Estimating Credit Index Market Beta After Adjusting for Spread DV01

Summary

The document explains how to estimate a credit index’s market beta when the index’s spread sensitivity, expressed as CD01, varies over time. It starts from a linear relationship between spread returns and market returns. If index returns scale with spread returns according to CD01, then estimating beta from raw index returns can mix the market relationship with changes in spread sensitivity.

The proposed adjustment is to divide each period’s index return by that period’s CD01, producing a spread-return series. Regressing this adjusted series against market returns estimates the beta in the stated relationship; multiplying by the index’s CD01 then relates the index to the market. The answer gives equations but no data, regression details, or validation. Its interpretation depends on the assumed linear relationship and on how index returns and CD01 are measured consistently over time.

Key ideas

• The method assumes spread returns vary linearly with market returns, up to a constant.
• Credit index returns are modeled as CD01 multiplied by spread returns.
• Divide each period’s index return by its CD01 to construct the spread-return series.
• Estimate the market beta using observed spread returns and market returns.
• The result relies on the assumed relationship and consistent time-varying CD01 measurements.

Tags

# Adjusting index betas for spread DV01


# Adjusting index betas for spread DV01












If you have an index and have measured its beta with respect to the overall market, how would you go about adjusting it against spread dv01 and why would you want this number?

## Answer by Brian B (score 2, accepted)

https://quant.stackexchange.com/a/19577

If you believe that the fundamental economic relationship is

$$ r_{\text{Spread}} = \beta \, r_{\text{Market}} + \text{const} $$

Then in order to obtain the beta of a credit index $I$ with CD01 $c$ to the market you would write

$$ r_I = c \, r_{\text{Spread}} $$

and thus

$$ r_I = c\, \beta \, r_{\text{Market}} + \text{const} $$

Now you need to estimate $\beta$ from observed data. To do so, you need a time series of $r_{\text{Market}}$ and $r_{\text{Spread}}$. To obtain the $r_{\text{Spread}}$ you simply take

$$ r_{\text{Spread}}^{(t)} = r_{I}^{(t)} / c^{(t)} $$

This is the "adjusting it against spread dv01" that you have observed.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.