Arbitrage profit using default swap

[sayjina]

Suppose a risky bond has a yield of 20%. If the return on U.S. Treasuries is 5% and the default swap premium on the bonds is 19%, what will the arbitrageur’s position be?

A) Go long the Treasury, buy the default swap, and short the risky bond.
B) Short the Treasury, buy the default swap, and invest in the risky bond.
C) Short the Treasury, sell the default swap, and invest in the risky bond.
D) Go long the Treasury, sell the default swap, and short the risky bond.


I understand that I need to sell the default swap, but I don't quite get the position of treasury bond and risky bond to create arbitrage profit.

 

[ravishankar80]

Hi David,

The investor is short the bond , as he has transferred the credit risk to default swap seller . He pays a premium of 19% for this.He also gets 20% from the bond.So he shorts the bond and buys a default swap . He is making a profit of 1% as long as bond does not default .Is this correct? So what is the role of the T-bond here.
Another question I have about CDS is that if the investor is buying protection on a reference asset but does not own the asset how with the settlement happen in case of a default. Since he cannot deliver the reference asset will it only be a cash settlement and no physical settlement

Regards
Ravi

 

[sayjina]

Answer to this question is D)
Recall the formula: risk-free bond return + default swap premium = risky bond return. An inequality tells the arbitrageur which position to take. Here it is 5% + 19% > 20%. So the arbitrageur needs to go long the left side (invest in the Treasury and earn the 19% swap premium by taking credit exposure), while shorting the right side (shorting the risky bond). The profit would be 4%. Note that interest rate and liquidity risk remain.

"risk-free bond return + default swap premium = risky bond return" <- I don't quite intuitively get this equality.
hope it will help and someone can help me to understand further

Best,
Jina

 

[ravishankar80]

Thanks, useful formula to remember.

 

[David Harper CFA FRM]

Hi Jina,

Re: Risk-free bond return + CDS premium = risky bond return

I think de Servigny (Ch 2) shows this nicely by using the rearrangement:
Risk-free bond return = risky bond return - CDS premium

So, on the right hand side. You start with a risky bond (e.g., long the 20% yield). Then you purchase default protection (long the CDS, paying 19% premium). So your risky bond is now protected. But 20%-29% = 1% does not make it worthwhile: you are making less than riskless 5%.

Or, starting from yours:
risk-free bond return + default swap premium = risky bond return

The left hand side is just a maneuver to simulate owning the risky bond: selling credit protection is to be synthetically long the underlying reference.

Hope that helps, David