Generating and interpreting betas for credit spreads

Question

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.

Answer 1

1) assuming these are time-series regressions between a credit spread y and the benchmark credit spread x, the decision on using levels vs differences depends on the stationarity of the processes. If the levels are not stationary or exhibit significant serial dependency, consider differencing the data. There’s also the possibility that the series are cointegrated (or fractionally cointegrated) but I don’t think we need to address that here given the scope of the exercise.

2) one could interpret the coefficient B1 of the differenced equation as “if the benchmark spread widens by 1 unit, the Y spread tends to widen by B1 units” (assuming a positive B1)

3) the intercept here can be interpreted as the expected change in the spread of Y given no change in the basis of the benchmark (X). In a differenced equation, a significantly positive (negative) intercept term would indicate a persistent widening (tightening) trend in the spread