Measuring Bond Mutual Fund Performance with Portfolio Characteristics

Transcription

1 Measuring Bond Mutual Fund Performance with Portfolio Characteristics FABIO MONETA This draft: March 2012 ABSTRACT This paper studies the performance of U.S. taxable bond mutual funds using measures constructed from a novel data set of portfolio weights. Active fund managers exhibit outperformance before costs and fees generating, on average, gross returns of 1% per annum over the benchmark portfolio constructed using past holdings (approximately the same magnitude as expenses and transaction costs combined). This suggests that fund managers are able to earn back their fees and costs. There is evidence of neutral ability to time different portfolio allocations (sector, credit quality, and portfolio maturity allocations) and only a subgroup of bond funds exhibit successful timing ability. One performance measure based on portfolio holdings predicts future fund performance and provides information not contained in the standard measures. These results provide the first evidence of the value of active management in bond mutual funds. JEL # G11, G23 Keywords: Bond mutual funds, Performance evaluation, Portfolio holdings Queen s University, Queen s School of Business, 143 Union Street, Kingston, Ontario, Canada, K7L 3N6. fmoneta@business.queensu.ca. This paper is based on my dissertation at Boston College. I am very grateful to my advisors Pierluigi Balduzzi and Wayne Ferson, and my committee members David Chapman and Alan Marcus for their support and helpful comments. I am also grateful to Ludwig Chincarini, Ian Cooper, Roger Edelen, Richard Evans, Jeff Pontiff, Selim Topaloglu, and seminar participants at Boston College, HEC Montréal, Erasmus University, Federal Reserve Board, Queen s University, Norwegian School of Management BI, Bocconi University, Swiss Finance Institute, 7th Trans-Atlantic Doctoral Conference at London Business School, the 2008 EFA and FMA Annual Meetings, and the 2009 NFA Annual Meetings for their valuable comments and suggestions.

2 Measuring Bond Mutual Fund Performance with Portfolio Characteristics This draft: March 2012 ABSTRACT This paper studies the performance of U.S. taxable bond mutual funds using measures constructed from a novel data set of portfolio weights. Active fund managers exhibit outperformance before costs and fees generating, on average, gross returns of 1% per annum over the benchmark portfolio constructed using past holdings (approximately the same magnitude as expenses and transaction costs combined). This suggests that fund managers are able to earn back their fees and costs. There is evidence of neutral ability to time different portfolio allocations (sector, credit quality, and portfolio maturity allocations) and only a subgroup of bond funds exhibit successful timing ability. One performance measure based on portfolio holdings predicts future fund performance and provides information not contained in the standard measures. These results provide the first evidence of the value of active management in bond mutual funds. JEL # G11, G23 Keywords: Bond mutual funds, Performance evaluation, Portfolio holdings

3 I. Introduction An important and recurrent debate in the mutual fund literature is about the value of active investment. The recent literature has documented that while examining mutual fund net returns there is no evidence of investment ability, using portfolio holdings information reveals the presence of investment skills among equity fund managers (see, inter alia, Grinblatt and Titman 1993, Daniel et al. 1997, Wermers 2000, Chen et al. 2000, Kacperczyk et al. 2005, and Jiang et al. 2007). Although this debate is at an early stage for bond mutual funds, the evidence to date does not support active management. It is conceivable to have a different result for bond fund managers when the differences between the equity and fixedincome markets are considered. For instance, fixed-income markets are considered to be populated by more sophisticated investors than the equity market. This paper contributes to the existing literature by using a large sample of mutual funds and holdings information to study bond fund performance, hence uncovering the first evidence of the value of active investing in the bond market. One challenge in assessing the performance of a managed portfolio is deciding how to deal with the dynamics created by the portfolio weights changes and the potential time-variation in returns and portfolio characteristics. This is likely to be particularly relevant for bond portfolios, because characteristics such as duration and credit quality change over time. Moreover, there is evidence of significant active trading at the security and portfolio level. To date, most studies of bond fund performance have used a returns-based approach. Although this has some benefits, due to its minimal information requirement, it has its limitations. Indeed, early studies such as Jensen (1972) and Grinblatt and Titman (1989) show that the traditional Jensen measure is biased for a market-timing investment strategy and can assign negative performance to a market timer. 1 Ferson and Schadt (1996) show that inferences about managerial performance can change significantly after adjusting for time-variation in risk loadings. However, when information about portfolio weights is available, the literature indicates that it is possible to infer abnormal performance in a more robust and powerful manner. 2 1 Roll (1978) demonstrates that, if the benchmark is inefficient, it is always possible to find another inefficient benchmark that switches the performance ranking based on Jensen alpha. Dybvig and Ross (1985) show that a manager with superior information can appear to observers to have inferior performance using the security market line except when the superior information is only security specific. 2 Comer (2006) shows, by simulations, that using holdings information gives greater power to detect a fund managers 1

