Comparing Regression Methods for Measuring Bond Fund Positioning
Summary
The document considers how to estimate an active bond fund’s positioning relative to its benchmark using returns on rates, credit spreads, and other sub-indices as explanatory factors. It compares subtracting factor betas estimated from separate fund and benchmark regressions with directly regressing the fund’s excess returns on those factors. A panel regression with fund-specific interactions is also raised as an option.
The response cautions that subtracting betas may be inappropriate because beta reflects volatility-related exposure. It recommends first checking the correlation and beta between the fund and benchmark, then comparing exposures if the relationship supports doing so. Of the proposed methods, it favors a panel regression, with excess-return regression as another possible approach. The document provides conceptual guidance rather than a worked analysis or empirical comparison, so it does not establish which approach performs best in a particular dataset. The reported fit differences suggest that fund returns may be less fully explained by the chosen factors than benchmark returns, but the causes are not explored.
Key ideas
- Check the fund’s correlation and beta with its benchmark before comparing factor exposures.
- Subtracting betas from separate regressions may not provide a sound measure of relative positioning.
- Regressing fund excess returns on factors is one proposed way to estimate active exposures.
- A panel regression with fund-specific factor interactions is another candidate approach.
- The document offers recommendations but no empirical test that establishes a universally superior method.
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Full text
# Modelling fund positioning using fund returns and linear regression
# Modelling fund positioning using fund returns and linear regression
I want to measure the positioning of an active bond mutual fund vs. its benchmark via rolling linear regression of returns vs several factors. The intuition of using linear regression is that the returns of the index or of the fund ($r$) should be a linear function of the returns of several sub indices (i.e. rates $r_{\text{10yr}}$, credit spreads $r_{\text{cred spreads}}$, etc..).
The regression takes the form: $$r = \beta_1 \times r_{\text{10yr}} + \beta_2 \times r_{\text{cred spreads}} + \cdots$$
The R-squared of the regression of the index vs. the sub-indices is ~95%. Likewise the R-squared of the regression of the mutual fund vs. the sub indices is ~85%.
I want to know whether it is better to measure relative positioning using the difference in the Betas to each factor from the regressions, i.e $\beta_{\text{fund}}$ - $\beta_{\text{index}}$ or if it is better to run a single regression of excess returns of the fund over the benchmark vs. the same set of factors:
$$(r_{\text{fund}}-r_{\text{index}}) = \beta_1 \times r_{\text{10yr}} + \beta_2 \times r_{\text{cred spreads}} + \cdots $$
I believe running separate regressions allows for the error terms to be estimated with different variances but what other factors should I think about? A third possibility is to run a panel regression were sensitivities are estimated simultaneously but the marginal effect is captured through an interaction term for each variable/fund combo.
## Answer by sen_saven (score 2)
https://quant.stackexchange.com/a/34622
That's a quite interesting problem, a few thoughts on how to attack it:
- Calculate the correlation and beta between the benchmark and the fund.
- If the above imply a link between these two then proceed with the betas' comparison.
- Regarding the three approaches you mention, the one which subtracts the betas sounds mathematically-speaking wrong since beta is a volatility-based measure.
- So I would go either for the panel regression or the one where you apply the regression on (rfund−rindex) - probably for the panel regression.
Hope that helps.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.