About this article
Published Online: Mar 22, 2024
Page range: 79 - 98
DOI: https://doi.org/10.2478/fprj-2022-0004
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© 2022 Riza Emekter et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.
Lists and Characteristics of Exchange Traded Funds (ETFs) (June 2007 to December 2017)
| Ticker | Name | Total Assets (million Dollars) | Fund Objective | Fund Geographical Focus | Fund Asset Class | Fund Strategy | Market Cap Focus | History Length (Days) | |
|---|---|---|---|---|---|---|---|---|---|
| 1 | SPY | SPDR S&P 500 ETF TRUST | 272,676 | Large-cap | United States | Equity | Blend | Large-cap | 9107 |
| 2 | VTI | VANGUARD TOTAL STOCK MKT ETF | 93,194 | Broad Market | United States | Equity | Blend | Broad Market | 6063 |
| 3 | EFA | ISHARES MSa EAFE ETF | 85,325 | International | International | Equity | Blend | Large-cap | 5985 |
| 4 | VEA | VANGUARD FΓSE DEVELOPED ETF | 69,281 | International | International | Equity | Blend | Large-cap | 3816 |
| 5 | VWO | VANGUARD ELSE EMERGING MARKE | 68,452 | Emerging Markets | International | Equity | Blend | Broad Market | 4684 |
| 6 | QQQ | POWERSHARES QQQ TRUST SERIES | 57,747 | Large-cap | United States | Equity | Growth | Large-cap | 6876 |
| 7 | AGG | ISHARES CORE U.S. AGGREGATE | 53,629 | Aggregate Bond | United States | Fixed Income | Aggregate | N.A. | 5215 |
| 8 | UH | ISHARES CORE S&P MIDCAP ETF | 44,841 | Mid-cop | United States | Equity | Blend | Mid-cap | 6433 |
| 9 | IWM | ISHARES RUSSELL 2000 ETF | 42,166 | Small-cap | United Stales | Equity | Blend | Small-cap | 6433 |
| 10 | IWD | ISHARES RUSSELL 1000 VALUE E | 41,631 | Large-cap | United States | Equity | Value | Large-cap | 6433 |
| 11 | IWF | ISHARES RUSSELL 1000 GROWTH | 40,961 | Lorg©-cap | United States | Equity | Growth | Large-cap | 6433 |
| 12 | LQD | ISHARES IBOXX INVESTMENT GRA | 38,431 | Corporate | United States | Fixed Income | Corporate | N.A. | 5642 |
| 13 | GLD | SPDR GOLD SHARES | 35,343 | Precious Metals | Global | Commodity | Precious Metals | N.A. | 4796 |
| 14 | VNQ | VANGUARD RETT ETF | 34,626 | Real Estate | United Stales | Equity | Blend | Broad Market | 4846 |
| 15 | TIP | ISHARES TIPS BOND ETF | 24,339 | Inflation Protected | United States | Fixed Income | Inflation Protected | N.A. | 5145 |
| 16 | BSV | VANGUARD SHORT-TERM BOND ETF | 23,884 | Aggregate Bond | United States | Fixed Income | Aggregate | N.A. | 3923 |
| 17 | VEU | VANGUARD FTSE ALL-WORLD EX-U | 23,484 | International | International | Equity | Blend | Large-cap | 3956 |