4 Following Daniel et al. (1997), mutual fund returns and costs are decomposed in the Characteristic Timing (CT) measure, in a benchmark portfolio return called Average Style (AS), and in a residual component called Return Gap (RG), following Kacperczyk et al. (2008). This study, however, uses asset class weights (the proportions of the portfolio invested in different sectors, credit quality, and maturity), rather than information about the individual securities that compose the portfolio. This choice is determined by data availability, and further motivated by the fact that the fixed-income market is a natural setting to use aggregate weights. 3 CT captures timing ability in rotating a portfolio across different asset classes, while RG includes a selectivity component, i.e., the ability of the manager to select securities that deliver better returns than the securities in the benchmark indices. Non-linearities and options components are common in the securities held by bond funds. As pointed out by Chen et al. (2010), this creates another challenge when evaluating the performance of a fixedincome managed portfolio. However, the approach adopted in this paper appears particularly attractive in this context for two reasons. First, because the CT measure does not use net fund returns, it avoids the bias that option-like features in the underlying assets can induce in returns-based measures, as emphasized by Jagannathan and Korajczyk (1986). Second, since the bond indices used in this paper to construct the benchmarks include bonds with optionality (e.g., callable bonds), the benchmarks should capture the behavior of returns of bonds with option components. 4 Using a sample of almost 1000 funds for the period , this paper provides evidence that bond funds engage in active strategies. Active bond fund managers trade frequently and considerably more than managers of index funds. Whereas the traditional alpha is significantly negative, the net RG measure (after expenses and transaction costs) is close to zero and becomes positive (although not statistically significant) for some subgroups of funds such as high yield, corporate bond general, ability for government bond funds. Kothari and Warner (2001) show a similar finding for equity funds. 3 In contrast to equities, it is not feasible to find returns data for all the bonds in the portfolio. Indeed, the universe of fixed-income securities is broader than that of equity securities and the data are less available. When these data are available, there are concerns about their accuracy (see, for example, Cici et al. 2011). Moreover, unlike equities, which are difficult to group into meaningful categories, bonds have closely specified characteristics (that also have a risk interpretation) and cash flows that make them easy to classify. Bond portfolio s returns are also well explained by aggregate benchmark portfolios returns. 4 This is valid if mutual funds and the benchmarks have a similar composition of bonds with optionality. The robustness section includes an analysis that shows that the systematic risk of the two portfolios is similar and that the results are not affected by a difference in systematic risk. 2

5 and multi-sector funds. The gross RG measure indicates that, on average, active managers generate gross returns of 1% over the benchmarks constructed using past holdings. This is approximately of the same magnitude as expenses and transaction costs combined. This suggests that fund managers hold securities that beat their holdings-based benchmarks by almost enough to cover their expenses and transaction costs. Although the average mutual fund exhibits neutral timing ability (the CT measure is close to zero), multi-sector bond funds exhibit timing ability rebalancing portfolios across different credit ratings. This paper also provides support for the Berk and Green (2004) model in the bond market. Indeed, the performance measures only exhibit short-term persistence and there is evidence of both diseconomies of scale and of a negative impact of past flows on performance. Moreover, the relation between expenses and RG is positive and statistically significant before fees, and insignificant after fees. This provides further evidence that bond fund managers are able to earn back their fees. Consistent with the interpretation of RG as being related to selectivity ability, RG is positively associated with Morningstar ratings and alphas. Finally, this study shows that RG helps to predict future mutual fund performance. Bond funds with a favorable past RG deliver an annualized 2.3% return more than funds with a poor past RG. This is greater than what could be obtained by selecting funds using past alphas. RG also contains information about future fund returns that is not contained in alpha, while alpha contains little or no additional information beyond RG, as shown by double sorts (sorting first on alpha, then on RG, and vice versa). These findings provide further evidence that RG reveals the presence of skill and is a helpful tool for investors to choose mutual funds in the context of the bond market for which it has been difficult to detect any investment ability. II. Related Literature on Bond Mutual Funds Few studies have examined the performance of bond mutual funds. As noted by Ferson et al. (2006), Recent years have witnessed an explosion of research on the performance of mutual funds, with most of the attention focused on equity-style funds. The amount of work on fixed-income funds is small in 3

6 relation to their importance in the economy. In one of the first and most cited studies on bond fund performance, Blake et al. (1993) concluded that the lack of available bond index funds for individual investors, coupled with the high transaction costs that accompany small purchases, might account for the past appeal of actively managed bond funds, despite substantial underperformance. However, more than a decade later, the opportunities for retail investors have improved substantially. Currently, there are more than 30 bond index funds and several bond Exchange-Traded Funds (ETF) to choose from. Furthermore, transaction costs are much lower now and investors can choose from low-cost strategies such as buying newly issued government bonds directly from the Treasury. 5 Nevertheless, the most costly active bond funds experienced intense growth during the last two decades. 6 It looks like, to paraphrase Gruber (1996), we have yet another puzzle in the growth of active bond funds. This puzzle remains unsolved, since more recent studies on bond fund performance such as Ferson et al. (2006), Chen et al. (2010), and Cici and Gibson (2011) did not find evidence of superior performance looking at selectivity and market timing ability. 7 This debate is important to justify the high expenses that active funds charge. For example, the difference between the expense ratio of the average active bond fund and of the largest bond index fund (Vanguard Total Bond Index fund) is roughly 60 basis points, which amounts to more than $8 billion per year, considering that active bond funds manage approximately $1.4 trillion in assets. Only two recent studies use holdings to study bond mutual fund performance. However, they focus on a specific type of bond mutual funds and they find poor bond-selection ability and little evidence of timing ability. In particular, Cici and Gibson (2011) use holdings of corporate bonds to study their performance in portfolios of corporate bond mutual funds. They find no evidence of investment ability, in particular bond-selection, and they conclude that the costs of active management on average appear 5 See, for instance, Jonathan Clemens, Yield Chase: Boost Income by Slashing Investment Costs, Wall Street Journal, February 14, At the end of 2006, active bond mutual funds had $1.4 trillion of assets under management compared with $243.1 billion at the end of 1988 (source Investment Company Institute). 7 Cornell and Green (1991) examine the performance of low-grade bond funds documenting that their risk-adjusted returns are similar to high-grade bond funds. Boney et al. (2009) examine timing ability in a sample of 84 high quality corporate bond funds. They find evidence of perverse (negative) market timing ability. Huij and Derwall (2008) find some evidence of performance persistence in funds alphas in a large sample of bond funds (without, however, aggregating the share classes of the same fund) from 1990 to

