Maturity-Matched Bond Fund Performance

Abstract

Performance regressions lever expected benchmark returns linearly to the risk exposures of the fund. The interest rate (IR) risk premium, however, usually follows a decreasingly upward-sloping yield curve, characterizing the nonlinearity between expected return and IR risk exposure—for example, maturity or duration. If the exposures of the fund and the benchmark differ, this discrepancy causes alpha to deviate from the active bond selection performance it is supposed to measure. Performance ratings and investor flows are affected by this alpha deviation. Our simple remedy is to individually match funds and benchmarks using their durations. Beta and R² are candidates for alternative matchings.

Disclosure: The authors report no conflicts of interest.

Editor’s Note:

Submitted 10 July 2020

Accepted 9 December 2020 by Stephen J. Brown

This article was externally reviewed using our double-blind peer-review process. When the article was accepted for publication, the authors thanked the reviewers in their acknowledgments. Quan Wen and one anonymous reviewer were the reviewers for this article.

Acknowledgments

We thank Rainer Baule, Henk Berkman, Stephen Brown (the executive editor), Ilja Dergunov, Oliver Entrop, Iraj Fooladi, Raquel Gaspar, Daniel Giamouridis (co-editor), Alexander Hillert, Christian Koziol, David Maslar, Steffen Mayer, Fabio Moneta, Sebastian Müller, Andreas Neuhierl, Nial O’Sullivan, Andreas Rathgeber, Heidi Raubenheimer, CFA, Ryan Riordan, Hendrik Scholz, Jules van Binsbergen, Stijn van Nieuwerburgh, Andreas Walter, Florian Weigert, David Yermack, and the participants at the 2017 European Retail Investment Conference in Stuttgart, the 2017 Meeting of the German Association of Business Research at the University of St. Gallen, the 2017 FMA European Conference at ISEG Lisbon, the 2017 World Finance Conference at the University of Cagliari, the 2017 Meeting of the German Finance Association at the University of Ulm, and the 2019 FMA International Annual Meeting in New Orleans for very helpful comments and suggestions. We are responsible for all remaining errors.

Notes

¹ Sharpe (1992) defined the style benchmark return as the sum of beta-weighted factor returns. Daniel, Grinblatt, Titman, and Wermers (1997) used the term average style return. Other popular terms, such as smart beta (e.g., Kahn and Lemmon 2016) and factor investing (e.g., Clarke, de Silva, and Thorley 2016), describe the same kind of investment decision. In the context of corporate bond funds specifically, Choi and Kronlund (2018) showed that many funds reach for yield by choosing high long-term exposures to interest rate risk and default risk.

² A wide range of studies have found that mutual funds in general and bond funds in particular show no relevant market-timing performance (e.g., Treynor and Mazuy 1966; Henriksson and Merton 1981; Chen, Ferson, and Peters 2010). Bunnenberg, Rohleder, Scholz, and Wilkens (2019) showed that constant-beta models, such as Jensen’s (1968) alpha, capture the aggregate of selection and timing as total active performance (approximately). Therefore, we concentrate on alpha and trust that it captures total active performance, including timing.

³ Another popular approach is to use a zero-investment factor to capture IR risk exposure constructed as the return difference between a long-term and a short-term Treasury bond index (e.g., Fama and French 1993). However, in unreported tests, we found that such a factor amplifies the problem discussed in our article rather than solving it. See Table A1 in Appendix A for an overview of the bond fund performance measures applied in the most influential bond fund research papers of the past 30 years.

⁴ ${\text{ε}}_{i,t}$ is an error term with E(${\epsilon }_{i,t}$) = 0.

⁵ We obtained the index data for January 1990 to December 2014 from www.theice.com/market-data/indices.

⁶ Table A2 in Appendix A shows the details of the various expected excess returns and linear regression parameters (alpha, beta), as well as mean durations, of the 10 US Treasury total return indexes.

⁷ This finding corresponds to durations (maturity ranges) shorter than that of the broad index; see Table A2 in Appendix A.

⁸ Panel A of Figure A1 in Appendix A shows a similar exercise using the shortest-maturity-range index as the benchmark. All betas are less than 1, all alphas are negative, and average alpha is –0.7086% p.a. Likewise, in Panel B, with the longest-maturity-range index as the benchmark, all betas are greater than 1, all alphas are positive, and average alpha is 0.7739% p.a.

⁹ We used duration instead of maturity for the matching because it is the better measure of IR risk exposure (Macaulay 1938).

¹⁰ In unreported tests, we instead used returns gross of expenses. The results were similar.

¹¹ According to Cici, Gibson, and Merrick (2011), corporate bond funds in particular may have substantial discretion in the valuation of their holdings, which could lead to autocorrelation due to smoothed returns. Details on the unsmoothing procedure are available upon request.

¹² In unreported robustness checks, we alternatively used the added value proposed as a performance measure by Berk and van Binsbergen (2015), which scales gross alpha by TNA. The results are economically in line with our main results.

¹³ In unreported robustness checks, we extended the baseline model in Equation 2$e{r}_{i,t}= {\alpha }_i^{}+ {\beta }_{i,Treasury}^{} e{r}_{Treasury,t}^{} + {\beta }_{i,Def}^{}{\text{Def}}_t+ {\beta }_{i, Option}^{} {\text{Option}}_t+ {\beta }_{i,mkt}^{} e{r}_{mkt,t}+ {\epsilon }_{i,t},$ (2) with several additional bond risk factors. Many are freely available from the authors listed in this note but cover only (in some cases, very short) subperiods of our sample period. We used several alternative liquidity or illiquidity factors provided by Dick-Nielsen, Feldhütter, and Lando (2012); Schestag, Schuster, and Uhrig-Homburg (2016); and Bai, Bali, and Wen (2019). We used bond momentum and reversal factors from Jostova, Nikolova, Philipov, and Stahel (2013) and Bai et al. (2019). We used macro factors from Ludvigson and Ng (2009). We used two self-constructed factors capturing corporate issuer size (bond SMB) and constraints (constrained minus unconstrained, or CMU) based on ICE indexes. Using various combinations of these factors renders our main findings and conclusions economically and quantitatively unchanged.

¹⁴ For example, D_1,10,i,t indicates that fund i is in Decile 1 according to broad alpha and in Decile 10 according to MM alpha in montht.

¹⁵ We considered funds to be institutional if more than 50% of their TNA are invested in their institutional share classes. The high-yield denomination is based on the Morningstar Broad Category Groups.