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Efficient Asset Allocation for Individual Investors in the ETF World

Riza Emekter
Riza Emekter
, 
Benjamas Jirasakuldech
Benjamas Jirasakuldech
 and 
Robert Beaves
Robert Beaves
   | Mar 22, 2024
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Published Online: Mar 22, 2024
Page range: 79 - 98
DOI: https://doi.org/10.2478/fprj-2022-0004
© 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
Panel A: Performance of Optimized Portfolio
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
Panel B: Performance of Individual ETFs
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
Lowest Risk/Return 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
Highest Risk/Return 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
Panel A: Performance of Optimized Portfolio based on 60-Months Optimization
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
Panel B: Performance of Optimized Portfolio based on 40-Monfhs Optimization
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
Panel C: Performance of Optimized Portfolio based on Cumulative Optimization
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
Panel A: Performance of Optimized Portfolio based on Annual Optimization
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
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