| 18 | VGK | VANGUARD FTSE EUROPE ETF | 18,598 | European Region | European Region | Equity | Blend | Large-cap | 4684 |
| 19 | HYG | ISHARES IBOXX USD HIGH YIELD | 17,946 | Corporate | United States | Fixed Income | Corporate | N.A. | 3922 |
| 20 | PFF | ISHARES US PREFERRED STOCK E | 17,653 | Preferred | United States | Fixed Income | Preferred | N.A. | 3934 |
| 21 | BIV | VANGUARD INTERMEDIATE-TERM B | 15,303 | Aggregate Bond | United States | Fixed Income | Aggregate | N.A. | 3923 |
| 22 | VBR | VANGUARD SMALL-CAP VALUE ETF | 12,763 | Small-cap | United Stales | Equity | Value | Small-cap | 5089 |
| 23 | MBB | ISHARES MBS ETF | 11,859 | Mortgage-Backed | United States | Fixed Income | Mortgage-Backed | N.A. | 3948 |
| 24 | SHY | ISHARES 1-3 YEAR TREASURY BO | 11,261 | Government | United States | Fixed Income | Government | N.A. | 5642 |
| 25 | IWS | ISHARES RUSSELL MIDCAP VALU | 11,125 | Mid-cap | United States | Equity | Value | Mid-cap | 6009 |
| 26 | IWO | ISHARES RUSSELL 2000 GROWTH | 9,188 | Smalkcap | United States | Equity | Growth | Small-cap | 6370 |
| 27 | IWP | ISHARES RUSSELL MIDCAP GROW | 8,615 | Midcap | United States | Equity | Growth | Mid-cap | 6001 |
| 28 | SHV | ISHARES SHORT TREASURY BOND | 8,057 | Government | United States | Fixed Income | Government | N.A. | 4012 |
| 29 | TLT | ISHARES 20+ YEAR TREASURY BOND | 7,185 | Government | United States | Fixed Income | Government | N.A. | 5642 |
| 30 | SLV | ISHARES SILVERTRUST | 5,454 | Precious Metals | Global | Commodity | Precious Metals | N.A. | 4270 |
| 31 | RWX | SPDR DJ INTERNATIONAL REAL E | 3,765 | Real Estate | International | Equity | Blend | Broad Market | 4039 |
| 32 | EFG | ISHARES MSCI EAFE GROWTH ETF | 3,600 | International | International | Equity | Growth | Large-cap | 4536 |
| 33 | DBC | POWERSHARES DB COMMODITY IND | 2,292 | Broad Based | Global | Commodity | Broad Based | N.A. | 4354 |
| 34 | USO | UNITED STATES OIL FUND LP | 2,077 | Energy | United States | Commodity | Energy | N.A. | 4288 |
The Performance of Optimized Portfolios Using The Modified Variance Covariance Matrix with the Shrinkage Technique (August 2012-Decemer 2017)
| Portfolio | Return | Risk | Sharpe Ratio | |
|---|---|---|---|---|
| Lowest Risk/Return | Portfolio 1 | 0.0000 | 0.1000 | -20.7570 |
| Portfolio 2 | 1.0000 | 1.2000 | -0.9540 | |
| Portfolio 3 | 2.0000 | 2.5000 | -0.0880 | |
| Portfolio 4 | 2.9000 | 3.7000 | 0.1830 | |
| Portfolio 5 | 3.7000 | 5.0000 | 0.3130 | |
