## BoE Research: Decomposing Corporate Bond Spreads

The fascinating Chart 1.18 in the April 2008 BoE Financial Stability Report led me to a paper in their 2007Q4 Bulletin by Lewis Webber & Rohan Churm, that seeks to decompose corporate bond spreads.

They use a Merton Model with a default boundary to estimate intrinsic default probabilities, which is similar to the Bank of Canada CDS Pricing research mentioned briefly on March 20. Further, the intrinsic default risk is differentiated from the premium demanded due to uncertainty regarding this intrinsic default risk by:

It is assumed that, in practice, corporate bond investors demand compensation for bearing both expected and unexpected default losses. The sum of these two components is calculated using the model by assuming that investors recognise the uncertainty surrounding the firmâ€™s asset value growth rate. They therefore discount the future cash flows they expect in practice at a risky rate of return to reflect the possibility of default occurring looking forward. To isolate the compensation demanded for expected default losses, it is assumed that investors continue to expect risky rates of return, but instead discount expected cash flows at the default risk-free rate. Compensation for bearing the risk of unexpected default losses can then be obtained as the difference between these two values.

Equivalently, the total compensation investors demand for bearing expected and unexpected default losses is calculated in the model using risk-neutral valuation methods. This involves calculating the expected default frequency used in equation (5) under the risk-neutral probability measure. Compensation for expected default losses is isolated by calculating the expected default frequency used in equation (5) under the real-world probability measure.

Finally, they assign the residual between calculated and market yields – mostly a liquidity premium:

In addition, there may be a residual part of observed corporate bond spreads that the model cannot explain. This contains compensation for all non-credit factors, including a premium for the relative illiquidity of the corporate bond market compared to the government bond market. This gives three contributions to observed corporate spreads: the compensation investors demand for expected default losses; compensation for uncertainty about default losses; and a non-credit related residual.

There are many fascinating graphs!

### 5 Responses to “BoE Research: Decomposing Corporate Bond Spreads”

1. […] corporate spread vs. governments using a structure “Merton” model, very similar to the BoE research previously reported on PrefBlog – the BoE is thanked for supplying code in note 16. For investment-grade firms issuing Canadian […]

2. […] that they calculate credit spreads that are much lower than those observed in the market. The Bank of England and the Bank of Canada take what I feel is a sensible course and ascribe the excess spread to […]

3. […] Decomposing corporate bond spreads by Webber and Churn, Bank of England Quarterly Bulletin 2007 Q4 (this has been discussed on PrefBlog) […]

4. […] use of Moody’s KMV methodology to determine intrinsic default probability is similar to the Bank of England approach, but different from the recently published Bank of Canada liquidity research which, essentially, […]

5. […] decomposing credit spreads according to the BoC methodology, which I dislike, as opposed to the Webber & Churm methodology used in the […]