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Estimating Credit Spread Exposure from Corporate and Treasury Bonds

Article Quant Q&A · Author: Kingvader Wong
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Summary

This question examines why a corporate bond’s yield spread may not appear as the return on a portfolio formed by buying the corporate bond and shorting a Treasury bond with matching cash flows. The reply frames spread exposure in terms of the bond’s average price over its life, approximated using its current price and face value, rather than the cash left over from comparing the two initial prices.

Using the stated bond prices and spread, the reply estimates average credit exposure and applies the spread to that amount, producing a result close to the spread intuition. This is a rough approximation, not a full replication or derivation of spread returns. The discussion does not reconcile the portfolio’s financing, reinvestment, or detailed cash flows, so it offers a useful intuition rather than a complete valuation method.

Key ideas

  • Credit spread exposure changes as a bond’s price approaches face value.
  • The reply approximates lifetime exposure with the average of the current bond price and face value.
  • Applying the spread to average exposure gives an approximate spread-related amount.
  • The explanation does not fully account for financing or cash-flow timing.

Tags

Fixed incomeRisk management
Full text
# Credit Spread Replication by Long/ Short Bonds


# Credit Spread Replication by Long/ Short Bonds












I am trying to derive the credit spread using an hypothetical portfolio of a long corporate bond plus a short treasury bond, which have the exact cashflows. I should be able to get the credit spread in theory but they don't seem to match. Here are the assumptions.

|  |  |
| maturity | 2 yr |
| annualised coupon ( for both bonds) | 20 USD |
| face value | 100 USD |
| credit spread | 600 bps |
| t bond yield (first year) | 100 bps |
| t bond yield (second year) | 300 bps |
| t bond price now | 152.2404 |
| corporate bond now | 137.4558 |

I calculated the bond price with

where r = t bond yield (t bond) and t bond yield + spread (corp)

In theory I paid 137.4558 for the corporate bond and receive 152.2404 from the T bond, which leaves me 14.78466 USD in the bank account. How does that translate to the credit spread return? It doesn't match if I calculate it as (1 + 14.78466 / 100)^(1/2) = 7.1376013%. Am I missing the lending rate? If I calculate the lending rate using the t bond yield curve = 1.148529% and deduct, it gives me 5.6523%, which still doesn't match the credit spread.

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/75813

The approximate exposure to credit risk during the life of the bond = avg (bond price now,100) = approx 118.6. 6% of that is 7.12. That seems quite close.

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