| Portfolio 6 | 4.6000 | 6.3000 | 0.3940 | |
| Portfolio 7 | 5.5000 | 7.5000 | 0.4500 | |
| Portfolio 8 | 6.9000 | 8.5000 | 0.5520 | |
| Portfolio 9 | 8.2000 | 10.4000 | 0.5760 | |
| Highest Risk/Return | Portfolio 10 | 5.5000 | 16.5000 | 0.2040 |
Comparison of Performances of Optimized Portfolio and Individual Exchange Traded Funds Based on Actual Return (August 2012 to December 2017)
| Portfolio | Return | Risk | Sharpe Ratio | |
|---|---|---|---|---|
| Lowest Risk/Return | Portfolio 1 | 0.0004 | 0.0012 | -18.3066 |
| Portfolio 2 | 0.0177 | 0.0134 | -0.3074 | |
| Portfolio 3 | 0.0350 | 0.0268 | 0.4910 | |
| Portfolio 4 | 0.0523 | 0.0404 | 0.7544 | |
| Portfolio 5 | 0.0695 | 0.0540 | 0.8840 | |
| Portfolio 6 | 0.0868 | 0.0677 | 0.9608 | |
| Portfolio 7 | 0.1041 | 0.0818 | 1, 006l | |
| Portfolio 8 | 0.1214 | 0.0994 | 1.0018 | |
| Portfolio 9 | 0.1387 | 0.1246 | 0.9387 | |
| Highest Risk/Return | Portfolio 10 | 0.1560 | 0.1804 | 0.7441 |
| QQQ | POWERSHARES QQQ TRUST SERIES | 16.2000 | 12.1000 | 1.1 600 |
| IWF | ISHARES RUSSELL 1000 GROWTH | 13.8000 | 9.8000 | 1.1900 |
| IWO | ISHARES RUSSELL 2000 GROWTH | 13.5000 | 14.1000 | 0.8000 |
| IWP | ISHARES RUSSELL MID-GAP GROW | 13.2000 | l0.6000 | 1.0400 |
| IJH | ISHARES CORE S&P MIDCAP ETF | 13.0000 | l0.9000 | 0.9900 |
| VBR | VANGUARD SMALL-GAP VALUE ETF | 12.4000 | 12.0000 | 0.8500 |
| VTI | VANGUARD TOTAL STOCK MKT ETF | 12.3000 | 9.6000 | 1, 0600 |
| IWM | ISHARES RUSSELL 2000 ETF | 12.3000 | 13.4000 | 0.7500 |
| SPY | SPDR S&P 500 ETF TRUST | 12.2000 | 9.3000 | 1.0800 |
| IWS | ISHARES RUSSELL MIDGAP VALU | 12.0000 | 10.0000 | 0.9900 |
| IWD | ISHARES RUSSELL 1000 VALUE E | l0.9000 | 9.5000 | 0.9200 |
| EFG | ISHARES MSCI EAFE GROWTH ETF | 7.5000 | 11.1000 | 0.4800 |
| VEA | VANGUARD FTSE DEVELOPED ETF | 6.4000 | 11,3000 | 0.3800 |
| EFA | ISHARES MSCI EAFE ETF | 6.3000 | 11,6000 | 0.3500 |
| VGK | VANGUARD FTSE EUROPE ETF | 5.9000 | 12.8000 | 0.2900 |
| VEU | VANGUARD FTSE ALL-WORLD EX-U | 5.2000 | 11,4000 | 0.2700 |
| VNQ | VANGUARD REIT ETF | 4.0000 | 13.2000 | 0.1400 |
| VWO | VANGUARD FTSE EMERGING MARKE | 2.5000 | 14.5000 | 0.0200 |
| RWX | SPDR DJ INTERNATIONAL REAL E | 1.2000 | 12.7000 | -0.0800 |
| LQD | ISHARES IBOXX INVESTMENT GRA | 0.0000 | 4.9000 | 0.4400 |
| SHV | ISHARES SHORT TREASURY BOND | 0.0000 | 0.l000 | -21,3300 |
| SHY | ISHARES 1-3 YEAR TREASURY BO | -0.1000 | 0.7000 | -3.2100 |
| TLT | ISHARES 20+YEAR TREASURY BOND | -0.4000 | 11, 0000 | -0.2400 |
| MBB | ISHARES MBS ETF | -0.4000 | 2.4000 | -1, 0600 |
