According to a Fitch survey of European fixed-income investors1 overseeing about US$7.1 trillion of assets, 2011 saw a major reallocation of cash from sovereign to corporate bonds. For example, the year saw a total outflow from euro sovereign bond funds of €33 billion, as investors became increasingly concerned about the ability of European governments to solve the sovereign debt crisis. The anti-sovereign, pro-corporate bond trend is set to continue this year, the survey’s respondents told Fitch.
In recent years, investors have also been making increasing use of indices to manage their bond investments. When the first corporate bond exchange-traded fund (ETF) was launched by iShares in the United States in 2002, there were only a few fixed-income ETFs, whereas there are now more than 70 based on corporate bonds alone. According to the ETF Industry Association2, bond ETF assets grew from about US$129 billion in 2010 to nearly US$180 billion at the end of last year: an impressive growth rate of 39.5%, compared to the 5% overall growth of the ETF industry. Furthermore, bond ETF inflows reached US$45 billion (38% of the industry’s total inflows). These numbers convey the recent increase in interest in passive investing in this asset class, but only recently have practitioners and academics begun to discuss the qualities of the indices underlying such funds.3
The bond indices offered by existing providers face a number of challenges. The major one for standard corporate bond indices, which simply weight the debt issues by their market value, is the so-called “bums’ problem” (Siegel 2003). This is the result of the large share of the total debt market accounted for by issuers with substantial outstanding debt. Market-value-weighted corporate bond indices will thus have a tendency to overweight bonds issued by highly indebted companies. It is often argued that such indices will thus give too much weight to riskier assets.
This is a problem not just for individual bond issues, but also for market sectors as a whole. While it is debatable whether debt-weighting really leads to overweighting in the most risky securities4, it is clear that market-value debt-weighted indices lead to more concentrated portfolios, something that conflicts with investors’ desire for a diversified portfolio. Barclays Capital, for instance, aims to limit such concentration in one benchmark by capping issuers’ weights to a fixed percentage of the index and then redistributing the excess weight across the other issuers (the Barclays Capital U.S. Corporate Aaa-A Capped Index is market-cap weighted with a 3% cap on any individual security’s weighting).
In addition to the problem of concentration, fluctuations in risk exposure, such as duration or credit risk, are pronounced in existing indices. Such uncontrolled time-variation in risk exposures is incompatible with investors’ requirements that these exposures be relatively stable, so that allocation decisions are not compromised by implicit choices made by an unstable index. Liquidity is also a concern. The recent EDHEC-Risk European Index Survey5 shows that, for corporate bond indices, 68.3% of respondents regard liquidity risk as an important or very important issue, while only 2.4% do not worry about it at all.
Recently, index providers have launched a number of alternative indices to try to address these concerns, and a variety of new approaches to index construction is now on offer. However, many of these approaches were first applied to equity indices and not designed for the bond markets per se. Despite this, index providers have started to apply the weighting principles from alternative equity indices to corporate bonds.
In this article, we examine two corporate bond index methods that use non-traditional weighting schemes. We then discuss the credit, interest rate and liquidity risks that investors face when investing in corporate bond indices.
NON-STANDARD CORPORATE BOND INDICES
An overview of corporate bond indices shows that market-value-weighted indices dominate index providers’ offerings. In the bond index universe, use of alternative weighting schemes is quite new and the recent crises in both corporate debt markets (especially for financials) and sovereign debt markets have drawn increasing investor attention to indices which offer less concentrated exposure to highly indebted issuers.
Equal-weighted index approaches seek to eliminate excessive concentration in individual index names. There is also no need to calculate issuers’ outstanding debt (which can at times be difficult6). Equal-weighted indices, however, face periodic rebalancing, resulting in elevated transaction costs, something that can be a particular problem in less liquid areas of the bond markets. However, equal-weighted indices are popular as (based on backtests) they have been found to have superior returns to capitalisation-weighted indices in several asset classes. Equal-weighting is also the naïve route to constructing well-diversified portfolios. Demiguel, Garlappi and Uppal (2006) find that 1/N equity portfolios have better returns and Sharpe ratios than capitalisation-weighted portfolios, based on studies in many different markets. Campani and Goltz (2011) show that the Dow Jones equally weighted corporate bond portfolio had higher Sharpe ratios than standard cap-weighted indices covering this sector.
