CDSs on US Treasuries

I’m thinking of this from a different POV.
Taking the actual prices of the spread from the link given above and being conservative (the move was a 25x increase, so lets assume 2bps and 44 bps for whole number sake)
So at 2bps.
You would have to pay $0.02 for every $100 of protection annually or $0.20 over a 10 years contract. Assuming the spread in the CDS dictates the probability of default, then the expected return in event of default is 0.002 x $60 (recovery rate) - $0.20 (cost of contract over its life) which equals -$0.08. So at this point there is a premium for the purchase of the contract due to the recovery rate assumption.
At the new price of 44bps:
You would have to pay $0.44 for every $100 of protection annully or $4.40 over the life of the contract. The expected return paying the $0.02/yr would be 0.044 x $60 - $0.20 equalling $2.44.
Wouldn’t the increase be approximately 25x as the probablility of default has come up and you have no investment except for the payments on the swap? The value of the $0.02/yr swap is now much higher as an equivalent swap now costs $0.44/yr.
Mind you, these probabilities are very primative yet there is some conservative calculation as this assumes all payments are made, although payments would stop when default occurs.
 
“Assuming the spread in the CDS dictates the probability of default,”
when is this the case?
 
actually it is the case but the math after that is what i have trouble with… the spread is the market, using the market you can then get a default probability, at a 5bps spread i get the arb free probability of 0.43% over the 5 year contract using 40% recovery.
 
Why would someone pay 25x more for something if the probability hasn’t increased dramatically?
The only idea about the probability of UST default is through what people will pay to protect against it.
 
Where are you getting your probabilities?
and if you can, can you calculate one for a 125 bps spread to compare to the 5bps spread?
 
Okay, so is it correct to say then that if you are calculating the risk free rate you should be using the treasury rate minus the CDS spread?
 
Yeah. That why my surprise. So the overall yield on the treasuries are falling AND the yield less credit risk is falling as a percentage of that. The CDS spread is pretty important when you take teh CDS into account.
Weird to say the least…
 
Black Swan Wrote:
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> Okay, so is it correct to say then that if you are
> calculating the risk free rate you should be using
> the treasury rate minus the CDS spread?
Interesting, I never thought of that… though I guess you also need a CDS on the counterparty and then on the counterparty’s counterparty… probably you can find some converging series or something.
 
Matt, In your calculation you are saying spread equals probability of default, which is not correct. By that rationale, there wouldn’t be a spread over 100 bp. That is a flawed assumption. Just PV your cash flows. Pay 2 bp on 10mm for 5yrs, receive 44 bp on 10mm for 5 yrs, assuming an instantaneous unwind of the position.
 
grover33 Wrote:
——————————————————-
> Matt, In your calculation you are saying spread
> equals probability of default, which is not
> correct. By that rationale, there wouldn’t be a
> spread over 100 bp. That is a flawed assumption.
> Just PV your cash flows. Pay 2 bp on 10mm for
> 5yrs, receive 44 bp on 10mm for 5 yrs, assuming an
> instantaneous unwind of the position.
You are the CDS buyer, so you are paying those amounts looking for the default to occur. You need to get a reasonable expectation of the probability of default to gauge the value of the swap should there be default. As this probability is completely unknown, we must only use this spread as our gauge for the probability of default as it is our instrument that attempts to price what a default would cost those who risk to protect against it. I don’t see how using an increase in the spread doesn’t help gauge the probability of default. I’m not saying that a 25x increase in the spread means a 25x increase in value, but I will stand by the fact that a 25x increase in the spread represents a large increase in the probability of default in UST, whether it be in perception of those who are buying this device, or in actuality.
Using your rationale of closing the swap out and receiving 42bps at that piont, your return is 100% correlated to the new price of the device which measures the risk of default so is 100% correlated to the risk of default.
a=b=c
 
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