Capitalization weighting is the prevailing choice for equity index investors, who can choose from low-cost index funds constructed with theoretically proven methodologies. But capitalization weighting in fixed-income markets enjoys no such theoretical foundation, leaving investors without a clear choice for a diversified core fixed-income holding. A portfolio of bond exchange-traded funds that optimizes the tradeoff between yield and risk gives investors a commendable way to own a broadly diversified core allocation.
John Bogle, the champion of indexing, has expressed concerns about the attributes and performance of the current generation of bond index funds. He focused on the Barclays Aggregate Bond Index (AGG), but his critique is relevant beyond that index. Rob Arnott’s firm, Research Affiliates, has also detailed problems with the current bond indexes. It is intriguing when Bogle and Arnott agree, particularly because they have historically been at odds on the subject of equity indexing.
The problems with capitalization-weighted bond indices
There are a variety of reasons why bond index funds have come under scrutiny. One of the common critiques of bond indices is the practice of capitalization-based weighting, using the outstanding market value of bonds. Companies with more debt have a higher allocation in a corporate bond index. There is no foundation for holding more of a company’s or country’s debt as it borrows more.
Another issue with cap-weighted bond indexes is style drift. The relative weighting of the aggregate bond index to government-backed bonds increased from 35% in 2007 to 47% in mid-2012. The higher allocation to government-backed securities increases interest-rate sensitivity. The effective style drift in AGG was not a one-time event, however. The history of this index shows a constantly varying allocation to different bond classes. A 2011 study of corporate bond indices found that their exposures to both credit risk and interest rate risk exhibit considerable drift through time.
A bond index with changing concentrations to specific fixed income classes is not inherently problematic, but it raises the question as to whether these allocations are broadly representative of the market or a quirk of the weighting methodology.
Another limitation of the aggregate bond index is that it does not include a number of bond classes, such as municipal bonds and high-yield bonds. Those bond sub-classes should not be ignored, since they are two of the few with substantial yields. Investors shouldn’t chase yield, but neither is it rational to exclude certain bond classes because they are high-risk.
There is a very good reason why investors should care whether a bond index consistently captures the entire bond market. A premise of portfolio theory is that for a portfolio to deliver the highest return for a given level of risk, it must be fully diversified. If the aggregate bond index is not fully diversified, investors are missing some fraction of the available return from the bond market. In the parlance of portfolio theory, the Aggregate Bond Index is not on the efficient frontier. This, in turn, means that a better core fixed-income portfolio should allow investors to reap more yield than the aggregate bond index, with no increase in risk. Bogle has suggested that this is the case, but he did not provide quantitative support nor did he propose a solution. Fortunately, as I will demonstrate, we can directly observe yield and risk for bond sub-classes and calculate portfolio yield and risk for combinations of these sub-asset classes, establishing that traditional bond indexes are inefficient at providing yield.
An alternate strategy
Arnott’s firm, Research Associates, has advocated a new approach to designing fixed income indices, but the results to date are inconclusive. Its approach is to weight bonds based on fundamental measures of a country’s or company’s prospective ability to repay debt, rather than upon the amount of outstanding debt. In its research, it found that a fundamentally weighted high-yield bond index had historically out-performed traditional high-yield indexes by an astounding 473 basis points per year. High-yield bonds exhibited the strongest benefit from fundamental weighting in their analysis, and other classes of bonds showed consistent benefits. This result suggests that traditional high-yield indexes are the most flawed as compared to other bond classes and thus present the biggest potential for improvement with a better-designed index.
The implementation of this strategy has not been successful, however. The PowerShares Fundamental High-Yield Bond Fund (PHB) has substantially under-performed Morningstar’s high-yield bond benchmark throughout its 5+ years of history, earning the fund a one-star rating. Some of the other funds using the fundamental bond index methodology have fared better, but the observed under-performance of PHB, for which the back testing showed the best results, is a concern.