Another popular weighting scheme, fundamental indexation, applies index weights based on a set of firm-level characteristics. The main objectives of this index approach are higher risk-adjusted performance and avoiding exposure to more indebted companies. In early 2012 Research Affiliates and Ryan partnered to launch a US corporate bond index series based on four company characteristics (five-year average cash flows, dividend payments, book value and sales). Research Affiliates and Citigroup have partnered to launch an alternative weighting scheme for sovereign bond indices based on another set of fundamental measures (GDP, energy consumption, population and rescaled land area).
Arnott et al. (2010) found that a fundamental index portfolio of investment grade bonds had historically outperformed a standard, capitalisation-weighted index by 42 basis points per annum. In less liquid markets like high-yield and emerging market bonds, annual outperformance was more pronounced (at 260 basis points and 143 basis points, respectively). How these indices will perform outside the back-test period remains to be seen. It is also apparent that, as the choice of fundamental criteria has a direct impact on the index performance, a set of fundamental parameters may be chosen a posteriori to lead to higher returns in the back-testing of the index.
Fundamental weighting approaches face another challenge in that some fundamental data is not accessible, since a number of bond issuers are not listed corporations (Arnott et al. (2010) recover only 84% of the accounting data for the US corporations included in their reference bond index). The decision not to include in the index those issuers for whom accounting data is unavailable obviously introduces a bond selection bias by comparison with standard, capitalisation-weighted bond indices.
After discussing these two non-debt-weighted approaches, below we focus on the risk exposures of corporate bond indices. Our focus will mainly be on the standard debt-weighted indices when discussing risks, as these indices have been studied more widely than their equal-weighted and fundamental-weighted counterparts. In particular, we will discuss the reliability of credit risk exposure, the stability of duration over time and liquidity risks.
MANAGING CREDIT RISK
The issuer’s willingness and ability to pay the debt and stick to the terms of the obligation is a key factor for fixed income investors. As a consequence, default risk is one of the first considerations in corporate bond indices and should be assessed and reflected in a reliable way. The typical credit risk classification used by bond index providers is straightforward. Index firms separate the bond universe into two parts: investment grade and high-yield corporate bond indices and then use credit rating agencies’ bond ratings to specify credit risk.
Using the ratings scales of the main three agencies: (Moody’s, S&P and Fitch7), the threshold between investment grade and high yield is set at Baa3/BBB-/BBB-. Index providers differ, however, on whether they include or exclude a bond when at the threshold rating, or how they handle a bond with a “split” rating from different agencies.8 Beyond the simple distinction between high yield and investment grade, it is rare to find corporate bond indices that focus on specific ratings categories. Thus investors will not easily find passive investment products which allow a specific sub-segment of the credit market to be captured.
The agency credit ratings underlying all these indices are based on accounting and fundamental data. Ratings are often narrow in focus (an accurate assessment of companies’ pension liabilities, for instance, is often difficult to achieve). Moody’s, S&P and Fitch describe their ratings as a long-term assessment of credit risk through the economic cycle (Altman and Rijken 2004), resulting in an approach that tends to be both stable and backward-looking.
Given this backward-looking approach and the bias towards ratings stability, it is perhaps not surprising that there is substantial empirical evidence that ratings lag the credit spreads observed in the market for corporate bonds. It is not surprising that market-based measures lead ratings changes. Both bond credit spreads and credit default swap (CDS) spreads for corporate issuers are market-based measures for assessing credit risk. There is a debate in academic literature over the information content of each of these measures. It is clear that both measures can be impacted by other effects not related to the pure default risk of the issuer, such as liquidity, supply and demand in the market of the respective instrument and other risk factors (Huang and Huang (2003), Colin-Dufresne, Goldstein, and Martin (2001), Longstaff, Mithal, and Neis (2005), Bao and Pan (2008) (2011), Aunon-Nerin et al. (2002) and Tang and Yan (2007)). However, such market-based measures have been found to be clearly more informative than ratings (Hull and White (2004), Blanco et al. (2005)). Given that investors ought to be concerned more about the current credit risk, rather than the past credit risk of constituents, it’s surprising they continue to rely on indices that make heavy use of agency credit ratings.
LACK OF STABILITY OF INTEREST RATE RISK EXPOSURE
The duration9 of debt-weighted and equally weighted indices shows severe fluctuations over time and across indices.10 This instability has major implications: even if a particular index matches an investor’s desired risk exposure today, it may not do so tomorrow. The fluctuations in this risk exposure are incompatible with investors’ requirements that duration exposures be relatively stable to protect allocation decisions from such fluctuations.