7 larger than the benefits. 8 Huang and Wang (2008) use the measure of Jiang et al. (2007) and holdings of Treasury securities to examine the market timing ability of a sample of 146 government bond funds. They provide evidence of some positive timing ability but only at the one-month forecasting horizon. This paper makes a number of contributions to this existing literature. First, this is the first paper that uses portfolio weights for many asset allocations and for a large sample of bond funds that include seven different investment objectives. It is important to take a broader perspective, because many bonds funds often change their investment style. Bond funds also tend to invest a significant part of their portfolio in the fixed-income space, but outside the asset class of their investment objective. Second, this paper provides a comprehensive analysis of timing ability intended as skill in rotating the portfolio across different dimensions of the portfolio (sectors, credit quality, and maturity). Third, this paper revisits the evidence about security selection ability using a new dataset and it provides positive evidence. The finding about RG is not simply an extension to bond funds of what has been documented for equity funds in Kacperczyk et al. (2008). Since aggregate weights are used, the RG measure used in this paper includes a selectivity component (absent in the original measure) which drives the results. Finally, RG helps to predict future mutual fund performance and contains a more precise signal than past alphas. This result further supports the interpretation of RG as related to skill. Therefore, this is the first paper to provide evidence about the value of active investing for the fixed-income market and also to reveal a helpful tool for investors to select bond funds. As pointed out by Cici and Gibson (2011), it might be more difficult to generate abnormal returns in the fixed-income market than in the equity market because of the small percentage of uninformed traders. This paper shows that the abnormal performance is higher in the high yield debt market. This is consistent with the idea that more valuation inefficiencies are present in this sector which can compensate for the lack of a large number of uninformed traders. 8 The authors obtain only 4% of their bond price information from Trade Reporting and Compliance Engine (TRACE). Before TRACE, it is a challenge to find reliable pricing information, especially of the less liquid bonds. Moreover, they only focus on corporate bond holdings, missing all the other holdings. As shown in Table 2 of Appendix C, corporate bond general and high-quality funds only invest, on average, almost 45% of their portfolios in corporate bonds. 5

8 III. A Mutual Fund Return Decomposition A portfolio invested in the most recently disclosed portfolio holdings can be considered a proxy for the gross return of the fund. Using this idea and following Daniel et al. (1997), an attribution analysis of bond fund performance can be computed. In particular, fund returns plus expenses and transaction costs can be decomposed into three components: the Characteristic Timing (CT) measure, the Average Style (AS) measure, and a residual component called Return Gap (RG). The CT measure captures timing ability, defined as the ability to increase (decrease) the portfolio investment on the asset class which is more likely to perform better (worse) in the near future. 9 This measure has strong theoretical foundations, because it is an application of the Grinblatt and Titman (1993) s measure to aggregate portfolio weights. 10 The AS measure was introduced by Daniel et al. (1997) for equity funds. In the fixed-income context, it captures the before cost returns earned by a fund due to that fund s tendency to hold fixed-income securities with certain characteristics. The decomposition is therefore: Rp i t + EXP i t + T Ci t = N wj,t 1R i j,t b + RG i t = j=1 N j=1 ( w i j,t 1 w j,t 1 k i ) R b j,t + N w j,t 1 k i Rb j,t + RG i t = CT i t + AS i t + RG i t (1) j=1 where Rp i t is the month t return of fund i,exp i t is an estimate of the monthly expenses (the annual expense ratio divided by 12), and T Ct i is an estimate of the monthly transaction costs, Rj,t b is the month t return of the benchmark bond index for sector (credit quality or maturity allocation) j, w i j,t 1 is the weight of fund i in sector j disclosed at the end of month t 1, and w j,t 1 k i is the buy-and-hold weight of fund i in sector j disclosed at the end of the previous k period. 11 Transaction costs are approximate, following Chen et al. (2010), using the reported average turnover multiplied by a round-trip transaction 9 Daniel et al. (1997) use security weights for CT. This is equivalent to using aggregate weights since the sum of the security weights for the same benchmark is equal to the aggregate weight corresponding to the benchmark. 10 Grinblatt and Titman (1993) propose a performance measure, based on portfolio weights, that does not require the use of an explicit asset pricing model and can detect superior performance even in the presence of a market-timing investment strategy. For a detailed analysis of the different portfolio holding measures see Wermers (2006). 11 Ferson and Khang (2002) is followed when considering buy-and-hold weights (using unadjusted weights deliver similar results). These weights for each sector j are calculated updating the disclosed weights w i j,t 1 k and taking into account the relative performance of the sector from t 1 k to t 1: w j,t 1 k i w i k j,t 1 k τ=1 (1 + Rj,t τ ) = ( N ) j=1 wj,t 1 k i k τ=1 (1 + Rj,t τ ) 6