An improved core fixed-income portfolio
My approach to building a core fixed-income allocation is quite simple. The goal of creating a core fixed-income portfolio is to combine bond ETFs so as to provide the highest yield for a given level of risk, controlling for interest-rate exposure. Rather than trying to create a representative basket of bonds, we are creating an efficient frontier of yield compared to risk (measured as volatility). I have demonstrated this approach in a number of previous articles. As I will show, using this approach, it is possible build a core fixed-income portfolio with a substantive increase in yield compared to the aggregate bond index with less interest-rate exposure and no additional risk. This demonstration serves to address the problem that Mr. Bogle identifies with the current aggregate bond index.
As with building a traditional efficient frontier, the starting point is to define a universe of relevant asset sub-classes. I have identified a series of potential candidates for inclusion in an improved core fixed-income portfolio.
Fixed income sub-classes and representative ETFs
|
Name
|
Ticker
|
Bond Type
|
Expense Ratio
|
Distribution Yield
|
|
ISHARES BARCLAYS 1-3 YEAR TREASURY BOND FUND
|
SHY
|
Short U.S. Treasury
|
0.15%
|
0.32%
|
|
SPDR BARCLAYS MORTGAGE BACKED BOND ETF
|
MBG
|
MBS
|
0.32%
|
0.49%
|
|
ISHARES BARCLAYS MBS BOND FUND
|
MBB
|
MBS
|
0.26%
|
1.50%
|
|
ISHARES BARCLAYS 7-10 YEAR TREASURY BOND FUND
|
IEF
|
Intermediate U.S. Treasury
|
0.15%
|
1.65%
|
|
ISHARES S&P/CITIGROUP INTL TREASURY BOND FUND
|
IGOV
|
International Treasury
|
0.35%
|
1.86%
|
|
SPDR BARCLAYS CAPITAL INTL TREASURY BOND ETF
|
BWX
|
International Treasury
|
0.50%
|
2.15%
|
|
ISHARES CORE US BOND MARKET ETF
|
AGG
|
Aggregate bond
|
0.08%
|
2.43%
|
|
ISHARES BARCLAYS 20+ YEAR TREASURY BOND FUND
|
TLT
|
Long U.S. Treasury
|
0.15%
|
2.58%
|
|
ISHARES S&P NATIONAL MUNICIPAL BOND FUND
|
MUB
|
Muni
|
0.25%
|
2.80%
|
|
ISHARES BARCLAYS INTERMEDIATE CREDIT BOND FUND
|
CIU
|
Credit
|
0.20%
|
3.02%
|
|
ISHARES IBOXX $ INVESTMENT GRADE CORP BOND FUND
|
LQD
|
Investment-grade corporate
|
0.15%
|
3.73%
|
|
SPDR BARCLAYS CONVERTIBLE SECURITIES ETF
|
CWB
|
Convertible
|
0.40%
|
3.76%
|
|
POWERSHARES INSURED NATIONAL MUNI BOND PORTFOLIO
|
PZA
|
Insured muni
|
0.28%
|
3.93%
|
|
ISHARES JPMORGAN USD EMERGING MARKETS BOND FUND
|
EMB
|
Emerging market
|
0.60%
|
4.20%
|
|
POWERSHARES FUNDAMENTAL HIGH YIELD CORP BOND FUND
|
PHB
|
High-yield corporate
|
0.50%
|
4.81%
|
|
MARKET VECTORS HIGH-YIELD MUNICIPAL INDEX ETF
|
HYD
|
High-yield muni
|
0.35%
|
4.93%
|
|
ISHARES IBOXX $ HIGH YIELD CORPORATE BOND FUND
|
HYG
|
High-yield corporate
|
0.50%
|
6.36%
|
These funds are sorted on the basis of yield, and the AGG is highlighted. The expense ratios show that there is a cost penalty associated with creating a higher-yield alternative to AGG. The average expense ratio across all of these funds is 0.31% versus 0.08% for AGG. The average yield for these funds is 2.97% vs. 2.43% for AGG.
Now we must determine whether including these higher-cost and higher-yield sub-classes will make the portfolio riskier and more expensive, offsetting the benefits of higher yield.
I included the fundamentally weighted high-yield bond fund (PHB) to determine whether there are diversification benefits associated with this fund that make it more worthwhile than its performance to date suggests.
