4.4.3.1 Average performance
Table 6 shows average alpha estimates aggregated over all government bond funds and benchmarked separately against all ten US Treasury indices, against the term factor as well as against the funds’ individually identified duration-adjusted benchmark. Panel A shows results for net returns in the overall sample period, while Panel B shows similar results using gross returns. The first interesting finding is that the average alpha of the funds in our sample increases with the duration of the benchmark index used with, e.g., αiSF in Panel A increasing almost monotonically from -0.3290% p.a. using the 1–3 index as the benchmark to 0.4981%
p.a. using the 10+ index. This is in line with our index based findings. Further, the average alpha using the broad index is similar to performance measured using the 5–10 index and the term factor produces the highest average alpha; both results are also in line with our index based analysis. The duration-adjusted average alpha with -0.1053% p.a. is below the average alpha measured using the broad index, which is in line with the majority of funds having average durations below that of the broad index which means that using the broad index for all funds systematically overestimates average government bond fund performance.
[Insert Table 6 here.]
Comparing the different factor models reveals that the SF model likely does not capture all relevant risks in government bond fund performance because the average alphas generated by the MF models are distinctively lower with duration-adjusted performance around -1.1% p.a.
In the case of the MF4 model, government bond fund performance is significantly negative using all Treasury indices, which is in line with the overall finding that on average active management does not add value for investors. The only exception is the average alpha using the term factor, which is significantly positive; another indication of the problems caused by using a term factor.
Comparing the results for net returns in Panel A with those for gross returns in Panel B reveals that, while the average gross alpha using the broad index is only slightly negative and statistically insignificant, the average gross duration-adjusted alpha is significantly negative with -0.3724% p.a. indicating that government bond funds do not even earn the fees they charge. This is in contrast to numerous findings on equity funds which show that average gross performance is zero on average (e.g., Sharpe, 1991; Fama and French, 2010).
About different market phases, Panels C and D show average government bond alphas using net returns during months with widening and contracting term spreads, respectively. The relations are in line with our index based analysis. Panel C shows that average alpha increases with higher benchmark duration while Panel D shows decreasing alpha with higher benchmark duration. Further, the differences between the average alphas using different indices are much higher, thereby creating even clearer patterns in both panels compared to Panel A. Regarding the average performance during both periods, the results using the duration-adjusted benchmark indicate that average performance during phases with widening term spread is much lower than the average performance during phases with contracting term spread. Moreover, this difference is more pronounced for the duration-adjusted alpha than for the broad Treasury alpha. This is consistent with the overall impression in Table 3 that bond returns are lower during phases of widening term-spread compared to phases with a contracting term-spread.
4.4.3.2 Duration bias in government bond fund performance
The results in the previous subsection on the average alpha performance of all funds show that there is a duration bias in government bond fund performance. To get into more detail on the magnitude and significance of the bias, Table 7 shows the results of an analysis similar to our pairwise Treasury index regressions presented in Table 2. Therefore, we sort all funds into groups according to their duration-adjusted benchmark. Then, for each group with at least five funds, we perform paired mean-comparison t-tests between the funds’ duration-adjusted
MF4-model alphas and the MF4-MF4-model alphas using the other nine Treasury indices.20 The figures represent the average alpha differences, i.e. duration-biases, for each duration group with respect to each Treasury index.
[Insert Table 7 here.]
Panel A shows results for the overall period while Panels B and C show results for the different market phases. Overall, the relations are as expected so that in Panels A and B using an index with a higher than appropriate duration leads to a positive duration bias while using a shorter than appropriate one leads to a negative duration bias. Panel C shows the reversed relation for market phases with contracting yield spread, consistent with our index based analysis in Table 2. Regarding the magnitude of the bias in different fund groups, we primarily look at the results for the broad Treasury index. While the bias decreases from left to right with growing bond fund duration, it is positive and significant for the first four groups which cover 96 of the total 127 funds in our sample (75.6%). This explains why the overall duration-adjusted performance in Table 6 is slightly lower than the alpha using the broad index as a benchmark.
Regarding single groups, the average duration-bias in Panel A may be as high as 0.5520% p.a. for the 24 funds sorted in group 1–3 which is clearly of economic relevance.
During phases of widening term spreads in Panel B, the duration bias of group 1–3 increases to 1.4663% p.a. while the largest duration bias during phases of contracting term-spread is reported in Panel C for the group 1–5 with -0.6104% p.a. Thus, depending on the market phase, using an index with an inappropriate duration as benchmark leads to economically significant duration-bias, consistent with our main research hypothesis.
20 Results for the SF- and the other MF-models are economically similar and available upon request. The same applies to results based on gross returns.