Basis for ABX Index

[Sidharth]

Gorton Reading

Imagine an investor who compares the market spread on the BBB subprime tranche (expressed as an annual percentage), Scash to the spread on the ABX index referencing that same bond, SCDS (also expressed as an annual percentage). The basis is SCDS – Scash. So, SCDS < Scash is a negative basis, and vice versa. The cash instrument has to be funded, so the difference SCDS – Scash should equal the cost of funding, say RCF.otherwise arbitrage exist.

RCF = 3.5%
Say for a security X having BBB rating is giving YTM of 7% while YTM on Zero-Coupon treasury Bond is 4%. Then Scash(Cash-Spread ) is 3% (7%-4%).

Now say Credit default payment per year for ABX index of BBB rated securities is $200 on notional principal is $10,000 which means SCDS of 2%.

Now as mentioned above SCDS-Scash should be equal to RCF here this is not there. but even in any realistic example it wont be possible to compare difference of CDS spread and cash spread to be RCF..

Because as we had studied earlier. Buying a bond is equal to ....buying a Treasury and selling CDS....so cash spread and CDS should be almost equal......... not that there difference should be RCF.

Am i right ??

 

[rahul.goyl]

Hi Sidh,

Would redirect to the below post.......... Awesome Post

http://www.acredittrader.com/?p=24

Regards,

Rahul

 

[Sidharth]

so when calculating difference we take absolute value and compare it with Rf.

so in this example |2%-7%| = 5%.
if Rf is 4% then arbitrage exist.

Is it right ?

 

[David Harper CFA FRM]

Sidharth -

Re: so in this example |2%-7%| = 5%. if Rf is 4% then arbitrage exist.
your example has a cash spread of 3% and a CDS premium of 2%, so under Gorton's model repo rate should = 1%
and there is an arbitrage if <>1%;
e.g., if repo = 0%, then funding is cheap and arbitrageur should fund (buy) the bond and buy protection:
+3% - 2% = +1% profit
if repo = 2%, then funding is rich and arb should write protection and short the bond:
collect 2% CDS premium, pay 3% on short bond and lend to earn +2% on repo = +2% - 3% + 2% = +1%

the valid confusion comes from "Buying a bond is equal to ....buying a Treasury and selling CDS"
this is correct only under a naive model the excludes funding cost (and funding risk).
Gorton is adding another factor to be more realistic
(in regards to CDS basis, even more factors can be added...)

David

 

[Sidharth]

thanks i got the concept