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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

enter image description here

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.

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  • $\begingroup$ 600 bps means a good chance that the corporte bond will default. Perhaps including probability of default (PD) and loss given default (LGD) in the calculations would make more economic sense. $\endgroup$
    – Dimitri Vulis
    Commented Jun 9, 2023 at 11:16

1 Answer 1

Reset to default
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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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  • $\begingroup$ Thanks, but how does it work with the cash flows? Does it mean the credit risk in USD is calculated as avg(bond price now, 100) * (bond price now - t bond price now)? $\endgroup$
    – Kingvader Wong
    Commented Jun 9, 2023 at 11:57
  • $\begingroup$ Not sure what you are asking. Credit risk at time t = market value of Corp bond at time t $\endgroup$
    – dm63
    Commented Jun 11, 2023 at 11:10
  • $\begingroup$ that doesn't make sense, shouldn't there be interest rate risk as well? $\endgroup$
    – Kingvader Wong
    Commented Jun 11, 2023 at 12:06

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