Indeed, it is no surprise that standard bond indices may not correspond to the levels of interest rate sensitivity that investors desire. Since standard corporate bond indices simply weight the debt issues by their market value, the duration structure of outstanding bonds will reflect the issuers’ preference for minimising their cost of capital and there is no reason why this cost minimisation should be aligned with the interests of investors.11 Also, each change of composition in the corporate bond index will affect its overall duration. Newly issued bonds, for example, are likely to differ from older outstanding debt in terms of duration. In addition to changes in the index composition, it is important to keep in mind that even if the bonds in an index and their relative weights remain unchanged, the indices’ average duration will decrease over time.
Campani and Goltz (2011) show that the average durations of several European corporate bond indices demonstrate severe fluctuations over time. For instance, their results show that for the same index, duration can vary from values of four to values of about seven over a ten year period: a very severe change of interest rate sensitivity. Figure 1 shows the average Macaulay duration over ten years of the iBoxx Liquid Euro Corporate investment grade index.
One solution to such fluctuations in risk exposure would be to build an index with more stable duration. There is currently a limited number of target duration indices, covering both corporate and sovereign bonds (see Figure 2).
Amongst target duration sovereign bond indices, iBoxx has target duration indices for US inflation-protected treasury bonds (TIPS). NASDAQ OMX Iceland (OMXI), Deutsche Bank and Barclays Capital also offer target duration indices for sovereign bonds.
Deutsche Bank offers an index which provides exposure to corporate credit risk through CDS while controlling interest rate risk using sovereign bonds. The index includes a portfolio of sovereign euro bonds and an exposure to the change in the level of corporate credit spreads (a portfolio of CDS on corporate issuers).
Lastly, Accretive Asset Management offers the “BulletShares USD Corporate Bond Indices”, which measure the performance of maturity-targeted segments of the US investment-grade corporate bond market. Each index tracks a basket of bonds with the same annual maturity and replicates a profile similar to that of an individual held-to-maturity bond, resulting in a series of fixed-income indices with successive annual maturities (from 2012 to 2021).
Benchmark indices generally consist of a very large number of bonds, which makes them difficult to replicate. Furthermore, bonds with special features or smaller amounts outstanding usually suffer from illiquidity, resulting in relatively large bid-offer spreads (Bias et al. 2006), especially during times of stress. For instance, Nielsen et al. (2011) show that corporate bond spreads increased dramatically with the onset of the subprime crisis. Old issues also tend to be illiquid as investors focus on newly issued bonds. Some corporate bond indices aim to address these deficiencies by limiting the number of bonds per index and excluding special bond types and old bonds, thus increasing liquidity.
The recent EDHEC-Risk European Index Survey12 shows that for corporate bond indices, liquidity risk is the most critical concern: 68.3% of respondents regard it as important or very important and only 2.4% do not worry about it at all.
Lack of trading and transaction data are a common feature for bonds, so it is especially important to monitor liquidity when selecting the components of a bond index. In fact, many studies have attributed deviations in corporate bond prices from their theoretical values to the influence of illiquidity in the market. Huang and Huang (2003) find that yield spreads for corporate bonds are too high to be explained by credit risk and question the economic content of the unexplained portion of yield spreads (see also Colin-Dufresne, Goldstein, and Martin (2001) and Longstaff, Mithal and Neis (2005)). Bao and Pan (2008) document a significant amount of transitory excess volatility in corporate bond returns and attribute this excess volatility to the illiquidity of corporate bonds. Bao and Pan (2011) also show that the illiquidity in corporate bonds is substantial, contributing to higher bond yield spreads than might be expected from bid–ask spreads alone. They find that the aggregate illiquidity explains the monthly changes in corporate yield spreads, all the more so for ratings A and above, where the illiquidity is by far the most important variable, explaining over 51% of the monthly variation in yield spreads for AAA-rated bonds, 47% for AA-rated bonds, and close to 60% for A-rated bonds. They also compare illiquidity-implied spreads with the estimated bid-ask spreads reported by Edwards, Harris, and Piwowar (2007). Bao and Pan find that estimates of implied spreads are between 50% higher and almost four times higher than those by Edwards, Harris, and Piwowar, depending on the size of the transaction.
