 |
| Investment weights (100% short sale with max 50% in one sector) | -9.12 % | -5.90 % | 50.00 % | 49.76 % | 49.90 % | -5.74 % | 28.49 % | -50.22 % | -7.18 % | 49.69 % | 23.04 % | 1.8526 |
| Investment weights (100% short sale with max 20% in one sector) | 9.58 % | 8.95 % | 20.00 % | 20.00 % | 20.00 % | 14.68 % | 20.00 % | -33.21 % | 20.00 % | 32.39 % | 16.00 % | 1.5872 |
Out of sample test result
| ASX | NSE | SSE | |||||||
|---|---|---|---|---|---|---|---|---|---|
| Optimal portfolio return | Portfolio standard deviation | Sharpe ratio | Optimal portfolio return | Portfolio standard deviation | Sharpe ratio | Optimal portfolio return | Portfolio standard deviation | Sharpe ratio | |
| Investment weights (no short sell) | 19.99% | 9.32% | 1.8770 | 16.53% | 11.12% | 0.8567 | 21.56% | 13.98% | 1.1134 |
| Investment weights (no short sell & maximum 20% weights in single sector) | 19.54% | 9.16% | 1.8602 | 15.03% | 12.25% | 0.6555 | 13.35% | 12.99% | 0.5659 |
| Investment weights (no short sell & maximum 50% weights in single sector) | 15.32% | 9.66% | 1.3271 | 13.53% | 10.05% | 0.6490 | 6.28% | 11.68% | 0.0243 |
| Investment weights (maximum 100% short sell) | 84.71% | 26.31% | 3.1249 | 79.67% | 35.43% | 2.0509 | 95.49% | 27.61% | 3.2411 |
| Investment weights (maximum 100% short sell & maximum 20% weights in single sector) | 48.57% | 17.17% | 2.6823 | 51.09% | 24.24% | 1.8184 | 54.80% | 19.10% | 2.5579 |
| Investment weights (maximum 100% short sell & maximum 50% weights in single sector) | 21.35% | 10.40% | 1.8119 | 20.80% | 17.08% | 0.8083 | 12.22% | 12.22% | 0.9052 |
Benchmark index
| ASX in Australia | NSE in India | SSE in China | |
|---|---|---|---|
| Portfolio mean Annual return | 8.35% | 15.74% | 19.54% |
| Portfolio standard deviation | 16.62% | 16.51% | 18.70% |
| Sharpe ratio | 0.3517 | 0.5296 | 0.7237 |
Sector indices list
| ASX Sector Index | Sector Index | Period | Observation |
| ASX 200 Consumer Discretionary Index | Consumer Discretionary | 2004/4/14-2012/4/13 | 2087 |
| ASX 200 Consumer Staples Index | Consumer Staples | 2004/4/14-2012/4/13 | 2087 |
| ASX 200 Energy Index | Energy | 2004/4/14-2012/4/13 | 2087 |
| ASX 200 Health Care Index | ASX 200 Health Care Index | 2004/4/14-2012/4/13 | 2087 |
| ASX 200 Industrials Index | Industries | 2004/4/14-2012/4/13 | 2087 |
| ASX 200 Information Technology Index | Information Technology | 2004/4/14-2012/4/13 | 2087 |
| ASX 200 Materials Index | Materials | 2004/4/14-2012/4/13 | 2087 |
| ASX 200 Real Estate Index | Real Estate | 2004/4/14-2012/4/13 | 2087 |
| ASX 200 Telecommunications Services Index | Telecommunications Services | 2004/4/14-2012/4/13 | 2087 |
| SSE Sector Index | Sector Index | Period | Observation |
| SSE Consumer Discretionary Sector Index | Consumer Discretionary | 2005/1/4-2012/4/13 | 1898 |
| SSE Consumer Staples Sector Index | Consumer Staples | 2005/1/4-2012/4/13 | 1898 |
| SSE Energy Sector Index | Energy | 2005/1/4-2012/4/13 | 1898 |
| SSE Financials Sector Index | Financials | 2005/1/4-2012/4/13 | 1898 |
| SSE Health Care Sector Index | Health Care | 2005/1/4-2012/4/13 | 1898 |
| SSE Industrials Sector Index | Industrials | 2005/1/4-2012/4/13 | 1898 |
| SSE Materials Index | Materials | 2005/1/4-2012/4/13 | 1898 |
| SSE Telecommunications Services Sector Index | Telecommunications Services | 2005/1/4-2012/4/13 | 1898 |
| SSE Utilities Sector Index | Utilities | 2005/1/4-2012/4/13 | 1898 |
| NSE Sector Index | Sector Index | Period | Observation |
| CNX Automobile Sector Index | Automobile | 2004/4/14-2012/4/13 | 2087 |
| CNX Banking Sector Index | Banking | 2004/4/14-2012/4/13 | 2087 |
| CNX Energy Sector Index | Energy | 2004/4/14-2012/4/13 | 2087 |
| CNX Financial Sector Index | Financial | 2004/4/14-2012/4/13 | 2087 |
| CNX Fast Moving Consumer Goods Sector Index | Fast Moving Consumer Goods | 2004/4/14-2012/4/13 | 2087 |
| CNX Information Technology Sector Index | Information Technology | 2004/4/14-2012/4/13 | 2087 |
| CNX Midea Sector | Midea | 2004/4/14-2012/4/13 | 2087 |
| CNX Metal Sector | Metal | 2004/4/14-2012/4/13 | 2087 |
| CNX Pharmaceuticals Sector Index | Pharmaceuticals | 2004/4/14-2012/4/13 | 2087 |