| BSV | VANGUARD SHORT-TERM BOND ETF | -0.5000 | 1,3000 | -2.0l00 |
| AGG | ISHARES CORE U.S. AGGREGATE | -0.5000 | 3.0000 | -0.9200 |
| PFF | ISHARES US PREFERRED STOCK E | -0.6000 | 4.5000 | -0.6300 |
| HYG | ISHARES IBOXX USD HIGH YIELD | -0.9000 | 5.1000 | -0.6100 |
| TIP | ISHARES TIPS BOND ETF | -1.2000 | 4.5000 | -0.7400 |
| BIV | VANGUARD INTERMEDIATE-TERM B | -1.3000 | 4.3000 | -0.8l00 |
| GLD | SPDR GOLD SHARES | -4.3000 | 15.8000 | -0.4l00 |
| DBC | POWERSHARES DB COMMODITY IND | -9.1000 | 14.7000 | -0.7700 |
| SLV | ISHARES SILVER TRUST | -9.8000 | 25.2000 | 0.4700 |
| USO | UNITED STATES OIL FUND LP | -18.5000 | 29.0000 | -0.7l00 |
Out of Sample Forecast Performance of Optimized Portfolios Using The Average Optimal Portfolio Weights (August 2012-December 2017)
| Portfolio | Return | Risk | Sharpe Ratio | |
|---|---|---|---|---|
| Portfolio 1 | 0.0000 | 0.1000 | -20.8870 | |
| Portfolio 2 | 1.3000 | 1.200C | -0.7410 | |
| Portfolio 3 | 2.6000 | 2.3000 | 0.1840 | |
| Portfolio 4 | 3.9000 | 3.4000 | 0.4950 | |
| Portfolio 5 | 5.2000 | 4.6000 | 0.6510 | |
| Portfolio 6 | 6.4000 | 5.7000 | 0.7460 | |
| Portfolio 7 | 7.7000 | 6.7000 | 0.8220 | |
| Portfolio 8 | 9.2000 | 7.6000 | 0.9180 | |
| Portfolio 9 | 10.9000 | 8.7000 | 1.0080 | |
| Portfolio 10 | 11.7000 | 10.6000 | 0.8990 |
Optimal Allocation based on Average Weights in each ETFs for Efficient Corner Portfolios (August 2012 to December 2017)
| Ticker | Name | Portfolio 1 Low Risk/Return | Portfolio 2 | Portfolio 3 | Portfolio 4 | Porlfolio 5 | Portfolio 6 | Portfolio 7 | Portfolio 8 | Portfolio 9 | Portfolio 10 Higt Risk/Return | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | TLT | ISHARES 20+ YEAR TREASURY BOND | 0.1100 | 0.1690 | 0.2290 | 0.2890 | 0.3200 | 0.2630 | 0.1210 | |||
| 2 | SHV | ISHARES 1G YEAR TREASURY BO | 0.9970 | 0.7210 | 0.5020 | 0.3590 | 0.2370 | 0.1200 | 0.0290 | 0.0020 | ||
| 3 | IWS | ISHARES RUSSELL MID-GAP VALU | 0.0160 | 0.0320 | 0.0480 | 0.0640 | 0.0800 | 0.1000 | 0.1000 | 0.0930 | ||
| 4 | SHY | ISHARES 1-3 YEAR TREASURY BO | 0.1180 | 0.1740 | 0.1520 | 0.1060 | 0.0600 | 0.0210 | 0.0020 | |||
| 5 | IWD | ISHARES RUSSELL 1000 VALUE E | 0.0100 | 0.0200 | 0.0300 | 0.0390 | 0.0490 | 0.0460 | 0.0040 | |||
| 6 | IWP | ISHARES RUSSELL MIDGAP GROW | 0.0040 | 0.0080 | 0.0120 | 0.0160 | 0.0190 | 0.0100 | 0.0030 | 0.0020 | ||
| 7 | IWF | ISHARES RUSSELL 1000 GROWTH | 0.0020 | 0.0030 | 0.0040 | 0.0050 | 0.0050 | 0.0060 | 0.0020 | |||
| 8 | MBB | ISHARES MBS ETF | 0.0020 | 0.0030 | 0.0050 | 0.0060 | 0.0030 | |||||