Bond illiquidity poses a significant challenge to fixed income ETF providers as a bond ETF has to track its index closely and efficiently. The lack of liquidity in the bond market, highlighted by the quasi-absence of a secondary market as most bonds are held until maturity, makes it even more difficult for a bond ETF price to converge to its stated NAV and fulfil its advertised promise of instant liquidity. This challenge is bigger for corporate bonds than for government bonds. Bond ETF providers will reduce this risk by limiting the number of bonds held to a representative number of the index’s constituents, although it’s often unclear how the choice of bonds is arrived at. For example, the Barclays Aggregate Bond Index contains more than 6,000 bonds, but the Barclays iShares Aggregate Bond Fund, which tracks the index, contains just over 100 of those bonds.
Another solution is to track a bond index made up of a limited number of bonds. Several corporate bond index providers (namely Barclays, Citigroup, Bank of America Merrill Lynch, J.P. Morgan, Dow Jones, iBoxx and Deutsche Bank), offer “liquid” versions of flagship indices, consisting of a limited number of bonds, typically those with the largest outstanding market value.13 However Campani and Goltz (2011) have shown that reducing the number of bonds could lead to higher instability of interest rate risk exposure of the index, and the smaller the number of bonds the greater the instability. As discussed previously, replacing a constituent with one with different characteristics will impact the overall risk exposure of the index. This impact will clearly be more important for an index with a small number of securities (say 50) than for an index with thousands of securities.
Overall, although liquidity risk is rightly one of the main concerns of index investors, the natural lack of liquidity in the corporate bond market makes it a problematic issue for anyone investing in this asset class. Index providers’ initiatives to provide liquid versions of their indices offer a potential solution but it should be noted that such indices also come with other pitfalls.
Despite their increased popularity, corporate bond indices and ETFs still rely on traditional market-value-weighted indices. Newer index versions, using equal or fundamental weighting, may partly address the well-known concentration problem of debt-weighted indices. However, alternative weighting schemes are often straightforward extensions of equity index methodologies and were never designed to address important challenges in bond index construction, such as duration instability, credit risk classification and liquidity.
When managing credit risk, most existing indices offer little granularity and rely on backward-looking information. Different approaches have been developed by bond index providers to manage indices’ interest rate exposures. Such approaches are often based on targeting specific market segments within single-issuer government bond indices.
For corporate bond indices, where one has to address questions of issuer diversification and interest rate risk control, such an approach may not be straightforward. Finally, many index providers offer corporate bond indices which control liquidity through security selection. Such indices, however, face a natural trade-off: it has been shown that higher investability will lead to higher instability of interest risk exposure.
Overall, it is clear that standard corporate bond indices serve a useful purpose as market benchmarks. They represent the performance of the average investor and thus allow for comparison with a peer group. However, relatively few indices allow investors’ specific requirements in managing credit, interest rate and liquidity risk to be integrated. At best, existing methodologies address only some of these questions. Index providers face a challenge in devising new methods of bond index construction without taking the easy route of simply transposing techniques used in building equity indices.
Endnotes And References
- Fitch, Q1-2012 Quarterly European Senior Fixed Income Survey.
- ETF Industry Association March 2012 ETF Data Reports, http://www.etf-ia.com/
- Sangvinatsos (2010) discusses how corporate bond indices could be integrated with other asset classes such as stocks and Treasuries in constructing optimal portfolios (also see Korn and Koziol (2006) and Meindl and Primbs (2006) who discuss bond portfolio optimisation). Cai and Jiang (2008) study corporate bond returns and volatility, and Arnott et al. (2010) apply characteristics-based indexing to fixed income.
- A higher weight for an issuer with a high market value of debt does not necessarily mean that the index is overweighting issuers with a high face value of debt. An issuer with a high amount of par value debt outstanding will only get a high weight if the market value is relatively close to par value, which implies that the issuer is not perceived to be very risky. It is therefore not clear why the market value-weighted index should become riskier. In addition, loading onto riskier issuers shouldn’t be a problem if this risk is rewarded by higher expected returns. Note that Davis et al. (2010) and Reinhart and Rogoff (2009) have argued that indebtedness doesn’t necessarily matter for default, nor for yields or returns, which suggests that the debt level is not associated with the riskiness of a bond.
- Goltz, F. EDHEC-Risk Institute. “Indices in Institutional Investment Management: results of a European survey 2010.”