9 cost specific to a given investment objective. 12 RG was proposed by Kacperczyk et al. (2008) for equity funds. RG is expected to be negatively related to hidden costs and positively related to hidden benefits of a mutual fund. The hidden costs include agency costs and negative investor externalities. 13 Hidden benefits (or costs) may derive from the unobserved interim trades between the last disclosure date and the month t. However, as discussed in Appendix A, in this study, RG also includes a selectivity component (absent in the original measure), since I am using asset class weights and returns instead of the weights of the securities in the portfolios. Therefore, a fund manager who selects securities which perform better than the securities in the index will lead to a positive RG. To test whether there is evidence of ability in rebalancing the porfolio across multiple dimensions, CT is calculated for different asset class breakdowns(see next section). I can then aggregate the CT measure across mutual funds and test whether the average is significantly different from zero. This test can be run for all funds or subgroups of funds to examine whether some specific subgroups exhibit positive timing ability. One natural advantage of a weights-based measure such as CT is that returns with different horizons can be used rather than just a specific holding-period return. In this way the horizon of the timing ability can be examined. IV. Data Data on bond mutual funds are drawn from more than 110 Morningstar Principia CD-ROMs from the beginning of 1997 to the end of The CDs provide different asset allocation breakdowns of the fund s portfolio holdings. Appendix C provides details about these data. Three portfolio allocations are examined: the allocation across different sectors of the fixed-income market (US government bonds, mortgage, credit, foreign bonds, and cash), different credit qualities, and different maturity ranges. One weakness of the data is that for many funds there is an irregular distribution of the portfolio 12 The round-trip transaction costs are taken from Chen et al. (2010): 75 basis points for high yield funds, 48 basis points for corporate general funds, 12.5 basis points for government-general and high quality funds, 20 basis points for mortgage funds, and 34 basis points for multi-sector funds. These costs are divided by 12 to obtain monthly figures. Other costs, such as load fees and taxes, which are not borne by all the investors are ignored. 13 As explained by Kacperczyk et al. (2008) these hidden costs include window dressing (Lakonishok et al. 1991), changes in risk taking behavior due to past performance (see Brown et al and Chevalier and Ellison 1997), and price impact among others. 7

10 weights observations. These data issues can cause a loss of power and work against finding evidence of investment ability. However, Comer (2006) shows, using simulations, that a performance measure based only on annual portfolio weights is more powerful than standard performance measures. Considering that the holdings used in this paper are more frequent than annual weights and that some significant results are found, these concerns should be mitigated. 14 These CDs also include information about fund returns, total net assets (TNA), turnover, fees, and several fund characteristics. Since past CDs are used, data on both dead and surviving funds are included. Only taxable U.S. bond mutual funds, as classified by Morningstar, are considered in this study. Index funds and bond ETFs are used as benchmarks. Similar to Chen et al. (2010), funds with less than $5 million in TNA are excluded. 15 Funds that do not have, in any portfolio allocation breakdown, at least 12 weight change observations (weights of the current portfolio minus weights of the past portfolio where k in equation 1 is less than or equal to 12 months) are also excluded. These filters can cause a survivorship bias. However, as documented by Blake et al. (1993), this bias is smaller for bond funds than equity funds. 16 Moreover, the survivorship bias should not affect the comparison between traditional returns-based performance measures and weights-based measures. Summary statistics of bond mutual funds for different investment styles for the period are presented in Table I. A sample of almost 1000 bond mutual funds is considered. The most important category, with respect to the number of funds and TNA, is general corporate bond funds followed by high quality and general government bond funds. Often, funds report different share classes which have the same holdings composition but different types of fees and loads (see Nanda et al. 2009). Since the holdings composition is the same for each share class, all the observations of the different share classes are aggregated into one figure. 17 The average expense ratio is 0.8%, slightly lower than that of 14 The robustness tests section addresses some further issues about whether the uneven reporting frequency of the funds affects the main results. 15 These are small funds, which are more likely to be subject to the incubation bias documented by Evans (2010). 16 This also applies to this sample. The difference between the return of an equally-weighted portfolio of all available funds and the return of only surviving funds is 0.16% per year. This is smaller than the survivorship bias found for equities (e.g., in Grinblatt and Titman, 1989, it is about 0.5% per year)). 17 TNA under management are summed across different share classes. For other quantitative attributes, I take the weighted averages of the values of the individual share classes with weights proportional to the lagged TNA of the individual share classes. 8