| 9 | IJH | ISHARES CORE S&P MIDCAP ETF | 0.0010 | 0.0020 | 0.0030 | 0.0030 | 0.0040 | 0.0040 | 0.0050 | |||
| 10 | LQD | ISHARES IBOXX INVESTMENT GRA | 0.0010 | 0.0020 | 0.0020 | 0.0030 | 0.0020 | |||||
| 11 | IIP | ISHARES TIPS BOND ETF | 0.0010 | 0.0020 | 0.0020 | 0.0010 | ||||||
| 12 | QQQ | POWERSHARES QQQ TRUST SERIES | 0.0010 | 0.0640 | 0.1240 | 0.1840 | 0.2450 | 0.3050 | 0.3830 | 0.5120 | 0.6390 | 0.7850 |
| 13 | SLV | ISHARES SILVER TRUST | 0.1080 | |||||||||
| 14 | GLD | SPDR GOLD SHARES | 0.0090 | 0.0210 | 0.0330 | 0.0460 | 0.0590 | 0.0770 | 0.1030 | 0.1370 | 0.0770 | |
| 15 | IWO | ISHARES RUSSELL 2000 GROWTH | 0.0010 | 0.0010 | 0.0020 | 0.0310 |
Historical Performances of Exchanges Traded Funds (August 2007 to December 2017)
| Ticker | Name | Mean | Standard Deviation | |
|---|---|---|---|---|
| 1 | QQQ | POWERSHARES QQQ TRUST SERIES | 11.4000 | 18.0800 |
| 2 | IWF | ISHARES RUSSELL l000 GROWTH | 8.0300 | 15.3500 |
| 3 | IWO | ISHARES RUSSELL 2000 GROWTH | 7.9000 | 20.1800 |
| 4 | IJH | ISHARES CORE S&P MIDCAP ETF | 7.7200 | 17.7100 |
| 5 | IWP | ISHARES RUSSELL MIDGAP GROW | 7.430C | 18.0600 |
| 6 | IWM | ISHARES RUSSELL 2000 ETF | 6.5400 | 19.6100 |
| 7 | VBR | VANGUARD SMALLGAP VALUE ETF | 6.2700 | 19.6000 |
| 8 | VTI | VANGUARD TOTAL STOCK MKT ETF | 6.1900 | 15.5900 |
| 9 | GLD | SPDR GOLD SHARES | 6.0600 | 19.0600 |
| 10 | SPY | SPDR S&P 500 ETF TRUST | 5.8100 | 15.0600 |
| 11 | IWS | ISHARES RUSSELL MIDGAP VALU | 5.6600 | 17.9600 |
| 12 | IWD | ISHARES RUSSELL l000VALUE E | 3.9000 | 15.7400 |
| 13 | TLT | ISHARES 20+YEAR TREASURY BOND | 3.5500 | 13.9300 |
| 14 | VNQ | VANGUARD REIT ETF | 2.3300 | 25.5100 |
| 15 | SLV | ISHARES SILVER TRUST | 2.1300 | 34.1 l00 |
| 16 | LQD | ISHARES IBOXX INVESTMENT GRA | 1,5700 | 7.7400 |
| 17 | TIP | ISHARES TIPS BOND ETF | 1.1900 | 6.3400 |
| 18 | BIV | VANGUARD INTERMEDIATE-TERM B | 1.1100 | 5.5500 |
| 19 | AGG | ISHARES CORE U.S. AGGREGATE | 0.9500 | 3.7800 |
| 20 | EFG | ISHARES MSCI EAFE GROWTH ETF | 0.7300 | 18.6200 |
| 21 | MBB | ISHARES MBS ETF | 0.6900 | 2.9700 |
| 22 | BSV | VANGUARD SHORT-TERM BOND ETF | 0.4600 | 2.4300 |
| 23 | SHY | ISHARES 1 -3 YEAR TREASURY BO | 0.3800 | 1.2800 |
| 24 | SHV | ISHARES SHORT TREASURY BOND | 0.0600 | 0.3300 |
| 25 | VWO | VANGUARD FTSE EMERGING MARKE | -0.2800 | 23.7500 |
| 26 | VEU | VANGUARD FTSE ALL-WORLD EX-U | -0.2800 | 19.9500 |
| 27 | VEA | VANGUARD FTSE DEVELOPED ETF | -0.6300 | 19.0900 |
| 28 | HYG | ISHARES IBOXX USD HIGH YIELD | -1, 0400 | 11.5100 |