- Outstanding debt changes over time and the information on changes is not always public. If an index includes callable bonds, for instance, the amount outstanding can change drastically over time (even when no bond matures), complicating the calculation of cap-weighted indices (Reilly et al. 1992).
- Sometimes, for Canadian dollar securities only, Fitch is replaced by DBRS in the rating selection.
- For instance, inclusion in an index could be based on the lowest rating (“most conservative”) of the three agencies, or the average of the ratings, or a median or “two out of three” rating. Index providers usually use a combination of methodologies.
- For the sake of simplicity and easy access to data we use duration in this article. However, Duration Time Spread (DTS) has been advocated to be a better and more robust measure of portfolio risk (Ben Dor et al. 2005).
- Goltz F., and C. Campani, EDHEC-Risk Institute, June 2011: “A Review of Corporate Bond Indices.”
- Siegel (2003) says the duration of an index is an “historical accident”. Duration is a measure of bonds’ risk exposure to interest rate changes, as beta is a stock’s risk exposure to market movements. Although the beta of the market is always 1, there is no “neutral” duration of the corporate bond market. Siegel (2003) concludes that the choice of duration is an active asset allocation decision that should not be left to the index.
- Goltz, F. EDHEC-Risk Institute “Indices in Institutional Investment Management: results of a European survey 2010.”
- The amount of debt outstanding is usually the main measure of liquidity. The iBoxx liquid indices are designed with investment-grade bonds representing “the most actively traded portion of the market”. All bonds must have a specific minimum amount outstanding in order to be eligible for the indices (Sovereigns €4bn, Sub-Sovereigns €2bn, corporates €750m, other bonds €1bn). A liquidity criterion specifies a minimum daily traded amount (€150m in nominal traded, for instance).
- Altman, E and H Rijken, 2004. “How rating agencies achieve rating stability.” Journal of Banking and Finance, vol 28, pp. 2679–714.
- Arnott, Robert, Hsu Jason, Li Feifei and Shepherd, Shane, 2010. “Valuation Indifferent Weighting for Bonds.” Journal of Portfolio Management, Volume 36 Number 3.
- Aunon-Nerin, D., D. Cossin, T. Hricko, and Z. Huang, 2002. “Exploring for the Determinants of Credit Risk in Credit Default Swap Transaction Data: Is Fixed Income Markets’ Information Sufficient to Evaluate Credit Risk?” Working Paper, HEC-University of Lausanne.
- Bao, Jack and Pan, Jun, Excess Volatility of Corporate Bonds, 2010. AFA 2009 San Francisco Meetings Paper; Charles A. Dice Center Working Paper No. 2010-20; Fisher College of Business Working Paper.
- Bao, Jack, Pan Jun, Jiang Wang, 2011. “The Illiquidity of Corporate Bonds.” Journal of Finance, volume 66, pp. 911-946, 2011.
- Ben Dor, A., L. Dynkin, P. Houweling, J. Hyman, E. Leeuwen, and O. Penninga. “DTS (Duration Times Spread): A New Measure of Spread Exposure in Credit Portfolios.” Lehman Brothers, June 2005
- Biais, B, F Declerck, J Dow, R Portes and E von Thadden, 2006. “European corporate bond markets: transparency, liquidity, efficiency.” Mimeograph, City of London, May.
- Blanco, R., Brennan, S., Marsh, I., 2005. “An Empirical Analysis of the Dynamic Relation between Investment-Grade Bonds and Credit Default Swaps.” Journal of Finance 60, pp.2255–2281.
- Boehmer, Ekkehart, and William L. Megginson, 1990. “Determinants of Secondary Market Prices for Developing Country Syndicated Loans.” Journal of Finance 45, pp. 1517-1540.
- Bühler, W., and M. Trapp, 2008. “Explaining the Bond-CDS Basis – The Role of Credit Risk and Liquidity.”
- Cai, N., and X. Jiang, 2008. “Corporate bond returns and volatility.” Financial Review 43:1–26.
- Campani, Carlos-Hector, Goltz, Felix, 2011. “A Review of Corporate Bond Indices: Construction Principles, Return Heterogeneity, and Fluctuations in Risk Exposures.”
- Collin-Dufresne, P., R. Goldstein, and S. Martin, 2001. “The determinants of credit spread changes.” Journal of Finance, 56, pp.2177-2207.