One of the most important critiques of the AGG is that it has too high an allocation to Treasury bonds, giving it a very high exposure to increases in interest rates. I measured this exposure using the correlation between fund returns and changes in the Chicago Board Options Exchange 10-year Treasury bond yield. AGG’s returns have a -0.85 correlation, making it highly sensitive to changes in interest rates. When rates rise, AGG’s value will move strongly downward.
Is it possible to build a portfolio with the same risk as AGG but with substantively higher yield by combining the ETFs listed above? The key is having a reliable estimate of risk for each of these bond funds and accurately measuring the correlations between them. Lower correlation corresponds to lower risk in a portfolio.
I used the Quantext Portfolio Planner (QPP) to create the risk analysis and projections. QPP’s projections have been extensively tested and benchmarked. QPP’s projected and historical risk levels for fixed-income asset classes are very similar, which provides an added affirmation of the model’s accuracy.
Four-year trailing and projected volatilities for individual ETFs
|
Ticker
|
Projected Volatility
|
Trailing Volatility
|
Yield
|
|
SHY
|
0.9%
|
0.9%
|
0.32%
|
|
MBG
|
3.1%
|
2.9%
|
0.49%
|
|
MBB
|
2.4%
|
2.3%
|
1.50%
|
|
IEF
|
6.7%
|
6.3%
|
1.65%
|
|
IGOV
|
9.3%
|
8.8%
|
1.86%
|
|
BWX
|
9.3%
|
8.8%
|
2.15%
|
|
AGG
|
3.2%
|
3.0%
|
2.43%
|
|
TLT
|
15.3%
|
14.5%
|
2.58%
|
|
MUB
|
6.0%
|
5.7%
|
2.80%
|
|
CIU
|
3.3%
|
3.2%
|
3.02%
|
|
LQD
|
6.3%
|
6.0%
|
3.73%
|
|
CWB
|
11.7%
|
11.0%
|
3.76%
|
|
PZA
|
6.6%
|
6.2%
|
3.93%
|
|
EMB
|
8.4%
|
7.9%
|
4.20%
|
|
PHB
|
7.5%
|
7.1%
|
4.81%
|
|
HYD
|
7.5%
|
7.1%
|
4.93%
|
|
HYG
|
10.0%
|
9.5%
|
6.36%
|
I have included yields in this table to provide a basis of comparison with the optimized portfolios presented below.
The optimization process uses trailing four-year returns (through May 2013) to calculate historical volatilities and correlations between the ETFs. The ETFs have sufficient data history and a variety of interest-rate environments.
QPP identified the portfolio with the highest yield that can be achieved with no more risk than AGG. I have created five portfolios with varying limits (3%, 5%, 10%, 15% and 20%) for the ETFs that could be combined with AGG to construct the optimal portfolio. Along with risk and yield, I provided the asset-weighted expense ratio for each portfolio and the correlation of its returns to the 10-year Treasury yield.
Optimized fixed income allocations
|
Ticker
|
Bond Type
|
AGG
|
Portfolio 1 (3% max)
|
Portfolio 2 (5% max)
|
Portfolio 3 (10% max)
|
Portfolio 4 (15% max)
|
Portfolio 5 (20% max)
|
|
SHY
|
Short U.S. Treasury
|
-
|
-
|
-
|
-
|
3.7%
|
4.5%
|
|
MBG
|
MBS
|
-
|
1.1%
|
-
|
-
|
-
|
-
|
|
MBB
|
MBS
|
-
|
2.4%
|
0.6%
|
2.5%
|
5.1%
|
4.0%
|
|
IEF
|
Intermediate U.S. Treasury
|
-
|
1.4%
|
-
|
-
|
-
|
-
|
|
IGOV
|
International Treasury
|
-
|
1.3%
|
-
|
-
|
-
|
-
|
|
BWX
|
International Treasury
|
-
|
0.7%
|
-
|
-
|
-
|
-
|
|
AGG
|
Aggregate bond
|
100%
|
67.5%
|
65.2%
|
62.6%
|
45.7%
|
41.6%
|
|
TLT
|
Long U.S. Treasury
|
-
|
-
|
-
|
-
|
-
|
-
|
|
MUB
|
Muni
|
-
|
1.5%
|
0.6%
|
-
|
-
|
-
|
|
CIU
|
Credit
|
-
|
3.0%
|
5.0%
|
4.3%
|
15.0%
|
20.0%
|
|
LQD
|
Investment-grade corporate
|
-
|
3.0%
|
2.3%
|
-
|
-
|
-
|
|
CWB
|
Convertible
|
-
|
3.0%
|
5.0%
|
2.3%
|
0.4%
|
-
|
|