| 29 | EFA | ISHARES MSCI EAFE ETF | -1.1100 | 19.2800 |
| 30 | VGK | VANGUARD FTSE EUROPE ETF | -2.1700 | 20.9500 |
| 31 | PFF | ISHARES US PREFERRED STOCK E | -2.2500 | 19.1300 |
| 32 | PWX | SPDR DJ INTERNATIONAL REAL E | -3.9500 | 21.1800 |
| 33 | DBC | POWERSHARES DB COMMODITY IND | -4.3700 | 20.6900 |
| 34 | USO | UNITED STATES OIL FUND LP | -15.2000 | 33.7700 |
Out of Sample Forecast of Optimized Portfolios Performance Using Historical Variance-Covariance Matrix (August 2012 to December 2017)
| Return | Risk | Sharpe Ratio | ||
|---|---|---|---|---|
| Lowest Risk/Return | Portfolio 1 | 0.0000 | 0.1000 | -20.0670 |
| Portfolio 2 | 1, 0000 | 1,3000 | -0.9660 | |
| Portfolio 3 | 1.9000 | 2.5000 | -0.1210 | |
| Portfolio 4 | 2.7000 | 3.8000 | 0.1470 | |
| Portfolio 5 | 3.6000 | 5.0000 | 0.2790 | |
| Portfolio 6 | 4.4000 | 6.3000 | 0.3600 | |
| Portfolio 7 | 5.5000 | 7.4000 | 0.4550 | |
| Portfolio 8 | 7.0000 | 8.5000 | 0.5720 | |
| Portfolio 9 | 8.0000 | l0.4000 | 0.5560 | |
| Highest Risk/Return | Portfolio 10 | 5.5000 | 16.5000 | 0.2040 |
| Lowest Risk/Return | Portfolio 1 | 0.0000 | 0.l000 | -20.7580 |
| Portfolio 2 | 1.0000 | 1,3000 | -0.8730 | |
| Portfolio 3 | 2.0000 | 2.6000 | -0.0490 | |
| Portfolio 4 | 3.l000 | 4.0000 | 0.2430 | |
| Portfolio 5 | 4.2000 | 5.3000 | 0.3810 | |
| Portfolio 6 | 5. 1000 | 6.6000 | 0.4330 | |
| Portfolio 7 | 6.0000 | 7.9000 | 0.4840 | |
| Portfolio 8 | 7.7000 | 9.2000 | 0.6010 | |
| Portfolio 9 | 8.9000 | 11.1000 | 0.60l0 | |
| Highest Risk/Return | Portfolio 10 | 9.7000 | 14.4000 | 0.5230 |
| Lowest Risk/Return | Portfolio 1 | 0.1000 | 0.1000 | -17.3720 |
| Portfolio 2 | 0.5000 | l.l000 | -1.4840 | |
| Portfolio 3 | 1.0000 | 2.3000 | -0.5110 | |
| Portfolio 4 | 1.5000 | 3.7000 | -0.1900 | |
| Portfolio 5 | 2.0000 | 5.0000 | -0.0420 | |
| Portfolio 6 | 2.5000 | 6.4000 | 0.0430 | |
| Portfolio 7 | 2.9000 | 7.8000 | 0.0890 | |
| Portfolio 8 | 2.4000 | 9.2000 | 0.0260 | |
| Portfolio 9 | 2.3000 | 11.0000 | 0.0110 | |
| Highest Risk/Return | Portfolio 10 | 0.3000 | 15.6000 | -0.1220 |
| Portfolio 1 | 0.0000 | 0.l000 | -I9.0260 | |
| Portfolio 2 | 0.8000 | 1,4000 | -0.9990 | |
| Portfolio 3 | 1,5000 | 2.7000 | -0.2540 | |
| Portfolio 4 | 2. l000 | 4.2000 | -0.0260 | |
| Portfolio 5 | 2.7000 | 5.6000 | 0.0950 | |
| Portfolio 6 | 3.3000 | 7.0000 | 0.1660 | |
| Portfolio 7 | 4.3000 | 8.5000 | 0.2470 | |
| Portfolio 8 | 5.4000 | 10.4000 | 0.3110 | |
| Portfolio 9 | 5.8000 | 12.3000 | 0.2970 | |
| Portfolio 10 | -1.0000 | 20.3000 | -0.1560 | |