- Davis, Joseph H., Roger Aliaga-Díaz, Donald G. Bennyhoff, Andrew J. Patterson, and Yan Zilbering. 2010. “Deficits, the Fed, and rising interest rates: Implications and considerations for bond investors”. Valley Forge, Pa.
- DeMiguel, Victor, Garlappi, Lorenzo and Uppal, Raman, 1/N (June 22, 2006). EFA 2006 Zurich Meetings.
- Duffie, Darrell, Lasse H. Pedersen, and Kenneth J. Singleton, 2003. “Modeling Sovereign Yield Spreads: A Case Study of Russian Debt.” Journal of Finance 58, pp.119-159.
- Edwards, A. K., L. E. Harris, and M. S. Piwowar, 2007. “Corporate bond market transaction costs and transparency.” Journal of Finance 62, pp.1421–1451.
- Elton, E., M. Gruber, D. Agrawal, and C. Mann, 2001. “Explaining the rate spread on corporate bonds.” Journal of Finance 56, pp.247–277.
- Ferreira, M. A., and P. M. Gama. 2007. “Does sovereign debt rating news spill over to international stock markets?” Journal of Banking and Finance 31 (10), pp. 3162–82.
- Huang, J., and M. Huang, 2003. “How much of the Corporate-Treasury yield spread is due to credit risk?” Working paper, Stanford University .
- Hull, J., M. Predescu, and A. White, 2004. “The Relationship between Credit Default Swap Spreads, Bond Yields, and Credit Rating Announcements.” Journal of Banking and Finance 28, pp.2789–2811.
- Kamin, Steven, and Karsten von Kleist, 1999. “The Evolution and Determinants of Emerging Market Credit Spreads in the 1990s.” Working paper No. 68, Bank for International Settlements.
- Korn, O., and C. Koziol, 2006. “Bond portfolio optimization: A risk-return approach.” Journal of Fixed Income 15 (4):pp. 48–60.
- Lloyd, W. T., and B. K. Manium, 2004. “Portfolio strategies for outperforming a benchmark.” In Handbook of European fixed income securities, ed. F. Fabozzi. Hoboken, N. J.: John Wiley & Sons.
- Longstaff, F., S. Mithal, and E. Neis, 2005. “Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit-Default Swap Market.” Journal of Finance 60, pp. 2213- 2254.
- Longstaff, Francis A., Jun Pan, Lasse H. Pedersen, and Kenneth J. Singleton, 2011. “How Sovereign is Sovereign Credit Risk?” American Economic Journal: Macroeconomics, forthcoming.
- Meindl, P. J., and J. Primbs, 2006. “Corporate bond portfolio optimization with transaction costs.” Working paper, Stanford University.
- Nielsen Jens Dick, Peter Feldhutter, David Lando, 2011. “Corporate bond liquidity before and after the onset of the subprime crisis.” Journal of Financial Economics 103 (2012) pp.471–492
- Pan, Jun, and Kenneth J. Singleton, 2008. “Default and Recovery Implicit in the Term Structure of Sovereign CDS Spreads.” Journal of Finance 63, pp.2345-2384.
- Reilly, F., and D. J. Wright, 1996. “Bond market indices.” In Handbook of fixed income securities, ed. F. Fabozzi. New York: McGraw-Hill.
- Reinhart, C and K Rogoff, 2010. “This time is different.” Princeton University Press
- Remolona, Eli, Michela Scatigna, and Eliza Wu, 2008. “The Dynamic Pricing of Sovereign Risk in Emerging Markets: Fundamentals and Risk Aversion.” Journal of Fixed Income 17, pp.57-71.
- Remolona. Eli, Michela Scatigna, Eliza Wu, 2007. “Interpreting Sovereign Spreads.” BIS Quarterly Review, March 2007.
- Sangvinatsos, A., 2010. “Strategic allocation: The role of corporate bond indices?” Working paper, University of Southern California.
- Siegel, L. B., 2003. “Benchmarks and investment management.” The Research Foundation of the Association for Investment Management and Research, Charlottesville, Virginia.
- Siegel, L. B., F. J. Enderle, and B. Pope, 2003. “Broad-capitalization indexes of the U.S. equity market.” Journal of Investing 12 (1): pp. 11–22.
- Tang, Dragon Yongjun and Yan, Hong, Liquidity and Credit Default Swap Spreads, 4 September 2007. AFA 2007 Chicago Meetings Paper; EFA 2008 Athens Meetings Paper.