# 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
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.

• 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. Jun 9 at 11:16