11 equity funds. The last two columns indicate the average yearly net return and the standard deviation. As a benchmark, the characteristics and returns of a portfolio of bond index funds and ETFs, which operated during the period, are reported. The Vanguard Total Bond Index fund is presented separately from the other index funds since it is the largest bond index fund and one of the largest bond funds. To calculate the performance measures, each asset class weight must be matched with a particular bond index (see Appendix D for more details). Merrill Lynch (ML), now Bank of America, provides an extensive number of broad and specialized bond market indices which cover all the asset classes considered by Morningstar. 18 V. Are Bond Mutual Funds Active? A priori it is unclear whether bond mutual fund managers make active investment decisions or whether their trading activity is mostly due to changes in the indexes that managers follow or passive changes in their underlying bond portfolios. To investigate this issue, both trading at the security and at the asset allocation levels are examined. The data show that bond fund managers actively trade and change their portfolio allocations. This evidence provides an additional motivation for using a dynamic benchmark based on portfolio weights information. Considering the security-level trading, Table II presents a measure of the fund s trading activity, the average security turnover rate, for different investment objectives. 19 Active bond fund managers trade frequently as high as 218% and higher than equity funds. Part of this trading is due to the fact that many bonds change characteristics such as maturity and credit quality or they simply mature (securities with maturities of less than one year are, however, excluded in the calculation). Indeed, the turnover rate for a passive bond index fund, such as the Vanguard Total Bond index is 85.6%. This is much higher than an equity passive fund such as the Vanguard 500 index (5% turnover), but still much lower 18 Another important provider is Lehman Brothers (now Barclays Capital). ML indices are used because they provide more daily data available since the beginning of These index returns are however highly correlated with the corresponding Lehman indices. The portfolios are indeed composed in a similar way. 19 Turnover rate is computed by Morningstar by taking the lesser of purchases or sales (excluding all securities with maturities of less than one year) and dividing this by the average monthly net assets. 9

12 than the bond active funds. Considering the asset allocation level, Appendix C presents some statistics for different bond style funds. Bond funds invest a significant part of the portfolio outside the main investment objective. For instance, Government bond-general funds invest, on average, 36% of their portfolios in mortgage securities and 10% in corporate bonds. Similarly, corporate bond-general funds invest more than 18% of their portfolios in Government securities and more than 21% in mortgage securities. The average standard deviation can be relatively high. To better understand whether this variability is due to active investing decisions and not to passive changes in the underlying bond portfolio, similar to Ferson and Khang (2002), I compute a measure of Active Portfolio Allocation Turnover (APAT). This is the average of the sum of the absolute difference of the weights divided by two. For fund i, it is the time-series average of: where w i j,t 12 AP AT i t = 1 N ( w i 2 j,t w j,t 12 i ) (2) j=1 is the past 12 months portfolio weight in sector j updated with a buy-and-hold strategy. This measure captures the departure of the portfolio s actual weights from the buy-and-hold weights. On average, almost 15% of the sector portfolio allocation is changed in a year (Table II). These variations are not explained by a differential in asset classes performance (captured by the buy-and-hold weights) and may instead suggest active investment decisions. Table II also presents the APAT for the Vanguard Total Bond Index fund. The active turnover figures suggest that, although a bond index fund is considered a passive fund, it exhibits significant portfolio changes. Nevertheless, using a Wilcoxon signed rank test, the median fund presents an average portfolio allocation turnover significantly higher than that of the index fund in all three allocations. 20 These findings suggest that bond mutual funds are actively trading and changing the portfolio weights significantly more than passive index funds. This trading activity can change the exposure of the portfolio and make the task of evaluating manager s performance more challenging. In particular, a traditional returns-based approach (unconditional Jensen alpha that assumes that the exposure to 20 This turnover can also cause a drift in a fund s style and risk (see Chan et al and Huang et al. 2011, for evidence on equity mutual funds). I found that 76% of bond funds change style and 39% change investment category (as defined by Morningstar) at least once over the life of the funds. 10

13 systematic risks is constant) is likely to be inaccurate. VI. Return Decomposition: CT and RG For the attribution analysis, it is important to construct a benchmark portfolio that delivers the best possible proxy of the gross return of the fund. If only the sector analysis is used, two funds, with the same sector allocation but different maturity and credit quality exposures, are assigned the same benchmark portfolio. The government, mortgage, and corporate ML indices that match the corresponding sectors have their own credit ratings and average maturities. The ratings and maturities of the fund may be different. As explained in Appendix B, I adjust the sector allocation for the credit quality and maturity differences between the fund and the government, corporate, and mortgage ML indices. Table III presents the return decomposition results for an equally weighted and a value-weighted portfolio of funds. To maximize the number of observations, the most recent past weights up to one year in the past (k 12) are used. The number of funds with at least 12 weight observations is 683. To ensure that there are no missing values in the time series, up to a 12-month horizon is used. The average CT is positive but very close to zero. RG is instead significantly positive. On average, considering both an equally and value weighted portfolio of funds, active managers generate gross returns of 1% over the benchmark portfolio constructed using past holdings. There are also some cross-sectional variations with high RG concentrated among corporate funds. In particular, corporate high yield funds generate gross returns of 2% over the benchmark. To the extent that in the high yield sector more valuation inefficiencies and opportunities are present, one could expect managers to exploit them. Table III also present RG after subtracting expenses and transaction costs (net RG). This measure is the difference between the fund returns and the gross returns from the portfolio-weights benchmarks. The traditional Jensen s alpha can also be interpreted as the difference between the fund returns and the gross returns from a benchmark portfolio. Following Blake et al. (1993), the alphas are obtained from a regression of bond portfolio excess returns on the excess returns of six indices (Treasury, mortgage, investment grade corporate, high yield corporate, foreign bond and S&P500). 21 The net RG measures 21 For Treasury funds, three Treasury indices with different maturity ranges (1-3 year, 5-7 year, and more than 10 years) 11

