My goal is to model individual credits spreads against a "benchmark" credit spread in order to generate a beta that is the fixed-income equivalent of the market beta used in capital asset pricing models in equity markets. (E.g. in CAPM, a $ \beta $ > 1 indicates that the individual stock has more systematic risk than the market as a whole). With this, I hope to be able to say how 'risky' each credit spread is compared to the benchmark credit spread.
Edit: (Note: What is a credit spread? A credit spread is the difference in yield between a U.S. Treasury bond and a debt security with the same maturity but of lesser quality. It essentially quantifies how much riskier a bond is compared to a risk-free U.S. government bond.)
In my case, instead of the risk relative to the market I want to know the risk relative to another credit spread.
Currently, my approach has been to regress the period-over-period change in the credit spread on the period-over-period change of the benchmark credit.
i.e. $$ \Delta(Credit Spread) = \beta_0 +\beta_1(\Delta(Benchmark Credit Spread))$$
However, I am unsure if using the differences is the correct approach.
1) Should I instead be using the spread levels?
2) If using first differences is appropriate, what is the exact interpretation of the coefficient? Does the beta represent the marginal effect of a change, of a change in the benchmark credit? I would like to be able to say given a 1 basis point change in the benchmark credit, we expect this other credit spread to increase by "x" bps.
3) What does the intercept represent in a model where all variables are first differences?
I realize this is not a very sophisticated or nuanced model, but it is intended to be as simple as possible. Any help with my approach would be greatly appreciated.