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.
|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.