14 are higher (closer to zero) than the negative and statistically significant alphas. This finding is more evident when considering subgroups of funds such as corporate high yield, corporate bond general, and multi-sector funds for which the net RG is positive (although not statistically significant). On average, bond funds deliver net returns approximately equal to the gross returns of their holdingsbased benchmarks. This suggests that mutual fund managers hold securities that outperform their benchmarks by almost enough to cover their expenses and transaction costs (on average around 1.3% per year, considering 0.8% of expenses and 0.5% of transaction costs). 22 These findings are consistent with the equilibrium models of Grossman and Stiglitz (1980) and Berk and Green (2004). However, they are different than what has been found in previous literature using a returns-based approach. The weights-based benchmarks used in RG should be able to capture variations in risk exposure. An alternative way is to follow Ferson and Schadt (1996) and estimate a conditional regression with time-varying betas. 23 The conditional alphas are in general lower than the unconditional ones (see Table III). The only exception is for high yield funds where the alphas are higher in the conditional model (similar to the evidence for equity funds), but are still significantly negative. It is also important to examine different asset class decompositions. They indeed correspond to different skill sets for a bond mutual fund manager. Also, some mutual funds may constrain their investment policy. For example, a Treasury bond fund may be prohibited from investing in high yield bonds. When the credit quality allocation is considered, it makes sense to separately examine subgroups of funds that are allowed to invest in different credit qualities. Table IV (Panel A) presents CT for the credit quality for different horizons (one, six, and 12 months) for three types of corporate bond funds and for multi-sector funds. Generally, the average mutual fund exhibits a weakly positive timing ability across different credit quality allocations. Significant and positive CT measure is obtained by the multi-sector bond funds, although it tends to weaken with a longer horizon. Table IV (Panel B) are considered. Since high yield funds generally do not invest in Treasury and mortgage securities, the corresponding indices are excluded from the regression for high yield funds. 22 The only exception is for Government bond general funds where the net return gap is negative and statistically significant consistent with the results from the returns-based approach and some previous research (e.g., Ferson et al. 2006). 23 Chen et al. (2010) is followed for the choice of instrumental variables. 12

15 presents the results considering the maturity range allocation. 24 Since there are no clear restrictions on the maturity of the portfolio coming from the investment objectives, the results for all the investment objectives are presented. The timing ability is close to zero. In summary, the RG provides evidence of managerial ability mostly related to selectivity (see next section for results that corroborate this point). The evidence about timing ability is weak and limited to multi-sector funds. However, it is comforting to see that there is no evidence of poor (negative) timing ability as found in some studies that only use returns information (e.g., Boney et al., 2009). 25 From an investor s perspective, the holdings-based performance measures are relevant if they present some persistence and if they are useful to select bond funds. VII. Performance Persistence and Panel Data Analyses To test whether there is evidence of persistence in the CT and RG, funds used in Table III are sorted into quintiles according to their averaged lagged CT and RG. Next, the average CT and RG during subsequent periods are computed by weighting funds in each quintile equally. Table V presents these results using two ranking periods (the previous year and the previous two years) and three different holding periods (one-month, one-quarter, and one-year). The performance persistence is short-lived. Indeed, the difference between the fifth and first quintile portfolio is of the order of 64 basis points per year and statistically significant considering one-quarter holding period (Panel B). For the RG measure, the magnitude of the spread portfolio is larger, of the order of 1.6 and 1.3% per annum considering respectively one-month and one-quarter holding periods. This evidence is weaker for both the CT and RG measures when considering a one-year holding period. To better understand the findings of a lack of long-term persistence and to investigate whether some fund s characteristics are associated with the performance measures, a panel data analysis is performed. I only focus on RG since there is little evidence of timing ability. RG, RG after transaction costs, and net RG (the measure after both transaction costs and expenses) are regressed on the following fund 24 As explained in Appendix D, the benchmark ML indices for the maturity ranges change according to the fund s investment objective. 25 As pointed out by Becker et al. (1999, p. 134), negative timing makes no economic sense. If funds could really time the market but got the direction wrong, astute investors could profit by taking opposite positions. 13