PZA
|
Insured muni
|
-
|
3.0%
|
3.1%
|
-
|
-
|
-
|
|
EMB
|
Emerging market
|
-
|
3.0%
|
3.2%
|
-
|
-
|
-
|
|
PHB
|
High-yield corporate
|
-
|
3.0%
|
5.0%
|
8.2%
|
-
|
-
|
|
HYD
|
High-yield muni
|
-
|
3.0%
|
5.0%
|
10.0%
|
15.0%
|
15.4%
|
|
HYG
|
High-yield corporate
|
-
|
3.0%
|
5.0%
|
10.0%
|
15.0%
|
14.5%
|
|
Max Supplemental Allocation
|
0%
|
3%
|
5%
|
10%
|
15%
|
20%
|
|
Trailing Four-Year Volatility
|
3.0%
|
3.0%
|
3.0%
|
3.0%
|
3.0%
|
3.0%
|
|
Projected Volatility
|
3.2%
|
3.0%
|
3.0%
|
3.0%
|
2.8%
|
2.9%
|
|
Distribution Yield
|
2.4%
|
2.8%
|
3.1%
|
3.3%
|
3.4%
|
3.4%
|
|
Expense Ratio
|
0.08%
|
0.17%
|
0.18%
|
0.20%
|
0.21%
|
0.22%
|
|
Correlation to 10-Yr Treasury Yield
|
-86%
|
-66%
|
-53%
|
-46%
|
-45%
|
-45%
|
Portfolio 1 (a 3% maximum allocation to any ETF other than AGG) has a 40-basis-point higher yield than AGG, with no increase in risk. Its expense ratio is 9 basis points higher than AGG, but the expense is far smaller than the gain in yield. This portfolio has a lower correlation to 10-year Treasury yield than AGG, so it is less negatively impacted by an increase in interest rates.
As maximum allocations to the individual ETFs increase, the yield rises steadily. Despite the recent run-up in prices on high-yield bonds (and corresponding decline in yield), the optimizer selected portfolios with allocations to high-yield asset classes. Portfolio 2 has a 15% allocation to high-yield bonds and a 3.1% yield, adding 70 basis points to the 2.4% yield provided by AGG.
A yield as high as 3.4% can be obtained if investors are willing to take on a 30% allocation to high-yield bonds. The model portfolios had allocations to the fundamentally weighted PHB only when the maximum allowable allocations to other fixed-income classes were reached. In Portfolios 4 and 5, the optimizer put its high-yield allocation entirely into HYD and HYG.
In all five portfolios, the historical risk matched that of AGG. The projected risk levels of the new portfolios are somewhat lower than that of AGG, but the difference is too small to draw any meaningful conclusion.
Conclusions
Investors using AGG are saddled with low yield and high interest-rate exposure, largely as a result of its high allocation to Treasury bonds. That allocation flows from its capitalization-weighted construction, which over-weights the most indebted firms or countries. No theoretical justification exists for this methodology, validating Bogle and Arnott, who agree that AGG is substantially flawed.
My alternative core fixed-income portfolio provides the maximum yield compared to risk. It is efficient with regard to the tradeoff between yield and risk. With a maximum 5% allocation to any ETF other than AGG, one can add 70 basis points in yield to AGG.
This approach is highly transparent, although the allocations could change over time. Investors looking for the best available core bond allocation should be less concerned about holding a static mix of bond sub-classes than about efficiently generating yield.
Geoff Considine is founder of Quantext and the developer of Quantext Portfolio Planner, a portfolio management tool. More information is available at www.quantext.com.Quantext is a strategic adviser to Folio Investing, an innovative brokerage firm specializing in offering and trading portfolios for advisors and individual investors
Read more articles by Geoff Considine