16 characteristics: the log of TNA, the percentage of cash in the portfolio, the duration and the average credit quality of the portfolio, the turnover rate, the average APAT, the log of the age of the fund (expressed in years), the yield of the fund s distributions, the expense ratio, the Morningstar rating, the past alpha calculated by Morningstar, the net flows, and the previous year s volatility of flows. Net flows for fund i are calculated, following Chevalier and Ellison (1997), using the TNA difference between two consecutive months (or quarters) adjusted for the return of the fund divided by the TNA of the first period. 26 : Table VI shows the results using two different specifications. The first specification is with both fund-fixed effects and time dummies. This specification is best suited to capture time-series effects of variables that have significant time-series variations (e.g., TNA and flows). The second specification includes only time-fixed effects. In this case I focus on the explanatory power of the cross-section which is suitable for variables that have little time-series variation and large cross-sectional variations (e.g., expenses). Considering the first specification (Panel A), RG is negatively associated with the size of the fund. Smaller funds tend to exhibit higher RG. This suggests some diseconomies of scale also documented by Chen et al. (2004) for equity funds. 27 This result is also consistent with Berk and Green s (2004) model and sheds light on the lack of persistence in the RG measure. 28 One could expect that the effect of size could be particularly important for high yield funds considering the lack of liquidity in the low-rating corporate bond market. Indeed, when the TNA interacts with a dummy for high yield funds this interaction term is negative and statistically significant. I also find that funds which experienced large flows (especially lagged one quarter) and past volatility of flows tend to exhibit smaller RG. This result mirrors what has been found in the equity literature (Ferson and Warther 1996 and Edelen 1999) and it may contribute to the lack of persistence in RG. There is also a significant positive relationship between turnover and RG. This finding is partly due 26 The flows data are Winsorized at the top and bottom 1% because these outliers are likely caused by mergers. The monthly TNA information is obtained by CRSP. 27 This finding is different from Gutierrez et al. (2009) who find a positive association between size and alpha. The RG measure, although it is positively associated with alpha, is not the same as alpha. Indeed, if I use alpha as a dependent variable I find a result consistent with Gutierrez et al. (2009). 28 For the Berk and Green (2004) model to work, we need investors to chase past performance. This has been shown for bond mutual funds by Zhao (2005). 14

17 to the presence of trading costs. Considering the RG measure after transaction costs, the relationship between turnover and RG is weaker although still positive and marginally significant. This could suggest that fund trades create sufficient value to cover the transaction costs. Next, funds that report high income yields in the form of distributions are associated with a lower RG. A similar finding was also documented by Chen et al. (2010). One explanation is that some bond funds invest in high yield bonds which may have higher default probability that can hurt the ex-post performance. Indeed, this effect seems to be present in high yield funds as suggested by the interaction of the distribution yield with the high yield dummy. Finally, consistent with the interpretation that RG captures selectivity ability, RG is positively associated with the Morningstar rating and past alpha. Considering the second specification with only time-fixed effects (Table VI Panel B), funds that have a portfolio with higher duration and lower credit quality have a higher RG. Expenses are positively associated with RG. The relationship with net RG is close to zero. This suggests that managers are able to earn back their fees and this contrasts with the findings of Blake et al. (1993) of a negative and close to one coefficient in the regression of alphas on expenses (a percentage-point increase in expenses leads to a percentage-point decrease in performance). Therefore, investors are not always better off investing in low-cost funds as concluded by Blake et al. (1993). Finally, mutual funds that are more active in changing their portfolio allocations, as measured by the average APAT, are associated with a better RG. VIII. Predicting Mutual Fund Returns Net RG provides more favorable evidence of performance (it is closer to zero) compared to standard performance tests. The relevance of this finding could be undermined if traditional tests help to predict future fund performance better than RG. To examine this question, at the end of each month bond funds are sorted into quintiles based on average past year and two-year performance measured using alpha, RG, and net RG. The alphas are the unconditional Jensen alphas of Table III calculated using a two-year window. Similar to RG, the alphas are calculated for each month of the past year and twoyear period and then they are averaged. The returns and risk-adjusted returns of an equally-weighted 15

18 portfolio of funds in each quintile are calculated during the subsequent month. The risk-adjusted returns are measured using an unconditional Jensen alpha. Table VII Panel A shows that funds with the most favorable alphas (fifth quintile) deliver an annualized 0.9% return and 1.3% risk-adjusted return more than funds with poor past return alphas (first quintile). However, if an investor uses the past RG as sorting criterion (Table VII Panel B) she would obtain a 2.3% return and a 1.9% risk-adjusted return. The average return of the 5-1 RG sorted portfolio is higher than the 5-1 alpha sorted portfolio with a p-value of (not shown in the table). These findings are similar when the portfolios are sorted based on the past two-year performance rather than the past one-year performance or when the net RD is used as sorting criterion (Panel C). 29 To examine whether RG contains information about fund returns that is not contained in alpha, funds are sorted into quintiles based on their alpha and then, within each quintile, funds are sorted based on RG (the gross measure). Twenty-five portfolios are constructed every month and for each portfolio, the next-month fund returns are calculated. Panel A of Table VIII reports the average returns for these 25 portfolios and for 5 portfolios that buy funds with high RG and short funds with low RG within a given alpha quintile. These 5-1 portfolios suggest that RG contains significant information about future fund returns above and beyond alpha. On average, these portfolios deliver almost a 2% return per annum which is statistically significant. I also perform the opposite exercise, sorting first on RG and then on alpha. Panel B shows that alpha contains little or no additional information beyond RG. Controlling for RG, the average spread between the top and bottom alpha quintiles is only 0.49%. 30 IX. Robustness Tests This section addresses several concerns about RG and CT. To conserve space, I mostly focus on RG and do not tabulate the analyses. Instead, they are described below. A first concern is window dressing. This is the practice of trading securities at the end of a disclosure 29 These findings are also similar if I try to predict the mutual fund returns three months from the sorting date. The first two months were skipped to consider a potential lag in obtaining the portfolio weights. By law mutual funds have up to 60 days to report holdings information to the SEC. Some mutual funds voluntarily disclose more information directly to Morningstar. 30 An untabulated analysis shows that these results are confirmed if risk-adjusted returns are calculated for the 5-1 portfolios instead of raw returns. 16

19 period for the purpose of providing an inaccurate representation of the holdings of the funds. For equity funds, this consists of selling poor performing stocks and buying recent winners (Lakonishok et al. 1991). For bond funds, Morey and O Neal (2006) find some evidence that corporate bond funds increase the holdings in government bonds and decrease the holdings in AAA bonds during disclosure periods. To test whether this can bias the RG results, two analyses are performed. Following Morey and O Neal (2006), daily CRSP mutual fund price returns are regressed on the excess returns of six indices (Treasury, mortgage, investment grade corporate, high yield corporate, foreign bond and S&P500) including dummy variables that interact with the betas. These dummy variables are equal to 1 for the 10 days surrounding the reporting periods. The SEC requires funds to disclose their holdings at their fiscal year-end and six months later (in 2004 this was changed to a quarterly disclosure). The dummy variable associated with the additional exposure to Treasury during reporting periods is tested to determine whether it is significant and positive. In a sample of 636 funds for which daily data from 2001 are available, only 32 funds have a T-statistic greater than 1.96 associated with the Treasury interaction term. This is approximately 5% of the total number of funds. Excluding these funds does not affect the results. 31 Next, RG of an equally weighted portfolio of funds is regressed on monthly dummies. This is to test whether RG is different around the most common disclosure months which coincide with the fiscal year-end months of September, October, and December. Therefore, I use a dummy for these months and for the following 6th month (March, April, and June). A dummy for the months following each of these months is also considered because in RG the benchmark uses lagged weights. The results reveal that the dummies are not significant whereas the intercept is still positive and statistically significant. A second concern is whether there is some residual risk exposure in RG that may be due to trades occurring after the disclosed weights or to investments in securities with different risk-return characteristics than the securities in the indices. To control for the former, I test whether RG is correlated with any risk or style factors. RG is regressed on the excess returns of six indices (Treasury, mortgage, investment 31 One should expect that window dressing would be more likely to be present among funds that report less frequently. However, the average RG for an equally-weighted portfolio of a group of 226 funds that report more frequently (at least six times per year) is 1.3%, similar to the other funds which is 1%. 17

20 grade corporate, high yield corporate, foreign bond and S&P500). No evidence of significant loadings is found and the intercept is positive and statistically significant. 32 To address the latter concern - that the RG results are due to the investment in securities that have a different systematic risk than the securities in the indices - the adjusted R-squared from a regression of mutual fund excess returns on the excess returns of the above six indices is calculated. The average RG for an equally-weighted portfolio of funds with below median R-squared is equal to 1.19% which is not statistically different from the funds with R-squared above the median. A third concern is that RG could capture a liquidity premium instead of managerial skill. Illiquidity indeed is likely to be pronounced in some bond portfolios. I focus here on the systematic component of liquidity (liquidity risk) that has been shown to be a priced risk factor in the cross-section of stock returns (Pástor and Stambaugh 2003) and Treasury bond returns (Li et al. 2009). The test whether RG captures a systematic exposure to liquidity risk, RG is regressed on the liquidity measures of Pástor and Stambaugh (2003) available on WRDS. The slope coefficients are insignificant while the intercepts are positive and statistically significant using both the traded and non-traded liquidity factors. Using Sadka s (2006) liquidity measures provide similar results. 33 This analysis does not exclude the possibility that fund managers could be compensated for the idiosyncratic component of liquidity risk. 34 This however could be part of the bond-selection ability of a manager. A fourth concern is that the findings are partly driven by the uneven reporting frequency of the funds. 35 As aforementioned, RG of funds that disclose more frequently is not different from RG of funds that disclose less frequently. Since the reporting frequency has improved in recent years, I also examine 32 Another concern is that RG captures excess returns not due to active management decisions but to passive changes of the portfolio due to bonds maturing or credit quality changes. To try to control for these effects, I also included in the regression the return of a portfolio of 20 index funds. The slope coefficient is not significant. 33 These measures are obtained from common stocks data. However, Chordia et al. (2005) suggest the existence of a common liquidity factor in stock and bond markets and similar measures were used by Sadka (2010) to control the exposure of hedge funds that also invest in the fixed-income market. 34 In the context of bond funds we still know very little about the managers liquidity preferences for their portfolios. For equity funds, Chen et al. (2000) show that fund managers prefer stocks with greater liquidity. 35 A related concern is whether this uneven reporting frequency causes some funds to obtain a noisy measure of holdings and this drives the RG results. This does not appear to be the case. Indeed, if funds are sorted according to the adjusted R-squareds of a regression of net returns on the gross returns obtained from the most recent holdings and divided in two groups, the group with high R-squareds has a higher average RG than the group with low R-squareds (1.23% vs. 1.01% annual for an equally-weighted portfolio). I also calculated RG only for the month after the disclosure months: the average RG for an equally-weighted portfolio is 1.2% per year. 18